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This is the kenzo Reference Manual, version 1.1.9, generated automatically by Declt version 4.0 beta 2 "William Riker" on Wed Jun 15 04:54:21 2022 GMT+0.
Next: Systems, Previous: The kenzo Reference Manual, Up: The kenzo Reference Manual [Contents][Index]
Kenzo is a Symbolic Software for Effective Homology Computation and should be of interest to students and researchers in algebraic topology.
This repository contains a repackaged version of the Kenzo program developed 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 updates its infrastructure by providing the following:
The primary source of documentation is the excellent Kenzo Handbook.
The easiest way to get started with Kenzo is to peruse a matching set of
Jupyter notebooks. In the notebooks
folder,
there is one notebook for each chapter in the Kenzo handbook. NOTE: The
first time you try to access the
Kenzo JupterHub
site, you will be prompted to authenticate via GitHub.
Please consult the Wiki for news, different installation methods, and other Kenzo topics.
Enjoy!
Next: Modules, Previous: Introduction, Up: The kenzo Reference Manual [Contents][Index]
The main system appears first, followed by any subsystem dependency.
Next: Files, Previous: Systems, Up: The kenzo Reference Manual [Contents][Index]
Modules are listed depth-first from the system components tree.
Next: kenzo/src/kenzo-7, Previous: Modules, Up: Modules [Contents][Index]
kenzo (system).
Next: kenzo/src/kenzo-8, Previous: kenzo/src, Up: Modules [Contents][Index]
src (module).
Next: kenzo/src/kenzo-9, Previous: kenzo/src/kenzo-7, Up: Modules [Contents][Index]
src (module).
Previous: kenzo/src/kenzo-8, Up: Modules [Contents][Index]
src (module).
Next: Packages, Previous: Modules, Up: The kenzo Reference Manual [Contents][Index]
Files are sorted by type and then listed depth-first from the systems components trees.
Next: kenzo/src/kenzo-7/package.lisp, Previous: Lisp, Up: Lisp [Contents][Index]
Next: kenzo/src/kenzo-7/kenzo.lisp, Previous: kenzo/kenzo.asd, Up: Lisp [Contents][Index]
Next: kenzo/src/kenzo-7/abbreviations.lisp, Previous: kenzo/src/kenzo-7/package.lisp, Up: Lisp [Contents][Index]
kenzo-7 (module).
Next: kenzo/src/kenzo-7/macros.lisp, Previous: kenzo/src/kenzo-7/kenzo.lisp, Up: Lisp [Contents][Index]
kenzo-7 (module).
Next: kenzo/src/kenzo-7/various.lisp, Previous: kenzo/src/kenzo-7/abbreviations.lisp, Up: Lisp [Contents][Index]
kenzo-7 (module).
Next: kenzo/src/kenzo-7/classes.lisp, Previous: kenzo/src/kenzo-7/macros.lisp, Up: Lisp [Contents][Index]
kenzo-7 (module).
Next: kenzo/src/kenzo-7/combinations.lisp, Previous: kenzo/src/kenzo-7/various.lisp, Up: Lisp [Contents][Index]
kenzo-7 (module).
Next: kenzo/src/kenzo-7/chain-complexes.lisp, Previous: kenzo/src/kenzo-7/classes.lisp, Up: Lisp [Contents][Index]
kenzo-7 (module).
Next: kenzo/src/kenzo-7/chcm-elementary-op.lisp, Previous: kenzo/src/kenzo-7/combinations.lisp, Up: Lisp [Contents][Index]
kenzo-7 (module).
Next: kenzo/src/kenzo-7/effective-homology.lisp, Previous: kenzo/src/kenzo-7/chain-complexes.lisp, Up: Lisp [Contents][Index]
kenzo-7 (module).
Next: kenzo/src/kenzo-7/homology-groups.lisp, Previous: kenzo/src/kenzo-7/chcm-elementary-op.lisp, Up: Lisp [Contents][Index]
kenzo-7 (module).
Next: kenzo/src/kenzo-7/searching-homology.lisp, Previous: kenzo/src/kenzo-7/effective-homology.lisp, Up: Lisp [Contents][Index]
kenzo-7 (module).
