The kenzo Reference Manual

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The kenzo Reference Manual

This is the kenzo Reference Manual, version 1.1.7, generated automatically by Declt version 2.3 "Robert April" on Wed Mar 14 04:06:50 2018 GMT+0.


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1 Introduction

Welcome to Kenzo

GPLv3 Logo Travis Status

According to the title of its handbook, Kenzo is a "Symbolic Software for Effective Homology Computation" and its main audience might be students and researchers in algebraic topology. Have a look at the overview to get a sense for what's there for you to discover.

It is also a remarkable piece of LISP code, albeit in need of a little touch-up. This repository contains a repackaged version of the Kenzo program by Francis Sergeraert and collaborators. The original version of the program can be found at http://www-fourier.ujf-grenoble.fr/~sergerar/Kenzo/ . This version aims to update its infrastructure by providing the following:

  1. A simple regression test suite based on FiveAM
  2. Support for the great freely available Lisp compilers out there, including CCL, [ECL] (https://common-lisp.net/project/ecl/), SBCL, etc.
  3. Installation via the Quicklisp library manager
  4. Updated documentation and examples runnable from cl-jupyter

This work is well underway, but there are several outstanding issues.

Getting up and running

There are several methods to get going:

  1. Just play with it a little! (Live)
  2. Just give me a Docker container!
  3. Local installation via Quicklisp or ASDF

Plain ASDF

To load Kenzo as provided by this repo, make sure ASDF knowns where to find the source, e.g. by creating a link to this directory at

  ~/.local/share/common-lisp/source/

Then in your Lisp (e.g., in ECL) type

(require :asdf)
(require :kenzo)

Quicklisp

Assuming you have Quicklisp, there isn't really much to say here:

* (ql:quickload :kenzo)
To load "kenzo":
  Install 1 Quicklisp release:
    kenzo
; Fetching #<URL "http://beta.quicklisp.org/archive/kenzo/2015-08-04/kenzo-20150804-git.tgz">
; 1835.57KB
==================================================
1,879,625 bytes in 1.48 seconds (1236.91KB/sec)
; Loading "kenzo"
[package cat].....................................
..................................................
..............................
(:KENZO)
*

Verify that you're good to go by loading and running the Kenzo regression test suite. For example, in an SBCL prompt you should see something like this:

* (ql:quickload :kenzo-test)
To load "kenzo-test":
  Load 1 ASDF system:
    kenzo-test
; Loading "kenzo-test"
.
(:KENZO-TEST)
* (fiveam:run!)

Running test suite KENZO
 Running test F-CMPR ..........
 Running test L-CMPR ..........
 Running test S-CMPR .....
 ...
---done---
Did 1482 checks.
    Pass: 1482 (100%)
    Skip: 0 ( 0%)
    Fail: 0 ( 0%)

Similarly, you'd load Kenzo via (ql:quickload :kenzo).


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2 Systems

The main system appears first, followed by any subsystem dependency.


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2.1 kenzo

Author

Francis Sergeraert <Francis.Sergeraert@ujf-grenoble.fr>

License

GPLv3

Description

A Symbolic Software for Effective Homology Computation by Francis Sergeraert

Version

1.1.7

Source

kenzo.asd (file)

Components

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3 Modules

Modules are listed depth-first from the system components tree.


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3.1 kenzo/src

Dependency

package.lisp (file)

Parent

kenzo (system)

Location

src/

Components

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4 Files

Files are sorted by type and then listed depth-first from the systems components trees.


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4.1 Lisp


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4.1.1 kenzo.asd

Location

kenzo.asd

Systems

kenzo (system)

Packages

kenzo-asd


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4.1.2 kenzo/package.lisp

Parent

kenzo (system)

Location

package.lisp

Packages

cat


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4.1.3 kenzo/src/kenzo.lisp

Parent

src (module)

Location

src/kenzo.lisp

Exported Definitions
Internal Definitions

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4.1.4 kenzo/src/abbreviations.lisp

Parent

src (module)

Location

src/abbreviations.lisp

Exported Definitions

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4.1.5 kenzo/src/macros.lisp

Parent

src (module)

Location

src/macros.lisp

Exported Definitions
Internal Definitions

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4.1.6 kenzo/src/various.lisp

Parent

src (module)

Location

src/various.lisp

Exported Definitions

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4.1.7 kenzo/src/classes.lisp

Parent

src (module)

Location

src/classes.lisp

Exported Definitions
Internal Definitions

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4.1.8 kenzo/src/combinations.lisp

Parent

src (module)

Location

src/combinations.lisp

Exported Definitions
Internal Definitions

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4.1.9 kenzo/src/chain-complexes.lisp

Parent

src (module)

Location

src/chain-complexes.lisp

Exported Definitions
Internal Definitions

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4.1.10 kenzo/src/chcm-elementary-op.lisp

Parent

src (module)

Location

src/chcm-elementary-op.lisp

Exported Definitions
Internal Definitions

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4.1.11 kenzo/src/effective-homology.lisp

Parent

src (module)

Location

src/effective-homology.lisp

Exported Definitions
Internal Definitions

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4.1.12 kenzo/src/homology-groups.lisp

Parent

src (module)

Location

src/homology-groups.lisp

Exported Definitions
Internal Definitions

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4.1.13 kenzo/src/searching-homology.lisp

Parent

src (module)

Location

src/searching-homology.lisp

Exported Definitions
Internal Definitions

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4.1.14 kenzo/src/cones.lisp

Parent

src (module)

Location

src/cones.lisp

Exported Definitions
Internal Definitions

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4.1.15 kenzo/src/bicones.lisp

Parent

src (module)

Location

src/bicones.lisp

Exported Definitions
Internal Definitions

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4.1.16 kenzo/src/tensor-products.lisp

Parent

src (module)

Location

src/tensor-products.lisp

Exported Definitions
Internal Definitions

search-efhm (method)


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4.1.17 kenzo/src/coalgebras.lisp

Parent

src (module)

Location

src/coalgebras.lisp

Internal Definitions

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4.1.18 kenzo/src/cobar.lisp

Parent

src (module)

Location

src/cobar.lisp

Exported Definitions
Internal Definitions

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4.1.19 kenzo/src/algebras.lisp

Parent

src (module)

Location

src/algebras.lisp

Exported Definitions
Internal Definitions

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4.1.20 kenzo/src/bar.lisp

Parent

src (module)

Location

src/bar.lisp

Exported Definitions
Internal Definitions

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4.1.21 kenzo/src/simplicial-sets.lisp

Parent

src (module)

Location

src/simplicial-sets.lisp

Exported Definitions
Internal Definitions

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4.1.22 kenzo/src/simplicial-mrphs.lisp

Parent

src (module)

Location

src/simplicial-mrphs.lisp

Exported Definitions
Internal Definitions

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4.1.23 kenzo/src/delta.lisp

Parent

src (module)

Location

src/delta.lisp

Exported Definitions
Internal Definitions

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4.1.24 kenzo/src/special-smsts.lisp

Parent

src (module)

Location

src/special-smsts.lisp

Exported Definitions
Internal Definitions

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4.1.25 kenzo/src/suspensions.lisp

Parent

src (module)

Location

src/suspensions.lisp

Exported Definitions
Internal Definitions

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4.1.26 kenzo/src/disk-pasting.lisp

Parent

src (module)

Location

src/disk-pasting.lisp

Exported Definitions
Internal Definitions

search-efhm (method)


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4.1.27 kenzo/src/cartesian-products.lisp

Parent

src (module)

Location

src/cartesian-products.lisp

Exported Definitions
Internal Definitions

crpr-print (function)


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4.1.28 kenzo/src/eilenberg-zilber.lisp

Parent

src (module)

Location

src/eilenberg-zilber.lisp

Exported Definitions
Internal Definitions

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4.1.29 kenzo/src/kan.lisp

Parent

src (module)

Location

src/kan.lisp

Exported Definitions

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4.1.30 kenzo/src/simplicial-groups.lisp

Parent

src (module)

Location

src/simplicial-groups.lisp

Exported Definitions

smgr (function)

Internal Definitions

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4.1.31 kenzo/src/fibrations.lisp

Parent

src (module)

Location

src/fibrations.lisp

Exported Definitions

fibration-total (function)

Internal Definitions

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4.1.32 kenzo/src/loop-spaces.lisp

Parent

src (module)

Location

src/loop-spaces.lisp

Exported Definitions
Internal Definitions

loop-space-face* (function)


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4.1.33 kenzo/src/ls-twisted-products.lisp

Parent

src (module)

Location

src/ls-twisted-products.lisp

Exported Definitions

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4.1.34 kenzo/src/lp-space-efhm.lisp

Parent

src (module)

Location

src/lp-space-efhm.lisp

Exported Definitions
Internal Definitions

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4.1.35 kenzo/src/classifying-spaces.lisp

Parent

src (module)

Location

src/classifying-spaces.lisp

Exported Definitions
Internal Definitions

gbar-print (function)


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4.1.36 kenzo/src/k-pi-n.lisp

Parent

src (module)

Location

src/k-pi-n.lisp

Exported Definitions
Internal Definitions

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4.1.37 kenzo/src/serre.lisp

Parent

src (module)

Location

src/serre.lisp

Exported Definitions
Internal Definitions

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4.1.38 kenzo/src/cs-twisted-products.lisp

Parent

src (module)

Location

src/cs-twisted-products.lisp

Exported Definitions
Internal Definitions

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4.1.39 kenzo/src/cl-space-efhm.lisp

Parent

src (module)

Location

src/cl-space-efhm.lisp

Exported Definitions
Internal Definitions

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4.1.40 kenzo/src/whitehead.lisp

Parent

src (module)

Location

src/whitehead.lisp

Exported Definitions
Internal Definitions

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4.1.41 kenzo/src/smith.lisp

Parent

src (module)

Location

src/smith.lisp

Exported Definitions
Internal Definitions

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5 Packages

Packages are listed by definition order.


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5.1 kenzo-asd

Source

kenzo.asd

Use List

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5.2 cat

Source

package.lisp (file)

Use List

common-lisp

Exported Definitions
Internal Definitions

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6 Definitions

Definitions are sorted by export status, category, package, and then by lexicographic order.


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6.1 Exported definitions


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6.1.1 Constants

Constant: +abbreviations+
Package

cat

Source

abbreviations.lisp (file)

Constant: +empty-list+
Package

cat

Source

kenzo.lisp (file)


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6.1.2 Special variables

Special Variable: *bc*
Package

cat

Source

kenzo.lisp (file)

Special Variable: *bdd*
Package

cat

Source

kenzo.lisp (file)

Special Variable: *chcm-list*
Package

cat

Source

kenzo.lisp (file)

Special Variable: *cmbn-control*
Package

cat

Source

kenzo.lisp (file)

Special Variable: *df-fd*
Package

cat

Source

kenzo.lisp (file)

Special Variable: *dg-gd*
Package

cat

Source

kenzo.lisp (file)

Special Variable: *fh*
Package

cat

Source

kenzo.lisp (file)

Special Variable: *hg*
Package

cat

Source

kenzo.lisp (file)

Special Variable: *hh*
Package

cat

Source

kenzo.lisp (file)

Special Variable: *homology-verbose*
Package

cat

Source

kenzo.lisp (file)

Special Variable: *id-fg*
Package

cat

Source

kenzo.lisp (file)

Special Variable: *id-gf-dh-hd*
Package

cat

Source

kenzo.lisp (file)

Special Variable: *list-list*

The variable *LIST-LIST* is bound to a list of variable names, which are bound to lists of user created objects such as chain complexes, morphisms, etc.

Package

cat

Source

kenzo.lisp (file)

Special Variable: *mrph-list*
Package

cat

Source

kenzo.lisp (file)

Special Variable: *results-verbose*
Package

cat

Source

kenzo.lisp (file)

Special Variable: *tc*
Package

cat

Source

kenzo.lisp (file)

Special Variable: *tdd*
Package

cat

Source

kenzo.lisp (file)

Special Variable: *tnpr-with-degrees*
Package

cat

Source

kenzo.lisp (file)

Special Variable: +null-abar+
Package

cat

Source

bar.lisp (file)

Special Variable: +null-gbar+
Package

cat

Source

classifying-spaces.lisp (file)

Special Variable: +null-loop+
Package

cat

Source

loop-spaces.lisp (file)

Special Variable: +too-much-time+
Package

cat

Source

kenzo.lisp (file)


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6.1.3 Macros

Macro: -1-expt-n N
Package

cat

Source

macros.lisp (file)

Macro: -1-expt-n+1 N
Package

cat

Source

macros.lisp (file)

Macro: -1-expt-n-1 N
Package

cat

Source

macros.lisp (file)

Macro: 2-exp N
Package

cat

Source

macros.lisp (file)

Macro: ? &rest REST
Package

cat

Source

macros.lisp (file)

Macro: absm DGOP GMSM
Package

cat

Source

macros.lisp (file)

Macro: absm1 CRPR
Package

cat

Source

macros.lisp (file)

Macro: absm2 CRPR
Package

cat

Source

macros.lisp (file)

Macro: apowr DGOP GMSM EXPN
Package

cat

Source

macros.lisp (file)

Macro: aprd &rest REST
Package

cat

Source

macros.lisp (file)

Macro: basis &rest REST

—————————————————————–[macro-doc] BASIS
Args: (&rest rest)
Args: (chcm)
Args: (chcm n)
Args: (chcm n :dgnr)
When invoked with only one argument, returns the function attached to the slot BASIS of the chain complex.
When invoked with two arguments, returns the basis of the group of degree N of the chain complex.
When invoked with three arguments, the keyword :DGNR, it also returns the degenerate elements of the basis in degree N.
This function returns an error if the chain complex is locally effective. ——————————————————————————

Package

cat

Source

macros.lisp (file)

Macro: bcc &rest REST

—————————————————————–[macro-doc] BCC
Args: (&rest rest)
Args: (rdct)
Args: (rdct cmbn)
Args: (rdct degr gnrt)
With only one argument, a reduction RDCT, this macro returns the bottom chain complex of the reduction. Otherwise, it applies the differential of the bottom chain complex of RDCT to a combination provided in additional arguments such as CMBN or DEGR GNRT. ——————————————————————————

Package

cat

Source

macros.lisp (file)

Macro: bcnb GNRT

(BCNB GNRT) returns the representation of the generator GNRT belonging to the chain complex B.

Package

cat

Source

macros.lisp (file)

Macro: bcnc GNRT

(BCNC GNRT) returns the representation of the generator GNRT belonging to the chain complex C.

Package

cat

Source

macros.lisp (file)

Macro: bcnd GNRT

(BCND GNRT) returns the representation of the generator GNRT belonging to the chain complex D.

Package

cat

Source

macros.lisp (file)

Macro: binomial-p-q P Q
Package

cat

Source

macros.lisp (file)

Macro: bndr &rest REST
Package

cat

Source

macros.lisp (file)

Macro: brgn DEGR GNRT
Package

cat

Source

macros.lisp (file)

Macro: bspn SMST
Package

cat

Source

macros.lisp (file)

Macro: cbgn DEGR GNRT
Package

cat

Source

macros.lisp (file)

Macro: cffc TERM

—————————————————————–[macro-doc] CFFC
Args: (term)
Returns the the coefficient (integer) of a term. ——————————————————————————

Package

cat

Source

macros.lisp (file)

Macro: cmbn-non-zero-p CMBN

—————————————————————–[macro-doc] CMBN-NON-ZERO-P
Args: (cmbn)
Tests if the combination CMBN is a non-null combination of any degree. ——————————————————————————

Package

cat

Source

macros.lisp (file)

Macro: cmbn-zero-p CMBN

—————————————————————–[macro-doc] CMBN-ZERO-P
Args: (cmbn)
Tests if the combination CMBN is the null combination of any degree. ——————————————————————————

Package

cat

Source

macros.lisp (file)

Macro: cmpr &rest REST

—————————————————————–[macro-doc] CMPR
Args: (&rest rest)
Args: (chcm gnrt1 gnrt2)
Typically invoked with a chain complex CHCM and two generators GNRT1 and GNRT2. Applies the comparison function associated with CHCM to GNRT1 and GNRT2, and return the result. ——————————————————————————

Package

cat

Source

macros.lisp (file)

Macro: column-minus-5 MTRX-LIST BEGIN COLUMN
Package

cat

Source

macros.lisp (file)

Macro: column-op-5 MTRX-LIST BEGIN LAMBDA COLUMN1 COLUMN2
Package

cat

Source

macros.lisp (file)

Macro: column-swap-5 MTRX-LIST BEGIN COLUMN1 COLUMN2
Package

cat

Source

macros.lisp (file)

Macro: con0 GNRT
Package

cat

Source

macros.lisp (file)

Macro: con1 GNRT
Package

cat

Source

macros.lisp (file)

Macro: cprd &rest REST
Package

cat

Source

macros.lisp (file)

Macro: crpr &rest REST
Package

cat

Source

macros.lisp (file)

Macro: d IGMSM
Package

cat

Source

macros.lisp (file)

Macro: def NAME VALUE

—————————————————————–[macro-doc] DEF
Args: (name value)
Defines a dynamic variable NAME in the CL-USER package, assigns it VALUE, and returns VALUE. ——————————————————————————

Package

cat

Source

macros.lisp (file)

Macro: degenerate-p ABSM
Package

cat

Source

macros.lisp (file)

Macro: dffr &rest REST

—————————————————————–[macro-doc] DFFR
Args: (&rest rest)
Args: (chcm cmbn)
Args: (chcm degr gnrt)
Applies the differential morphism of the chain complex CHCM to a combination CMBN or a generator GNRT of a degree DEGR.
See also the macro ?. ——————————————————————————

Package

cat

Source

macros.lisp (file)

Macro: dgnl &rest REST
Package

cat

Source

macros.lisp (file)

Macro: f &rest REST

—————————————————————–[macro-doc] F
Args: (&rest rest)
Args: (rdct)
Args: (rdct cmbn)
Args: (rdct degr gnrt)
With only one argument, a reduction RDCT, this macro returns the morphism f of the reduction. Otherwise, it applies f to a combination provided in additional arguments such as CMBN or DEGR GNRT. ——————————————————————————

Package

cat

Source

macros.lisp (file)

Macro: face &rest REST
Package

cat

Source

macros.lisp (file)

Macro: g &rest REST

—————————————————————–[macro-doc] G
Args: (&rest rest)
Args: (rdct)
Args: (rdct cmbn)
Args: (rdct degr gnrt)
With only one argument, a reduction RDCT, this macro returns the morphism g of the reduction. Otherwise, it applies g to a combination provided in additional arguments such as CMBN or DEGR GNRT. ——————————————————————————

Package

cat

Source

macros.lisp (file)

Macro: gnrt TERM

—————————————————————–[macro-doc] GNRT
Args: (term)
Returns the the generator of a term. ——————————————————————————

Package

cat

Source

macros.lisp (file)

