/*
* $Id$
*/
package edu.jas.application;
import java.io.IOException;
import java.io.Reader;
import java.io.StringReader;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.List;
import java.util.Map;
import java.util.Random;
import org.apache.log4j.Logger;
import edu.jas.kern.PrettyPrint;
import edu.jas.kern.Scripting;
import edu.jas.poly.ExpVector;
import edu.jas.poly.GenPolynomial;
import edu.jas.poly.GenPolynomialRing;
import edu.jas.poly.GenPolynomialTokenizer;
import edu.jas.poly.GenSolvablePolynomial;
import edu.jas.poly.GenSolvablePolynomialRing;
import edu.jas.poly.RecSolvablePolynomial;
import edu.jas.poly.RecSolvablePolynomialRing;
import edu.jas.poly.RelationTable;
import edu.jas.poly.TermOrder;
import edu.jas.structure.GcdRingElem;
import edu.jas.structure.RingElem;
import edu.jas.structure.RingFactory;
/**
* ResidueSolvablePolynomialRing generic solvable polynomial with residue
* coefficients factory implementing RingFactory and extending
* GenSolvablePolynomialRing factory. Factory for n-variate ordered solvable
* polynomials over solvable residue coefficients. The non-commutative
* multiplication relations are maintained in a relation table and the
* non-commutative multiplication relations between the coefficients and the
* main variables are maintained in a coefficient relation table. Almost
* immutable object, except variable names and relation table contents.
* @param coefficient type.
* @author Heinz Kredel
*/
public class ResidueSolvablePolynomialRing> extends
GenSolvablePolynomialRing> {
/*
* The solvable multiplication relations between variables and coefficients.
*/
//public final RelationTable> coeffTable;
/**
* Recursive solvable polynomial ring with polynomial coefficients.
*/
public final RecSolvablePolynomialRing polCoeff;
/**
* The constant polynomial 0 for this ring. Hides super ZERO.
*/
public final ResidueSolvablePolynomial ZERO;
/**
* The constant polynomial 1 for this ring. Hides super ONE.
*/
public final ResidueSolvablePolynomial ONE;
private static final Logger logger = Logger.getLogger(ResidueSolvablePolynomialRing.class);
private final boolean debug = logger.isDebugEnabled();
/**
* The constructor creates a solvable polynomial factory object with the
* default term order and commutative relations.
* @param cf factory for coefficients of type C.
* @param n number of variables.
*/
public ResidueSolvablePolynomialRing(RingFactory> cf, int n) {
this(cf, n, new TermOrder(), null, null);
}
/**
* The constructor creates a solvable polynomial factory object with the
* default term order.
* @param cf factory for coefficients of type C.
* @param n number of variables.
* @param rt solvable multiplication relations.
*/
public ResidueSolvablePolynomialRing(RingFactory> cf, int n,
RelationTable> rt) {
this(cf, n, new TermOrder(), null, rt);
}
/**
* The constructor creates a solvable polynomial factory object with the
* given term order and commutative relations.
* @param cf factory for coefficients of type C.
* @param n number of variables.
* @param t a term order.
*/
public ResidueSolvablePolynomialRing(RingFactory> cf, int n, TermOrder t) {
this(cf, n, t, null, null);
}
/**
* The constructor creates a solvable polynomial factory object with the
* given term order.
* @param cf factory for coefficients of type C.
* @param n number of variables.
* @param t a term order.
* @param rt solvable multiplication relations.
*/
public ResidueSolvablePolynomialRing(RingFactory> cf, int n, TermOrder t,
RelationTable> rt) {
this(cf, n, t, null, rt);
}
/**
* The constructor creates a solvable polynomial factory object with the
* given term order and commutative relations.
* @param cf factory for coefficients of type C.
* @param n number of variables.
* @param t a term order.
* @param v names for the variables.
*/
public ResidueSolvablePolynomialRing(RingFactory> cf, int n, TermOrder t, String[] v) {
this(cf, n, t, v, null);
}
/**
* The constructor creates a solvable polynomial factory object with the
* given term order and commutative relations.
* @param cf factory for coefficients of type C.
* @param t a term order.
* @param v names for the variables.
*/
public ResidueSolvablePolynomialRing(RingFactory> cf, TermOrder t, String[] v) {
this(cf, v.length, t, v, null);
}
/**
* The constructor creates a solvable polynomial factory object with the
* default term order.
* @param cf factory for coefficients of type C.
* @param v names for the variables.
*/
public ResidueSolvablePolynomialRing(RingFactory> cf, String[] v) {
this(cf, v.length, new TermOrder(), v, null);
}
/**
* The constructor creates a solvable polynomial factory object with the
* given term order.
* @param cf factory for coefficients of type C.
