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/*
* $Id: PolyGBUtil.java 4049 2012-07-25 17:10:49Z kredel $
*/
package edu.jas.gbufd;
import java.util.ArrayList;
import java.util.List;
import org.apache.log4j.Logger;
import edu.jas.gb.GroebnerBaseAbstract;
import edu.jas.poly.ExpVector;
import edu.jas.poly.GenPolynomial;
import edu.jas.poly.GenPolynomialRing;
import edu.jas.poly.PolyUtil;
import edu.jas.structure.GcdRingElem;
import edu.jas.structure.RingElem;
/**
* Package gbufd utilities.
* @author Heinz Kredel
*/
public class PolyGBUtil {
private static final Logger logger = Logger.getLogger(PolyGBUtil.class);
private static boolean debug = logger.isDebugEnabled();
/**
* Test for resultant.
* @param A generic polynomial.
* @param B generic polynomial.
* @param r generic polynomial.
* @return true if res(A,B) isContained in ideal(A,B), else false.
*/
public static >
boolean isResultant(GenPolynomial A, GenPolynomial B, GenPolynomial r) {
if (r == null || r.isZERO()) {
return true;
}
GroebnerBaseAbstract bb = GBFactory. getImplementation(r.ring.coFac);
List> F = new ArrayList>(2);
F.add(A);
F.add(B);
List> G = bb.GB(F);
//System.out.println("G = " + G);
GenPolynomial n = bb.red.normalform(G, r);
//System.out.println("n = " + n);
return n.isZERO();
}
/**
* Top pseudo reduction wrt the main variables.
* @param P generic polynomial.
* @param A list of generic polynomials sorted according to appearing main variables.
* @return top pseudo remainder of P wrt. A for the appearing variables.
*/
public static >
GenPolynomial topPseudoRemainder(List> A, GenPolynomial P) {
if (A == null || A.isEmpty()) {
return P.monic();
}
if (P.isZERO()) {
return P;
}
//System.out.println("remainder, P = " + P);
GenPolynomialRing pfac = A.get(0).ring;
if (pfac.nvar <= 1) { // recursion base
GenPolynomial R = PolyUtil. baseSparsePseudoRemainder(P, A.get(0));
return R.monic();
}
// select polynomials according to the main variable
GenPolynomialRing> rfac = pfac.recursive(1);
GenPolynomial Q = A.get(0); // wrong, must eventually search polynomial
GenPolynomial> qr = PolyUtil. recursive(rfac, Q);
GenPolynomial> pr = PolyUtil. recursive(rfac, P);
GenPolynomial> rr;
if (qr.isONE()) {
return P.ring.getZERO();
}
if (qr.degree(0) > 0) {
rr = PolyUtil. recursiveSparsePseudoRemainder(pr, qr);
//System.out.println("remainder, pr = " + pr);
//System.out.println("remainder, qr = " + qr);
//System.out.println("remainder, rr = " + rr);
} else {
rr = pr;
}
if (rr.degree(0) > 0) {
GenPolynomial R = PolyUtil. distribute(pfac, rr);
return R.monic();
// not further reduced wrt. other variables = top-reduction only
}
List> zeroDeg = zeroDegrees(A);
GenPolynomial R = topPseudoRemainder(zeroDeg, rr.leadingBaseCoefficient());
R = R.extend(pfac, 0, 0L);
return R.monic();
}
/**
* Top coefficient pseudo remainder of the leading coefficient of P wrt A in the main variables.
* @param P generic polynomial in n+1 variables.
* @param A list of generic polynomials in n variables sorted according to appearing main variables.
* @return pseudo remainder of the leading coefficient of P wrt A.
*/
public static >
GenPolynomial topCoefficientPseudoRemainder(List> A, GenPolynomial P) {
if (A == null || A.isEmpty()) {
return P.monic();
}
if (P.isZERO()) {
return P;
}
GenPolynomialRing pfac = P.ring;
GenPolynomialRing pfac1 = A.get(0).ring;
if (pfac1.nvar <= 1) { // recursion base
GenPolynomial a = A.get(0);
GenPolynomialRing> rfac = pfac.recursive(pfac.nvar - 1);
GenPolynomial> pr = PolyUtil. recursive(rfac, P);
// ldcf(P,x_m) = q a + r
GenPolynomial> rr = PolyGBUtil. coefficientPseudoRemainderBase(pr, a);
GenPolynomial R = PolyUtil. distribute(pfac, rr);
return R.monic();
}
// select polynomials according to the main variable
GenPolynomialRing> rfac1 = pfac1.recursive(1);
int nv = pfac.nvar - pfac1.nvar;
GenPolynomialRing> rfac = pfac.recursive(1 + nv);
GenPolynomialRing>> rfac2 = rfac.recursive(nv);
if (debug) {
logger.info("rfac =" + rfac);
}
GenPolynomial> pr = PolyUtil. recursive(rfac, P);
GenPolynomial>> pr2 = PolyUtil.> recursive(rfac2, pr);
//System.out.println("recursion, pr2 = " + pr2);
GenPolynomial Q = A.get(0);
GenPolynomial> qr = PolyUtil. recursive(rfac1, Q);
GenPolynomial>> rr;
if (qr.isONE()) {
return P.ring.getZERO();
}
if (qr.degree(0) > 0) {
// pseudo remainder: ldcf(P,x_m) = a q + r
rr = PolyGBUtil. coefficientPseudoRemainder(pr2, qr);
//System.out.println("recursion, qr = " + qr);
//System.out.println("recursion, pr = " + pr2);
//System.out.println("recursion, rr = " + rr);
} else {
rr = pr2;
}
// reduction wrt. the other variables
List> zeroDeg = zeroDegrees(A);
GenPolynomial> Rr = PolyUtil.> distribute(rfac, rr);
GenPolynomial R = PolyUtil. distribute(pfac, Rr);
R = topCoefficientPseudoRemainder(zeroDeg, R);
return R.monic();
}
/**
* Polynomial leading coefficient pseudo remainder.
