symexpress3 0.0.14

A Python module for symbolic calculations

Python Symbolic Expression 3

A Python module for symbolic calculations

Usage

Optimize expression

>>> import symexpress3
>>> objExpress = symexpress3.SymFormulaParser( '(x+1) * (x+2)' )
>>> objExpress.optimizeExtended()
>>> print( objExpress )
x^2 + x * 3 + 2

Supported operators

+   -   *   /   (   )   ^   ^^
^ gives root values by fractions ^^ gives principal root values by fractions

>>> import symexpress3
>>> objExpress = symexpress3.SymFormulaParser( '(4)^(1/2)' )
>>> objExpress.optimizeExtended()
>>> print( objExpress )
[ (-2) | 2 ]
>>> objExpress = symexpress3.SymFormulaParser( '(4)^^(1/2)' )
>>> objExpress.optimizeExtended()
>>> print( objExpress )
2

Numeric values

Only integers are supported. For fractions use /

>>> import symexpress3
>>> objExpress = symexpress3.SymFormulaParser( '7/10 + 3/11' )
>>> objExpress.optimizeExtended()
>>> print( objExpress )
(107/110)

Get the real value

If there is more the one value, it gives an array back

>>> import symexpress3
>>> objExpress = symexpress3.SymFormulaParser( '7/10 + 3/11' )
>>> objExpress.optimizeExtended()
>>> print( objExpress.getValue() )
0.9727272727272728
>>> objExpress = symexpress3.SymFormulaParser( '(4)^(1/2)' )
>>> objExpress.optimizeExtended()
>>> print( objExpress.getValue() )
[-2, 2]

Get all defined functions

Get a dictionary of all the defined functions. Key is the functions syntax, value is the description

>>> import symexpress3
>>> print( symexpress3.GetAllFunctions() )

Get all defined optimize actions

Get a dictionary of all the optimize actions. Key is the optimize action, value is the description

>>> import symexpress3
>>> print( symexpress3.GetAllOptimizeActions() )

Get all fixed variables

Get a dictionary of all the fixed variables. Key is the variable name, value is the description

>>> import symexpress3
>>> print( symexpress3.GetFixedVariables() )

Predefined optimization methods

The optimizeNormal method use the multiply, onlyOneRoot, i, power and add optimize actions The power action do not optimize roots. onlyOneRoot get radicals in it lowest form.

>>> import symexpress3
>>> objExpress = symexpress3.SymFormulaParser( '5 * 2^2 + i * i + (4)^(1/2)' )
>>> objExpress.optimizeNormal()
>>> print( objExpress )
19 + 4^(1/2)

The optimizeExtended method use the optimizeNormal method and the following optimize actions: rootToPrincipalRoot, powerArrays,arrayPower, functionToValues, negRootToI, functionToValues, unnestingRadicals, functionToValues, radicalDenominatorToCounter, rootIToSinCos, functionToValues, rootOfImagNumToCosISin, functionToValues, nestedRadicals, imaginairDenominator, sinTwoCosTwo, cosXplusYtoSinCos, sinXplusYtoSinCos, splitDenominator and expandArrays

>>> import symexpress3
>>> objExpress = symexpress3.SymFormulaParser( '5 * 2^2 + i * i + (4)^(1/2)' )
>>> objExpress.optimizeExtended()
>>> print( objExpress )
19 + [ (-2) | 2 ]
>>> print( objExpress.getValue() )
[17, 21]

Optimize expression

Use the optimize method for optimization

Remove unnecessary () and optimize the internal structure

>>> import symexpress3
>>> objExpress = symexpress3.SymFormulaParser( '((2) + (3))' )
>>> objExpress.optimize( None )
>>> print( objExpress )
2 + 3

Use of the optimize actions. Use after SymFormulaParser and each optimize() an optimize( None ) Most of the time use optimizeNormal() instead of optimize( None )

>>> import symexpress3
>>> objExpress = symexpress3.SymFormulaParser( 'cos( pi/4 )' )
>>> objExpress.optimize( None )
>>> objExpress.optimize( 'functionToValues' )
>>> objExpress.optimize( None )
>>> print( objExpress )
2^^(1/2) * (1/2)

Output formats

MathMl output

>>> import symexpress3
>>> objExpress = symexpress3.SymFormulaParser( 'cos( pi/4 )' )
>>> objExpress.optimize( None )
>>> print( objExpress.mathMl() )

Html output with expression in MathMl and string format. It create the symexpress3_demo.html file in the current directory.

>>> import symexpress3
>>> objExpress = symexpress3.SymFormulaParser( 'cos( pi/4 )' )
>>> objExpress.optimize( None )
>>> objOutput = symexpress3.SymToHtml( "symexpress3_demo.html", "SymExpress 3 demo" )
>>> objOutput.writeSymExpress( objExpress )
>>> objOutput.writeLine( str( objExpress ))
>>> objOutput.closeFile()

Calculate value with variables

Define a dictionary for the variables. The key is the variable name and de value is a number.

>>> import symexpress3
>>> objExpress = symexpress3.SymFormulaParser( '(x+1) (y+2)' )
>>> dictVar = {}
>>> dictVar[ 'x' ] = 0.33333
>>> dictVar[ 'y' ] = 3
>>> valueExpression = objExpress.getValue( dictVar )
>>> print( valueExpression )
6.66665

Command line

python -m symexpress3

• Help: python -m symexpress3 -h
• Direct optimize: python -m symexpress3 "cos( pi / 4 )^^(1/3)"

Notes

• By big numbers set mpmatch precision accordingly (mpmath.mp.dps)
• Graphical user interface: https://github.com/SWVandenEnden/websym3