com.perisic.ring
Class UniversalPolynomialRing

java.lang.Object
  com.perisic.ring.Ring
      com.perisic.ring.UniversalRing
          com.perisic.ring.UniversalPolynomialRing

public class UniversalPolynomialRing
extends UniversalRing

The field of polynomials over all allowed variable names as variables. That is, say in this ring you can add a polynomial a^2 + b of Z[a][b] with b - c of Z[b][c] and get as result a polynomial of the ring Z[a][b][c] (the order of the variables is undefined and may vary).

• Generated January 16, 2003.
• Last Change: April 18, 2003: Exception list of variables.
• Last Change: 13.12.2003: GPL MC.
• Last Change: 01.05.2011: Added methods evaluatePolynomial
• Copyright:(c) Marc Conrad, 2002, 2003,2011
• Email: ring@perisic.com. Please let me know if you use this software.
• WWW: www.ring.perisic.com
• The com.perisic.ring library is distributed under the terms of the GNU Lesser General Public License (LGPL).
• If you require the package under a different licence please contact me.
• disclaimer: The classes are provided "as is". There is no warranty implied by using the com.perisic.ring package.

Example:

public static void main(String [] args) {
// Define a polynomial ring over R
        UniversalPolynomialRing U = new UniversalPolynomialRing(Ring.R);
        RingElt poly1 = U.map("0.5 * ((x1 - x2)^2 - a * (x1 + x2)^2)");
        System.out.println("poly1="+poly1+" of "+poly1.getRing());

// 1st Example to substitute variables:
        String [] variables = { "x1", "x2" }; 
        RingElt [] values = { Ring.R.map(2.3), Ring.R.map(1.7) };
        RingElt poly2 = U.evaluatePolynomial(poly1, variables, values); 
        System.out.println("Example1: poly2="+poly2+" of "+poly2.getRing());

//      2nd Example to substitute variables:
        RingElt poly3 = U.evaluatePolynomial(poly1, "a", Ring.R.map(-1)); 
        System.out.println("Example2: poly3="+poly3+" of "+poly3.getRing());

//      3rd Example to substitute variables:
        RingElt poly4 = U.evaluatePolynomial(poly3, variables, values); 
        System.out.println("Example3: poly4="+poly4+" of "+poly4.getRing());
}

Produces the following output:

poly1=(0.5 + -0.5*a)*x2^2 + ((-1.0 + -1.0*a)*x2)*x1 + (0.5 + -0.5*a)*x1^2 of R[a][x2][x1]
Example1: poly2=0.18000000000000016 + -7.999999999999999*a of R[a]
Example2: poly3=1.0*x2^2 + 1.0*x1^2 of R[x2][x1]
Example3: poly4=8.18 of R

Version:

0.4

Author:

Marc Conrad

Field Summary

Fields inherited from class com.perisic.ring.Ring

C, F2, Q, R, Z

Constructor Summary

UniversalPolynomialRing(Ring coefficientRing)
Construct the universal polynomial field by the ring of coefficients.

Method Summary

RingElt	evaluatePolynomial(RingElt p, java.lang.String[] var, RingElt[] b) Evaluates the polynomial p at the variables var[i] with the values b[i].
RingElt	evaluatePolynomial(RingElt p, java.lang.String var, RingElt b) Evaluates the Polynomial p (which may be defined over more than one variable) at b for the variable var.
Ring	findRing() A suitable ring able to map 0 (and 1).
Ring	findRing(RingElt a) The ring over the coefficient ring with the variables of a.getRing().
Ring	findRing(RingElt a, RingElt b) The result is the coefficient ring over the variables of a.getRing() and the variables of b.getRing().
boolean	isUFD() true if the coefficient ring and therefore also the polynomial ring is an uniqe factorization domain.
static void	main(java.lang.String[] args) Simple test method.
RingElt	map(java.lang.String str) All Java identifiers are allowed as variables.
RingElt	reduceVariables(RingElt p) Reduces the polynomial into a polynomial of the polynomial ring with the fewest variables.
java.lang.String	toString()

Methods inherited from class com.perisic.ring.UniversalRing

add, ediv, equalZero, gcd, inv, map, mod, mult, neg, one, tdiv, zero

Methods inherited from class com.perisic.ring.Ring

div, eltToString, equal, evaluatePolynomial, isEuclidian, isField, map, map, map, pow, pow, sub

Methods inherited from class java.lang.Object

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

Constructor Detail

UniversalPolynomialRing

public UniversalPolynomialRing(Ring coefficientRing)

Construct the universal polynomial field by the ring of coefficients.

Method Detail

toString

public java.lang.String toString()

Overrides:

toString in class UniversalRing

Returns:

"R[...]" where R is the coefficient ring.

isUFD

public boolean isUFD()

true if the coefficient ring and therefore also the polynomial ring is an uniqe factorization domain. False otherwise.

Overrides:

isUFD in class Ring

Returns:

true if the polynomial ring is an UFD

map

public RingElt map(java.lang.String str)

All Java identifiers are allowed as variables. That means the first character is true with java.lang.Character.isJavaIdentifierStart(), the following chracters return true with Character.isJavaIdentifierPart()

Overrides:

map in class UniversalRing

findRing

public Ring findRing()

Description copied from class: UniversalRing

A suitable ring able to map 0 (and 1).

Specified by:

findRing in class UniversalRing

Returns:

the ring of coefficients.

findRing

public Ring findRing(RingElt a)

The ring over the coefficient ring with the variables of a.getRing().

Specified by:

findRing in class UniversalRing

findRing

public Ring findRing(RingElt a,
                     RingElt b)

The result is the coefficient ring over the variables of a.getRing() and the variables of b.getRing().

Specified by:

findRing in class UniversalRing

reduceVariables

public RingElt reduceVariables(RingElt p)

Reduces the polynomial into a polynomial of the polynomial ring with the fewest variables. For instance if p = a^2 + b^2 is an element of Z[x][a][y][b][c] then reduceVariables(p) = a^2 + b^2 in Z[a][b].

evaluatePolynomial

public RingElt evaluatePolynomial(RingElt p,
                                  java.lang.String[] var,
                                  RingElt[] b)

Evaluates the polynomial p at the variables var[i] with the values b[i]. The lengths of var and b must be the same and is not checked.

evaluatePolynomial

public RingElt evaluatePolynomial(RingElt p,
                                  java.lang.String var,
                                  RingElt b)

Evaluates the Polynomial p (which may be defined over more than one variable) at b for the variable var. If p is not a polynomial or if p (as a polynomial) does not contain the variable var the polynomial p is returned (p is the considered a constant in respect to var).

main

public static void main(java.lang.String[] args)

Simple test method.

Parameters:

args -