The mini-cas Reference Manual

This is the mini-cas Reference Manual, generated automatically by Declt version 4.0 beta 2 "William Riker" on Wed May 15 06:16:02 2024 GMT+0.

Table of Contents


1 Introduction


2 Systems

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


2.1 mini-cas

Source

mini-cas.asd.

Child Components

3 Files

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


3.1 Lisp


3.1.1 mini-cas/mini-cas.asd

Source

mini-cas.asd.

Parent Component

mini-cas (system).

ASDF Systems

mini-cas.


3.1.2 mini-cas/mini-cas.lisp

Source

mini-cas.asd.

Parent Component

mini-cas (system).

Packages

mini-cas.


3.1.3 mini-cas/basic-ops.lisp

Dependency

mini-cas.lisp (file).

Source

mini-cas.asd.

Parent Component

mini-cas (system).

Public Interface
Internals

3.1.4 mini-cas/full-derivative.lisp

Dependency

basic-ops.lisp (file).

Source

mini-cas.asd.

Parent Component

mini-cas (system).

Public Interface

full-derivative (generic function).

Internals

3.1.5 mini-cas/simplify.lisp

Dependency

full-derivative.lisp (file).

Source

mini-cas.asd.

Parent Component

mini-cas (system).

Internals

3.1.6 mini-cas/arrays.lisp

Dependency

simplify.lisp (file).

Source

mini-cas.asd.

Parent Component

mini-cas (system).

Public Interface

full-derivative (method).

Internals

3.1.7 mini-cas/substitute.lisp

Dependency

arrays.lisp (file).

Source

mini-cas.asd.

Parent Component

mini-cas (system).

Internals

cas-substitute (generic function).


3.1.8 mini-cas/test.lisp

Dependency

substitute.lisp (file).

Source

mini-cas.asd.

Parent Component

mini-cas (system).

Internals

4 Packages

Packages are listed by definition order.


4.1 mini-cas

Source

mini-cas.lisp.

Use List

common-lisp.

Public Interface
Internals

5 Definitions

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


5.1 Public Interface


5.1.1 Ordinary functions

Function: cas* (&rest args)
Package

mini-cas.

Source

basic-ops.lisp.

Function: cas+ (&rest args)
Package

mini-cas.

Source

basic-ops.lisp.

Function: cas- (arg)
Package

mini-cas.

Source

basic-ops.lisp.

Function: cas-cos (x)
Package

mini-cas.

Source

basic-ops.lisp.

Function: cas-sin (x)
Package

mini-cas.

Source

basic-ops.lisp.

Function: cas/ (num den)
Package

mini-cas.

Source

basic-ops.lisp.


5.1.2 Generic functions

Generic Function: full-derivative (form var)
Package

mini-cas.

Source

full-derivative.lisp.

Methods
Method: full-derivative ((form array) var)
Source

arrays.lisp.

Method: full-derivative ((form list) var)
Method: full-derivative ((form number) var)
Method: full-derivative ((form symbol) var)
Method: full-derivative (form var)

5.2 Internals


5.2.1 Special variables

Special Variable: *partial*

set true to enable partial derivatives

Package

mini-cas.

Source

full-derivative.lisp.


5.2.2 Macros

Macro: check (form expected)
Package

mini-cas.

Source

test.lisp.


5.2.3 Ordinary functions

Function: /den (quotient)
Package

mini-cas.

Source

basic-ops.lisp.

Function: /num (quotient)
Package

mini-cas.

Source

basic-ops.lisp.

Function: cas*? (form)
Package

mini-cas.

Source

basic-ops.lisp.

Function: cas+? (form)
Package

mini-cas.

Source

basic-ops.lisp.

Function: cas-? (form)
Package

mini-cas.

Source

basic-ops.lisp.

Function: cas-cos? (form)
Package

mini-cas.

Source

basic-ops.lisp.

Function: cas-list-pred (car form &optional length)
Package

mini-cas.

Source

basic-ops.lisp.

Function: cas-sin? (form)
Package

mini-cas.

