Package org.lsmp.djep.sjep

An advanced simplification/expansion/comparison algorithm.

See: Description

Interface Summary

Interface	Description
PNodeI	An element in a polynomial representation of an expression.

Class Summary

Class	Description
AbstractPNode	Default methods, when more specific methods do not work.
Monomial	Represents an imutable monomial a x^i * y^j * ...
MutiableMonomial	A mutable monomial representing a * x^i * y^j * ...
MutiablePolynomial	A mutable polynomial representing a + b + c.
PConstant	Represents a constant.
PFunction	Represents a function.
Polynomial	Represents a polynomial.
PolynomialCreator	Main entry point for simplification routines.
POperator	Represents an operator.
PVariable	Represents a variable.

Package org.lsmp.djep.sjep Description

An advanced simplification/expansion/comparison algorithm. To use

PolynomialCreator pc = new PolynomialCreator(jep);
Node simp = pc.simplify(node);
Node expand = pc.expand(node);
boolean flag = pc.equals(node1,node2);
int res = pc.compare(node1,node2);
PNodeI poly = pc.createPoly(node);

How it works

The basic idea is to reduce each equation to a canonical form based on a total ordering of the terms. For example a polynomial in x will always be in the form a+b x+c x^2+d x^3. This makes comparison of two polynomials easy as it is just necessary to compare term by term, whereas it is difficult to compare x^2-1 with (x+1)*(x-1) without any simplification or reordering.

The precise total ordering is intentionally not defined as it may be later modified. As an illustration some of the rules for the ordering are 0<1<2, 5<x, x<x^2<x^3, x<y.

A polynomial is constructed from a set of monomials by arranging the monomials in order. Likewise a monomial is constructed from a set of variables by arranging the variables in name order.

The algorithm can also work with non-polynomial equations. Functions are order by the name of the function and the ordering of their arguments. Hence cos(x)<sin(x)<sin(y).