The mini-cas Reference Manual

3.1.1 mini-cas/mini-cas.asd

Source

mini-cas.asd.

Parent Component

mini-cas (system).

ASDF Systems

mini-cas.

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3.1.2 mini-cas/mini-cas.lisp

Source

mini-cas.asd.

Parent Component

mini-cas (system).

Packages

mini-cas.

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3.1.3 mini-cas/basic-ops.lisp

Dependency

mini-cas.lisp (file).

Source

mini-cas.asd.

Parent Component

mini-cas (system).

Public Interface

• cas* (function).
• cas+ (function).
• cas- (function).
• cas-cos (function).
• cas-sin (function).
• cas/ (function).

Internals

• /den (function).
• /num (function).
• cas*? (function).
• cas+? (function).
• cas-? (function).
• cas-cos? (function).
• cas-list-pred (function).
• cas-sin? (function).
• cas/? (function).

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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

• *partial* (special variable).
• full-derivative-list (generic function).
• partial-derivative (generic function).

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3.1.5 mini-cas/simplify.lisp

Dependency

full-derivative.lisp (file).

Source

mini-cas.asd.

Parent Component

mini-cas (system).

Internals

• *reduce (generic function).
• +reduce (generic function).
• /reduce (generic function).
• canonic-order (generic function).
• canonic-order-list (generic function).
• canonic-order-pred (generic function).
• canonic-order-rank (generic function).
• cas-equal (generic function).
• full-simplify (function).
• simplify (generic function).
• simplify-list (generic function).

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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

• *reduce (method).
• *reduce (method).
• +reduce (method).
• simplify (method).
• transpose (function).

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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).

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3.1.8 mini-cas/test.lisp

Dependency

substitute.lisp (file).

Source

mini-cas.asd.

Parent Component

mini-cas (system).

Internals

• check (macro).
• test-full-derivative (function).
• test-simplification (function).

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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.

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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) ¶

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5.2.1 Special variables

Special Variable: *partial* ¶

set true to enable partial derivatives

Package

mini-cas.

Source

full-derivative.lisp.

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5.2.2 Macros

Macro: check (form expected) ¶

Package

mini-cas.

Source

test.lisp.

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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.

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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) ¶

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