Source

basic-ops.lisp.

Function: cas/? (form)
Package

mini-cas.

Source

basic-ops.lisp.

Function: full-simplify (form)

Keep simplifying the form until a fixed point is reached.

Package

mini-cas.

Source

simplify.lisp.

Function: test-full-derivative ()
Package

mini-cas.

Source

test.lisp.

Function: test-simplification ()
Package

mini-cas.

Source

test.lisp.

Function: transpose (array)
Package

mini-cas.

Source

arrays.lisp.


5.2.4 Generic functions

Generic Function: *reduce (a b)

Methods for reducing added pairs - return nil or the sum

Package

mini-cas.

Source

simplify.lisp.

Methods
Method: *reduce (a (b array))
Source

arrays.lisp.

Method: *reduce ((a array) (b array))
Source

arrays.lisp.

Method: *reduce ((a number) (b number))
Method: *reduce ((a (eql 0)) b)
Method: *reduce ((a (eql 1)) b)
Method: *reduce (a b)
Generic Function: +reduce (a b)

Methods for reducing added pairs - return nil or the sum

Package

mini-cas.

Source

simplify.lisp.

Methods
Method: +reduce ((a array) (b array))
Source

arrays.lisp.

Method: +reduce ((a number) (b number))
Method: +reduce ((a (eql 0)) b)
Method: +reduce (a b)
Generic Function: /reduce (a b)

Methods for reducing a/b. Return nil if no reduction is possible.

Package

mini-cas.

Source

simplify.lisp.

Methods
Method: /reduce ((a number) (b number))
Method: /reduce (a b)
Generic Function: canonic-order (form)
Package

mini-cas.

Source

simplify.lisp.

Methods
Method: canonic-order ((form list))
Method: canonic-order (form)
Generic Function: canonic-order-list (car cdr)
Package

mini-cas.

Source

simplify.lisp.

Methods
Method: canonic-order-list ((car (eql *)) cdr)
Method: canonic-order-list ((car (eql +)) cdr)
Method: canonic-order-list (car cdr)
Generic Function: canonic-order-pred (a b)

predicate for sorting terms, extend for entries in the same class

Package

mini-cas.

Source

simplify.lisp.

Methods
Method: canonic-order-pred ((a list) (b list))
Method: canonic-order-pred (a b)
Method: canonic-order-pred ((a number) (b number))
Method: canonic-order-pred ((a symbol) (b symbol))
Generic Function: canonic-order-rank (form)

ordering of form types

Package

mini-cas.

Source

simplify.lisp.

Methods
Method: canonic-order-rank ((form number))
Method: canonic-order-rank ((form symbol))
Method: canonic-order-rank ((form list))
Method: canonic-order-rank ((form array))
Generic Function: cas-equal (a b)
Package

mini-cas.

Source

simplify.lisp.

Methods
Method: cas-equal ((a array) (b array))
Method: cas-equal ((a list) (b list))
Method: cas-equal (a b)
Generic Function: cas-substitute (new old form)

Like CL:substitute, but do a deep recursive replacement.

Package

mini-cas.

Source

substitute.lisp.

Methods
Method: cas-substitute (new old (form array))
Method: cas-substitute (new old (form list))
Method: cas-substitute (new old form)
Generic Function: full-derivative-list (car cdr var)
Package

mini-cas.

Source

full-derivative.lisp.

Methods
Method: full-derivative-list ((car (eql cos)) cdr var)
Method: full-derivative-list ((car (eql sin)) cdr var)
Method: full-derivative-list ((car (eql /)) cdr var)
Method: full-derivative-list ((car (eql *)) cdr var)
Method: full-derivative-list ((car (eql -)) cdr var)
Method: full-derivative-list ((car (eql +)) cdr var)
Method: full-derivative-list (car cdr var)
Generic Function: partial-derivative (form var)
Package

mini-cas.

Source

full-derivative.lisp.

Methods
Method: partial-derivative (form var)
Generic Function: simplify (form)
Package

mini-cas.

