org.matheclipse.core.reflection.system

Class Apart

java.lang.Object

org.matheclipse.core.eval.interfaces.AbstractEvaluator

org.matheclipse.core.eval.interfaces.AbstractFunctionEvaluator

org.matheclipse.core.reflection.system.Apart

All Implemented Interfaces:

IFunctionEvaluator, IEvaluator

public class Apart
extends AbstractFunctionEvaluator

Evaluate the partial fraction decomposition of a univariate polynomial fraction. See Wikipedia - Partial fraction decomposition

Constructor Summary

Constructors

Constructor and Description
Apart()

Method Summary

Modifier and Type	Method and Description
IExpr	evaluate(IAST ast, EvalEngine engine) Symbolic evaluation of a function.
static IExpr[]	getFractionalParts(IExpr arg, boolean trig) Split the expression into numerator and denominator parts, by separating positive and negative powers.
static IExpr[]	getFractionalPartsPower(IAST powerAST, boolean trig) Return the denominator for the given Power[...]
static IExpr[]	getFractionalPartsRational(IExpr arg) Split the expression into numerator and denominator parts, by separating positive and negative powers.
static IExpr[]	getFractionalPartsTimes(IAST timesAST, boolean splitNumeratorOne, boolean splitFractionalNumbers, boolean trig, boolean evalParts) Return the numerator and denominator for the given Times[...]
static IAST	partialFractionDecompositionInteger(IExpr[] parts, IAST variableList) Deprecated. untested at the moment
static IExpr	partialFractionDecompositionRational(IPartialFractionGenerator pf, IExpr[] parts, ISymbol x) Returns an AST with head Plus, which contains the partial fraction decomposition of the numerator and denominator parts.

Methods inherited from class org.matheclipse.core.eval.interfaces.AbstractFunctionEvaluator

createRuleFromMethod, getNormalizedNegativeExpression, getNormalizedNegativeExpression, getPeriodicParts, getPureImaginaryPart, getRuleAST, initSerializedRules, isNegativeExpression, setUp

Methods inherited from class org.matheclipse.core.eval.interfaces.AbstractEvaluator

numericEval

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

Apart

public Apart()

Method Detail

evaluate

public IExpr evaluate(IAST ast,
                      EvalEngine engine)

Description copied from class: AbstractFunctionEvaluator

Symbolic evaluation of a function. ast.get(0) (or alternatively ast.head()) contains the head (i.e. the function symbol) of this abstract syntax tree (AST).
From ast.arg1() to ast.get(n) the ast contains the first to n-th argument of the function (alternatively you get the first to fifth argument with the methods arg1(), arg2(),... arg5()).
If necessary use the methods from the Validate class to check the number or types of arguments in the evaluate method.
Note: if the symbolic evaluation isn't possible or no result is found the evaluate method returns with a null value without throwing an exception!

Specified by:

evaluate in interface IFunctionEvaluator

Specified by:

evaluate in class AbstractFunctionEvaluator

Parameters:

ast - the abstract syntax tree (AST) which should be evaluated

engine - the users current evaluation engine

Returns:

the evaluated object or null, if evaluation isn't possible

See Also:

Validate, IExpr.head(), IAST.arg1(), IAST.arg2(), IAST.arg3()

partialFractionDecompositionInteger

@Deprecated
public static IAST partialFractionDecompositionInteger(IExpr[] parts,
                                                                    IAST variableList)

Deprecated. untested at the moment

Returns an AST with head Plus, which contains the partial fraction decomposition of the numerator and denominator parts.

Parameters:

parts -

variableList -

Returns:

null if the partial fraction decomposition wasn't constructed

partialFractionDecompositionRational

public static IExpr partialFractionDecompositionRational(IPartialFractionGenerator pf,
                                                         IExpr[] parts,
                                                         ISymbol x)

Returns an AST with head Plus, which contains the partial fraction decomposition of the numerator and denominator parts.

Parameters:

parts -

variableList -

Returns:

F.NIL if the partial fraction decomposition wasn't constructed

getFractionalPartsRational

public static IExpr[] getFractionalPartsRational(IExpr arg)

Split the expression into numerator and denominator parts, by separating positive and negative powers.

Parameters:

arg -

Returns:

the numerator and denominator expression

getFractionalParts

public static IExpr[] getFractionalParts(IExpr arg,
                                         boolean trig)

Split the expression into numerator and denominator parts, by separating positive and negative powers.

Parameters:

arg -

trig - determine the denominator by splitting up functions like Tan[9,Cot[], Csc[],...

Returns:

the numerator and denominator expression or null if no denominator was found.

getFractionalPartsTimes

public static IExpr[] getFractionalPartsTimes(IAST timesAST,
                                              boolean splitNumeratorOne,
                                              boolean splitFractionalNumbers,
                                              boolean trig,
                                              boolean evalParts)

Return the numerator and denominator for the given Times[...] AST, by separating positive and negative powers.

Parameters:

timesAST - a times expression (a*b*c....)

splitNumeratorOne - split a fractional number into numerator and denominator, only if the numerator is 1, if true, ignore splitFractionalNumbers parameter.

splitFractionalNumbers - split a fractional number into numerator and denominator

trig - try to find a trigonometric numerator/denominator form (Example: Csc[x] gives 1 / Sin[x])

Returns:

the numerator and denominator expression and an optional fractional number (maybe null), if splitNumeratorOne is true.

getFractionalPartsPower

public static IExpr[] getFractionalPartsPower(IAST powerAST,
                                              boolean trig)

Return the denominator for the given Power[...] AST, by separating positive and negative powers.

Parameters:

powerAST - a power expression (a^b)

trig - TODO

Returns:

the numerator and denominator expression