org.lsmp.djep.sjep

Class PolynomialCreator

java.lang.Object

org.lsmp.djep.xjep.DoNothingVisitor

org.lsmp.djep.sjep.PolynomialCreator

All Implemented Interfaces:

ParserVisitor

public class PolynomialCreator
extends DoNothingVisitor

Main entry point for simplification routines.

Uses a complete reworking of the ways equations are represented. A tree structure is built from Polynomials, Monomials, PVariable etc. An equation like

1+2 x^2+3 x y+4 x sin(y)

is represented as

Polynomial([
  Monomial(2.0,[PVariable(x)],[2])]),
  Monomial(3.0,[x,y],[1,1]),
  Monomial(4.0,[x,Function(sin,arg)],[1,1])
])

A total ordering of all expressions is used. As the representation is constructed the total ordering of terms is maintained. This helps ensure that polynomials are always in their simplest form and also allows comparison of equations.

The following sequence illustrates current ordering. This ordering may change without warning.

• -1 numbers sorted by values
• 0
• 1 numbers before monomials
• a^-2 powers in increasing order
• a^-1
• a
• a^2
• a^3
• a^x numeric powers before symbolic powers
• a b single variable monomials before multiple variables
• a^2 b
• b variables sorted alphabetically
• cos(a) monomials before functions
• sin(a) function names sorted alphabetically
• a+b functions before polynomials
• a+b+c

Constructor Summary

Constructors

Constructor and Description
PolynomialCreator(XJep j)

Method Summary

Modifier and Type	Method and Description
int	compare(Node node1, Node node2) Compares two nodes.
PNodeI	createPoly(Node node) Converts an expression into the polynomial representation.
boolean	equals(Node node1, Node node2) Compares two nodes.
Node	expand(Node node) Expands an expression.
Node	simplify(Node node) Simplifies an expression.
Object	visit(ASTConstant node, Object data)
Object	visit(ASTFunNode node, Object data)
Object	visit(ASTVarNode node, Object data)

Methods inherited from class org.lsmp.djep.xjep.DoNothingVisitor

visit, visit

Methods inherited from class java.lang.Object

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

Constructor Detail

PolynomialCreator

public PolynomialCreator(XJep j)

Method Detail

createPoly

public PNodeI createPoly(Node node)
                  throws ParseException

Converts an expression into the polynomial representation.

Parameters:

node - top node of expression

Returns:

top node of polynomial form of expression

Throws:

ParseException - if expression cannot be converted.

simplify

public Node simplify(Node node)
              throws ParseException

Simplifies an expression.

Parameters:

node - top node to expression to be simplified.

Returns:

a simplified expression

Throws:

ParseException

expand

public Node expand(Node node)
            throws ParseException

Expands an expression. Will always expand brackets for multiplication and simple powers. For instance (1+x)^3 -> 1+3x+3x^2+x^3

Parameters:

node - top node to expression to be simplified.

Returns:

a simplified expression

Throws:

ParseException

compare

public int compare(Node node1,
                   Node node2)
            throws ParseException

Compares two nodes. Uses a total ordering of expressions. Expands equations before comparison.

Parameters:

node1 -

node2 -

Returns:

-1 if node1node2

Throws:

ParseException

equals

public boolean equals(Node node1,
                      Node node2)
               throws ParseException

Compares two nodes. Uses a total ordering of expressions. May give some false negatives is simplification cannot reduce two equal expressions to the same canonical form. Expands equations before comparison.

Parameters:

node1 -

node2 -

Returns:

true if two nodes represents same expression.

Throws:

ParseException

visit

public Object visit(ASTConstant node,
                    Object data)
             throws ParseException

Specified by:

visit in interface ParserVisitor

Overrides:

visit in class DoNothingVisitor

Throws:

ParseException

visit

public Object visit(ASTVarNode node,
                    Object data)
             throws ParseException

Specified by:

visit in interface ParserVisitor

Overrides:

visit in class DoNothingVisitor

Throws:

ParseException

visit

public Object visit(ASTFunNode node,
                    Object data)
             throws ParseException

Specified by:

visit in interface ParserVisitor

Overrides:

visit in class DoNothingVisitor

Throws:

ParseException