Next: kenzo/src/kenzo-7/cones.lisp, Previous: kenzo/src/kenzo-7/homology-groups.lisp, Up: Lisp [Contents][Index]
kenzo-7 (module).
search-efhm (generic function).
Next: kenzo/src/kenzo-7/bicones.lisp, Previous: kenzo/src/kenzo-7/searching-homology.lisp, Up: Lisp [Contents][Index]
kenzo-7 (module).
Next: kenzo/src/kenzo-7/tensor-products.lisp, Previous: kenzo/src/kenzo-7/cones.lisp, Up: Lisp [Contents][Index]
kenzo-7 (module).
Next: kenzo/src/kenzo-7/coalgebras.lisp, Previous: kenzo/src/kenzo-7/bicones.lisp, Up: Lisp [Contents][Index]
kenzo-7 (module).
search-efhm (method).
Next: kenzo/src/kenzo-7/cobar.lisp, Previous: kenzo/src/kenzo-7/tensor-products.lisp, Up: Lisp [Contents][Index]
kenzo-7 (module).
print-object (method).
Next: kenzo/src/kenzo-7/algebras.lisp, Previous: kenzo/src/kenzo-7/coalgebras.lisp, Up: Lisp [Contents][Index]
kenzo-7 (module).
Next: kenzo/src/kenzo-7/bar.lisp, Previous: kenzo/src/kenzo-7/cobar.lisp, Up: Lisp [Contents][Index]
kenzo-7 (module).
Next: kenzo/src/kenzo-7/simplicial-sets.lisp, Previous: kenzo/src/kenzo-7/algebras.lisp, Up: Lisp [Contents][Index]
kenzo-7 (module).
Next: kenzo/src/kenzo-7/simplicial-mrphs.lisp, Previous: kenzo/src/kenzo-7/bar.lisp, Up: Lisp [Contents][Index]
kenzo-7 (module).
Next: kenzo/src/kenzo-7/delta.lisp, Previous: kenzo/src/kenzo-7/simplicial-sets.lisp, Up: Lisp [Contents][Index]
kenzo-7 (module).
Next: kenzo/src/kenzo-7/special-smsts.lisp, Previous: kenzo/src/kenzo-7/simplicial-mrphs.lisp, Up: Lisp [Contents][Index]
kenzo-7 (module).
Next: kenzo/src/kenzo-7/suspensions.lisp, Previous: kenzo/src/kenzo-7/delta.lisp, Up: Lisp [Contents][Index]
kenzo-7 (module).
Next: kenzo/src/kenzo-7/disk-pasting.lisp, Previous: kenzo/src/kenzo-7/special-smsts.lisp, Up: Lisp [Contents][Index]
kenzo-7 (module).
Next: kenzo/src/kenzo-7/cartesian-products.lisp, Previous: kenzo/src/kenzo-7/suspensions.lisp, Up: Lisp [Contents][Index]
kenzo-7 (module).
search-efhm (method).
Next: kenzo/src/kenzo-7/eilenberg-zilber.lisp, Previous: kenzo/src/kenzo-7/disk-pasting.lisp, Up: Lisp [Contents][Index]
kenzo-7 (module).
crpr-print (function).
Next: kenzo/src/kenzo-7/kan.lisp, Previous: kenzo/src/kenzo-7/cartesian-products.lisp, Up: Lisp [Contents][Index]
kenzo-7 (module).
Next: kenzo/src/kenzo-7/simplicial-groups.lisp, Previous: kenzo/src/kenzo-7/eilenberg-zilber.lisp, Up: Lisp [Contents][Index]
kenzo-7 (module).
Next: kenzo/src/kenzo-7/fibrations.lisp, Previous: kenzo/src/kenzo-7/kan.lisp, Up: Lisp [Contents][Index]
kenzo-7 (module).
Next: kenzo/src/kenzo-7/loop-spaces.lisp, Previous: kenzo/src/kenzo-7/simplicial-groups.lisp, Up: Lisp [Contents][Index]
kenzo-7 (module).
fibration-total (function).
Next: kenzo/src/kenzo-7/ls-twisted-products.lisp, Previous: kenzo/src/kenzo-7/fibrations.lisp, Up: Lisp [Contents][Index]
kenzo-7 (module).
loop-space-face* (function).