Macro: gnrt-name I
Package

cat

Source

macros.lisp (file)

Macro: grin SMGR &rest REST
Package

cat

Source

macros.lisp (file)

Macro: grml SMGR &rest REST
Package

cat

Source

macros.lisp (file)

Macro: h &rest REST

—————————————————————–[macro-doc] H
Args: (&rest rest)
Args: (rdct)
Args: (rdct cmbn)
Args: (rdct degr gnrt)
With only one argument, a reduction RDCT, this macro returns the morphism h of the reduction. Otherwise, it applies h to a combination provided in additional arguments such as CMBN or DEGR GNRT. ——————————————————————————

Package

cat

Source

macros.lisp (file)

Macro: i-add MRPH1 &rest REST
Package

cat

Source

macros.lisp (file)

Macro: i-cmps MRPH1 &rest REST
Package

cat

Source

macros.lisp (file)

Macro: i-sbtr MRPH1 MRPH2 &rest REST
Package

cat

Source

macros.lisp (file)

Macro: kfll &rest REST
Package

cat

Source

macros.lisp (file)

Macro: lexico &rest REST
Package

cat

Source

macros.lisp (file)

Macro: lf &rest REST
Package

cat

Source

macros.lisp (file)

Macro: lg &rest REST
Package

cat

Source

macros.lisp (file)

Macro: line-minus-5 MTRX-LIST BEGIN LINE
Package

cat

Source

macros.lisp (file)

Macro: line-op-5 MTRX-LIST BEGIN LAMBDA LINE1 LINE2
Package

cat

Source

macros.lisp (file)

Macro: line-swap-5 MTRX-LIST BEGIN LINE1 LINE2
Package

cat

Source

macros.lisp (file)

Macro: mask N
Package

cat

Source

macros.lisp (file)

Macro: non-degenerate-p ABSM
Package

cat

Source

macros.lisp (file)

Macro: rbcc &rest REST
Package

cat

Source

macros.lisp (file)

Macro: rf &rest REST
Package

cat

Source

macros.lisp (file)

Macro: rg &rest REST
Package

cat

Source

macros.lisp (file)

Macro: tcc &rest REST

—————————————————————–[macro-doc] TCC
Args: (&rest rest)
Args: (rdct)
Args: (rdct cmbn)
Args: (rdct degr gnrt)
With only one argument, a reduction RDCT, this macro returns the top
chain complex of the reduction. Otherwise, it applies the differential of the top chain complex of RDCT to a combination provided in additional arguments such as CMBN or DEGR GNRT. ——————————————————————————

Package

cat

Source

macros.lisp (file)

Macro: term CFFC GNRT
Package

cat

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macros.lisp (file)

Macro: term-cmbn DEGR CFFC GNRT

—————————————————————–[macro-doc] TERM-CMBN
Args: (degr cffc gnrt)
Returns the combination of degree DEGR with the only term CFFC*GNRT. ——————————————————————————

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macros.lisp (file)

Macro: tnpr DEGR1 GNRT1 DEGR2 GNRT2
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macros.lisp (file)

Macro: with--term (CFFC GNRT) MARK . BODY
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macros.lisp (file)

Macro: with-absm (DGOP-VAR GMSM-VAR) ABSM . BODY
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macros.lisp (file)

Macro: with-cmbn (DEGR LIST) CMBN . BODY
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macros.lisp (file)

Macro: with-crpr &rest REST
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macros.lisp (file)

Macro: with-term (CFFC GNRT) TERM . BODY
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macros.lisp (file)

Macro: with-tnpr (DEGR1 GNRT1 DEGR2 GNRT2) TNPR . BODY
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macros.lisp (file)


Next: , Previous: , Up: Exported definitions   [Contents][Index]

6.1.4 Functions

Function: 1dgnr INDX ABSM
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simplicial-sets.lisp (file)

Function: 1dgop*dgop 1DGOP DGOP
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simplicial-sets.lisp (file)

Function: 1dlop-dgop 1DLOP DGOP
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simplicial-sets.lisp (file)

Function: 2absm-acrpr ABSM1 ABSM2
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cartesian-products.lisp (file)

Function: 2cmbn-add CMPR CMBN1 CMBN2

————————————————————–[function-doc] 2CMBN-ADD
Args: (cmpr cmbn1 cmbn2)
Returns the combination, which is the sum of CMBN1 and CMBN2. The first argument, CMPR, must be a function or macro, which is used to compare the generators of the combination arguments and to order the terms of the result combination. ——————————————————————————

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combinations.lisp (file)

Function: 2cmbn-sbtr CMPR CMBN1 CMBN2

————————————————————–[function-doc] 2CMBN-SBTR
Args: (cmpr cmbn1 cmbn2)
Returns the combination, which is the difference of CMBN1 and CMBN2. The first argument, CMPR, must be a function or macro, which is used to compare the generators of the combination arguments and to order the terms of the result combination. ——————————————————————————

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combinations.lisp (file)

Function: 2cmbn-tnpr CMBN1 CMBN2
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tensor-products.lisp (file)

Function: 2n-2cmbn CMPR N1 CMBN1 N2 CMBN2

————————————————————–[function-doc] 2N-2CMBN
Args: (cmpr n1 cmbn1 n2 cmbn2)
Returns the combination N1*CMBN1+N2*CMBN2. Both integers N1 and N2 must be non-zero. The first argument, CMPR, must be a function or macro, which is used to compare the generators of the input combinations and to order the terms of the result combination. ——————————————————————————

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combinations.lisp (file)

Function: <a-b< A B
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various.lisp (file)

Function: <a-b> A B
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various.lisp (file)

Function: >a-b< A B
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various.lisp (file)

Function: >a-b> A B
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various.lisp (file)

Function: a-cmpr3 CMPR ABSM1 ABSM2
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simplicial-sets.lisp (file)

Function: a-face4 FACE INDX DMNS ABSM
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simplicial-sets.lisp (file)

Function: abar &rest LIST
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bar.lisp (file)

Function: abar-list INSTANCE
Function: (setf abar-list) VALUE INSTANCE
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classes.lisp (file)

Function: absm-ext-int VLIST
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special-smsts.lisp (file)

Function: absm-int-ext ABSM
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special-smsts.lisp (file)

Function: absm-loopabsm CMPR DMNS ABSM LOOP-ABSM
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ls-twisted-products.lisp (file)

Function: absm-p OBJECT
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classes.lisp (file)

Function: absm-print ABSM STREAM DEPTH
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simplicial-sets.lisp (file)

Function: all-objects ()

————————————————————–[function-doc] ALL-OBJECTS
Args: ()
Return a string representation of a user created objects. ——————————————————————————

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chain-complexes.lisp (file)

Function: allp &rest LIST
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cobar.lisp (file)

Function: allp-list INSTANCE
Function: (setf allp-list) VALUE INSTANCE
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classes.lisp (file)

Function: apowr-face4 FACE INDX DMNS APOWR
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loop-spaces.lisp (file)

Function: apowr-lastface4 CMPR FACE DMNS APOWR
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loop-spaces.lisp (file)

Function: apowr-niloop CMPR APOWR NILOOP
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loop-spaces.lisp (file)

Function: aw SMST1 SMST2 &aux CRTS-PRDC TNSR-PRDC FACE1 FACE2
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eilenberg-zilber.lisp (file)

Function: bar-basis BASIS
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bar.lisp (file)

Function: bar-basis-length BASIS DEGR LENGTH
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bar.lisp (file)

Function: bar-cmpr CMPR
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bar.lisp (file)

Function: bar-hrzn-dffr ALGB
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bar.lisp (file)

Function: bar-intr-hrzn-dffr APRD
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bar.lisp (file)

Function: bar-intr-vrtc-dffr DFFR
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bar.lisp (file)

Function: bicn-cmbn-cmbnb CMBN

(BICN-CMBN-CMBNB CMBN) extracts from the bicone combination CMBN of degree n the B-component as a legal combination of degree n in B. If the B-component is empty, the null combination of degree n in B is returned.

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bicones.lisp (file)

Function: bicn-cmbn-cmbnc CMBN

(BICN-CMBN-CMBNC CMBN) extracts from the bicone combination CMBN of degree n the C-component as a legal combination of degree n+1 in C. If the C-component is empty, the null combination of degree n+1 in C is returned.

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bicones.lisp (file)

Function: bicn-cmbn-cmbnd CMBN

(BICN-CMBN-CMBND CMBN) extracts from the bicone combination CMBN of degree n the D-component as a legal combination of degree n in D. If the D-component is empty, the null combination of degree n in D is returned.

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bicones.lisp (file)

Function: bicone RDCT1 RDCT2

(BICONE RDCT1 RDCT2) returns the bicone chain complex from the reductions RDCT1 and RDCT2. B is the top chain complex of RDCT1 and D is the top chain complex of RDCT2. The bottom chain complexes of RDCT1 and RDCT2 must be the same, and C is that chain complex.

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bicones.lisp (file)

Function: bicone-basis BASISB BASISC BASISD

(BICONE-BASIS BASISB BASISC BASISD) returns a bicone basis function built from the basis functions BASISB, BASISC and BASISD. If at least one is locally effective, the function returns the symbol :locally-effective.

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bicones.lisp (file)

Function: bicone-cmpr CMPRB CMPRC CMPRD

(BICONE-CMPR CMPRB CMPRC CMPRD) returns a comparison function for bicone generators, which is contructed from the comparison functions CMPRB, CMPRC and CMPRD.

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bicones.lisp (file)

Function: binomial-n-p N P
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various.lisp (file)

Function: brown-reduction FIBRATION &aux BASE FIBRE TOTAL EZ T-PERTURBATION
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serre.lisp (file)

Function: bspn-p CMPR BSPN DMNS ABSM
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simplicial-sets.lisp (file)

Function: build-chcm &key CMPR BASIS BSGN INTR-DFFR STRT ORGN

————————————————————–[function-doc] BUILD-CHCM
Args: (&key cmpr basis bsgn intr-dffr strt orgn)
Returns an instance of the class CHAIN-COMPLEX. The keyword arguments are as follows:

:CMPR CMPR, the comparison function for generators

:BASIS BASIS, the function defining the basis of the freee Z-modules C_p or the the keyword :LOCALLY-EFFECTIVE

:BSGN BSGN, a generator, the base point of the underlying set

:INTR-DFFR INTR-DFFR, a Lisp function defining the differential homomorphism for each p (d_p: C_p -> C_{p-1}

:STRT STRT, one of the keywords :GNRT or :CMBN, defining the mapping strategy of the differential homomorphism, either by generator or by combination. The default is :GNRT

:ORGN ORGN, a list which is the copy of a Lisp statement, in principle the statement which was at the origin of the creation of this Kenzo object. A caching process, using this slot, prevents the creation of multiple copies of the same mathematical object, which is important for efficiency. It is used also for debugging and analyzing the program.

Use this function instead of creating instances via the standard constructor MAKE-INSTANCE. ——————————————————————————

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chain-complexes.lisp (file)

Function: build-finite-ss LIST
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special-smsts.lisp (file)

Function: build-mrph &key SORC TRGT DEGR INTR STRT ORGN

————————————————————–[function-doc] BUILD-MRPH
Args: (&key sorc trgt degr intr strt orgn)
Returns an instance of the class MORPHISM. The keyword arguments are as follows:

:SORC SORC, the source object, a CHAIN-COMPLEX type object

:TRGT TRGT, the target object, a CHAIN-COMPLEX type object

:DEGR DEGR, the degree of the morphism, an integer

:INTR INTR, the Lisp function defining the effective mapping

:STRT STRT, one of the keywords :GNRT or :CMBN, defining the mapping strategy of the differential homomorphism, either by generator or by combination. The default is :GNRT

:ORGN ORGN, a list which is the copy of a Lisp statement, in principle the statement which was at the origin of the creation of this Kenzo object. A caching process, using this slot, prevents the creation of multiple copies of the same mathematical object, which is important for efficiency. It is used also for debugging and analyzing the program.

Use this function instead of creating instances via the standard constructor MAKE-INSTANCE. ——————————————————————————

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chain-complexes.lisp (file)

Function: build-rdct &key F G H ORGN

————————————————————–[function-doc] BUILD-RDCT
Args: (&key f g h orgn)
Returns an instance of the class REDUCTION. The keyword arguments are as follows:

:F F, an object of type MORPHISM representing the chain morphism f of a reduction

:G G, an object of type MORPHISM representing the chain morphism g of a reduction

:H H, an object of type MORPHISM representing the morphism of graded modules h of a reduction

:ORGN ORGN, a list which is the copy of a Lisp statement, in principle the statement which was at the origin of the creation of this Kenzo object. A caching process, using this slot, prevents the creation of multiple copies of the same mathematical object, which is important for efficiency. It is used also for debugging and analyzing the program.

Use this function instead of creating instances via the standard constructor MAKE-INSTANCE. ——————————————————————————

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effective-homology.lisp (file)

Function: build-smmr &key SORC TRGT DEGR SINTR INTR STRT ORGN
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simplicial-mrphs.lisp (file)

Function: build-smst &key CMPR BASIS BSPN FACE FACE* INTR-BNDR BNDR-STRT INTR-DGNL DGNL-STRT ORGN
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simplicial-sets.lisp (file)

Function: cat-init ()

————————————————————–[function-doc] CAT-INIT
Args: ()
Initialize Kenzo internal data structures and clear, among other things, the list of user created chain complexes *CHCM-LIST* and reset the global counter to 0. ——————————————————————————

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chain-complexes.lisp (file)

Function: change-chcm-to-algb CHCM &key INTR-APRD APRD-STRT ORGN
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algebras.lisp (file)

Function: chcm IDNM

————————————————————–[function-doc] CHCM
Args: (idnm)
Return from the list *CHCM-LIST* the chain complex instance with Kenzo identifier IDNUM or NIL, if it doesn’t exist. ——————————————————————————

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chain-complexes.lisp (file)

Function: chcm-disk-pasting CHCM DMNS NEW BNDR
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disk-pasting.lisp (file)

Function: chcm-homology CC N
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homology-groups.lisp (file)

Function: chcm-homology-gen CC N
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homology-groups.lisp (file)

Function: chcm-mat CHCM N
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homology-groups.lisp (file)

Function: chcm-mtrx CHCM DEGR
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smith.lisp (file)

Function: check-cmbn CHCM CMBN

————————————————————–[function-doc] CHECK-CMBN
Args: (chcm cmbn)
Tests if the combination CMBN is a valid combination of chain complex CHCM. CHECK-CMBN raises an error if the generators of CMBN are out-of-order. ——————————————————————————

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combinations.lisp (file)

Function: check-faces CMPR FACE DMNS GMSM
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simplicial-sets.lisp (file)

Function: check-hat KAN INDX DMNS HAT
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kan.lisp (file)

Function: check-kan KAN INDX DMNS HAT
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kan.lisp (file)

Function: check-rdct ()

————————————————————–[function-doc] CHECK-RDCT
Args: ()
Maps combinations of the top and bottom chain complexes of a reduction using the morphisms created by PRE-CHECK-RDCT. Having no parameters, the combinations must be provided via the Lisp global variables *TC* and *BC*, for the top and bottom chain complex, respectively. If the morphisms are coherent, the result of each mapping is a null combination.

Note: This function is intended for interactive use. It pauses after each evaluation for the user to inspect the result. Resume execution, by pressing the <Enter> key. ——————————————————————————

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effective-homology.lisp (file)

Function: check-rdct-no-wait ()

————————————————————–[function-doc] CHECK-RDCT-NO-WAIT
Args: ()
Maps combinations of the top and bottom chain complexes of a reduction using the morphisms created by PRE-CHECK-RDCT. Having no parameters, the combinations must be provided via the Lisp global variables *TC* and *BC*, for the top and bottom chain complex, respectively. If the morphisms are coherent, the result of each mapping is a null combination. ——————————————————————————

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effective-homology.lisp (file)

Function: check-smst SMST DMNS1 &optional DMNS2
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simplicial-sets.lisp (file)

Function: chml-clss CHCM FIRST
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smith.lisp (file)

Function: chml-clss-intr CHCM FIRST
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smith.lisp (file)

Function: circle ()
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k-pi-n.lisp (file)

Function: classifying-space-basis BASIS
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classifying-spaces.lisp (file)

Function: classifying-space-cmpr CMPR
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classifying-spaces.lisp (file)

Function: classifying-space-face FACE SINTR-GRML
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classifying-spaces.lisp (file)

Function: classifying-space-grin-sintr SINTR-GRIN
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classifying-spaces.lisp (file)

Function: classifying-space-grml-sintr IDNT SINTR-GRML
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classifying-spaces.lisp (file)

Function: clock ()
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various.lisp (file)

Function: cmbn DEGR &rest REST

————————————————————–[function-doc] CMBN
Args: (degr &rest rest)
Returns a combination of degree DEGR from a sum of terms provided as a sequence CF1 GNRT1 CF2 GNRT2 ... CFn GNRTn of coefficient / generator pairs in REST. REST can be of arbitrary length including NIL, in which case the combination is an instance of the null combination of degree DEGR. ——————————————————————————

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combinations.lisp (file)

Function: cmbn-? MRPH CMBN
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chain-complexes.lisp (file)

Function: cmbn-cmbn CMPR N-CMBN-LIST

————————————————————–[function-doc] CMBN-CMBN
Args: (cmpr n-cmbn-list)
Returns the linear combination of a list of integer/combination pairs. The first argument, CMPR, must be a function or macro, which is used to compare the generators of the input combinations and to order the terms of the result combination. The second argument, N-CMBN-LIST, is a list dotted pairs (CONSes), where the first element is a non-zero integer and the second element is a combination. ——————————————————————————

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combinations.lisp (file)

Function: cmbn-con0 CMBN
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cones.lisp (file)

Function: cmbn-con1 CMBN
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cones.lisp (file)

Function: cmbn-degr INSTANCE
Function: (setf cmbn-degr) VALUE INSTANCE
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classes.lisp (file)

Function: cmbn-list INSTANCE
Function: (setf cmbn-list) VALUE INSTANCE
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classes.lisp (file)

Function: cmbn-opps CMBN

————————————————————–[function-doc] CMBN-OPPS
Args: (cmbn)
Returns the combination opposite combination of CMBN. ——————————————————————————

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combinations.lisp (file)

Function: cobar-basis BASIS
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cobar.lisp (file)

Function: cobar-basis-length BASIS DEGR LENGTH
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cobar.lisp (file)

Function: cobar-cmpr CMPR
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cobar.lisp (file)

Function: cobar-hrzn-dffr CLGB
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cobar.lisp (file)

Function: cobar-intr-hrzn-dffr CPRD
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cobar.lisp (file)

Function: cobar-intr-vrtc-dffr DFFR
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cobar.lisp (file)

Function: column-minus MTRX BEGIN COLUMN
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smith.lisp (file)

Function: column-op MTRX BEGIN LAMBDA COLUMN1 COLUMN2
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smith.lisp (file)

