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Redberry is an open source computer algebra system designed for tensor
manipulation. It implements basic computer algebra system routines as well as
complex tools for real computations in physics.
This is Redberry core, which contains the implementation of the basic
computer algebra routines and general-purpose transformations.
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/*
* JAS: Java Algebra System.
*
* Copyright (c) 2000-2014:
* Heinz Kredel
*
* This file is part of Java Algebra System (JAS).
*
* JAS is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 2 of the License, or
* (at your option) any later version.
*
* JAS is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with JAS. If not, see > extends GreatestCommonDivisorAbstract {
/**
* Univariate GenPolynomial greatest comon divisor. Uses pseudoRemainder for
* remainder.
*
* @param P univariate GenPolynomial.
* @param S univariate GenPolynomial.
* @return gcd(P, S).
*/
@Override
public GenPolynomial baseGcd(GenPolynomial P, GenPolynomial S) {
if (S == null || S.isZERO()) {
return P;
}
if (P == null || P.isZERO()) {
return S;
}
if (P.ring.nvar > 1) {
throw new IllegalArgumentException(this.getClass().getName() + " no univariate polynomial");
}
boolean field = P.ring.coFac.isField();
long e = P.degree(0);
long f = S.degree(0);
GenPolynomial q;
GenPolynomial r;
if (f > e) {
r = P;
q = S;
long g = f;
f = e;
e = g;
} else {
q = P;
r = S;
}
C c;
if (field) {
r = r.monic();
q = q.monic();
c = P.ring.getONECoefficient();
} else {
r = r.abs();
q = q.abs();
C a = baseContent(r);
C b = baseContent(q);
c = gcd(a, b); // indirection
r = divide(r, a); // indirection
q = divide(q, b); // indirection
}
if (r.isONE()) {
return r.multiply(c);
}
if (q.isONE()) {
return q.multiply(c);
}
GenPolynomial x;
while (!r.isZERO()) {
x = PolyUtil.baseSparsePseudoRemainder(q, r);
q = r;
if (field) {
r = x.monic();
} else {
r = x;
}
}
q = basePrimitivePart(q);
return (q.multiply(c)).abs();
}
/**
* Univariate GenPolynomial recursive greatest comon divisor. Uses
* pseudoRemainder for remainder.
*
* @param P univariate recursive GenPolynomial.
* @param S univariate recursive GenPolynomial.
* @return gcd(P, S).
*/
@Override
public GenPolynomial> recursiveUnivariateGcd(GenPolynomial> P,
GenPolynomial> S) {
if (S == null || S.isZERO()) {
return P;
}
if (P == null || P.isZERO()) {
return S;
}
if (P.ring.nvar > 1) {
throw new IllegalArgumentException(this.getClass().getName() + " no univariate polynomial");
}
boolean field = P.leadingBaseCoefficient().ring.coFac.isField();
long e = P.degree(0);
long f = S.degree(0);
GenPolynomial> q;
GenPolynomial> r;
if (f > e) {
r = P;
q = S;
long g = f;
f = e;
e = g;
} else {
q = P;
r = S;
}
if (field) {
r = PolyUtil.monic(r);
q = PolyUtil.monic(q);
} else {
r = r.abs();
q = q.abs();
}
GenPolynomial a = recursiveContent(r);
GenPolynomial b = recursiveContent(q);
GenPolynomial c = gcd(a, b); // go to recursion
r = PolyUtil.recursiveDivide(r, a);
q = PolyUtil.recursiveDivide(q, b);
if (r.isONE()) {
return r.multiply(c);
}
if (q.isONE()) {
return q.multiply(c);
}
GenPolynomial> x;
while (!r.isZERO()) {
x = PolyUtil.recursivePseudoRemainder(q, r);
q = r;
if (field) {
r = PolyUtil.monic(x);
} else {
r = x;
}
}
q = recursivePrimitivePart(q);
q = q.abs().multiply(c);
return q;
}
/**
* Univariate GenPolynomial resultant.
*
* @param P univariate GenPolynomial.
* @param S univariate GenPolynomial.
* @return res(P, S).