Next: kenzo/src/kenzo-7/lp-space-efhm.lisp, Previous: kenzo/src/kenzo-7/loop-spaces.lisp, Up: Lisp [Contents][Index]
kenzo-7 (module).
Next: kenzo/src/kenzo-7/classifying-spaces.lisp, Previous: kenzo/src/kenzo-7/ls-twisted-products.lisp, Up: Lisp [Contents][Index]
kenzo-7 (module).
Next: kenzo/src/kenzo-7/k-pi-n.lisp, Previous: kenzo/src/kenzo-7/lp-space-efhm.lisp, Up: Lisp [Contents][Index]
kenzo-7 (module).
gbar-print (function).
Next: kenzo/src/kenzo-7/serre.lisp, Previous: kenzo/src/kenzo-7/classifying-spaces.lisp, Up: Lisp [Contents][Index]
kenzo-7 (module).
Next: kenzo/src/kenzo-7/cs-twisted-products.lisp, Previous: kenzo/src/kenzo-7/k-pi-n.lisp, Up: Lisp [Contents][Index]
kenzo-7 (module).
Next: kenzo/src/kenzo-7/cl-space-efhm.lisp, Previous: kenzo/src/kenzo-7/serre.lisp, Up: Lisp [Contents][Index]
kenzo-7 (module).
Next: kenzo/src/kenzo-7/whitehead.lisp, Previous: kenzo/src/kenzo-7/cs-twisted-products.lisp, Up: Lisp [Contents][Index]
kenzo-7 (module).
Next: kenzo/src/kenzo-7/smith.lisp, Previous: kenzo/src/kenzo-7/cl-space-efhm.lisp, Up: Lisp [Contents][Index]
kenzo-7 (module).
Next: kenzo/src/kenzo-8/package.lisp, Previous: kenzo/src/kenzo-7/whitehead.lisp, Up: Lisp [Contents][Index]
kenzo-7 (module).
Next: kenzo/src/kenzo-8/cat-init.lisp, Previous: kenzo/src/kenzo-7/smith.lisp, Up: Lisp [Contents][Index]
Next: kenzo/src/kenzo-8/macros.lisp, Previous: kenzo/src/kenzo-8/package.lisp, Up: Lisp [Contents][Index]
kenzo-8 (module).
Next: kenzo/src/kenzo-8/various.lisp, Previous: kenzo/src/kenzo-8/cat-init.lisp, Up: Lisp [Contents][Index]
kenzo-8 (module).
Next: kenzo/src/kenzo-8/classes.lisp, Previous: kenzo/src/kenzo-8/macros.lisp, Up: Lisp [Contents][Index]
kenzo-8 (module).
Next: kenzo/src/kenzo-8/combinations.lisp, Previous: kenzo/src/kenzo-8/various.lisp, Up: Lisp [Contents][Index]
kenzo-8 (module).
Next: kenzo/src/kenzo-8/chain-complexes.lisp, Previous: kenzo/src/kenzo-8/classes.lisp, Up: Lisp [Contents][Index]
kenzo-8 (module).
+zero-negative-cmbn+ (constant).
Next: kenzo/src/kenzo-8/chcm-elementary-op.lisp, Previous: kenzo/src/kenzo-8/combinations.lisp, Up: Lisp [Contents][Index]
kenzo-8 (module).
Next: kenzo/src/kenzo-8/effective-homology.lisp, Previous: kenzo/src/kenzo-8/chain-complexes.lisp, Up: Lisp [Contents][Index]
kenzo-8 (module).
Next: kenzo/src/kenzo-8/homology-groups.lisp, Previous: kenzo/src/kenzo-8/chcm-elementary-op.lisp, Up: Lisp [Contents][Index]
kenzo-8 (module).
Next: kenzo/src/kenzo-8/searching-homology.lisp, Previous: kenzo/src/kenzo-8/effective-homology.lisp, Up: Lisp [Contents][Index]
kenzo-8 (module).
Next: kenzo/src/kenzo-8/cones.lisp, Previous: kenzo/src/kenzo-8/homology-groups.lisp, Up: Lisp [Contents][Index]
kenzo-8 (module).
search-efhm (generic function).