Function: column-swap MTRX BEGIN COLUMN1 COLUMN2
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smith.lisp (file)

Function: cone MRPH
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cones.lisp (file)

Function: cone-2cmbn-append CMBN0 CMBN1
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cones.lisp (file)

Function: cone-2mrph-diag SORC-CONE TRGT-CONE MRPH0 MRPH1
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cones.lisp (file)

Function: cone-2mrph-diag-impl MRPH0 MRPH1
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cones.lisp (file)

Function: cone-3mrph-triangle SORC-CONE TRGT-CONE MRPH0 MRPH1 PHI
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cones.lisp (file)

Function: cone-3mrph-triangle-impl CMPR0 MRPH0 MRPH1 PHI
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cones.lisp (file)

Function: cone-basis BASIS0 BASIS1
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cones.lisp (file)

Function: cone-cmbn-split CMBN
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cones.lisp (file)

Function: cone-cmpr CMPR0 CMPR1
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cones.lisp (file)

Function: copy-mtrx MTRX
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smith.lisp (file)

Function: crts-contraction SPACE &aux TWISTED-CRTS-PRDC
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ls-twisted-products.lisp (file)

Function: crts-contraction-intr BASE-CMPR BASE-BSPN BASE-FACE CRTS-CMPR
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ls-twisted-products.lisp (file)

Function: crts-prdc SMST1 SMST2
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cartesian-products.lisp (file)

Function: crts-prdc-basis BASIS1 BASIS2
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cartesian-products.lisp (file)

Function: crts-prdc-cmpr CMPR1 CMPR2
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cartesian-products.lisp (file)

Function: crts-prdc-face FACE1 FACE2
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cartesian-products.lisp (file)

Function: crts-prdc-face* FACE1 FACE2
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cartesian-products.lisp (file)

Function: cs-hat-t-u SMGR &aux BAR FIBRATION BROWN TWISTED-TNSR-PRDC HAT-U-U
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cl-space-efhm.lisp (file)

Function: cs-hat-u-t SMGR &aux HAT-U-U HAT-RIGHT-PERTURBATION
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cl-space-efhm.lisp (file)

Function: cs-left-hmeq SMGR
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cl-space-efhm.lisp (file)

Function: cs-left-hmeq-hat SMGR &aux HAT-T-U HAT-RIGHT-PERTURBATION
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cl-space-efhm.lisp (file)

Function: cs-left-hmeq-left-reduction SMGR &aux PRE-LEFT-HMEQ-LEFT-REDUCTION HAT-LEFT-PERTURBATION
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cl-space-efhm.lisp (file)

Function: cs-left-hmeq-right-reduction SMGR &aux PRE-REDUCTION PERTURBATION
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cl-space-efhm.lisp (file)

Function: cs-pre-left-hmeq-left-reduction SMGR
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cl-space-efhm.lisp (file)

Function: cs-pre-left-hmeq-left-reduction-intr-f CMBN
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cl-space-efhm.lisp (file)

Function: cs-pre-left-hmeq-left-reduction-intr-g IDNT
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cl-space-efhm.lisp (file)

Function: cs-pre-left-hmeq-right-reduction SMGR
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cl-space-efhm.lisp (file)

Function: cs-pre-left-hmeq-right-reduction-intr-f CMBN
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cl-space-efhm.lisp (file)

Function: cs-pre-left-hmeq-right-reduction-intr-g IDNT
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cl-space-efhm.lisp (file)

Function: delta DMNS
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delta.lisp (file)

Function: delta-bndr DMNS GMSM
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delta.lisp (file)

Function: delta-dgnl DMNS GMSM
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delta.lisp (file)

Function: delta-face INDX DMNS GMSM
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delta.lisp (file)

Function: delta-infinity ()
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delta.lisp (file)

Function: delta-n-basis N
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delta.lisp (file)

Function: deltab ()
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delta.lisp (file)

Function: deltab2 ()
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delta.lisp (file)

Function: deltab2-bndr DMNS GMSM
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delta.lisp (file)

Function: deltab2-dgnl DMNS GMSM
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delta.lisp (file)

Function: dgop INSTANCE
Function: (setf dgop) VALUE INSTANCE
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classes.lisp (file)

Function: dgop*dgop DGOP1 DGOP2
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simplicial-sets.lisp (file)

Function: dgop-ext-int EXT-DGOP
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simplicial-sets.lisp (file)

Function: dgop-int-ext DGOP
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simplicial-sets.lisp (file)

Function: dgop/dgop DGOP1 DGOP2
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simplicial-sets.lisp (file)

Function: dgop1 INSTANCE
Function: (setf dgop1) VALUE INSTANCE
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classes.lisp (file)

Function: dgop2 INSTANCE
Function: (setf dgop2) VALUE INSTANCE
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classes.lisp (file)

Function: disk-pasting SMST DMNS NEW FACES
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disk-pasting.lisp (file)

Function: disk-pasting-basis BASIS DMNS NEW
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disk-pasting.lisp (file)

Function: disk-pasting-cmpr CMPR NEW
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disk-pasting.lisp (file)

Function: disk-pasting-face CMPR FACE DMNS NEW FACES
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disk-pasting.lisp (file)

Function: disk-pasting-intr-dffr OLD-DFFR DEGR NEW BNDR
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disk-pasting.lisp (file)

Function: dispatch-bicn-cmbn CMBN

(DISPATCH-BICN-CMBN CMBN) splits the bicone combination CMBN into three combinations and returns 3 values.

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bicones.lisp (file)

Function: dlop-ext-int EXT-DLOP
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simplicial-sets.lisp (file)

Function: dlop-int-ext DLOP
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simplicial-sets.lisp (file)

Function: do-control CMPR CMBN
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chain-complexes.lisp (file)

Function: done ()
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various.lisp (file)

Function: dstr-add-term-to-cmbn CMPR CFFC GNRT CMBN

————————————————————–[function-doc] DSTR-ADD-TERM-TO-CMBN
Args: (cmpr cffc gnrt cmbn)
Returns a combination, which is the result of adding the term CFFC*GNRT to the combination CMBN. The first argument, CMPR, must be a function or macro, which is used to compare the generators of the inputs and to order the terms of the result combination. ——————————————————————————

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combinations.lisp (file)

Function: dtau-d SPACE &aux LOOP-SPACE CRTS-PRDC CRTS-PRDC-CMPR CRTS-PRDC-FACE TWISTED-CRTS-PRDC TWISTED-CRTS-PRDC-FACE
Package

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Source

ls-twisted-products.lisp (file)

Function: dtau-d-intr CRTS-PRDC-CMPR CRTS-PRDC-FACE TWISTED-CRTS-PRDC-FACE
Package

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Source

ls-twisted-products.lisp (file)

Function: echcm CHCM
Package

cat

Source

searching-homology.lisp (file)

Function: echcm-kill-epi ECHCM FIRST
Package

cat

Source

smith.lisp (file)

Function: echcm-kill-epi-f-intr CMPR FIRST N M F+1-BASIS MTRX-LIST
Package

cat

Source

smith.lisp (file)

Function: echcm-kill-epi-g-intr FIRST N M F+1-BASIS MTRX-LIST
Package

cat

Source

smith.lisp (file)

Function: echcm-kill-epi-h-intr CMPR FIRST N M F-BASIS F+1-BASIS MTRX-LIST
Package

cat

Source

smith.lisp (file)

Function: eml SMST1 SMST2
Package

cat

Source

eilenberg-zilber.lisp (file)

Function: extract-common-dgop DGOP1 DGOP2
Package

cat

Source

cartesian-products.lisp (file)

Function: ez SMST1 SMST2
Package

cat

Source

eilenberg-zilber.lisp (file)

Function: f-cmpr N1 N2

————————————————————–[function-doc] F-CMPR
Args: (n1 n2)
Returns :LESS, :EQUAL, or :GREATER, according to the result of the canonical comparison of the integers N1 and N2. ——————————————————————————

Package

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Source

combinations.lisp (file)

Function: face*-bndr CMPR FACE*
Package

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Source

simplicial-sets.lisp (file)

Function: face-bndr CMPR FACE
Package

cat

Source

simplicial-sets.lisp (file)

Function: fibration-dtau-d FIBRATION &aux BASE FIBRE UTOTAL
Package

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Source

serre.lisp (file)

Function: fibration-dtau-d-intr FIBRATION &aux BASE BFACE FIBRE FFACE SINTR-GRML FBSPN SINTR-TWIST TOTAL TOTAL-CMPR
Package

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Source

serre.lisp (file)

Function: fibration-total FIBRATION &aux BASE FIBRE UNTWISTED-PRDC
Package

cat

Source

fibrations.lisp (file)

Function: finite-ss-pre-table LIST
Package

cat

Source

special-smsts.lisp (file)

Function: finite-ss-pre-table-table PRE-TABLE
Package

cat

Source

special-smsts.lisp (file)

Function: finite-ss-table LIST
Package

cat

Source

special-smsts.lisp (file)

Function: gbar DMNS &rest REST
Package

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Source

classifying-spaces.lisp (file)

Function: gdeltab ()
Package

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Source

loop-spaces.lisp (file)

Function: gmsm INSTANCE
Function: (setf gmsm) VALUE INSTANCE
Package

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Source

classes.lisp (file)

Function: gmsm-cocycle FACE SMALL-DMNS HIGH-DMNS GMSM CHML-CLSS
Package

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Source

k-pi-n.lisp (file)

Function: gmsm1 INSTANCE
Function: (setf gmsm1) VALUE INSTANCE
Package

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Source

classes.lisp (file)

Function: gmsm2 INSTANCE
Function: (setf gmsm2) VALUE INSTANCE
Package

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Source

classes.lisp (file)

Function: gmsms-subsmst SMST GMSMS &aux DMNS CMPR=
Package

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Source

special-smsts.lisp (file)

Function: gnrt-? MRPH DEGR GNRT
Package

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Source

chain-complexes.lisp (file)

Function: gnrt-name-basis N
Package

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Source

smith.lisp (file)

Function: hmeq-disk-pasting HMEQ DMNS NEW BNDR &key NEW-LBCC
Package

cat

Source

disk-pasting.lisp (file)

Function: hmtp-vrtc-bar-intr H GF
Package

cat

Source

bar.lisp (file)

Function: hmtp-vrtc-cobar-intr H GF
Package

cat

Source

cobar.lisp (file)

Function: homologie M N
Package

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Source

homology-groups.lisp (file)

Function: hopf IDNM
Package

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Source

algebras.lisp (file)

Function: hopf-fibration N
Package

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Source

k-pi-n.lisp (file)

Function: hopf-fibration-sintr N
Package

cat

Source

k-pi-n.lisp (file)

Function: how-many-objects ()

————————————————————–[function-doc] HOW-MANY-OBJECTS
Args: ()
Return the number of user created objects by object type. ——————————————————————————

Package

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Source

chain-complexes.lisp (file)

Function: hyphenize-list LIST
Package

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Source

simplicial-sets.lisp (file)

Function: idnt-mrph CHCM
Package

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Source

chcm-elementary-op.lisp (file)

Function: idnt-mtrx N
Package

cat

Source

smith.lisp (file)

Function: interesting-faces FACE SMALL-DMNS HIGH-DMNS GMSM
Package

cat

Source

k-pi-n.lisp (file)

Function: intr-aw FACE1 FACE2
Package

cat

Source

eilenberg-zilber.lisp (file)

Function: intr-diagonal FACE
Package

cat

Source

simplicial-sets.lisp (file)

Function: intr-eml CMBN
Package

cat

Source

eilenberg-zilber.lisp (file)

Function: intr-phi SMST1 SMST2 &aux CRTS-PRDC CMPR FACE1 FACE2
Package

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Source

eilenberg-zilber.lisp (file)

Function: k IDNM

————————————————————–[function-doc] K
Args: (idnm)
Returns the IDNM-th Kenzo object. ——————————————————————————

Package

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Source

chain-complexes.lisp (file)

Function: k-z N
Package

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Source

k-pi-n.lisp (file)

Function: k-z-1 ()
Package

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Source

k-pi-n.lisp (file)

Function: k-z-1-cmpr GNRT1 GNRT2
Package

cat

Source

k-pi-n.lisp (file)

Function: k-z-1-face INDX DMNS GMSM
Package

cat

Source

k-pi-n.lisp (file)

Function: k-z-1-grin DMNS BAR
Package

cat

Source

k-pi-n.lisp (file)

Function: k-z-1-grml DMNS CRPR
Package

cat

Source

k-pi-n.lisp (file)

Function: k-z-fundamental-class N
Package

cat

Source

k-pi-n.lisp (file)

Function: k-z2 N
Package

cat

Source

k-pi-n.lisp (file)

Function: k-z2-1 ()
Package

cat

Source

k-pi-n.lisp (file)

Function: k-z2-fundamental-class N
Package

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Source

k-pi-n.lisp (file)

Function: kan IDNM
Package

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Source

kan.lisp (file)

Function: kd IDNM

————————————————————–[function-doc] KD
Args: (idnm)
Return the type of Kenzo object number IDNM and print the comment list (SLOT :ORGN) of the object. ——————————————————————————

Package

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Source

chain-complexes.lisp (file)

Function: kd2 IDNM

————————————————————–[function-doc] KD2
Args: (idnm)
Return the type of Kenzo object number IDNM, print the comment list
(SLOT :ORGN) of the object and, recursively, return the same information for all Kenzo objects of the same type in relation with this object. Return the list of object numbers. ——————————————————————————

Package

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Source

chain-complexes.lisp (file)

Function: kenzo-version ()
Package

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Source

kenzo.lisp (file)

Function: kill-epi CHCM FIRST
Package

cat

Source

smith.lisp (file)

Function: kill-epis CHCM FIRST END
Package

cat

Source

smith.lisp (file)

Function: kz1-rdct ()
Package

cat

Source

k-pi-n.lisp (file)

Function: kz1-rdct-f-intr CMBN
Package

cat

Source

k-pi-n.lisp (file)

Function: kz1-rdct-h-intr DMNS BAR
Package

cat

Source

k-pi-n.lisp (file)

Function: l-cmpr LIST1 LIST2

————————————————————–[function-doc] L-CMPR
Args: (list1 list2)
Returns :LESS, :EQUAL, or :GREATER, according to the lexicographical ordering of the generator lists LIST1 and LIST2. ——————————————————————————

Package

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Source

combinations.lisp (file)

Function: left-submatrix MTRX K
Package

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Source

smith.lisp (file)

Function: line-minus MTRX BEGIN LINE
Package

cat

Source

smith.lisp (file)

Function: line-op MTRX BEGIN LAMBDA LINE1 LINE2
Package

cat

Source

smith.lisp (file)

Function: line-swap MTRX BEGIN LINE1 LINE2
Package

cat

Source

smith.lisp (file)

Function: list-smith MTRX-LIST
Package

cat

Source

smith.lisp (file)

Function: loop-list INSTANCE
Function: (setf loop-list) VALUE INSTANCE
Package

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Source

classes.lisp (file)

Function: loop-print LOOP STREAM DEPTH
Package

cat

Source

loop-spaces.lisp (file)

Function: loop-space SMST &optional N
Package

cat

Source

loop-spaces.lisp (file)

Function: loop-space-cmpr CMPR
Package

cat

Source

loop-spaces.lisp (file)

Function: loop-space-face CMPR FACE
Package

cat

Source

loop-spaces.lisp (file)

Function: loop-space-grin-sintr DMNS LOOP
Package

cat

Source

loop-spaces.lisp (file)

Function: loop-space-grml-sintr CMPR
Package

cat

Source

loop-spaces.lisp (file)

Function: loop3 &rest LIST
Package

cat

Source

loop-spaces.lisp (file)

Function: ls-hat-t-u SPACE &aux LS-HAT-U-U LS-HAT-LEFT-PERTURBATION
Package

cat

Source

lp-space-efhm.lisp (file)

Function: ls-hat-u-t SPACE &aux COBAR TWISTED-TNSR-PRDC LS-HAT-U-U
Package

cat

Source

lp-space-efhm.lisp (file)

Function: ls-left-hmeq SPACE
Package

cat

Source

lp-space-efhm.lisp (file)

Function: ls-left-hmeq-hat SPACE &aux LS-HAT-U-T LS-HAT-LEFT-PERTURBATION
Package

cat

Source

lp-space-efhm.lisp (file)

Function: ls-left-hmeq-left-reduction SPACE &aux LS-PRE-LEFT-HMEQ-LEFT-REDUCTION LS-HAT-RIGHT-PERTURBATION
Package

cat

Source

lp-space-efhm.lisp (file)

Function: ls-left-hmeq-left-reduction-g-intr BSPN
Package

cat

Source

lp-space-efhm.lisp (file)

Function: ls-left-hmeq-right-reduction SPACE &aux PRE-REDUCTION PERTURBATION
Package

cat

Source

lp-space-efhm.lisp (file)

Function: ls-pre-left-hmeq-left-reduction SPACE
Package

cat

Source

lp-space-efhm.lisp (file)

Function: ls-pre-left-hmeq-left-reduction-h-intr SPACE &aux LS-HAT-T-U CMPR
Package

cat

Source

lp-space-efhm.lisp (file)

Function: ls-pre-left-hmeq-left-reduction-intr-f CMBN
Package

cat

Source

lp-space-efhm.lisp (file)

Function: ls-pre-left-hmeq-right-reduction SPACE
Package

cat

Source

lp-space-efhm.lisp (file)

Function: ls-pre-left-hmeq-right-reduction-intr-f CMBN
Package

cat

Source

lp-space-efhm.lisp (file)

Function: ls-pre-left-hmeq-right-reduction-intr-g BSPN
Package

cat

Source

lp-space-efhm.lisp (file)

Function: make-abar &key (LIST LIST)
Package

cat

Source

classes.lisp (file)

Function: make-absm &key (DGOP DGOP) (GMSM GMSM)
Package

cat

Source

classes.lisp (file)

Function: make-allp &key (LIST LIST)
Package

cat

Source

classes.lisp (file)

Function: make-bicn-cmbn CMBNB CMBNC CMBND

(MAKE-BICN-CMBN CMBNB CMBNC CMBND) constructs a bicone combination from CMBNB, CMBNC and CMBND, which belong to chain complexes B, C, D, respectively. Combinations CMBNB and CMBND must be of the same degree n and combination CMBNC must be of degree n+1, yiedling a bicone combination of degree n.