*/
@Override
public GenPolynomial baseResultant(GenPolynomial P, GenPolynomial S) {
if (S == null || S.isZERO()) {
return S;
}
if (P == null || P.isZERO()) {
return P;
}
if (P.ring.nvar > 1 || P.ring.nvar == 0) {
throw new IllegalArgumentException("no univariate polynomial");
}
long e = P.degree(0);
long f = S.degree(0);
if (f == 0 && e == 0) {
return P.ring.getONE();
}
if (e == 0) {
return Power.power(P.ring, P, f);
}
if (f == 0) {
return Power.power(S.ring, S, e);
}
GenPolynomial q;
GenPolynomial r;
int s = 0; // sign is +, 1 for sign is -
if (e < f) {
r = P;
q = S;
long t = e;
e = f;
f = t;
if ((e % 2 != 0) && (f % 2 != 0)) { // odd(e) && odd(f)
s = 1;
}
} else {
q = P;
r = S;
}
RingFactory cofac = P.ring.coFac;
boolean field = cofac.isField();
C c = cofac.getONE();
GenPolynomial x;
long g;
do {
if (field) {
x = q.remainder(r);
} else {
x = PolyUtil.baseSparsePseudoRemainder(q, r);
}
if (x.isZERO()) {
return x;
}
e = q.degree(0);
f = r.degree(0);
if ((e % 2 != 0) && (f % 2 != 0)) { // odd(e) && odd(f)
s = 1 - s;
}
g = x.degree(0);
C c2 = r.leadingBaseCoefficient();
for (int i = 0; i < (e - g); i++) {
c = c.multiply(c2);
}
q = r;
r = x;
} while (g != 0);
C c2 = r.leadingBaseCoefficient();
for (int i = 0; i < f; i++) {
c = c.multiply(c2);
}
if (s == 1) {
c = c.negate();
}
x = P.ring.getONE().multiply(c);
return x;
}
/**
* Univariate GenPolynomial recursive resultant.
*
* @param P univariate recursive GenPolynomial.
* @param S univariate recursive GenPolynomial.
* @return res(P, S).
*/
@Override
public GenPolynomial> recursiveUnivariateResultant(GenPolynomial> P,
GenPolynomial> S) {
if (S == null || S.isZERO()) {
return S;
}
if (P == null || P.isZERO()) {
return P;
}
if (P.ring.nvar > 1 || P.ring.nvar == 0) {
throw new IllegalArgumentException("no recursive univariate polynomial");
}
long e = P.degree(0);
long f = S.degree(0);
if (f == 0 && e == 0) {
// if coeffs are multivariate (and non constant)
// otherwise it would be 1
GenPolynomial t = resultant(P.leadingBaseCoefficient(), S.leadingBaseCoefficient());
return P.ring.getONE().multiply(t);
}
if (e == 0) {
return Power.power(P.ring, P, f);
}
if (f == 0) {
return Power.power(S.ring, S, e);
}
GenPolynomial> q;
GenPolynomial> r;
int s = 0; // sign is +, 1 for sign is -
if (f > e) {
r = P;
q = S;
long g = f;
f = e;
e = g;
if ((e % 2 != 0) && (f % 2 != 0)) { // odd(e) && odd(f)
s = 1;
}
} else {
q = P;
r = S;
}
GenPolynomial> x;
RingFactory> cofac = P.ring.coFac;
GenPolynomial c = cofac.getONE();
long g;
do {
x = PolyUtil.recursiveSparsePseudoRemainder(q, r);
//x = PolyUtil.recursiveDensePseudoRemainder(q,r);
if (x.isZERO()) {
return x;
}
//no: x = recursivePrimitivePart(x);
e = q.degree(0);
f = r.degree(0);
if ((e % 2 != 0) && (f % 2 != 0)) { // odd(e) && odd(f)
s = 1 - s;
}
g = x.degree(0);
GenPolynomial c2 = r.leadingBaseCoefficient();
for (int i = 0; i < (e - g); i++) {
c = c.multiply(c2);
}
q = r;
r = x;
} while (g != 0);
GenPolynomial c2 = r.leadingBaseCoefficient();
for (int i = 0; i < f; i++) {
c = c.multiply(c2);
}
if (s == 1) {
c = c.negate();
}
x = P.ring.getONE().multiply(c);
return x;
}
}