Next: kenzo/src/kenzo-8/bicones.lisp, Previous: kenzo/src/kenzo-8/searching-homology.lisp, Up: Lisp [Contents][Index]
kenzo-8 (module).
Next: kenzo/src/kenzo-8/tensor-products.lisp, Previous: kenzo/src/kenzo-8/cones.lisp, Up: Lisp [Contents][Index]
kenzo-8 (module).
bicone-intr-dffr (function).
Next: kenzo/src/kenzo-8/coalgebras.lisp, Previous: kenzo/src/kenzo-8/bicones.lisp, Up: Lisp [Contents][Index]
kenzo-8 (module).
search-efhm (method).
Next: kenzo/src/kenzo-8/cobar.lisp, Previous: kenzo/src/kenzo-8/tensor-products.lisp, Up: Lisp [Contents][Index]
kenzo-8 (module).
print-object (method).
Next: kenzo/src/kenzo-8/algebras.lisp, Previous: kenzo/src/kenzo-8/coalgebras.lisp, Up: Lisp [Contents][Index]
kenzo-8 (module).
Next: kenzo/src/kenzo-8/bar.lisp, Previous: kenzo/src/kenzo-8/cobar.lisp, Up: Lisp [Contents][Index]
kenzo-8 (module).
Next: kenzo/src/kenzo-8/simplicial-sets.lisp, Previous: kenzo/src/kenzo-8/algebras.lisp, Up: Lisp [Contents][Index]
kenzo-8 (module).
Next: kenzo/src/kenzo-8/simplicial-mrphs.lisp, Previous: kenzo/src/kenzo-8/bar.lisp, Up: Lisp [Contents][Index]
kenzo-8 (module).
Next: kenzo/src/kenzo-8/delta.lisp, Previous: kenzo/src/kenzo-8/simplicial-sets.lisp, Up: Lisp [Contents][Index]
kenzo-8 (module).
Next: kenzo/src/kenzo-8/special-smsts.lisp, Previous: kenzo/src/kenzo-8/simplicial-mrphs.lisp, Up: Lisp [Contents][Index]
kenzo-8 (module).
Next: kenzo/src/kenzo-8/suspensions.lisp, Previous: kenzo/src/kenzo-8/delta.lisp, Up: Lisp [Contents][Index]
kenzo-8 (module).
Next: kenzo/src/kenzo-8/disk-pasting.lisp, Previous: kenzo/src/kenzo-8/special-smsts.lisp, Up: Lisp [Contents][Index]
kenzo-8 (module).
Next: kenzo/src/kenzo-8/cartesian-products.lisp, Previous: kenzo/src/kenzo-8/suspensions.lisp, Up: Lisp [Contents][Index]
kenzo-8 (module).
search-efhm (method).
Next: kenzo/src/kenzo-8/eilenberg-zilber.lisp, Previous: kenzo/src/kenzo-8/disk-pasting.lisp, Up: Lisp [Contents][Index]
kenzo-8 (module).
Next: kenzo/src/kenzo-8/kan.lisp, Previous: kenzo/src/kenzo-8/cartesian-products.lisp, Up: Lisp [Contents][Index]
kenzo-8 (module).
Next: kenzo/src/kenzo-8/simplicial-groups.lisp, Previous: kenzo/src/kenzo-8/eilenberg-zilber.lisp, Up: Lisp [Contents][Index]
kenzo-8 (module).
*kan-list* (special variable).
Next: kenzo/src/kenzo-8/fibrations.lisp, Previous: kenzo/src/kenzo-8/kan.lisp, Up: Lisp [Contents][Index]
kenzo-8 (module).
Next: kenzo/src/kenzo-8/loop-spaces.lisp, Previous: kenzo/src/kenzo-8/simplicial-groups.lisp, Up: Lisp [Contents][Index]
kenzo-8 (module).
fibration-total (function).
Next: kenzo/src/kenzo-8/ls-twisted-products.lisp, Previous: kenzo/src/kenzo-8/fibrations.lisp, Up: Lisp [Contents][Index]
kenzo-8 (module).
loop-space-face* (function).