Source

simplify.lisp.

Methods
Method: simplify ((form array))
Source

arrays.lisp.

Method: simplify ((form list))
Method: simplify (form)
Generic Function: simplify-list (car cdr)
Package

mini-cas.

Source

simplify.lisp.

Methods
Method: simplify-list ((car (eql cos)) cdr)
Method: simplify-list ((car (eql sin)) cdr)
Method: simplify-list ((car (eql mini-cas::d)) cdr)
Method: simplify-list ((car (eql /)) cdr)
Method: simplify-list ((car (eql -)) cdr)
Method: simplify-list ((car (eql *)) cdr)
Method: simplify-list ((car (eql +)) cdr)
Method: simplify-list (car cdr)

Appendix A Indexes


A.1 Concepts


A.2 Functions

Jump to:   *   +   /  
C   F   G   M   P   S   T  
Index Entry  Section

*
*reduce: Private generic functions
*reduce: Private generic functions
*reduce: Private generic functions
*reduce: Private generic functions
*reduce: Private generic functions
*reduce: Private generic functions
*reduce: Private generic functions

+
+reduce: Private generic functions
+reduce: Private generic functions
+reduce: Private generic functions
+reduce: Private generic functions
+reduce: Private generic functions

/
/den: Private ordinary functions
/num: Private ordinary functions
/reduce: Private generic functions
/reduce: Private generic functions
/reduce: Private generic functions

C
canonic-order: Private generic functions
canonic-order: Private generic functions
canonic-order: Private generic functions
canonic-order-list: Private generic functions
canonic-order-list: Private generic functions
canonic-order-list: Private generic functions
canonic-order-list: Private generic functions
canonic-order-pred: Private generic functions
canonic-order-pred: Private generic functions
canonic-order-pred: Private generic functions
canonic-order-pred: Private generic functions
canonic-order-pred: Private generic functions
canonic-order-rank: Private generic functions
canonic-order-rank: Private generic functions
canonic-order-rank: Private generic functions
canonic-order-rank: Private generic functions
canonic-order-rank: Private generic functions
cas*: Public ordinary functions
cas*?: Private ordinary functions
cas+: Public ordinary functions
cas+?: Private ordinary functions
cas-: Public ordinary functions
cas-?: Private ordinary functions
cas-cos: Public ordinary functions
cas-cos?: Private ordinary functions
cas-equal: Private generic functions
cas-equal: Private generic functions
cas-equal: Private generic functions
cas-equal: Private generic functions
cas-list-pred: Private ordinary functions
cas-sin: Public ordinary functions
cas-sin?: Private ordinary functions
cas-substitute: Private generic functions
cas-substitute: Private generic functions
cas-substitute: Private generic functions
cas-substitute: Private generic functions
cas/: Public ordinary functions
cas/?: Private ordinary functions
check: Private macros

F
full-derivative: Public generic functions
full-derivative: Public generic functions
full-derivative: Public generic functions
full-derivative: Public generic functions
full-derivative: Public generic functions
full-derivative: Public generic functions
full-derivative-list: Private generic functions
full-derivative-list: Private generic functions
full-derivative-list: Private generic functions
full-derivative-list: Private generic functions
full-derivative-list: Private generic functions
full-derivative-list: Private generic functions
full-derivative-list: Private generic functions
full-derivative-list: Private generic functions
full-simplify: Private ordinary functions
Function, /den: Private ordinary functions
Function, /num: Private ordinary functions
Function, cas*: Public ordinary functions
Function, cas*?: Private ordinary functions
Function, cas+: Public ordinary functions
Function, cas+?: Private ordinary functions
Function, cas-: Public ordinary functions
Function, cas-?: Private ordinary functions
Function, cas-cos: Public ordinary functions
Function, cas-cos?: Private ordinary functions
Function, cas-list-pred: Private ordinary functions
Function, cas-sin: Public ordinary functions
Function, cas-sin?: Private ordinary functions
Function, cas/: Public ordinary functions
Function, cas/?: Private ordinary functions
Function, full-simplify: Private ordinary functions
Function, test-full-derivative: Private ordinary functions
Function, test-simplification: Private ordinary functions
Function, transpose: Private ordinary functions