* @param P generic polynomial in n+1 variables.
* @param A generic polynomial in n variables.
* @return pseudo remainder of the leading coefficient of P wrt A, with
* ldcf(A)m' P = quotient * A + remainder.
*/
public static >
GenPolynomial>> coefficientPseudoRemainder(
GenPolynomial>> P, GenPolynomial> A) {
if (A == null || A.isZERO()) { // findbugs
throw new ArithmeticException(P + " division by zero " + A);
}
if (A.isONE()) {
return P.ring.getZERO();
}
if (P.isZERO() || P.isONE()) {
return P;
}
GenPolynomialRing>> pfac = P.ring;
GenPolynomialRing> afac = A.ring; // == pfac.coFac
GenPolynomial>> r = P;
GenPolynomial> h;
GenPolynomial>> hr;
GenPolynomial> ldcf = P.leadingBaseCoefficient();
long m = ldcf.degree(0);
long n = A.degree(0);
GenPolynomial c = A.leadingBaseCoefficient();
GenPolynomial> cc = afac.getZERO().sum(c);
//System.out.println("cc = " + cc);
ExpVector e = A.leadingExpVector();
for (long i = m; i >= n; i--) {
if (r.isZERO()) {
return r;
}
GenPolynomial> p = r.leadingBaseCoefficient();
ExpVector g = r.leadingExpVector();
long k = p.degree(0);
if (i == k) {
GenPolynomial pl = p.leadingBaseCoefficient();
ExpVector f = p.leadingExpVector();
f = f.subtract(e);
r = r.multiply(cc); // coeff cc
h = A.multiply(pl, f); // coeff ac
hr = new GenPolynomial>>(pfac, h, g);
r = r.subtract(hr);
} else {
r = r.multiply(cc);
}
//System.out.println("r = " + r);
}
if (r.degree(0) < P.degree(0)) { // recursion for degree
r = coefficientPseudoRemainder(r, A);
}
return r;
}
/**
* Polynomial leading coefficient pseudo remainder, base case.
* @param P generic polynomial in 1+1 variables.
* @param A generic polynomial in 1 variable.
* @return pseudo remainder of the leading coefficient of P wrt. A, with
* ldcf(A)m' P = quotient * A + remainder.
*/
public static >
GenPolynomial> coefficientPseudoRemainderBase(
GenPolynomial> P, GenPolynomial A) {
if (A == null || A.isZERO()) { // findbugs
throw new ArithmeticException(P + " division by zero " + A);
}
if (A.isONE()) {
return P.ring.getZERO();
}
if (P.isZERO() || P.isONE()) {
return P;
}
GenPolynomialRing> pfac = P.ring;
GenPolynomialRing afac = A.ring; // == pfac.coFac
GenPolynomial> r = P;
GenPolynomial h;
GenPolynomial> hr;
GenPolynomial ldcf = P.leadingBaseCoefficient();
long m = ldcf.degree(0);
long n = A.degree(0);
C c = A.leadingBaseCoefficient();
GenPolynomial cc = afac.getZERO().sum(c);
//System.out.println("cc = " + cc);
ExpVector e = A.leadingExpVector();
for (long i = m; i >= n; i--) {
if (r.isZERO()) {
return r;
}
GenPolynomial p = r.leadingBaseCoefficient();
ExpVector g = r.leadingExpVector();
long k = p.degree(0);
if (i == k) {
C pl = p.leadingBaseCoefficient();
ExpVector f = p.leadingExpVector();
f = f.subtract(e);
r = r.multiply(cc); // coeff cc
h = A.multiply(pl, f); // coeff ac
hr = new GenPolynomial>(pfac, h, g);
r = r.subtract(hr);
} else {
r = r.multiply(cc);
}
//System.out.println("r = " + r);
}
if (r.degree(0) < P.degree(0)) { // recursion for degree
r = coefficientPseudoRemainderBase(r, A);
}
return r;
}
/**
* Extract polynomials with degree zero in the main variable.
* @param A list of generic polynomials in n variables.
* @return Z = [a_i] with deg(a_i,x_n) = 0 and in n-1 variables.
*/
public static > List> zeroDegrees(List> A) {
if (A == null || A.isEmpty()) {
return A;
}
GenPolynomialRing pfac = A.get(0).ring;
GenPolynomialRing> rfac = pfac.recursive(1);
List> zeroDeg = new ArrayList>(A.size());
for (int i = 0; i < A.size(); i++) {
GenPolynomial q = A.get(i);
GenPolynomial> fr = PolyUtil. recursive(rfac, q);
if (fr.degree(0) == 0) {
zeroDeg.add(fr.leadingBaseCoefficient());
}
}
return zeroDeg;
}
}
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