Next: kenzo/src/kenzo-8/lp-space-efhm.lisp, Previous: kenzo/src/kenzo-8/loop-spaces.lisp, Up: Lisp [Contents][Index]
kenzo-8 (module).
Next: kenzo/src/kenzo-8/classifying-spaces.lisp, Previous: kenzo/src/kenzo-8/ls-twisted-products.lisp, Up: Lisp [Contents][Index]
kenzo-8 (module).
Next: kenzo/src/kenzo-8/k-pi-n.lisp, Previous: kenzo/src/kenzo-8/lp-space-efhm.lisp, Up: Lisp [Contents][Index]
kenzo-8 (module).
Next: kenzo/src/kenzo-8/serre.lisp, Previous: kenzo/src/kenzo-8/classifying-spaces.lisp, Up: Lisp [Contents][Index]
kenzo-8 (module).
Next: kenzo/src/kenzo-8/cs-twisted-products.lisp, Previous: kenzo/src/kenzo-8/k-pi-n.lisp, Up: Lisp [Contents][Index]
kenzo-8 (module).
Next: kenzo/src/kenzo-8/cl-space-efhm.lisp, Previous: kenzo/src/kenzo-8/serre.lisp, Up: Lisp [Contents][Index]
kenzo-8 (module).
Next: kenzo/src/kenzo-8/whitehead.lisp, Previous: kenzo/src/kenzo-8/cs-twisted-products.lisp, Up: Lisp [Contents][Index]
kenzo-8 (module).
Next: kenzo/src/kenzo-8/smith.lisp, Previous: kenzo/src/kenzo-8/cl-space-efhm.lisp, Up: Lisp [Contents][Index]
kenzo-8 (module).
Next: kenzo/src/kenzo-9/package.lisp, Previous: kenzo/src/kenzo-8/whitehead.lisp, Up: Lisp [Contents][Index]
kenzo-8 (module).
Next: kenzo/src/kenzo-9/cat-init.lisp, Previous: kenzo/src/kenzo-8/smith.lisp, Up: Lisp [Contents][Index]
Next: kenzo/src/kenzo-9/macros.lisp, Previous: kenzo/src/kenzo-9/package.lisp, Up: Lisp [Contents][Index]
kenzo-9 (module).
Next: kenzo/src/kenzo-9/various.lisp, Previous: kenzo/src/kenzo-9/cat-init.lisp, Up: Lisp [Contents][Index]
kenzo-9 (module).
Next: kenzo/src/kenzo-9/classes.lisp, Previous: kenzo/src/kenzo-9/macros.lisp, Up: Lisp [Contents][Index]
kenzo-9 (module).
Next: kenzo/src/kenzo-9/combinations.lisp, Previous: kenzo/src/kenzo-9/various.lisp, Up: Lisp [Contents][Index]
kenzo-9 (module).
Next: kenzo/src/kenzo-9/chain-complexes.lisp, Previous: kenzo/src/kenzo-9/classes.lisp, Up: Lisp [Contents][Index]
kenzo-9 (module).
+zero-negative-cmbn+ (constant).
Next: kenzo/src/kenzo-9/chain-complexes-dvf.lisp, Previous: kenzo/src/kenzo-9/combinations.lisp, Up: Lisp [Contents][Index]
kenzo-9 (module).
Next: kenzo/src/kenzo-9/chcm-elementary-op.lisp, Previous: kenzo/src/kenzo-9/chain-complexes.lisp, Up: Lisp [Contents][Index]
kenzo-9 (module).
print-object (method).
Next: kenzo/src/kenzo-9/effective-homology.lisp, Previous: kenzo/src/kenzo-9/chain-complexes-dvf.lisp, Up: Lisp [Contents][Index]
kenzo-9 (module).
Next: kenzo/src/kenzo-9/homology-groups.lisp, Previous: kenzo/src/kenzo-9/chcm-elementary-op.lisp, Up: Lisp [Contents][Index]
kenzo-9 (module).
Next: kenzo/src/kenzo-9/searching-homology.lisp, Previous: kenzo/src/kenzo-9/effective-homology.lisp, Up: Lisp [Contents][Index]
kenzo-9 (module).