* @param n number of variables.
* @param t a term order.
* @param v names for the variables.
* @param rt solvable multiplication relations.
*/
public ResidueSolvablePolynomialRing(RingFactory> cf, int n, TermOrder t, String[] v,
RelationTable> rt) {
super(cf, n, t, v, rt);
//if (rt == null) { // handled in super }
SolvableResidueRing cfring = (SolvableResidueRing) cf; // == coFac
polCoeff = new RecSolvablePolynomialRing(cfring.ring, n, t, v);
if (table.size() > 0) { // TODO
ExpVector e = null;
ExpVector f = null;
GenSolvablePolynomial> p = null;
polCoeff.table.update(e, f, p); // from rt
}
//coeffTable = polCoeff.coeffTable; //new RelationTable>(polCoeff, true);
ZERO = new ResidueSolvablePolynomial(this);
SolvableResidue coeff = coFac.getONE();
//evzero = ExpVector.create(nvar); // from super
ONE = new ResidueSolvablePolynomial(this, coeff, evzero);
}
/**
* The constructor creates a solvable polynomial factory object with the the
* same term order, number of variables and variable names as the given
* polynomial factory, only the coefficient factories differ and the
* solvable multiplication relations are empty.
* @param cf factory for coefficients of type C.
* @param o other solvable polynomial ring.
*/
public ResidueSolvablePolynomialRing(RingFactory> cf, ResidueSolvablePolynomialRing o) {
this(cf, o.nvar, o.tord, o.getVars(), null);
}
/**
* Get the String representation.
* @see java.lang.Object#toString()
*/
@Override
public String toString() {
String res = super.toString();
if (PrettyPrint.isTrue()) {
//res += "\n" + table.toString(vars);
res += "\n" + polCoeff.coeffTable.toString(vars);
} else {
res += ", #rel = " + table.size() + " + " + polCoeff.coeffTable.size();
}
return res;
}
/**
* Get a scripting compatible string representation.
* @return script compatible representation for this Element.
* @see edu.jas.structure.Element#toScript()
*/
@Override
public String toScript() {
StringBuffer s = new StringBuffer();
switch (Scripting.getLang()) {
case Ruby:
s.append("SolvPolyRing.new(");
break;
case Python:
default:
s.append("SolvPolyRing(");
}
if (coFac instanceof RingElem) {
s.append(((RingElem>) coFac).toScriptFactory());
} else {
s.append(coFac.toScript().trim());
}
s.append(",\"" + varsToString() + "\",");
String to = tord.toString();
if (tord.getEvord() == TermOrder.INVLEX) {
to = "PolyRing.lex";
}
if (tord.getEvord() == TermOrder.IGRLEX) {
to = "PolyRing.grad";
}
s.append(to);
if (table.size() > 0) {
String rel = table.toScript();
s.append(",rel=");
s.append(rel);
}
if (polCoeff.coeffTable.size() > 0) {
String rel = polCoeff.coeffTable.toScript();
s.append(",coeffrel=");
s.append(rel);
}
s.append(")");
return s.toString();
}
/**
* Comparison with any other object.
* @see java.lang.Object#equals(java.lang.Object)
*/
@Override
@SuppressWarnings("unchecked")
public boolean equals(Object other) {
if (!(other instanceof ResidueSolvablePolynomialRing)) {
return false;
}
ResidueSolvablePolynomialRing oring = null;
try {
oring = (ResidueSolvablePolynomialRing) other;
} catch (ClassCastException ignored) {
}
if (oring == null) {
return false;
}
// do a super.equals( )
if (!super.equals(other)) {
return false;
}
// check same base relations
//if ( ! table.equals(oring.table) ) { // done in super
// return false;
//}
if (!polCoeff.coeffTable.equals(oring.polCoeff.coeffTable)) {
return false;
}
return true;
}
/**
* Hash code for this polynomial ring.
* @see java.lang.Object#hashCode()
*/
@Override
public int hashCode() {
int h;
h = super.hashCode();
h = 37 * h + table.hashCode(); // may be different after some computations
h = 37 * h + polCoeff.coeffTable.hashCode(); // may be different
return h;
}
/**
* Get the zero element.
* @return 0 as ResidueSolvablePolynomial.
*/
@Override
public ResidueSolvablePolynomial getZERO() {
return ZERO;
}
/**
* Get the one element.
* @return 1 as ResidueSolvablePolynomial.
*/
@Override
public ResidueSolvablePolynomial getONE() {
return ONE;
}
/**
* Query if this ring is commutative.
* @return true if this ring is commutative, else false.