G
Generic Function, *reduce: Private generic functions
Generic Function, +reduce: Private generic functions
Generic Function, /reduce: Private generic functions
Generic Function, canonic-order: Private generic functions
Generic Function, canonic-order-list: Private generic functions
Generic Function, canonic-order-pred: Private generic functions
Generic Function, canonic-order-rank: Private generic functions
Generic Function, cas-equal: Private generic functions
Generic Function, cas-substitute: Private generic functions
Generic Function, full-derivative: Public generic functions
Generic Function, full-derivative-list: Private generic functions
Generic Function, partial-derivative: Private generic functions
Generic Function, simplify: Private generic functions
Generic Function, simplify-list: Private generic functions

M
Macro, check: Private macros
Method, *reduce: Private generic functions
Method, *reduce: Private generic functions
Method, *reduce: Private generic functions
Method, *reduce: Private generic functions
Method, *reduce: Private generic functions
Method, *reduce: Private generic functions
Method, +reduce: Private generic functions
Method, +reduce: Private generic functions
Method, +reduce: Private generic functions
Method, +reduce: Private generic functions
Method, /reduce: Private generic functions
Method, /reduce: Private generic functions
Method, canonic-order: Private generic functions
Method, canonic-order: Private generic functions
Method, canonic-order-list: Private generic functions
Method, canonic-order-list: Private generic functions
Method, canonic-order-list: Private generic functions
Method, canonic-order-pred: Private generic functions
Method, canonic-order-pred: Private generic functions
Method, canonic-order-pred: Private generic functions
Method, canonic-order-pred: Private generic functions
Method, canonic-order-rank: Private generic functions
Method, canonic-order-rank: Private generic functions
Method, canonic-order-rank: Private generic functions
Method, canonic-order-rank: Private generic functions
Method, cas-equal: Private generic functions
Method, cas-equal: Private generic functions
Method, cas-equal: Private generic functions
Method, cas-substitute: Private generic functions
Method, cas-substitute: Private generic functions
Method, cas-substitute: Private generic functions
Method, full-derivative: Public generic functions
Method, full-derivative: Public generic functions
Method, full-derivative: Public generic functions
Method, full-derivative: Public generic functions
Method, full-derivative: Public generic functions
Method, full-derivative-list: Private generic functions
Method, full-derivative-list: Private generic functions
Method, full-derivative-list: Private generic functions
Method, full-derivative-list: Private generic functions
Method, full-derivative-list: Private generic functions
Method, full-derivative-list: Private generic functions
Method, full-derivative-list: Private generic functions
Method, partial-derivative: Private generic functions
Method, simplify: Private generic functions
Method, simplify: Private generic functions
Method, simplify: Private generic functions
Method, simplify-list: Private generic functions
Method, simplify-list: Private generic functions
Method, simplify-list: Private generic functions
Method, simplify-list: Private generic functions
Method, simplify-list: Private generic functions
Method, simplify-list: Private generic functions
Method, simplify-list: Private generic functions
Method, simplify-list: Private generic functions

P
partial-derivative: Private generic functions
partial-derivative: Private generic functions

S
simplify: Private generic functions
simplify: Private generic functions
simplify: Private generic functions
simplify: Private generic functions
simplify-list: Private generic functions
simplify-list: Private generic functions
simplify-list: Private generic functions
simplify-list: Private generic functions
simplify-list: Private generic functions
simplify-list: Private generic functions
simplify-list: Private generic functions
simplify-list: Private generic functions
simplify-list: Private generic functions

T
test-full-derivative: Private ordinary functions
test-simplification: Private ordinary functions
transpose: Private ordinary functions


A.3 Variables

Jump to:   *  
S  
Index Entry  Section

*
*partial*: Private special variables

S
Special Variable, *partial*: Private special variables