Next: kenzo/src/kenzo-9/cones.lisp, Previous: kenzo/src/kenzo-9/homology-groups.lisp, Up: Lisp [Contents][Index]
kenzo-9 (module).
search-efhm (generic function).
Next: kenzo/src/kenzo-9/bicones.lisp, Previous: kenzo/src/kenzo-9/searching-homology.lisp, Up: Lisp [Contents][Index]
kenzo-9 (module).
Next: kenzo/src/kenzo-9/tensor-products.lisp, Previous: kenzo/src/kenzo-9/cones.lisp, Up: Lisp [Contents][Index]
kenzo-9 (module).
Next: kenzo/src/kenzo-9/coalgebras.lisp, Previous: kenzo/src/kenzo-9/bicones.lisp, Up: Lisp [Contents][Index]
kenzo-9 (module).
Next: kenzo/src/kenzo-9/cobar.lisp, Previous: kenzo/src/kenzo-9/tensor-products.lisp, Up: Lisp [Contents][Index]
kenzo-9 (module).
Next: kenzo/src/kenzo-9/algebras.lisp, Previous: kenzo/src/kenzo-9/coalgebras.lisp, Up: Lisp [Contents][Index]
kenzo-9 (module).
Next: kenzo/src/kenzo-9/bar.lisp, Previous: kenzo/src/kenzo-9/cobar.lisp, Up: Lisp [Contents][Index]
kenzo-9 (module).
Next: kenzo/src/kenzo-9/simplicial-sets.lisp, Previous: kenzo/src/kenzo-9/algebras.lisp, Up: Lisp [Contents][Index]
kenzo-9 (module).
Next: kenzo/src/kenzo-9/simplicial-mrphs.lisp, Previous: kenzo/src/kenzo-9/bar.lisp, Up: Lisp [Contents][Index]
kenzo-9 (module).
Next: kenzo/src/kenzo-9/delta.lisp, Previous: kenzo/src/kenzo-9/simplicial-sets.lisp, Up: Lisp [Contents][Index]
kenzo-9 (module).
Next: kenzo/src/kenzo-9/special-smsts.lisp, Previous: kenzo/src/kenzo-9/simplicial-mrphs.lisp, Up: Lisp [Contents][Index]
kenzo-9 (module).
Next: kenzo/src/kenzo-9/suspensions.lisp, Previous: kenzo/src/kenzo-9/delta.lisp, Up: Lisp [Contents][Index]
kenzo-9 (module).
Next: kenzo/src/kenzo-9/disk-pasting.lisp, Previous: kenzo/src/kenzo-9/special-smsts.lisp, Up: Lisp [Contents][Index]
kenzo-9 (module).
Next: kenzo/src/kenzo-9/cartesian-products.lisp, Previous: kenzo/src/kenzo-9/suspensions.lisp, Up: Lisp [Contents][Index]
kenzo-9 (module).
Next: kenzo/src/kenzo-9/eilenberg-zilber.lisp, Previous: kenzo/src/kenzo-9/disk-pasting.lisp, Up: Lisp [Contents][Index]
kenzo-9 (module).
crpr-print (function).
Next: kenzo/src/kenzo-9/kan.lisp, Previous: kenzo/src/kenzo-9/cartesian-products.lisp, Up: Lisp [Contents][Index]
kenzo-9 (module).
Next: kenzo/src/kenzo-9/simplicial-groups.lisp, Previous: kenzo/src/kenzo-9/eilenberg-zilber.lisp, Up: Lisp [Contents][Index]
kenzo-9 (module).
*kan-list* (special variable).
Next: kenzo/src/kenzo-9/fibrations.lisp, Previous: kenzo/src/kenzo-9/kan.lisp, Up: Lisp [Contents][Index]
kenzo-9 (module).
Next: kenzo/src/kenzo-9/fibrations-dvf.lisp, Previous: kenzo/src/kenzo-9/simplicial-groups.lisp, Up: Lisp [Contents][Index]
kenzo-9 (module).
fibration-total (function).
Next: kenzo/src/kenzo-9/loop-spaces.lisp, Previous: kenzo/src/kenzo-9/fibrations.lisp, Up: Lisp [Contents][Index]
kenzo-9 (module).