Package

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Source

bicones.lisp (file)

Function: make-cmbn &key (DEGR DEGR) (LIST LIST)
Package

cat

Source

classes.lisp (file)

Function: make-gbar &key (DMNS DMNS) (LIST LIST)
Package

cat

Source

classes.lisp (file)

Function: make-loop &key (LIST LIST)
Package

cat

Source

classes.lisp (file)

Function: make-result &key (GNRT GNRT) (VALUE VALUE) (CLNM CLNM) (RNTM RNTM)
Package

cat

Source

classes.lisp (file)

Function: maplexico CMPR LIST1 LIST2
Package

cat

Source

combinations.lisp (file)

Function: mat-aleat N1 N2 DENS X
Package

cat

Source

homology-groups.lisp (file)

Function: minimal-rest-1 MATRIX BEGIN
Package

cat

Source

smith.lisp (file)

Function: minimal-rest-2 MATRIX BEGIN
Package

cat

Source

smith.lisp (file)

Function: minimal-term MATRIX BEGIN
Package

cat

Source

smith.lisp (file)

Function: minimal-term-top-left MTRX-LIST BEGIN IL IC
Package

cat

Source

smith.lisp (file)

Function: moore PII DMNS
Package

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Source

special-smsts.lisp (file)

Function: mrph N

Return from the list *MRPH-LIST* the morphism instance with Kenzo identifier IDNUM or NIL, if it doesn’t exist.

Package

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Source

chain-complexes.lisp (file)

Function: mrph-disk-pasting MRPH NEW-SORC NEW-TRGT DMNS NEW NEW-IM
Package

cat

Source

disk-pasting.lisp (file)

Function: mrph-disk-pasting-intr MRPH TRGT-CMPR DMNS NEW NEW-IM
Package

cat

Source

disk-pasting.lisp (file)

Function: mrph-vrtc-bar-intr MRPH
Package

cat

Source

bar.lisp (file)

Function: mrph-vrtc-cobar-intr MRPH
Package

cat

Source

cobar.lisp (file)

Function: mtrx-prdc MTRX1 MTRX2
Package

cat

Source

smith.lisp (file)

Function: n-cmbn N CMBN

————————————————————–[function-doc] N-CMBN
Args: (n cmbn)
Returns N times the combination CMBN. N must be non-zero. ——————————————————————————

Package

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Source

combinations.lisp (file)

Function: n-mrph N MRPH
Package

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Source

chcm-elementary-op.lisp (file)

Function: ncmbn-add CMPR CMBN &rest REST

————————————————————–[function-doc] NCMBN-ADD
Args: (cmpr cmbn &rest rest)
Returns the sum of an arbitrary number of combinations. The first argument, CMPR, must be a function or macro, which is used to compare the generators of the input combinations and to order the terms of the result combination. ——————————————————————————

Package

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Source

combinations.lisp (file)

Function: ncmbn-bar CMBN-LIST
Package

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Source

bar.lisp (file)

Function: ncmbn-cobar CMBN-LIST
Package

cat

Source

cobar.lisp (file)

Function: ndgnr DGOP ABSM
Package

cat

Source

simplicial-sets.lisp (file)

Function: nface FACE DLOP DMNS GMSM
Package

cat

Source

simplicial-sets.lisp (file)

Function: normalize-gbar NIGBAR
Package

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Source

classifying-spaces.lisp (file)

Function: normalize-loop DMNS NILOOP
Package

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Source

loop-spaces.lisp (file)

Function: nterm-add CMPR DEGR &rest REST

————————————————————–[function-doc] NTERM-ADD
Args: (cmpr degr &rest rest)
Returns a combination of degree DEGR which is the sum of terms supplied in REST. The first argument, CMPR, must be a function or macro, which is used to compare the generators of the input terms and to order the terms of the result combination. If REST is NIL, an instance of the null combination of degree DEGR is returned. ——————————————————————————

Package

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Source

combinations.lisp (file)

Function: opps MRPH
Package

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Source

chcm-elementary-op.lisp (file)

Function: phi SMST1 SMST2
Package

cat

Source

eilenberg-zilber.lisp (file)

Function: pivott MTRX-LIST BEGIN
Package

cat

Source

smith.lisp (file)

Function: pop-first-absm DMNS ILOOP
Package

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Source

ls-twisted-products.lisp (file)

Function: pre-check-rdct RDCT

————————————————————–[function-doc] PRE-CHECK-RDCT
Args: (rdct)
Assigns the following Lisp global variables, using morphisms from RDCT and the differentials and identity morphisms of the underlying chain complexes, according to these formulas:

*TDD* = d ° d
^ ^
C C

*BDD* = d ° d
C C

*ID-FG* = Id - f ° g
C

*ID-GF-DH-HD* = Id - g ° f - (d ° h + h ° d )
^ ^ ^
C C C

*HH* = h ° h
*FH* = f ° h
*HG* = h ° g

*DF-FD* = d ° f - f ° d
C ^
C

*DG-GD* = d ° g - g ° d
^ C
C

——————————————————————————

Package

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Source

effective-homology.lisp (file)

Function: r-proj-space &rest ARGS
Package

cat

Source

special-smsts.lisp (file)

Function: r-proj-space-basis K L
Package

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Source

special-smsts.lisp (file)

Function: random-matrix LINE-N COLUMN-N MAX
Package

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smith.lisp (file)

Function: rdct N

————————————————————–[function-doc] RDCT
Args: (n)
Returns the N-th user-created reduction from the list *RDCT-LIST*. Returns NIL if it doesn’t exist. ——————————————————————————

Package

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Source

effective-homology.lisp (file)

Function: remove-bit N INDX
Package

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Source

simplicial-sets.lisp (file)

Function: right-serre-efhm FIBRATION &aux BASE FIBRE BASE-EFHM FIBRE-EFHM UPRDC-EFHM
Package

cat

Source

serre.lisp (file)

Function: s-cmpr SYMBOL1 SYMBOL2

————————————————————–[function-doc] S-CMPR
Args: (symbol1 symbol2)
Returns :LESS, :EQUAL, or :GREATER, according to the result of the Lisp string comparison function of the strings (SYMBOL-NAME SYMBOL1) and
(SYMBOL-NAME SYMBOL2). ——————————————————————————

Package

cat

Source

combinations.lisp (file)

Function: show-structure SMST DMNS

————————————————————–[function-doc] SHOW-STRUCTURE
Args: (smst dmns)
Shows the structure of the simplicial set SMST (i.e., generators and faces) from dimension 0 up to and including dimension DMNS. ——————————————————————————

Package

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Source

simplicial-sets.lisp (file)

Function: shuffle-sign DGOP
Package

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Source

eilenberg-zilber.lisp (file)

Function: smgr IDNM
Package

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Source

simplicial-groups.lisp (file)

Function: smgr-crts-contraction SMGR
Package

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Source

cs-twisted-products.lisp (file)

Function: smgr-fibration SMGR
Package

cat

Source

cs-twisted-products.lisp (file)

Function: smgr-tnpr-contraction SMGR &aux FIBRATION BROWN F G CHI
Package

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Source

cs-twisted-products.lisp (file)

Function: smst N
Package

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Source

simplicial-sets.lisp (file)

Function: smst-kan SMST KFLL
Package

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kan.lisp (file)

Function: soft-delta DMNS
Package

cat

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delta.lisp (file)

Function: soft-delta-bndr DMNS GMSM
Package

cat

Source

delta.lisp (file)

Function: soft-delta-cmpr GMSM1 GMSM2
Package

cat

Source

delta.lisp (file)

Function: soft-delta-dgnl DMNS GMSM
Package

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Source

delta.lisp (file)

Function: soft-delta-face INDX DMNS GMSM
Package

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delta.lisp (file)

Function: soft-delta-infinity ()
Package

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delta.lisp (file)

Function: soft-delta-n-basis N
Package

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delta.lisp (file)

Function: soft-dlop-p OBJECT
Package

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Source

classes.lisp (file)

Function: sphere DMNS
Package

cat

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special-smsts.lisp (file)

Function: sphere-face DMNS
Package

cat

Source

special-smsts.lisp (file)

Function: sphere-wedge &rest DMNS-LIST
Package

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Source

special-smsts.lisp (file)

Function: srandom MAX
Package

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various.lisp (file)

Function: suspension OBJ &optional N
Package

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suspensions.lisp (file)

Function: suspension-basis BASIS
Package

cat

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suspensions.lisp (file)

Function: suspension-cmpr CMPR
Package

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suspensions.lisp (file)

Function: suspension-face FACE
Package

cat

Source

suspensions.lisp (file)

Function: suspension-intr MRPH
Package

cat

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suspensions.lisp (file)

Function: suspension-intr-cprd CMBN
Package

cat

Source

suspensions.lisp (file)

Function: suspension-intr-dffr DFFR
Package

cat

Source

suspensions.lisp (file)

Function: szczarba SPACE &aux LOOP-SPACE TWISTED-CRTS-PRDC EZ DTAU-D
Package

cat

Source

ls-twisted-products.lisp (file)

Function: term-con0 TERM
Package

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cones.lisp (file)

Function: term-con1 TERM
Package

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Source

cones.lisp (file)

Function: term-uncon TERM
Package

cat

Source

cones.lisp (file)

Function: tnpr-contraction SPACE &aux SZCZARBA F G CRTS-CONTRACTION
Package

cat

Source

ls-twisted-products.lisp (file)

Function: tnpr-p OBJECT
Package

cat

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classes.lisp (file)

Function: tnpr-print TNPR STREAM DEPTH
Package

cat

Source

tensor-products.lisp (file)

Function: tnsr-prdc-basis BASIS1 BASIS2
Package

cat

Source

tensor-products.lisp (file)

Function: tnsr-prdc-cmpr CMPR1 CMPR2
Package

cat

Source

tensor-products.lisp (file)

Function: tnsr-prdc-intr MRPH1 MRPH2
Package

cat

Source

tensor-products.lisp (file)

Function: tnsr-prdc-intr-dffr DFFR1 DFFR2
Package

cat

Source

tensor-products.lisp (file)

Function: trivial-hmeq CHCM
Package

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Source

effective-homology.lisp (file)

Function: trivial-rdct CHCM

————————————————————–[function-doc] TRIVIAL-RDCT
Args: (chcm)
Builds the trivial reduction according to the following diagram, which involves the chain complex CHCM only:

Zero s
C ——-> C
^
| |
Id | | Id
| |
v
C

Zero is the zero morphism of degree 1 of C and Id is its identity morphism.

See also: ZERO-MRPH, IDNT-MRPH. ——————————————————————————

Package

cat

Source

effective-homology.lisp (file)

Function: tw-a-sintr3 SINTR DMNS ABSM BSPN
Package

cat

Source

simplicial-mrphs.lisp (file)

Function: twisted-crts-prdc SPACE &aux LOOP-SPACE CRTS-PRDC
Package

cat

Source

ls-twisted-products.lisp (file)

Function: twisted-crts-prdc-face CMPR SPACE-FACE LOOP-SPACE-FACE NON-TWISTED-FACE
Package

cat

Source

ls-twisted-products.lisp (file)

Function: twisted-tnsr-prdc SPACE &aux SZCZARBA
Package

cat

Source

ls-twisted-products.lisp (file)

Function: unnormalize-gbar ABSM IDNT
Package

cat

Source

classifying-spaces.lisp (file)

Function: unnormalize-loop ABSM
Package

cat

Source

loop-spaces.lisp (file)

Function: v<a-b> A B
Package

cat

Source

various.lisp (file)

Function: vertex-i ABSM I
Package

cat

Source

special-smsts.lisp (file)

Function: what-is KWD

WHAT-IS returns the full word or term for an abbreviation provided as a keyword, string, or symbol. It returns NIL for unknown abbreviations.

Package

cat

Source

abbreviations.lisp (file)

Function: z-absm-bar ABSM
Package

cat

Source

k-pi-n.lisp (file)

Function: z-bar-absm BAR
Package

cat

Source

k-pi-n.lisp (file)

Function: z-chcm ()

————————————————————–[function-doc] Z-CHCM
Args: ()
Build the unit chain complex. ——————————————————————————

Package

cat

Source

chcm-elementary-op.lisp (file)

Function: z-cocycle-gbar N DMNS COCYCLE
Package

cat

Source

k-pi-n.lisp (file)

Function: z-cocycle-gbar-head N DMNS COCYCLE
Package

cat

Source

k-pi-n.lisp (file)

Function: z-fundamental-gmsm DMNS PI-ELM
Package

cat

Source

k-pi-n.lisp (file)

Function: z-whitehead SMST CHML-CLSS &aux N
Package

cat

Source

whitehead.lisp (file)

Function: z-whitehead-sintr SMST N CHML-CLSS &aux FACE K-Z-N-1 IDNT EFHM
Package

cat

Source

whitehead.lisp (file)

Function: z2-absm-bar ABSM
Package

cat

Source

k-pi-n.lisp (file)

Function: z2-bar-absm BAR
Package

cat

Source

k-pi-n.lisp (file)

Function: z2-cocycle-gbar N DMNS COCYCLE
Package

cat

Source

k-pi-n.lisp (file)

Function: z2-cocycle-gbar-head N DMNS COCYCLE
Package

cat

Source

k-pi-n.lisp (file)

Function: z2-fundamental-gmsm DMNS PI-ELM
Package

cat

Source

k-pi-n.lisp (file)

Function: z2-whitehead SMST CHML-CLSS &aux N
Package

cat

Source

whitehead.lisp (file)

Function: z2-whitehead-sintr SMST N CHML-CLSS &aux FACE K-Z2-N-1 IDNT EFHM
Package

cat

Source

whitehead.lisp (file)

Function: zero-cmbn DEGR

————————————————————–[function-doc] ZERO-CMBN
Args: (degr)
Returns an instance of the null combination of degree DEGR. ——————————————————————————

Package

cat

Source

combinations.lisp (file)

Function: zero-intr-dffr CMBN

————————————————————–[function-doc] ZERO-INTR-DFFR
Args: (cmbn)
Returns the null combination of degree p-1, for any combination CMBN of degree p. ——————————————————————————

Package

cat

Source

combinations.lisp (file)

Function: zero-mrph CHCM1 &optional CHCM2 DEGR
Package

cat

Source

chcm-elementary-op.lisp (file)


Next: , Previous: , Up: Exported definitions   [Contents][Index]

6.1.5 Generic functions

Generic Function: ?2 CHCM-OR-MRPH CMBN
Package

cat

Source

chain-complexes.lisp (file)

Methods
Method: ?2 (CHCM chain-complex) CMBN
Method: ?2 (MRPH morphism) CMBN
Generic Function: ?3 CHCM-OR-MRPH DEGR GNRT
Package

cat

Source

chain-complexes.lisp (file)

Methods
Method: ?3 (SMMR simplicial-mrph) DMNS ABSM-OR-GMSM
Source

simplicial-mrphs.lisp (file)

Method: ?3 (CHCM chain-complex) DEGR GNRT
Method: ?3 (MRPH morphism) DEGR GNRT
Generic Function: add CHCM-OR-MRPH MORPHISM &optional STRT
Package

cat

Source

chcm-elementary-op.lisp (file)

Methods
Method: add (HMEQ homotopy-equivalence) (LB-PERTURBATION morphism) &optional DUMMY
Source

effective-homology.lisp (file)

Method: add (RDCT reduction) (PERTURBATION morphism) &optional DUMMY
Source

effective-homology.lisp (file)

Method: add (CHCM chain-complex) (PERTURBATION morphism) &optional STRT
Method: add (MRPH1 morphism) (MRPH2 morphism) &optional STRT
Generic Function: bar ALGEBRA-OR-HMEQ
Package

cat

Source

bar.lisp (file)

Methods
Method: bar (HMEQ homotopy-equivalence)
Method: bar (ALGEBRA algebra)
Generic Function: bsgn OBJECT
Package

cat

Methods
Method: bsgn (CHAIN-COMPLEX chain-complex)

automatically generated reader method

Source

classes.lisp (file)

Generic Function: build-hmeq KEYWORD LRDCT &key LG LH RF RG RH ORGN RRDCT
Package

cat

Source

effective-homology.lisp (file)

Methods
Method: build-hmeq (KEYWORD1 (eql lf)) LF &key LG LH RF RG RH ORGN
Method: build-hmeq (KEYWORD1 (eql lrdct)) LRDCT &key RRDCT ORGN
Generic Function: classifying-space SMGR
Package

cat

Source

classifying-spaces.lisp (file)

Methods
Method: classifying-space (SMGR ab-simplicial-group)
Method: classifying-space (SMGR simplicial-group)
Generic Function: cmps CHCM-OR-MRPH1 CHCM-OR-MRPH2 &optional STRT

—————————————————————[generic-doc] CMPS
Args: (arg1 arg2 &optional opt)
A generic function whose specializations implement the composition
ARG2 ° ARG1 modified by an optional argument OPT. A typical example is the composition of two morphisms, where the optional argument is a strategy. —————————————————————————–

Package

cat

Source

chcm-elementary-op.lisp (file)

Methods
Method: cmps (HMEQ1 homotopy-equivalence) (HMEQ2 homotopy-equivalence) &optional DUMMY

(CMPS HMEQ1 HMEQ2 &OPTIONAL DUMMY) constructs a homotopy equivalence by composition of the homotopy equivalences HMEQ1 and HMEQ2.

