| Sign in

SympyCore - an efficient pure Python Computer Algebra System

Project Home		Downloads		Wiki		Issues		Source

Search

Updated Apr 08, 2008 by pearu.peterson

ReviewConversionMethods3

Notes about conversion methods

Introduction

Currently Algebra.convert is used to convert algebra operation operands to operands algebra. This does not cover cases where different algebra convert method should be used. For example, the operand algebras of Logic.Lt and Logic.And are Calculus and Logic, respectively. In such a case the convert method depends on the expression head.

SOLUTION: See http://sympycore.googlecode.com/svn/trunk/doc/html/structure.html#how-does-it-work-in-sympycore

Please add questions and issues to comments.

Overview of existing algebras

All algebras may have APPLY operations or callable heads that must defined their own argument algebras.

`Verbatim` algebra

Operands algebras to all operations is Verbatim.

`CollectingField` algebra

`Calculus` algebra

Operation head	Operand LHS	Operand RHS
NUMBER	-	ll-number
SYMBOL	-	str
ADD, SUB, MUL, DIV	Calculus	Calculus
	ll-number	Calculus
	Calculus	ll-number
POW	Calculus	Calculus
	ll-number	Calculus
	Calculus	ll-number
APPLY	FunctionRing	argument algebras
callable	-	Calculus arguments

ll-number is low-level number (int, long, mpq, mpf, mpqc, mpc).

`Unit` algebra

Operation head	Operand LHS	Operand RHS
NUMBER	-	Calculus
	-	ll-nunber
SYMBOL	-	str
ADD, SUB, MUL, DIV	Unit	Unit
	ll-number	Unit
	Unit	ll-number
POW	Unit	int
APPLY	FunctionRing	argument algebras
callable	-	Unit arguments

`FunctionRing` algebra

Operation head	Operand LHS	Operand RHS
NUMBER	-	Calculus
	-	ll-number
SYMBOL	-	str
ADD, SUB, MUL, DIV	FunctionRing	FunctionRing
	ll-number	FunctionRing
	FunctionRing	ll-number
POW	FunctionRing	int
APPLY	FunctionRing	argument algebras
callable	-	FunctionRing arguments

`Differential` algebra

Operation head	Operand LHS	Operand RHS
NUMBER	-	Calculus
	-	ll-number
SYMBOL	-	Calculus
	-	str
ADD, SUB, MUL	Differential	Differential
	Calculus	Differential
	Differential	Calculus
	ll-number	Differential
	Differential	ll-number
DIV	Differential	Calculus
	Differential	ll-number
POW	Differential	int
APPLY	FunctionRing	argument algebras
callable	-	Differential arguments

`Logic` algebra

Operation head	Operand LHS	Operand RHS
NUMBER	-	bool
SYMBOL	-	str
AND, OR	Logic	Logic
NOT	-	Logic
LT, GT, LE, GE	Calculus	Calculus
EQ, NE	Calculus	Calculus
IN, NOTIN	object	Set
APPLY	FunctionRing	argument algebras
callable	-	Logic arguments

Need to implement quantifier support: ForAll, Exists, Any, All. Their argument algebras may vary.

`Set` algebra

Operation head	Operand LHS	Operand RHS
NUMBER	-	frozenset
SYMBOL	-	str
APPLY	FunctionRing	argument algebras
callable	-	Set arguments

Currently Set lacks operations but we need Union, Intersection etc.

Need to introduce optional Set element algebra, eg for Integers, Reals, and other set symbols.

`MatrixRing` algebra

Operation head	Operand LHS	Operand RHS
NUMBER	-	N/A
SYMBOL	-	N/A
ADD, SUB, MUL	MatrixRing	MatrixRing
	MatrixRing	element algebra
	element algebra	MatrixRing
DIV	MatrixRing	element algebra
POW	MatrixRing	int
APPLY	-	N/A
callable	-	N/A

Need to introduce optional Matrix element algebra.

`PolynomialRing` algebra

Operation head	Operand LHS	Operand RHS
NUMBER	-	dict
SYMBOL	-	N/A
ADD, SUB, MUL	PolynomialRing	PolynomialRing
	PolynomialRing	coefficent algebra
	coefficient algebra	PolynomialRing
DIV	PolynomialRing	coefficient algebra
POW	PolynomialRing	int
APPLY	-	N/A
callable	-	N/A

Convert methods

All algebras should use default convert class method. It first tries convert_number class method and then tries to do the conversion via Verbatim algebra as_algebra method. Here the proper conversion methods should be called. For that we need to have callback conversion methods to original algebras. The aim of this wiki page is to workout these callback hooks.

Sign in to add a comment

Hosted by