Next: kenzo/src/kenzo-9/ls-twisted-products.lisp, Previous: kenzo/src/kenzo-9/fibrations-dvf.lisp, Up: Lisp [Contents][Index]
kenzo-9 (module).
loop-space-face* (function).
Next: kenzo/src/kenzo-9/lp-space-efhm.lisp, Previous: kenzo/src/kenzo-9/loop-spaces.lisp, Up: Lisp [Contents][Index]
kenzo-9 (module).
Next: kenzo/src/kenzo-9/classifying-spaces.lisp, Previous: kenzo/src/kenzo-9/ls-twisted-products.lisp, Up: Lisp [Contents][Index]
kenzo-9 (module).
Next: kenzo/src/kenzo-9/classifying-spaces-dvf.lisp, Previous: kenzo/src/kenzo-9/lp-space-efhm.lisp, Up: Lisp [Contents][Index]
kenzo-9 (module).
Next: kenzo/src/kenzo-9/k-pi-n.lisp, Previous: kenzo/src/kenzo-9/classifying-spaces.lisp, Up: Lisp [Contents][Index]
kenzo-9 (module).
Next: kenzo/src/kenzo-9/serre.lisp, Previous: kenzo/src/kenzo-9/classifying-spaces-dvf.lisp, Up: Lisp [Contents][Index]
kenzo-9 (module).
Next: kenzo/src/kenzo-9/cs-twisted-products.lisp, Previous: kenzo/src/kenzo-9/k-pi-n.lisp, Up: Lisp [Contents][Index]
kenzo-9 (module).
Next: kenzo/src/kenzo-9/cl-space-efhm.lisp, Previous: kenzo/src/kenzo-9/serre.lisp, Up: Lisp [Contents][Index]
kenzo-9 (module).
Next: kenzo/src/kenzo-9/whitehead.lisp, Previous: kenzo/src/kenzo-9/cs-twisted-products.lisp, Up: Lisp [Contents][Index]
kenzo-9 (module).
Next: kenzo/src/kenzo-9/new-smith.lisp, Previous: kenzo/src/kenzo-9/cl-space-efhm.lisp, Up: Lisp [Contents][Index]
kenzo-9 (module).
Previous: kenzo/src/kenzo-9/whitehead.lisp, Up: Lisp [Contents][Index]
kenzo-9 (module).
Next: Definitions, Previous: Files, Up: The kenzo Reference Manual [Contents][Index]
Packages are listed by definition order.
common-lisp.
common-lisp.
common-lisp.
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Definitions are sorted by export status, category, package, and then by lexicographic order.
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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.
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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.
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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.
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(BCNB GNRT) returns the representation of the generator GNRT belonging to the chain complex B.
(BCNC GNRT) returns the representation of the generator GNRT belonging to the chain complex C.
(BCND GNRT) returns the representation of the generator GNRT belonging to the chain complex D.
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CFFC
Args: (term)
Returns the the coefficient (integer) of a term.
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CMBN-NON-ZERO-P
Args: (cmbn)
Tests if the combination CMBN is a non-null combination of any degree.
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CMBN-ZERO-P
Args: (cmbn)
Tests if the combination CMBN is the null combination of any degree.
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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.
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DEF
Args: (name value)
Defines a dynamic variable NAME in the CL-USER package, assigns it VALUE,
and returns VALUE.
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—————————————————————–[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 ?.
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—————————————————————–[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.
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—————————————————————–[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.
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GNRT
Args: (term)
Returns the the generator of a term.
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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.
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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.
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—————————————————————–[macro-doc]
TERM-CMBN
Args: (degr cffc gnrt)
Returns the combination of degree DEGR with the only term CFFC*GNRT.
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Next: Generic functions, Previous: Macros, Up: Public Interface [Contents][Index]
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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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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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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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list.
list.
list.
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ALL-OBJECTS
Args: ()
Return a string representation of a user created objects.
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list.
list.
list.
(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.
(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.
(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.
(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.
(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.
(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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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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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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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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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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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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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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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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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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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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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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degr.
degr.
degr.
list.
list.
list.
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CMBN-OPPS
Args: (cmbn)
Returns the combination opposite combination of CMBN.
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