Source

bicones.lisp (file)

Method: cmps (BRDCT reduction) (TRDCT reduction) &optional DUMMY
Source

effective-homology.lisp (file)

Method: cmps (MRPH1 morphism) (MRPH2 morphism) &optional STRT
Method: cmps (MRPH1 morphism) (CHCM2 chain-complex) &optional STRT
Method: cmps (CHCM1 chain-complex) (MRPH2 morphism) &optional STRT
Method: cmps (CHCM1 chain-complex) (CHCM2 chain-complex) &optional STRT
Generic Function: cobar CLGBR-OR-HMEQ
Package

cat

Source

cobar.lisp (file)

Methods
Method: cobar (HMEQ homotopy-equivalence)
Method: cobar (COALGEBRA coalgebra)
Generic Function: degr OBJECT
Package

cat

Methods
Method: degr (MORPHISM morphism)

automatically generated reader method

Source

classes.lisp (file)

Generic Function: dffr1 OBJECT
Package

cat

Methods
Method: dffr1 (CHAIN-COMPLEX chain-complex)

automatically generated reader method

Source

classes.lisp (file)

Generic Function: efhm OBJECT
Generic Function: (setf efhm) NEW-VALUE OBJECT
Package

cat

Methods
Method: efhm (CHAIN-COMPLEX chain-complex)

automatically generated reader method

Source

classes.lisp (file)

Method: (setf efhm) NEW-VALUE (CHAIN-COMPLEX chain-complex)

automatically generated writer method

Source

classes.lisp (file)

Generic Function: hmeq INTEGER
Package

cat

Source

effective-homology.lisp (file)

Methods
Method: hmeq (N integer)
Generic Function: homology CHCM DEGR1 &optional DEGR2
Package

cat

Source

searching-homology.lisp (file)

Methods
Method: homology (CHCM chain-complex) DEGR1 &optional DEGR2
Generic Function: idnm OBJECT
Package

cat

Methods
Method: idnm (HOMOTOPY-EQUIVALENCE homotopy-equivalence)

automatically generated reader method

Source

classes.lisp (file)

Method: idnm (REDUCTION reduction)

automatically generated reader method

Source

classes.lisp (file)

Method: idnm (MORPHISM morphism)

automatically generated reader method

Source

classes.lisp (file)

Method: idnm (CHAIN-COMPLEX chain-complex)

automatically generated reader method

Source

classes.lisp (file)

Generic Function: lrdct OBJECT
Package

cat

Methods
Method: lrdct (HOMOTOPY-EQUIVALENCE homotopy-equivalence)

automatically generated reader method

Source

classes.lisp (file)

Generic Function: orgn OBJECT
Package

cat

Methods
Method: orgn (HOMOTOPY-EQUIVALENCE homotopy-equivalence)

automatically generated reader method

Source

classes.lisp (file)

Method: orgn (REDUCTION reduction)

automatically generated reader method

Source

classes.lisp (file)

Method: orgn (MORPHISM morphism)

automatically generated reader method

Source

classes.lisp (file)

Method: orgn (CHAIN-COMPLEX chain-complex)

automatically generated reader method

Source

classes.lisp (file)

Generic Function: rrdct OBJECT
Package

cat

Methods
Method: rrdct (HOMOTOPY-EQUIVALENCE homotopy-equivalence)

automatically generated reader method

Source

classes.lisp (file)

Generic Function: sbtr CHCM-OR-MRPH MORPHISM &optional STRT
Package

cat

Source

chcm-elementary-op.lisp (file)

Methods
Method: sbtr (MRPH1 morphism) (MRPH2 morphism) &optional STRT
Generic Function: sintr OBJECT
Package

cat

Methods
Method: sintr (SIMPLICIAL-MRPH simplicial-mrph)

automatically generated reader method

Source

classes.lisp (file)

Generic Function: sorc OBJECT
Package

cat

Methods
Method: sorc (MORPHISM morphism)

automatically generated reader method

Source

classes.lisp (file)

Generic Function: tnsr-prdc CHCM-HMEQ-MRPH-RDCT1 CHCM-HMEQ-MRPH-RDCT2
Package

cat

Source

tensor-products.lisp (file)

Methods
Method: tnsr-prdc (HMEQ1 homotopy-equivalence) (HMEQ2 homotopy-equivalence)
Method: tnsr-prdc (RDCT1 reduction) (RDCT2 reduction)
Method: tnsr-prdc (MRPH1 morphism) (MRPH2 morphism)
Method: tnsr-prdc (CHCM1 chain-complex) (CHCM2 chain-complex)
Generic Function: vrtc-bar CHCM-HMEQ-MRPH
Package

cat

Source

bar.lisp (file)

Methods
Method: vrtc-bar (HMEQ homotopy-equivalence)
Method: vrtc-bar (RDCT reduction)
Method: vrtc-bar (MRPH morphism)
Method: vrtc-bar (CHCM chain-complex)
Generic Function: vrtc-cobar CHCM-OR-HMEQ-OR-RDCT
Package

cat

Source

cobar.lisp (file)

Methods
Method: vrtc-cobar (HMEQ homotopy-equivalence)
Method: vrtc-cobar (RDCT reduction)
Method: vrtc-cobar (MRPH morphism)
Method: vrtc-cobar (CHCM chain-complex)

Next: , Previous: , Up: Exported definitions   [Contents][Index]

6.1.6 Structures

Structure: abar ()
Package

cat

Source

classes.lisp (file)

Direct superclasses

structure-object (structure)

Direct methods

print-object (method)

Direct slots
Slot: list
Initform

(:type (quote list))

Readers

abar-list (function)

Writers

(setf abar-list) (function)

Structure: absm ()
Package

cat

Source

classes.lisp (file)

Direct superclasses

structure-object (structure)

Direct methods

print-object (method)

Direct slots
Slot: dgop
Type

cat:dgop

Initform

0

Readers

dgop (function)

Writers

(setf dgop) (function)

Slot: gmsm
Type

cat:gmsm

Readers

gmsm (function)

Writers

(setf gmsm) (function)

Structure: allp ()
Package

cat

Source

classes.lisp (file)

Direct superclasses

structure-object (structure)

Direct methods

print-object (method)

Direct slots
Slot: list
Initform

(:type (quote cat::iallp))

Readers

allp-list (function)

Writers

(setf allp-list) (function)

Structure: cmbn ()

——————————————————————[type-doc] CMBN
Slots: (degr list)
A structure with two slots, DEGR and LIST, for the degree and the list of terms of a combination, of type FIXNUM and LIST, respectively. This is the internal representation of combinations. ——————————————————————————

Package

cat

Source

classes.lisp (file)

Direct superclasses

structure-object (structure)

Direct methods

print-object (method)

Direct slots
Slot: degr
Type

fixnum

Initform

-1

Readers

cmbn-degr (function)

Writers

(setf cmbn-degr) (function)

Slot: list
Type

list

Readers

cmbn-list (function)

Writers

(setf cmbn-list) (function)

Structure: cone ()
Package

cat

Source

classes.lisp (file)

Direct superclasses

structure-object (structure)

Direct methods

print-object (method)

Direct slots
Slot: conx
Initform

(:type (quote (member 0 1)))

Readers

conx (function)

Writers

(setf conx) (function)

Slot: icon
Initform

(:type (quote cat:gnrt))

Readers

icon (function)

Writers

(setf icon) (function)

Structure: crpr ()
Package

cat

Source

classes.lisp (file)

Direct superclasses

structure-object (structure)

Direct methods

print-object (method)

Direct slots
Slot: dgop1
Initform

(:type (quote cat:dgop))

Readers

dgop1 (function)

Writers

(setf dgop1) (function)

Slot: gmsm1
Initform

(:type (quote cat:gmsm))

Readers

gmsm1 (function)

Writers

(setf gmsm1) (function)

Slot: dgop2
Initform

(:type (quote cat:dgop))

Readers

dgop2 (function)

Writers

(setf dgop2) (function)

Slot: gmsm2
Initform

(:type (quote cat:gmsm))

Readers

gmsm2 (function)

Writers

(setf gmsm2) (function)

Structure: gbar ()
Package

cat

Source

classes.lisp (file)

Direct superclasses

structure-object (structure)

Direct methods

print-object (method)

Direct slots
Slot: dmns
Type

fixnum

Initform

-1

Readers

gbar-dmns (function)

Writers

(setf gbar-dmns) (function)

Slot: list
Type

list

Readers

gbar-list (function)

Writers

(setf gbar-list) (function)

Structure: tnpr ()
Package

cat

Source

classes.lisp (file)

Direct superclasses

structure-object (structure)

Direct methods

print-object (method)

Direct slots
Slot: degr1
Readers

degr1 (function)

Writers

(setf degr1) (function)

Slot: gnrt1
Readers

gnrt1 (function)

Writers

(setf gnrt1) (function)

Slot: degr2
Readers

degr2 (function)

Writers

(setf degr2) (function)

Slot: gnrt2
Readers

gnrt2 (function)

Writers

(setf gnrt2) (function)


Next: , Previous: , Up: Exported definitions   [Contents][Index]

6.1.7 Classes

Class: ab-simplicial-group ()
Package

cat

Source

classes.lisp (file)

Direct superclasses

simplicial-group (class)

Direct methods
Class: chain-complex ()

—————————————————————-[class-doc] CHAIN-COMPLEX
Slots: (cmps basis bsgn dffr grmd efhm idnm orgn)
Intances of this class represent chain complexes. The class has 8 slots:

1. CMPR, a comparison function or method for generators. Its reader function is CMPR1.

2. BASIS, a Lisp function, which returns the ordered basis of the free Z-modules (C_p), or the keyword :LOCALLY-EFFECTIVE. Its reader funtion is BASIS1.

3. BSGN, a Lisp object representing the base generator in dimension 0. Its reader function is BSGN.

4. DFFR, the differential morphism, an instance of the class MORPHISM. Its reader function is DFFR1.

5. GRMD, refers to some chain-complex considered as a reference for the underlying graded module structure. Sometimes, it is better to check two chain-complexes have the same underlying graded module. Typically if C1 is a chain-complex and C2 is obtained from C1 by perturbing the differential, then (eq (grmd C1) (grmd C2)) should return T. Its reader function is GRMD.

6. EFHM, if the effective homology of the chain complex has already been computed, then this slot points to the HOMOTOPY-EQUIVALENCE which IS the effective homology of this object. Otherwise the slot is unbound. Its reader function is EFHM.

7. IDNM, an integer, a system generated identifier for this object. Its reader function is IDNM.

8. ORGN, a list which is the copy of a Lisp statement, in principle the statement which was at the origin of the creation of this Kenzo object. A caching process, using this slot, prevents the creation of multiple copies of the same mathematical object, which is important for efficiency. It is used also for debugging and analyzing the program. —————————————————————————–

Package

cat

Source

classes.lisp (file)

Direct superclasses

standard-object (class)

Direct subclasses
Direct methods
Direct slots
Slot: cmpr
Type

cat::cmprf

Initargs

:cmpr

Readers

cmpr1 (generic function)

Slot: basis
Type

cat:basis

Initargs

:basis

Readers

basis1 (generic function)

Slot: bsgn
Type

cat:gnrt

Initargs

:bsgn

Readers

bsgn (generic function)

Slot: dffr
Type

cat:morphism

Initargs

:dffr

Readers

dffr1 (generic function)

Slot: grmd
Type

cat:chain-complex

Initargs

:grmd

Readers

grmd (generic function)

Slot: efhm
Type

cat:homotopy-equivalence

Initargs

:efhm

Readers

efhm (generic function)

Writers

(setf efhm) (generic function)

Slot: idnm
Type

fixnum

Initform

(incf cat::*idnm-counter*)

Readers

idnm (generic function)

Slot: orgn
Type

list

Initargs

:orgn

Readers

orgn (generic function)

Class: homotopy-equivalence ()

—————————————————————-[class-doc] HOMOTOPY-EQUIVALENCE
A homotopy-equivalence is essentially a pair of respective reductions from an intermediate chain complex TCC to the LBCC (left bottom) and RBCC (rigth bottom) chain complexes. It is an equivalence between LBCC and RBCC. —————————————————————————–

Package

cat

Source

classes.lisp (file)

Direct superclasses

standard-object (class)

Direct methods
Direct slots
Slot: lbcc
Type

cat:chain-complex

Initargs

:lbcc

Readers

lbcc1 (generic function)

Slot: tcc
Type

cat:chain-complex

Initargs

:tcc

Readers

tcc1 (generic function)

Slot: rbcc
Type

cat:chain-complex

Initargs

:rbcc

Readers

rbcc1 (generic function)

Slot: lf
Type

cat:morphism

Initargs

:lf

Readers

lf1 (generic function)

Slot: lg
Type

cat:morphism

Initargs

:lg

Readers

lg1 (generic function)

Slot: lh
Type

cat:morphism

Initargs

:lh

Readers

lh1 (generic function)

Slot: rf
Type

cat:morphism

Initargs

:rf

Readers

rf1 (generic function)

Slot: rg
Type

cat:morphism

Initargs

:rg

Readers

rg1 (generic function)

Slot: rh
Type

cat:morphism

Initargs

:rh

Readers

rh1 (generic function)

Slot: lrdct
Type

cat:reduction

Initargs

:lrdct

Readers

lrdct (generic function)

Slot: rrdct
Type

cat:reduction

Initargs

:rrdct

Readers

rrdct (generic function)

Slot: idnm
Type

fixnum

Initform

(incf cat::*idnm-counter*)

Readers

idnm (generic function)

Slot: orgn
Type

list

Initargs

:orgn

Readers

orgn (generic function)

Class: kan ()
Package

cat

Source

classes.lisp (file)

Direct superclasses

simplicial-set (class)

Direct subclasses

simplicial-group (class)

Direct methods
  • print-object (method)
  • kfll1 (method)
Direct slots
Slot: kfll
Type

cat:kfll

Initargs

:kfll

Readers

kfll1 (generic function)

Class: morphism ()

—————————————————————-[class-doc] MORPHISM
Slots: (sorc trgt degr intr strt ???-clnm ?-clnm rslts idnm orgn)
Intances of this class represent morphisms between chain complexes, and the differential homomorphism of a chain complex is treated as a morphism of degree -1. The class has 10 slots:

1. SORC, an object of type CHAIN-COMPLEX, the source chain complex of this morphism. Its reader function is SORC.

2. TRGT, an object of type CHAIN-COMPLEX, the target chain complex of this morphism. Its reader function is TRGT.

3. DEGR, an integer, the degree of the morphism. Its reader function is DEGR.

4. INTR, a Lisp INTeRnal function implementing the morphism, taking account of the strategy STRT. Its reader function is INTR.

5. STRT, a symbol, one of :GNRT or :CMBN. Its reader function is STRT.

If this slot is :GNRT, the implementation of INTR is a function: (function (degr gnrt) cmbn)
and for any call of this function, the result is stored in the slot RSLTS to avoid later a possibly long recalculation for the same argument.

If this slot is :CMBN, the implementation of INTR is a function: (function (cmbn) cmbn)
and the RSLTS slot is not used. Think for example to an identity or null function, where storing a result is wasted time.

6. ???-CLNM, an integer updated by the system for internal statistics. Its reader function is ???-CLNM.

7. ?-CLNM, another integer maintained by the system for internal pusposes. Its reader function is ?-CLNM.

8. RSLTS, an array of length +MAXIMAL-DIMENSION+ reserved by the system for caching intermediate results. Its reader function is RSLTS.

9. IDNM, an integer, a system-generated identifier for this object. Its reader function is IDNM.

10. ORGN, a list which is the copy of a Lisp statement, in principle the statement which was at the origin of the creation of this Kenzo object. A caching process, using this slot, prevents the creation of multiple copies of the same mathematical object, which is important for efficiency. It is used also for debugging and analyzing the program. —————————————————————————–

Package

cat

Source

classes.lisp (file)

Direct superclasses

standard-object (class)

Direct subclasses

simplicial-mrph (class)

Direct methods
Direct slots
Slot: sorc
Type

cat:chain-complex

Initargs

:sorc

Readers

sorc (generic function)

Slot: trgt
Type

cat:chain-complex

Initargs

:trgt

Readers

trgt (generic function)

Slot: degr
Type

fixnum

Initargs

:degr

Readers

degr (generic function)

Slot: intr
Type

cat::intr-mrph

Initargs

:intr

Readers

intr (generic function)

Slot: strt
Type

cat::strt

Initargs

:strt

Readers

strt (generic function)

Slot: ???-clnm
Type

fixnum

Initform

0

Readers

???-clnm (generic function)

Writers

(setf ???-clnm) (generic function)

Slot: ?-clnm
Type

fixnum

Initform

0

Readers

?-clnm (generic function)

Writers

(setf ?-clnm) (generic function)

Slot: rslts
Type

simple-vector

Readers

rslts (generic function)

Slot: idnm
Type

fixnum

Initform

(incf cat::*idnm-counter*)

Readers

idnm (generic function)

Slot: orgn
Type

list

Initargs

:orgn

Readers

orgn (generic function)

Class: reduction ()

—————————————————————-[class-doc] REDUCTION
Slots: (tcc bcc f g h idnm orgn)
Instances of this class represent reductions of chain complexes.

^ h s ^ f ° g = 1
C —–> C C
^ h ° d + d ° h = 1 - g ° f
| | ^
f | | g C
| | f ° h = 0
v h ° g = 0
C h ° h = 0

The class has 7 slots: ^
1. TCC, an object of type CHAIN-COMPLEX, the top chain complex C. Its reader function is TCC1.

2. BCC, an object of type CHAIN-COMPLEX, the bottom chain complex C. Its reader function is BCC1.

3. F, an object of type MORPHISM representing the chain morphism f. Its reader function is F1.

4. G, an object of type MORPHISM representing the chain morphism g. Its reader function is G1.

5. H, an object of type MORPHISM representing the morphism of graded modules h. Its reader function is H1.

6. IDNM, an integer, a system-generated identifier for this object. Its reader function is IDNM.

7. ORGN, a list which is the copy of a Lisp statement, in principle the statement which was at the origin of the creation of this Kenzo object. A caching process, using this slot, prevents the creation of multiple copies of the same mathematical object, which is important for efficiency. It is used also for debugging and analyzing the program. —————————————————————————–

Package

cat

Source

classes.lisp (file)

Direct superclasses

standard-object (class)

Direct methods
Direct slots
Slot: tcc
Type

cat:chain-complex

Initargs

:tcc

Readers

tcc1 (generic function)

Slot: bcc
Type

cat:chain-complex

Initargs

:bcc

Readers

bcc1 (generic function)

Slot: f
Type

cat:morphism

Initargs

:f

Readers

f1 (generic function)

Slot: g
Type

cat:morphism

Initargs

:g

Readers

g1 (generic function)

Slot: h
Type

cat:morphism

Initargs

:h

Readers

h1 (generic function)

Slot: idnm
Type

fixnum

Initform

(incf cat::*idnm-counter*)

Readers

idnm (generic function)

Slot: orgn
Type

list

Initargs

:orgn

Readers

orgn (generic function)

Class: simplicial-group ()
Package

cat

Source

classes.lisp (file)

Direct superclasses
Direct subclasses

ab-simplicial-group (class)

Direct methods
Direct slots
Slot: grml
Type

cat:simplicial-mrph

Initargs

:grml

Readers

grml1 (generic function)

Slot: grin
Type

cat:simplicial-mrph

Initargs

:grin

Readers

grin1 (generic function)

Class: simplicial-mrph ()
Package

cat

Source

classes.lisp (file)

Direct superclasses

morphism (class)

Direct methods
  • print-object (method)
  • ?3 (method)
  • sintr (method)
Direct slots
Slot: sintr
Type

cat:sintr

Initargs

:sintr

Readers

sintr (generic function)

Class: simplicial-set ()
Package

cat

Source

classes.lisp (file)

Direct superclasses

coalgebra (class)

Direct subclasses

kan (class)

Direct methods
Direct slots
Slot: face
Type

cat:face

Initargs

:face

Readers

face1 (generic function)


Previous: , Up: Exported definitions   [Contents][Index]

6.1.8 Types

Type: apowr ()
Package

cat

Source

classes.lisp (file)

Type: basis ()

——————————————————————[type-doc] BASIS
A derived type to represent the basis of a chain complex. In Kenzo, a basis is either a (basis-)generating function or, for not finitely-generated modules, the symbol :LOCALLY-EFFECTIVE. ——————————————————————————

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classes.lisp (file)

Type: brgn ()
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classes.lisp (file)

Type: cbgn ()
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classes.lisp (file)

Type: cffc ()

——————————————————————[type-doc] CFFC
A derived type to represent the coefficients of terms. In Kenzo, the set of coefficients it the set of objects which satisfy the CFFC-P predicate: non-zero FIXNUMs. ——————————————————————————

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classes.lisp (file)

Type: cmpr ()

——————————————————————[type-doc] CMPR
An enumerated type to represent the results of comparisons. ——————————————————————————

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classes.lisp (file)

