Package com.singularsys.extensions.polynomials

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.
Coeffs	Jep function to extract array of coefficients from a polynomial.
Compare	The compare(x,y) command.
Expand	The expand(x) command.
Monomial	Represents an immutable monomial a x^i * y^j * ... * z^k, a constant.
MutableMonomial	A mutable monomial representing a * x^i * y^j * ... * z^k.
MutablePolynomial	A mutable polynomial representing a + b + c.
PConstant	Represents a constant.
PFunction	Represents a function.
Polynomial	Represents a polynomial.
PolynomialCreator	A system for symbolic simplification, expansion and comparision based on conversion to a canonical polynomial representation.
POperator	Represents an operator.
PVariable	Represents a variable.
Simplify	The simplify(x) command.

Package com.singularsys.extensions.polynomials 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 dificult to compare x^2-1 with (x+1)*(x-1) without any simplification or reordering is tricky.

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).

Since:

Jep 3.5 / Extensions 2.0

See Also:

Polynomials documentation