Type: dgop ()
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classes.lisp (file)

Type: face ()
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classes.lisp (file)

Type: gmsm ()
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classes.lisp (file)

Type: gnrt ()

——————————————————————[type-doc] GNRT
A type to represent the generators of terms. In Kenzo, the set of coefficients it the set of all Lisp objects (T). ——————————————————————————

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classes.lisp (file)

Type: iabsm ()
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classes.lisp (file)

Type: kfll ()
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classes.lisp (file)

Type: sintr ()
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classes.lisp (file)

Type: soft-dlop ()
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classes.lisp (file)

Type: term ()

——————————————————————[type-doc] TERM
A derived type to represent terms. In Kenzo, the set of terms it the set of objects which satisfy the TERM-P predicate: CONSes whose CAR is of type CFFC and whose CDR is of type GNRT. ——————————————————————————

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classes.lisp (file)


Previous: , Up: Definitions   [Contents][Index]

6.2 Internal definitions


Next: , Previous: , Up: Internal definitions   [Contents][Index]

6.2.1 Constants

Constant: +2-exp+
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kenzo.lisp (file)

Constant: +f-empty-vector+
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kenzo.lisp (file)

Constant: +false+
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kenzo.lisp (file)

Constant: +gnrts-pckg+
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smith.lisp (file)

Constant: +mask+
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kenzo.lisp (file)

Constant: +s-empty-vector+
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kenzo.lisp (file)

Constant: +true+
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kenzo.lisp (file)

Constant: +zero-negative-cmbn+

————————————————————–[constant-doc] +ZERO-NEGATIVE-CMBN+ is bound to an instance of the null combination of degree -1. ——————————————————————————

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combinations.lisp (file)


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6.2.2 Special variables

Special Variable: *algb-list*
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kenzo.lisp (file)

Special Variable: *clgb-list*
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kenzo.lisp (file)

Special Variable: *future-display*
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kenzo.lisp (file)

Special Variable: *hmeq-list*
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kenzo.lisp (file)

Special Variable: *hopf-list*
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kenzo.lisp (file)

Special Variable: *idnm-counter*
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kenzo.lisp (file)

Special Variable: *kan-list*
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kenzo.lisp (file)

Special Variable: *rdct-list*
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kenzo.lisp (file)

Special Variable: *results-cmlt-tm*
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kenzo.lisp (file)

Special Variable: *results-coef*
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kenzo.lisp (file)

Special Variable: *results-max*
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kenzo.lisp (file)

Special Variable: *results-n*
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kenzo.lisp (file)

Special Variable: *smgr-list*
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kenzo.lisp (file)

Special Variable: *smmr-list*
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kenzo.lisp (file)

Special Variable: *smst-list*
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kenzo.lisp (file)

Special Variable: *start-stack*
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kenzo.lisp (file)

Special Variable: *time-interval*
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kenzo.lisp (file)

Special Variable: *wrong-cmbn*
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macros.lisp (file)

Special Variable: +maximal-dimension+
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kenzo.lisp (file)

Special Variable: +null-allp+
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cobar.lisp (file)


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6.2.3 Macros

Macro: -bdegr BRGN
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macros.lisp (file)

Macro: -bgnrt BRGN
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macros.lisp (file)

Macro: -cdegr CBGN
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macros.lisp (file)

Macro: -cffc MARK
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macros.lisp (file)

Macro: -cgnrt CBGN
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macros.lisp (file)

Macro: -gnrt MARK
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macros.lisp (file)

Macro: -term MARK
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macros.lisp (file)

Macro: apdgop APOWR
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macros.lisp (file)

Macro: apexpn APOWR
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macros.lisp (file)

Macro: apgmsm APOWR
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macros.lisp (file)

Macro: basecol MAT N
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macros.lisp (file)

Macro: baselig MAT N
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macros.lisp (file)

Macro: basis3 SMST DMNS KEYWORD
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macros.lisp (file)

Macro: bdegr BRGN
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macros.lisp (file)

Macro: bgnrt BRGN
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macros.lisp (file)

Macro: build-ab-smgr &rest REST
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macros.lisp (file)

Macro: cdegr CBGN
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macros.lisp (file)

Macro: cgnrt CBGN
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macros.lisp (file)

Macro: cmpr3 OBJECT ITEM1 ITEM2
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macros.lisp (file)

Macro: column-number MTRX
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macros.lisp (file)

Macro: control CMPR CMBN
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macros.lisp (file)

Macro: controln CMPR CMBN
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macros.lisp (file)

Macro: crpr2 ABSM1 ABSM2
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macros.lisp (file)

Macro: crpr4 DGOP1 GMSM1 DGOP2 GMSM2
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macros.lisp (file)

Macro: define-constant NAME VALUE &optional DOC
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kenzo.lisp (file)

Macro: eilenberg-zilber &rest REST
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macros.lisp (file)

Macro: expn POWR
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macros.lisp (file)

Macro: gnrt-allp-tnpr DEGR GNRT ALLP
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macros.lisp (file)

Macro: info-bndr GMSM-FACES-INFO
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macros.lisp (file)

Macro: info-face-i GMSM-FACES-INFO I
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macros.lisp (file)

Macro: info-faces GMSM-FACES-INFO
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macros.lisp (file)

Macro: info-gmsm GMSM-FACES-INFO
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macros.lisp (file)

Macro: kfll4 KAN INDX DMNS HAT
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macros.lisp (file)

Macro: lbcc &rest REST
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macros.lisp (file)

Macro: lh &rest REST
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macros.lisp (file)

Macro: line-number MTRX
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macros.lisp (file)

Macro: make-gmsm-faces-info &key GMSM FACES BNDR
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macros.lisp (file)

Macro: pgmsm POWR
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macros.lisp (file)

Macro: powr GMSM EXPN
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macros.lisp (file)

Macro: rh &rest REST
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macros.lisp (file)

Macro: with--brgn (BDEGR BGNRT) BRGN . BODY
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macros.lisp (file)

Macro: with--cbgn (CDEGR CGNRT) CBGN . BODY
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macros.lisp (file)

Macro: with-abar (LIST) ABAR . BODY
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macros.lisp (file)

Macro: with-allp (LIST) ALLP . BODY
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macros.lisp (file)

Macro: with-apowr (DGOP GMSM EXPN) APOWR . BODY
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macros.lisp (file)

Macro: with-bicn (BCNX IBICN) BICN . BODY
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macros.lisp (file)

Macro: with-brgn (BDEGR BGNRT) BRGN . BODY
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macros.lisp (file)

Macro: with-cbgn (CDEGR CGNRT) CBGN . BODY
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macros.lisp (file)

Macro: with-cone (CONX ICON) CONE . BODY
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macros.lisp (file)

Macro: with-crpr-2 (ABSM1 ABSM2) CRPR . BODY
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macros.lisp (file)

Macro: with-crpr-4 (DGOP1 GMSM1 DGOP2 GMSM2) CRPR . BODY
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macros.lisp (file)

Macro: with-gbar (DMNS LIST) GBAR . BODY
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macros.lisp (file)

Macro: with-powr (GMSM EXPN) POWR . BODY
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macros.lisp (file)


Next: , Previous: , Up: Internal definitions   [Contents][Index]

6.2.4 Functions

Function: a-basis2 BASIS DMNS
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simplicial-sets.lisp (file)

Function: a-grin4 SINTR-GRIN DMNS ABSM
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simplicial-groups.lisp (file)

Function: a-grml4 SINTR-GRML DMNS ABSM1 ABSM2
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simplicial-groups.lisp (file)

Function: abar-p OBJECT
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classes.lisp (file)

Function: abar-print ABAR STREAM DEPTH
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bar.lisp (file)

Function: algb IDNM
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algebras.lisp (file)

Function: allp-p OBJECT
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classes.lisp (file)

Function: allp-print ALLP STREAM DEPTH
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cobar.lisp (file)

Function: apowr-p OBJECT
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classes.lisp (file)

Function: bar-intr-dffr VRTC-DFFR HRZN-DFFR
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bar.lisp (file)

Function: basic-perturbation-lemma REDUCTION TOP-PERTURBATION
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effective-homology.lisp (file)

Function: basis2 OBJECT N
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chain-complexes.lisp (file)

Function: bcnx INSTANCE
Function: (setf bcnx) VALUE INSTANCE
Package

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classes.lisp (file)

Function: bicn-p OBJECT
Package

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classes.lisp (file)

Function: bicn-print BICN STREAM DEPTH
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bicones.lisp (file)

Function: bicone-intr-dffr CMPRC DFFRB DFFRC DFFRD F1 F2

(BICONE-INTR-DFFR CMPRC DFFRB DFFRC DFFRD F1 F2)

Package

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bicones.lisp (file)

Function: bpl-*-sigma HOMOTOPY PERTURBATION
Package

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effective-homology.lisp (file)

Function: brgn-p OBJECT
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classes.lisp (file)

Function: build-algb &key CMPR BASIS BSGN INTR-DFFR DFFR-STRT INTR-APRD APRD-STRT ORGN
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algebras.lisp (file)

Function: build-clgb &key CMPR BASIS BSGN INTR-DFFR DFFR-STRT INTR-CPRD CPRD-STRT ORGN
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coalgebras.lisp (file)

Function: build-smgr &key CMPR BASIS BSPN FACE FACE* INTR-BNDR BNDR-STRT INTR-DGNL DGNL-STRT SINTR-GRML SINTR-GRIN ORGN
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simplicial-groups.lisp (file)

Function: cbgn-p OBJECT
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classes.lisp (file)

Function: cffc-p OBJECT
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classes.lisp (file)

Function: change-chcm-to-clgb CHCM &key INTR-CPRD CPRD-STRT ORGN
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coalgebras.lisp (file)

Function: change-sorc-trgt MRPH &key NEW-SORC NEW-TRGT
Package

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chcm-elementary-op.lisp (file)

Function: chcm-homology-gen-old CC N
Package

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homology-groups.lisp (file)

Function: chercher-hor P IC
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homology-groups.lisp (file)

Function: chercher-ver P IL
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homology-groups.lisp (file)

Function: circle-basis DMNS
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k-pi-n.lisp (file)

Function: circle-cmpr GNRT1 GNRT2
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k-pi-n.lisp (file)

Function: classifying-space-efhm SMGR
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cat

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cl-space-efhm.lisp (file)

Function: clean-results &optional RESULTS-COEF
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chain-complexes.lisp (file)

Function: clgb IDNM
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coalgebras.lisp (file)

Function: cmbn-abar-cmbn-tnpr CMBN ABAR-CMBN
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bar.lisp (file)

Function: cmbn-allp-cmbn-tnpr CMBN ALLP-CMBN
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cobar.lisp (file)

Function: cmbn-gmsms CMBN
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special-smsts.lisp (file)

Function: cmbn-p OBJECT
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classes.lisp (file)

Function: cmbn-print CMBN STREAM DEPTH

————————————————————–[function-doc] CMBN-PRINT
Args: (cmbn stream depth)
Prints the combination CMBN to the stream STREAM. The third argument, DEPTH, is ignored. ——————————————————————————

Package

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combinations.lisp (file)

Function: cobar-intr-dffr VRTC-DFFR HRZN-DFFR
Package

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cobar.lisp (file)

Function: cone-efhm CONE
Package

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cones.lisp (file)

Function: cone-p OBJECT
Package

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classes.lisp (file)

Function: cone-print CONE STREAM DEPTH
Package

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cones.lisp (file)

Function: conx INSTANCE
Function: (setf conx) VALUE INSTANCE
Package

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classes.lisp (file)

Function: copier-matrice MAT
Package

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homology-groups.lisp (file)

Function: copy-abar INSTANCE
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classes.lisp (file)

Function: copy-absm INSTANCE
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classes.lisp (file)

Function: copy-allp INSTANCE
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classes.lisp (file)

Function: copy-bicn INSTANCE
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classes.lisp (file)

Function: copy-cmbn INSTANCE
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classes.lisp (file)

Function: copy-cone INSTANCE
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classes.lisp (file)

Function: copy-crpr INSTANCE
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classes.lisp (file)

Function: copy-gbar INSTANCE
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classes.lisp (file)

Function: copy-loop INSTANCE
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classes.lisp (file)

Function: copy-matrice INSTANCE
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classes.lisp (file)

Function: copy-result INSTANCE
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classes.lisp (file)

Function: copy-t-mat INSTANCE
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classes.lisp (file)

Function: copy-tnpr INSTANCE
Package

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classes.lisp (file)

Function: creer-matrice N1 N2
Package

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homology-groups.lisp (file)

Function: crpr-p OBJECT
Package

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classes.lisp (file)

Function: crpr-print CRPR STREAM DEPTH
Package

cat

Source

cartesian-products.lisp (file)

Function: cs-hat-left-perturbation SMGR &aux FIBRATION BAR HAT-U-T
Package

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Source

cl-space-efhm.lisp (file)

Function: cs-hat-right-perturbation SMGR &aux HAT-U-U
Package

cat

Source

cl-space-efhm.lisp (file)

Function: cs-hat-right-perturbation-intr SMGR
Package

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cl-space-efhm.lisp (file)

Function: cs-hat-u-u SMGR &aux BAR CL-SPACE CLSP-TNSR-SMGR
Package

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cl-space-efhm.lisp (file)

Function: cs-pre-left-hmeq-left-reduction-f SMGR &aux HAT-U-T CLASSIFYING-SPACE
Package

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cl-space-efhm.lisp (file)

Function: cs-pre-left-hmeq-left-reduction-g SMGR &aux HAT-U-T CLASSIFYING-SPACE
Package

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cl-space-efhm.lisp (file)

Function: cs-pre-left-hmeq-left-reduction-h SMGR &aux HAT-U-T
Package

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cl-space-efhm.lisp (file)

Function: cs-pre-left-hmeq-left-reduction-intr-h CMPR IDNT
Package

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cl-space-efhm.lisp (file)

Function: cs-pre-left-hmeq-right-reduction-f SMGR &aux HAT-T-U BAR
Package

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cl-space-efhm.lisp (file)

Function: cs-pre-left-hmeq-right-reduction-g SMGR &aux HAT-T-U BAR IDNT
Package

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cl-space-efhm.lisp (file)

Function: cs-pre-left-hmeq-right-reduction-h SMGR &aux BAR TNPR-CONTRACTION
Package

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cl-space-efhm.lisp (file)

Function: degr1 INSTANCE
Function: (setf degr1) VALUE INSTANCE
Package

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classes.lisp (file)

Function: degr2 INSTANCE
Function: (setf degr2) VALUE INSTANCE
Package

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classes.lisp (file)

Function: deltab-bndr DMNS GMSM
Package

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delta.lisp (file)

Function: deltab-cmpr GMSM1 GMSM2
Package

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delta.lisp (file)

Function: deltab2-face INDX DMNS GMSM
Package

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delta.lisp (file)

Function: disp-colonne MAT IC
Package

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homology-groups.lisp (file)

Function: disp-ligne MAT IL
Package

cat

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homology-groups.lisp (file)

Function: disp-matrice MAT
Package

cat

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homology-groups.lisp (file)

Function: disp-matrice-colonnes MAT
Package

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Source

homology-groups.lisp (file)

Function: disp-p P
Package

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homology-groups.lisp (file)

Function: disp-peigne PEIGNE
Package

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homology-groups.lisp (file)

Function: diviseur A B
Package

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homology-groups.lisp (file)

Function: dstr-change-sorc-trgt MRPH &key NEW-SORC NEW-TRGT
Package

cat

Source

chcm-elementary-op.lisp (file)

Function: easy-perturbation-lemma REDUCTION BOTTOM-PERTURBATION
Package

cat

Source

effective-homology.lisp (file)

Function: echcm-without-epi ECHCM FIRST N M INTR-F
Package

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Source

smith.lisp (file)

Function: expn-p OBJECT
Package

cat

Source

classes.lisp (file)

Function: face4 SMST INDX DMNS GMSM-OR-ABSM
Package

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Source

simplicial-sets.lisp (file)

Function: fibration-kfll TWIST &aux SINTR-TWIST BASE FIBRE FBSPN BKFLL FKFLL SINTR-GRML SINTR-GRIN
Package

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Source

fibrations.lisp (file)

Function: fibration-p OBJECT
Package

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classes.lisp (file)

Function: fibration-total-efhm FIBRATION
Package

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serre.lisp (file)

Function: fibration-total-face FIBRATION &aux BASE BFACE FIBR FBSPN FFACE GRML SINTR-GRML TOTL UFACE SINTR-TWIST
Package

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fibrations.lisp (file)

Function: finite-ss-basis TABLE
Package

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special-smsts.lisp (file)

Function: finite-ss-face IND-SMST TABLE
Package

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special-smsts.lisp (file)

Function: finite-ss-find-gmsm TABLE GMSM DMNS &optional MAX-DMNS
Package

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special-smsts.lisp (file)

Function: finite-ss-finish-entry TABLE ENTRY DMNS BSPN
Package

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special-smsts.lisp (file)

Function: finite-ss-finish-line TABLE DMNS BSPN
Package

cat

Source

special-smsts.lisp (file)

Function: finite-ss-finish-table TABLE BSPN
Package

cat

Source

special-smsts.lisp (file)

Function: finite-ss-intr-bndr IND-SMST TABLE
Package

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Source

special-smsts.lisp (file)

Function: gbar-dmns INSTANCE
Function: (setf gbar-dmns) VALUE INSTANCE
Package

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Source

classes.lisp (file)

Function: gbar-list INSTANCE
Function: (setf gbar-list) VALUE INSTANCE
Package

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Source

classes.lisp (file)

Function: gbar-p OBJECT
Package

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classes.lisp (file)

Function: gbar-print GBAR STREAM DEPTH
Package

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Source

classifying-spaces.lisp (file)

Function: generateur-torsion-h* B N P
Package

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Source

homology-groups.lisp (file)

Function: gnrt1 INSTANCE
Function: (setf gnrt1) VALUE INSTANCE
Package

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classes.lisp (file)

Function: gnrt2 INSTANCE
Function: (setf gnrt2) VALUE INSTANCE
Package

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classes.lisp (file)

Function: hmtp-vrtc-bar H GF
Package

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bar.lisp (file)

Function: hmtp-vrtc-cobar H GF
Package

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cobar.lisp (file)

Function: iabar-p OBJECT
Package

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classes.lisp (file)

Function: iabsm-p OBJECT
Package

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classes.lisp (file)

Function: iallp-p OBJECT
Package

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classes.lisp (file)

Function: ibicn INSTANCE
Function: (setf ibicn) VALUE INSTANCE
Package

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classes.lisp (file)

Function: icmbn-p OBJECT
Package

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Source

classes.lisp (file)

Function: icol INSTANCE
Function: (setf icol) VALUE INSTANCE
Package

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Source

classes.lisp (file)

Function: icon INSTANCE
Function: (setf icon) VALUE INSTANCE
Package

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Source

classes.lisp (file)

Function: identite N
Package

cat

Source

homology-groups.lisp (file)

Function: ilig INSTANCE
Function: (setf ilig) VALUE INSTANCE
Package

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Source

classes.lisp (file)

Function: iloop-p OBJECT
Package

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classes.lisp (file)

Function: init-peigne-hor MAT PTC
Package

cat

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homology-groups.lisp (file)

Function: init-peigne-ver MAT PTL
Package

cat

Source

homology-groups.lisp (file)

Function: inserer-terme PL PC VAL
Package

cat

Source

homology-groups.lisp (file)

Function: intr-phi-2 ARRAY-PQ CMPR
Package

cat

Source

eilenberg-zilber.lisp (file)

Function: k-z2-1-grin ()
Package

cat

Source

k-pi-n.lisp (file)

Function: k-z2-1-grin-intr DMNS GMSM
Package

cat

Source

k-pi-n.lisp (file)

Function: k-z2-1-grml ()
Package

cat

Source

k-pi-n.lisp (file)

Function: k-z2-1-grml-intr DMNS CRPR
Package

cat

Source

k-pi-n.lisp (file)

Function: kz1-efhm ()
Package

cat

Source

k-pi-n.lisp (file)

Function: kz1-rdct-f ()
Package

cat

Source

k-pi-n.lisp (file)

Function: kz1-rdct-g ()
Package

cat

Source

k-pi-n.lisp (file)

Function: kz1-rdct-g-intr CMBN
Package

cat

Source

k-pi-n.lisp (file)

Function: kz1-rdct-h ()
Package

cat

Source

k-pi-n.lisp (file)

Function: left INSTANCE
Function: (setf left) VALUE INSTANCE
Package

cat

Source

classes.lisp (file)

Function: left-crts-prdc-efhm SMST1 SMST2
Package

cat

Source

eilenberg-zilber.lisp (file)

Function: left-serre-efhm FIBRATION
Package

cat

Source

serre.lisp (file)

Function: leftcol INSTANCE
Function: (setf leftcol) VALUE INSTANCE
Package

cat

Source

classes.lisp (file)

Function: loop-p OBJECT
Package

cat

Source

classes.lisp (file)

Function: loop-space-efhm SPACE
Package

cat

Source

lp-space-efhm.lisp (file)

Function: loop-space-face* CMPR FACE
Package

cat

Source

loop-spaces.lisp (file)

Function: ls-hat-left-perturbation SPACE
Package

cat

Source

lp-space-efhm.lisp (file)

Function: ls-hat-left-perturbation-intr SPACE
Package

cat

Source

lp-space-efhm.lisp (file)

Function: ls-hat-right-perturbation SPACE &aux COBAR LS-HAT-T-U
Package

cat

Source

lp-space-efhm.lisp (file)

Function: ls-hat-u-u SPACE &aux COBAR LOOP-SPACE SPAC-TNSR-LPSP
Package

cat

Source

lp-space-efhm.lisp (file)

Function: ls-left-hmeq-left-reduction-g SPACE &aux BSPN LS-HAT-T-U LOOP-SPACE
Package

cat

Source

lp-space-efhm.lisp (file)

Function: ls-pre-left-hmeq-left-reduction-f SPACE &aux LS-HAT-T-U LOOP-SPACE
Package

cat

Source

lp-space-efhm.lisp (file)

Function: ls-pre-left-hmeq-left-reduction-h SPACE &aux LS-HAT-T-U
Package

cat

Source

lp-space-efhm.lisp (file)

Function: ls-pre-left-hmeq-right-reduction-f SPACE &aux LS-HAT-U-T COBAR
Package

cat

Source

lp-space-efhm.lisp (file)

Function: ls-pre-left-hmeq-right-reduction-g SPACE &aux LS-HAT-U-T COBAR BSPN
Package

cat

Source

lp-space-efhm.lisp (file)

Function: ls-pre-left-hmeq-right-reduction-h SPACE &aux COBAR TNPR-CONTRACTION
Package

cat

Source

lp-space-efhm.lisp (file)

Function: maj-colonne MAT IC LISTE
Package

cat

Source

homology-groups.lisp (file)

Function: maj-ligne MAT IL LISTE
Package

cat

Source

homology-groups.lisp (file)

Function: maj-matrice MAT LISTE
Package

cat

Source

homology-groups.lisp (file)

Function: maj-peigne-hor PEIGNE IC
Package

cat

Source

homology-groups.lisp (file)

Function: maj-peigne-ver PEIGNE IL
Package

cat

Source

homology-groups.lisp (file)

Function: maj-terme PL PC VAL
Package

cat

Source

homology-groups.lisp (file)

Function: make-bicn &key (BCNX BCNX) (IBICN IBICN)
Package

cat

Source

classes.lisp (file)

Function: make-cone &key (CONX CONX) (ICON ICON)
Package

cat

Source

classes.lisp (file)

Function: make-crpr &key (DGOP1 DGOP1) (GMSM1 GMSM1) (DGOP2 DGOP2) (GMSM2 GMSM2)
Package

cat

Source

classes.lisp (file)

Function: make-matrice &key (LEFTCOL LEFTCOL) (UPLIG UPLIG)
Package

cat

Source

classes.lisp (file)

Function: make-t-mat &key (VAL VAL) (ILIG ILIG) (ICOL ICOL) (LEFT LEFT) (UP UP)
Package

cat

Source

classes.lisp (file)

Function: make-tnpr &key (DEGR1 DEGR1) (GNRT1 GNRT1) (DEGR2 DEGR2) (GNRT2 GNRT2)
Package

cat

Source

classes.lisp (file)

Function: matrice-p OBJECT
Package

cat

Source

classes.lisp (file)

Function: moore-basis DMNS
Package

cat

Source

special-smsts.lisp (file)

Function: moore-cmpr GMSM1 GMSM2
Package

cat

Source

special-smsts.lisp (file)

Function: moore-face PII DMNS
Package

cat

Source

special-smsts.lisp (file)

Function: moore-intr-bndr PII DMNS
Package

cat

Source

special-smsts.lisp (file)

Function: mrph-cmbn SCMPR2 TCMPR2 INTR CMBN MEMORY
Package

cat

Source

chain-complexes.lisp (file)

Function: mrph-gnrt CMPR2 INTR DEGR GNRT MEMORY &optional LEFT RIGHT
Package

cat

Source

chain-complexes.lisp (file)

Function: n-col MAT
Package

cat

Source

homology-groups.lisp (file)

Function: n-lig MAT
Package

cat

Source

homology-groups.lisp (file)

Function: n-mrph-intr N MRPH
Package

cat

Source

chcm-elementary-op.lisp (file)

Function: ncol MAT
Package

cat

Source

homology-groups.lisp (file)

Function: nlig MAT
Package

cat

Source

homology-groups.lisp (file)

Function: nresults ()
Package

cat

Source

chain-complexes.lisp (file)

Function: op-col PTC1 PTC2 PEIGNE LAMBDA
Package

cat

Source

homology-groups.lisp (file)

Function: op-col-n MAT C1 C2 LAMBDA
Package

cat

Source

homology-groups.lisp (file)

Function: op-elem PL PC ALPHA
Package

cat

Source

homology-groups.lisp (file)

Function: op-lig PTL1 PTL2 PEIGNE LAMBDA
Package

cat

Source

homology-groups.lisp (file)

Function: op-lig-n MAT L1 L2 LAMBDA
Package

cat

Source

homology-groups.lisp (file)

Function: peigne-hor MAT PTC IC
Package

cat

Source

homology-groups.lisp (file)

Function: peigne-ver MAT PTL IL
Package

cat

Source

homology-groups.lisp (file)

Function: pivot MAT P
Package

cat

Source

homology-groups.lisp (file)

Function: pivot-parallele M N P
Package

cat

Source

homology-groups.lisp (file)

Function: powr-p OBJECT
Package

cat

Source

classes.lisp (file)

Function: r-proj-space-cmpr GMSM1 GMSM2
Package

cat

Source

special-smsts.lisp (file)

Function: r-proj-space-face K
Package

cat

Source

special-smsts.lisp (file)

Function: r-proj-space-intr-bndr K
Package

cat

Source

special-smsts.lisp (file)

Function: reste A B
Package

cat

Source

homology-groups.lisp (file)

Function: reste-minimal-colonne MAT P
Package

cat

Source

homology-groups.lisp (file)

Function: reste-minimal-ligne MAT P
Package

cat

Source

homology-groups.lisp (file)

Function: result-clnm INSTANCE
Function: (setf result-clnm) VALUE INSTANCE
Package

cat

Source

classes.lisp (file)

Function: result-gnrt INSTANCE
Function: (setf result-gnrt) VALUE INSTANCE
Package

cat

Source

classes.lisp (file)

Function: result-p OBJECT
Package

cat

Source

classes.lisp (file)

Function: result-print RESULT STREAM DEPTH
Package

cat

Source

chain-complexes.lisp (file)

Function: result-rntm INSTANCE
Function: (setf result-rntm) VALUE INSTANCE
Package

cat

Source

classes.lisp (file)

Function: result-value INSTANCE
Function: (setf result-value) VALUE INSTANCE
Package

cat

Source

classes.lisp (file)

Function: sintr-intr SINTR
Package

cat

Source

simplicial-mrphs.lisp (file)

Function: smgr-aprd SMGR
Package

cat

Source

simplicial-groups.lisp (file)

Function: smgr-crts-contraction-intr IDNT
Package

cat

Source

cs-twisted-products.lisp (file)

Function: smgr-fibration-sintr DMNS GBAR
Package

cat

Source

cs-twisted-products.lisp (file)

Function: smgr-kfll SMGR
Package

cat

Source

simplicial-groups.lisp (file)

Function: smgr-kfll-intr FACE SINTR-GRML SINTR-GRIN
Package

cat

Source

simplicial-groups.lisp (file)

Function: smith MATRIX
Package

cat

Source

smith.lisp (file)

Function: smmr IDNM
Package

cat

Source

simplicial-mrphs.lisp (file)

Function: special-bpl REDUCTION TOP-PERTURBATION
Package

cat

Source

effective-homology.lisp (file)

Function: special-bpl-2 REDUCTION TOP-PERTURBATION
Package

cat

Source

effective-homology.lisp (file)

Function: sphere-basis DMNS
Package

cat

Source

special-smsts.lisp (file)

Function: sphere-cmpr GMSM1 GMSM2
Package

cat

Source

special-smsts.lisp (file)

Function: sphere-wedge-basis DMNS-LIST
Package

cat

Source

special-smsts.lisp (file)

Function: sphere-wedge-face INDX DMNS GMSM
Package

cat

Source

special-smsts.lisp (file)

Function: supprimer-terme PL PC
Package

cat

Source

homology-groups.lisp (file)

Function: t-mat-p OBJECT
Package

cat

Source

classes.lisp (file)

Function: term-p OBJECT
Package

cat

Source

classes.lisp (file)

Function: terme MAT I J
Package

cat

Source

homology-groups.lisp (file)

Function: terme-minimal-matrice MAT
Package

cat

Source

homology-groups.lisp (file)

Function: terminer-h* B
Package

cat

Source

homology-groups.lisp (file)

Function: time-list ()
Package

cat

Source

chain-complexes.lisp (file)

Function: tuer-colonne MAT IC
Package

cat

Source

homology-groups.lisp (file)

Function: tuer-ligne MAT IL
Package

cat

Source

homology-groups.lisp (file)

Function: up INSTANCE
Function: (setf up) VALUE INSTANCE
Package

cat

Source

classes.lisp (file)

Function: uplig INSTANCE
Function: (setf uplig) VALUE INSTANCE
Package

cat

Source

classes.lisp (file)

Function: val INSTANCE
Function: (setf val) VALUE INSTANCE
Package

cat

Source

classes.lisp (file)

Function: z-wwhitehead-sintr SMST N CHML-CLSS &aux FACE K-Z-N IDNT EFHM
Package

cat

Source

whitehead.lisp (file)

Function: z2-wwhitehead-sintr SMST N CHML-CLSS &aux FACE K-Z2-N IDNT EFHM
Package

cat

Source

whitehead.lisp (file)


Next: , Previous: , Up: Internal definitions   [Contents][Index]

6.2.5 Generic functions

Generic Function: ?-clnm OBJECT
Generic Function: (setf ?-clnm) NEW-VALUE OBJECT
Package

cat

Methods
Method: ?-clnm (MORPHISM morphism)

automatically generated reader method

Source

classes.lisp (file)

Method: (setf ?-clnm) NEW-VALUE (MORPHISM morphism)

automatically generated writer method

Source

classes.lisp (file)

Generic Function: ???-clnm OBJECT
Generic Function: (setf ???-clnm) NEW-VALUE OBJECT
Package

cat

Methods
Method: ???-clnm (MORPHISM morphism)

automatically generated reader method

Source

classes.lisp (file)

Method: (setf ???-clnm) NEW-VALUE (MORPHISM morphism)

automatically generated writer method

Source

classes.lisp (file)

Generic Function: aprd1 OBJECT
Package

cat

Methods
Method: aprd1 (ALGEBRA algebra)

automatically generated reader method

Source

classes.lisp (file)

Generic Function: basis1 OBJECT
Package

cat

Methods
Method: basis1 (CHAIN-COMPLEX chain-complex)

automatically generated reader method

Source

classes.lisp (file)

Generic Function: bcc1 OBJECT
Package

cat

Methods
Method: bcc1 (REDUCTION reduction)

automatically generated reader method

Source

classes.lisp (file)

Generic Function: cmpr1 OBJECT
Package

cat

Methods
Method: cmpr1 (CHAIN-COMPLEX chain-complex)

automatically generated reader method

Source

classes.lisp (file)

Generic Function: cprd1 OBJECT
Package

cat

Methods
Method: cprd1 (COALGEBRA coalgebra)

automatically generated reader method

Source

classes.lisp (file)

Generic Function: f1 OBJECT
Package

cat

Methods
Method: f1 (REDUCTION reduction)

automatically generated reader method

Source

classes.lisp (file)

Generic Function: face1 OBJECT
Package

cat

Methods
Method: face1 (SIMPLICIAL-SET simplicial-set)

automatically generated reader method

Source

classes.lisp (file)

Generic Function: g1 OBJECT
Package

cat

Methods
Method: g1 (REDUCTION reduction)

automatically generated reader method

Source

classes.lisp (file)

Generic Function: grin1 OBJECT
Package

cat

Methods
Method: grin1 (SIMPLICIAL-GROUP simplicial-group)

automatically generated reader method

Source

classes.lisp (file)

Generic Function: grmd OBJECT
Package

cat

Methods
Method: grmd (CHAIN-COMPLEX chain-complex)

automatically generated reader method

Source

classes.lisp (file)

Generic Function: grml1 OBJECT
Package

cat

Methods
Method: grml1 (SIMPLICIAL-GROUP simplicial-group)

automatically generated reader method

Source

classes.lisp (file)

Generic Function: h1 OBJECT
Package

cat

Methods
Method: h1 (REDUCTION reduction)

automatically generated reader method

Source

classes.lisp (file)

Generic Function: intr OBJECT
Package

cat

Methods
Method: intr (MORPHISM morphism)

automatically generated reader method

Source

classes.lisp (file)

Generic Function: kfll1 OBJECT
Package

cat

Methods
Method: kfll1 (KAN kan)

automatically generated reader method

Source

classes.lisp (file)

Generic Function: lbcc1 OBJECT
Package

cat

Methods
Method: lbcc1 (HOMOTOPY-EQUIVALENCE homotopy-equivalence)

automatically generated reader method

Source

classes.lisp (file)

Generic Function: lf1 OBJECT
Package

cat

Methods
Method: lf1 (HOMOTOPY-EQUIVALENCE homotopy-equivalence)

automatically generated reader method

Source

classes.lisp (file)

Generic Function: lg1 OBJECT
Package

cat

Methods
Method: lg1 (HOMOTOPY-EQUIVALENCE homotopy-equivalence)

automatically generated reader method

Source

classes.lisp (file)

Generic Function: lh1 OBJECT
Package

cat

Methods
Method: lh1 (HOMOTOPY-EQUIVALENCE homotopy-equivalence)

automatically generated reader method

Source

classes.lisp (file)

Generic Function: print-keycons CAR CDR STREAM
Package

cat

Source

delta.lisp (file)

Methods
Method: print-keycons (CAR (eql delt)) CDR STREAM
Generic Function: rbcc1 OBJECT
Package

cat

Methods
Method: rbcc1 (HOMOTOPY-EQUIVALENCE homotopy-equivalence)

automatically generated reader method

Source

classes.lisp (file)

Generic Function: rf1 OBJECT
Package

cat

Methods
Method: rf1 (HOMOTOPY-EQUIVALENCE homotopy-equivalence)

automatically generated reader method

Source

classes.lisp (file)

Generic Function: rg1 OBJECT
Package

cat

Methods
Method: rg1 (HOMOTOPY-EQUIVALENCE homotopy-equivalence)

automatically generated reader method

Source

classes.lisp (file)

Generic Function: rh1 OBJECT
Package

cat

Methods
Method: rh1 (HOMOTOPY-EQUIVALENCE homotopy-equivalence)

automatically generated reader method

Source

classes.lisp (file)

Generic Function: rslts OBJECT
Package

cat

Methods
Method: rslts (MORPHISM morphism)

automatically generated reader method

Source

classes.lisp (file)

Generic Function: search-efhm CHCM ORGN
Package

cat

Source

searching-homology.lisp (file)

Methods
Method: search-efhm CLASSIFYING-SPACE (ORGN (eql classifying-space))
Source

cl-space-efhm.lisp (file)

Method: search-efhm SMST (ORGN (eql fibration-total))
Source

serre.lisp (file)

Method: search-efhm K-Z-1 (ORGN (eql k-z-1))
Source

k-pi-n.lisp (file)

Method: search-efhm LOOP-SPACE (ORGN (eql loop-space))
Source

lp-space-efhm.lisp (file)

Method: search-efhm SMST (ORGN (eql crts-prdc))
Source

eilenberg-zilber.lisp (file)

Method: search-efhm SMST (ORGN (eql disk-pasting))
Source

disk-pasting.lisp (file)

Method: search-efhm SUSPENSION (ORGN (eql suspension))
Source

suspensions.lisp (file)

Method: search-efhm CHCM (ORGN (eql tnsr-prdc))
Source

tensor-products.lisp (file)

Method: search-efhm CHCM (ORGN (eql cone))
Source

cones.lisp (file)

Method: search-efhm CHCM ORGN
Generic Function: strt OBJECT
Package

cat

Methods
Method: strt (MORPHISM morphism)

automatically generated reader method

Source

classes.lisp (file)

Generic Function: suspension-1 X
Package

cat

Source

suspensions.lisp (file)

Methods
Method: suspension-1 (HMEQ homotopy-equivalence)
Method: suspension-1 (RDCT reduction)
Method: suspension-1 (MRPH morphism)
Method: suspension-1 (SMST simplicial-set)
Method: suspension-1 (CLGB coalgebra)
Method: suspension-1 (CHCM chain-complex)
Generic Function: tcc1 OBJECT
Package

cat

Methods
Method: tcc1 (HOMOTOPY-EQUIVALENCE homotopy-equivalence)

automatically generated reader method

Source

classes.lisp (file)

Method: tcc1 (REDUCTION reduction)

automatically generated reader method

Source

classes.lisp (file)

Generic Function: trgt OBJECT
Package

cat

Methods
Method: trgt (MORPHISM morphism)

automatically generated reader method

Source

classes.lisp (file)


Next: , Previous: , Up: Internal definitions   [Contents][Index]

6.2.6 Structures

Structure: bicn ()
Package

cat

Source

classes.lisp (file)

Direct superclasses

structure-object (structure)

Direct methods

print-object (method)

Direct slots
Slot: bcnx
Initform

(:type (quote (member :bcnb :bcnc :bcnd)))

Readers

bcnx (function)

Writers

(setf bcnx) (function)

Slot: ibicn
Initform

(:type (quote cat:gnrt))

Readers

ibicn (function)

Writers

(setf ibicn) (function)

Structure: matrice ()

——————————————————————[type-doc] MATRICE
Slots: (leftcol uplig)
A MATRICE is made of two vectors LEFTCOL and UPLIG. LEFTCOL is a
vector of size m+1 if m is the number of rows of the matrix, UPLIG is
a vector of size n+1 if n is the number of columns.
Every element of LEFTCOL and UPLIG is a T-MAT with the value NIL indicating it is a fake term. ——————————————————————————

Package

cat

Source

classes.lisp (file)

Direct superclasses

structure-object (structure)

Direct methods

print-object (method)

Direct slots
Slot: leftcol
Readers

leftcol (function)

Writers

(setf leftcol) (function)

Slot: uplig
Readers

uplig (function)

Writers

(setf uplig) (function)

Structure: result ()
Package

cat

Source

classes.lisp (file)

Direct superclasses

structure-object (structure)

Direct methods

print-object (method)

Direct slots
Slot: gnrt
Type

cat:gnrt

Readers

result-gnrt (function)

Writers

(setf result-gnrt) (function)

Slot: value
Type

cat:cmbn

Readers

result-value (function)

Writers

(setf result-value) (function)

Slot: clnm
Type

fixnum

Initform

0

Readers

result-clnm (function)

Writers

(setf result-clnm) (function)

Slot: rntm
Type

single-float

Initform

0.0

Readers

result-rntm (function)

Writers

(setf result-rntm) (function)

Structure: t-mat ()

——————————————————————[type-doc] T-MAT
Slots: (val ilig icol left up)
A T-MAT (= Terme de Matrice) has five components:

VAL = A value, an integer, in principle a non-null integer.
ILIG = the line (row is better) index of this term
ICOL = the column index of this term
LEFT = a pointer to the next term on the left on the same line,
or to a fake term, an element of LEFTCOL of the matrice.
UP = a pointer to the next term above on the same column,
or to a fake term, an element of UPLIG of the matrice. ——————————————————————————

Package

cat

Source

classes.lisp (file)

Direct superclasses

structure-object (structure)

Direct slots
Slot: val
Readers

val (function)

Writers

(setf val) (function)

Slot: ilig
Readers

ilig (function)

Writers

(setf ilig) (function)

Slot: icol
Readers

icol (function)

Writers

(setf icol) (function)

Slot: left
Readers

left (function)

Writers

(setf left) (function)

Slot: up
Readers

up (function)

Writers

(setf up) (function)


Next: , Previous: , Up: Internal definitions   [Contents][Index]

6.2.7 Classes

Class: algebra ()
Package

cat

Source

classes.lisp (file)

Direct superclasses

chain-complex (class)

Direct subclasses

hopf-algebra (class)

Direct methods
  • bar (method)
  • print-object (method)
  • aprd1 (method)
Direct slots
Slot: aprd
Type

cat:morphism

Initargs

:aprd

Readers

aprd1 (generic function)

Class: coalgebra ()
Package

cat

Source

classes.lisp (file)

Direct superclasses

chain-complex (class)

Direct subclasses
Direct methods
Direct slots
Slot: cprd
Type

cat:morphism

Initargs

:cprd

Readers

cprd1 (generic function)

Class: hopf-algebra ()
Package

cat

Source

classes.lisp (file)

Direct superclasses
Direct subclasses

simplicial-group (class)

Direct methods

print-object (method)


Previous: , Up: Internal definitions   [Contents][Index]

6.2.8 Types

Type: any ()

——————————————————————[type-doc] ANY
A derived type that is equivalent to Lisp’s system class T, which includes all Lisp objects. ——————————————————————————

Package

cat

Source

classes.lisp (file)

Type: cmprf ()

——————————————————————[type-doc] CMPRF
A derived type to represent comparison functions. ——————————————————————————

Package

cat

Source

classes.lisp (file)

Type: dlop ()
Package

cat

Source

classes.lisp (file)

Type: expn ()
Package

cat

Source

classes.lisp (file)

Type: face* ()
Package

cat

Source

classes.lisp (file)

Type: fibration ()
Package

cat

Source

classes.lisp (file)

Type: iabar ()
Package

cat

Source

classes.lisp (file)

Type: iallp ()
Package

cat

Source

classes.lisp (file)

Type: icmbn ()
Package

cat

Source

classes.lisp (file)

Type: iloop ()
Package

cat

Source

classes.lisp (file)

Type: intr-mrph ()
Package

cat

Source

classes.lisp (file)

Type: matrix ()
Package

cat

Source

smith.lisp (file)

Type: powr ()
Package

cat

Source

classes.lisp (file)

Type: strt ()

—————————————————————–[type-doc] STRT
A derived type, which represents the mapping strategy of morphisms. ——————————————————————————

Package

cat

Source

classes.lisp (file)


Previous: , Up: Top   [Contents][Index]

Appendix A Indexes


Next: , Previous: , Up: Indexes   [Contents][Index]

A.1 Concepts

Jump to:   F   K   L   M  
Index Entry  Section

F
File, Lisp, kenzo.asd: The kenzo<dot>asd file
File, Lisp, kenzo/package.lisp: The kenzo/package<dot>lisp file
File, Lisp, kenzo/src/abbreviations.lisp: The kenzo/src/abbreviations<dot>lisp file
File, Lisp, kenzo/src/algebras.lisp: The kenzo/src/algebras<dot>lisp file
File, Lisp, kenzo/src/bar.lisp: The kenzo/src/bar<dot>lisp file
File, Lisp, kenzo/src/bicones.lisp: The kenzo/src/bicones<dot>lisp file
File, Lisp, kenzo/src/cartesian-products.lisp: The kenzo/src/cartesian-products<dot>lisp file
File, Lisp, kenzo/src/chain-complexes.lisp: The kenzo/src/chain-complexes<dot>lisp file
File, Lisp, kenzo/src/chcm-elementary-op.lisp: The kenzo/src/chcm-elementary-op<dot>lisp file
File, Lisp, kenzo/src/cl-space-efhm.lisp: The kenzo/src/cl-space-efhm<dot>lisp file
File, Lisp, kenzo/src/classes.lisp: The kenzo/src/classes<dot>lisp file
File, Lisp, kenzo/src/classifying-spaces.lisp: The kenzo/src/classifying-spaces<dot>lisp file
File, Lisp, kenzo/src/coalgebras.lisp: The kenzo/src/coalgebras<dot>lisp file
File, Lisp, kenzo/src/cobar.lisp: The kenzo/src/cobar<dot>lisp file
File, Lisp, kenzo/src/combinations.lisp: The kenzo/src/combinations<dot>lisp file
File, Lisp, kenzo/src/cones.lisp: The kenzo/src/cones<dot>lisp file
File, Lisp, kenzo/src/cs-twisted-products.lisp: The kenzo/src/cs-twisted-products<dot>lisp file
File, Lisp, kenzo/src/delta.lisp: The kenzo/src/delta<dot>lisp file
File, Lisp, kenzo/src/disk-pasting.lisp: The kenzo/src/disk-pasting<dot>lisp file
File, Lisp, kenzo/src/effective-homology.lisp: The kenzo/src/effective-homology<dot>lisp file
File, Lisp, kenzo/src/eilenberg-zilber.lisp: The kenzo/src/eilenberg-zilber<dot>lisp file
File, Lisp, kenzo/src/fibrations.lisp: The kenzo/src/fibrations<dot>lisp file
File, Lisp, kenzo/src/homology-groups.lisp: The kenzo/src/homology-groups<dot>lisp file
File, Lisp, kenzo/src/k-pi-n.lisp: The kenzo/src/k-pi-n<dot>lisp file
File, Lisp, kenzo/src/kan.lisp: The kenzo/src/kan<dot>lisp file
File, Lisp, kenzo/src/kenzo.lisp: The kenzo/src/kenzo<dot>lisp file
File, Lisp, kenzo/src/loop-spaces.lisp: The kenzo/src/loop-spaces<dot>lisp file
File, Lisp, kenzo/src/lp-space-efhm.lisp: The kenzo/src/lp-space-efhm<dot>lisp file
File, Lisp, kenzo/src/ls-twisted-products.lisp: The kenzo/src/ls-twisted-products<dot>lisp file
File, Lisp, kenzo/src/macros.lisp: The kenzo/src/macros<dot>lisp file
File, Lisp, kenzo/src/searching-homology.lisp: The kenzo/src/searching-homology<dot>lisp file
File, Lisp, kenzo/src/serre.lisp: The kenzo/src/serre<dot>lisp file
File, Lisp, kenzo/src/simplicial-groups.lisp: The kenzo/src/simplicial-groups<dot>lisp file
File, Lisp, kenzo/src/simplicial-mrphs.lisp: The kenzo/src/simplicial-mrphs<dot>lisp file
File, Lisp, kenzo/src/simplicial-sets.lisp: The kenzo/src/simplicial-sets<dot>lisp file
File, Lisp, kenzo/src/smith.lisp: The kenzo/src/smith<dot>lisp file
File, Lisp, kenzo/src/special-smsts.lisp: The kenzo/src/special-smsts<dot>lisp file
File, Lisp, kenzo/src/suspensions.lisp: The kenzo/src/suspensions<dot>lisp file
File, Lisp, kenzo/src/tensor-products.lisp: The kenzo/src/tensor-products<dot>lisp file
File, Lisp, kenzo/src/various.lisp: The kenzo/src/various<dot>lisp file
File, Lisp, kenzo/src/whitehead.lisp: The kenzo/src/whitehead<dot>lisp file

K
kenzo.asd: The kenzo<dot>asd file
kenzo/package.lisp: The kenzo/package<dot>lisp file
kenzo/src: The kenzo/src module
kenzo/src/abbreviations.lisp: The kenzo/src/abbreviations<dot>lisp file
kenzo/src/algebras.lisp: The kenzo/src/algebras<dot>lisp file
kenzo/src/bar.lisp: The kenzo/src/bar<dot>lisp file
kenzo/src/bicones.lisp: The kenzo/src/bicones<dot>lisp file
kenzo/src/cartesian-products.lisp: The kenzo/src/cartesian-products<dot>lisp file
kenzo/src/chain-complexes.lisp: The kenzo/src/chain-complexes<dot>lisp file
kenzo/src/chcm-elementary-op.lisp: The kenzo/src/chcm-elementary-op<dot>lisp file
kenzo/src/cl-space-efhm.lisp: The kenzo/src/cl-space-efhm<dot>lisp file
kenzo/src/classes.lisp: The kenzo/src/classes<dot>lisp file
kenzo/src/classifying-spaces.lisp: The kenzo/src/classifying-spaces<dot>lisp file
kenzo/src/coalgebras.lisp: The kenzo/src/coalgebras<dot>lisp file
kenzo/src/cobar.lisp: The kenzo/src/cobar<dot>lisp file
kenzo/src/combinations.lisp: The kenzo/src/combinations<dot>lisp file
kenzo/src/cones.lisp: The kenzo/src/cones<dot>lisp file
kenzo/src/cs-twisted-products.lisp: The kenzo/src/cs-twisted-products<dot>lisp file
kenzo/src/delta.lisp: The kenzo/src/delta<dot>lisp file
kenzo/src/disk-pasting.lisp: The kenzo/src/disk-pasting<dot>lisp file
kenzo/src/effective-homology.lisp: The kenzo/src/effective-homology<dot>lisp file
kenzo/src/eilenberg-zilber.lisp: The kenzo/src/eilenberg-zilber<dot>lisp file
kenzo/src/fibrations.lisp: The kenzo/src/fibrations<dot>lisp file
kenzo/src/homology-groups.lisp: The kenzo/src/homology-groups<dot>lisp file
kenzo/src/k-pi-n.lisp: The kenzo/src/k-pi-n<dot>lisp file
kenzo/src/kan.lisp: The kenzo/src/kan<dot>lisp file
kenzo/src/kenzo.lisp: The kenzo/src/kenzo<dot>lisp file
kenzo/src/loop-spaces.lisp: The kenzo/src/loop-spaces<dot>lisp file
kenzo/src/lp-space-efhm.lisp: The kenzo/src/lp-space-efhm<dot>lisp file
kenzo/src/ls-twisted-products.lisp: The kenzo/src/ls-twisted-products<dot>lisp file
kenzo/src/macros.lisp: The kenzo/src/macros<dot>lisp file
kenzo/src/searching-homology.lisp: The kenzo/src/searching-homology<dot>lisp file
kenzo/src/serre.lisp: The kenzo/src/serre<dot>lisp file
kenzo/src/simplicial-groups.lisp: The kenzo/src/simplicial-groups<dot>lisp file
kenzo/src/simplicial-mrphs.lisp: The kenzo/src/simplicial-mrphs<dot>lisp file
kenzo/src/simplicial-sets.lisp: The kenzo/src/simplicial-sets<dot>lisp file
kenzo/src/smith.lisp: The kenzo/src/smith<dot>lisp file
kenzo/src/special-smsts.lisp: The kenzo/src/special-smsts<dot>lisp file
kenzo/src/suspensions.lisp: The kenzo/src/suspensions<dot>lisp file
kenzo/src/tensor-products.lisp: The kenzo/src/tensor-products<dot>lisp file
kenzo/src/various.lisp: The kenzo/src/various<dot>lisp file
kenzo/src/whitehead.lisp: The kenzo/src/whitehead<dot>lisp file

L
Lisp File, kenzo.asd: The kenzo<dot>asd file
Lisp File, kenzo/package.lisp: The kenzo/package<dot>lisp file
Lisp File, kenzo/src/abbreviations.lisp: The kenzo/src/abbreviations<dot>lisp file
Lisp File, kenzo/src/algebras.lisp: The kenzo/src/algebras<dot>lisp file
Lisp File, kenzo/src/bar.lisp: The kenzo/src/bar<dot>lisp file
Lisp File, kenzo/src/bicones.lisp: The kenzo/src/bicones<dot>lisp file
Lisp File, kenzo/src/cartesian-products.lisp: The kenzo/src/cartesian-products<dot>lisp file
Lisp File, kenzo/src/chain-complexes.lisp: The kenzo/src/chain-complexes<dot>lisp file
Lisp File, kenzo/src/chcm-elementary-op.lisp: The kenzo/src/chcm-elementary-op<dot>lisp file
Lisp File, kenzo/src/cl-space-efhm.lisp: The kenzo/src/cl-space-efhm<dot>lisp file
Lisp File, kenzo/src/classes.lisp: The kenzo/src/classes<dot>lisp file
Lisp File, kenzo/src/classifying-spaces.lisp: The kenzo/src/classifying-spaces<dot>lisp file
Lisp File, kenzo/src/coalgebras.lisp: The kenzo/src/coalgebras<dot>lisp file
Lisp File, kenzo/src/cobar.lisp: The kenzo/src/cobar<dot>lisp file
Lisp File, kenzo/src/combinations.lisp: The kenzo/src/combinations<dot>lisp file
Lisp File, kenzo/src/cones.lisp: The kenzo/src/cones<dot>lisp file
Lisp File, kenzo/src/cs-twisted-products.lisp: The kenzo/src/cs-twisted-products<dot>lisp file
Lisp File, kenzo/src/delta.lisp: The kenzo/src/delta<dot>lisp file
Lisp File, kenzo/src/disk-pasting.lisp: The kenzo/src/disk-pasting<dot>lisp file
Lisp File, kenzo/src/effective-homology.lisp: The kenzo/src/effective-homology<dot>lisp file
Lisp File, kenzo/src/eilenberg-zilber.lisp: The kenzo/src/eilenberg-zilber<dot>lisp file
Lisp File, kenzo/src/fibrations.lisp: The kenzo/src/fibrations<dot>lisp file
Lisp File, kenzo/src/homology-groups.lisp: The kenzo/src/homology-groups<dot>lisp file
Lisp File, kenzo/src/k-pi-n.lisp: The kenzo/src/k-pi-n<dot>lisp file
Lisp File, kenzo/src/kan.lisp: The kenzo/src/kan<dot>lisp file
Lisp File, kenzo/src/kenzo.lisp: The kenzo/src/kenzo<dot>lisp file
Lisp File, kenzo/src/loop-spaces.lisp: The kenzo/src/loop-spaces<dot>lisp file
Lisp File, kenzo/src/lp-space-efhm.lisp: The kenzo/src/lp-space-efhm<dot>lisp file
Lisp File, kenzo/src/ls-twisted-products.lisp: The kenzo/src/ls-twisted-products<dot>lisp file
Lisp File, kenzo/src/macros.lisp: The kenzo/src/macros<dot>lisp file
Lisp File, kenzo/src/searching-homology.lisp: The kenzo/src/searching-homology<dot>lisp file
Lisp File, kenzo/src/serre.lisp: The kenzo/src/serre<dot>lisp file
Lisp File, kenzo/src/simplicial-groups.lisp: The kenzo/src/simplicial-groups<dot>lisp file
Lisp File, kenzo/src/simplicial-mrphs.lisp: The kenzo/src/simplicial-mrphs<dot>lisp file
Lisp File, kenzo/src/simplicial-sets.lisp: The kenzo/src/simplicial-sets<dot>lisp file
Lisp File, kenzo/src/smith.lisp: The kenzo/src/smith<dot>lisp file
Lisp File, kenzo/src/special-smsts.lisp: The kenzo/src/special-smsts<dot>lisp file
Lisp File, kenzo/src/suspensions.lisp: The kenzo/src/suspensions<dot>lisp file
Lisp File, kenzo/src/tensor-products.lisp: The kenzo/src/tensor-products<dot>lisp file
Lisp File, kenzo/src/various.lisp: The kenzo/src/various<dot>lisp file
Lisp File, kenzo/src/whitehead.lisp: The kenzo/src/whitehead<dot>lisp file

M
Module, kenzo/src: The kenzo/src module

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A.2 Functions

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