*/
@Override
public boolean isCommutative() {
if (polCoeff.coeffTable.size() == 0) {
return super.isCommutative();
}
// todo: check structure of relations
return false;
}
/**
* Query if this ring is associative. Test if the relations between the mian
* variables and the coefficient generators define an associative solvable
* ring.
* @return true, if this ring is associative, else false.
*/
@Override
public boolean isAssociative() {
ResidueSolvablePolynomial Xi, Xj, Xk, p, q;
List>> gens = generators();
int ngen = gens.size();
for (int i = 0; i < ngen; i++) {
Xi = (ResidueSolvablePolynomial) gens.get(i);
for (int j = i + 1; j < ngen; j++) {
Xj = (ResidueSolvablePolynomial) gens.get(j);
for (int k = j + 1; k < ngen; k++) {
Xk = (ResidueSolvablePolynomial) gens.get(k);
p = Xk.multiply(Xj).multiply(Xi);
q = Xk.multiply(Xj.multiply(Xi));
if (!p.equals(q)) {
if (true || debug) {
logger.info("Xk = " + Xk + ", Xj = " + Xj + ", Xi = " + Xi);
logger.info("p = ( Xk * Xj ) * Xi = " + p);
logger.info("q = Xk * ( Xj * Xi ) = " + q);
}
return false;
}
}
}
}
return coFac.isAssociative();
}
/**
* Get a (constant) ResidueSolvablePolynomial<C> element from a long
* value.
* @param a long.
* @return a ResidueSolvablePolynomial<C>.
*/
@Override
public ResidueSolvablePolynomial fromInteger(long a) {
return new ResidueSolvablePolynomial(this, coFac.fromInteger(a), evzero);
}
/**
* Get a (constant) ResidueSolvablePolynomial<C> element from a
* BigInteger value.
* @param a BigInteger.
* @return a ResidueSolvablePolynomial<C>.
*/
@Override
public ResidueSolvablePolynomial fromInteger(BigInteger a) {
return new ResidueSolvablePolynomial(this, coFac.fromInteger(a), evzero);
}
/**
* Random solvable polynomial. Generates a random solvable polynomial with k
* = 5, l = n, d = (nvar == 1) ? n : 3, q = (nvar == 1) ? 0.7 : 0.3.
* @param n number of terms.
* @return a random solvable polynomial.
*/
@Override
public ResidueSolvablePolynomial random(int n) {
return random(n, random);
}
/**
* Random solvable polynomial. Generates a random solvable polynomial with k
* = 5, l = n, d = (nvar == 1) ? n : 3, q = (nvar == 1) ? 0.7 : 0.3.
* @param n number of terms.
* @param rnd is a source for random bits.
* @return a random solvable polynomial.
*/
@Override
public ResidueSolvablePolynomial random(int n, Random rnd) {
if (nvar == 1) {
return random(5, n, n, 0.7f, rnd);
}
return random(5, n, 3, 0.3f, rnd);
}
/**
* Generate a random solvable polynomial.
* @param k bitsize of random coefficients.
* @param l number of terms.
* @param d maximal degree in each variable.
* @param q density of nozero exponents.
* @return a random solvable polynomial.
*/
@Override
public ResidueSolvablePolynomial random(int k, int l, int d, float q) {
return random(k, l, d, q, random);
}
/**
* Random solvable polynomial.
* @param k size of random coefficients.
* @param l number of terms.
* @param d maximal degree in each variable.
* @param q density of nozero exponents.
* @param rnd is a source for random bits.
* @return a random solvable polynomial.
*/
@Override
public ResidueSolvablePolynomial random(int k, int l, int d, float q, Random rnd) {
ResidueSolvablePolynomial r = getZERO(); // copy( ZERO );
ExpVector e;
SolvableResidue a;
// add random coeffs and exponents
for (int i = 0; i < l; i++) {
e = ExpVector.EVRAND(nvar, d, q, rnd);
a = coFac.random(k, rnd);
r = (ResidueSolvablePolynomial) r.sum(a, e);
// somewhat inefficient but clean
}
return r;
}
/**
* Copy polynomial c.
* @param c
* @return a copy of c.
*/
public ResidueSolvablePolynomial copy(ResidueSolvablePolynomial c) {
return new ResidueSolvablePolynomial(this, c.getMap());
}
/**
* Parse a solvable polynomial with the use of GenPolynomialTokenizer
* @param s String.
* @return ResidueSolvablePolynomial from s.
*/
@Override
public ResidueSolvablePolynomial parse(String s) {
return parse(new StringReader(s));
}
/**
* Parse a solvable polynomial with the use of GenPolynomialTokenizer
* @param r Reader.
* @return next ResidueSolvablePolynomial from r.
*/
@Override
@SuppressWarnings("unchecked")
public ResidueSolvablePolynomial parse(Reader r) {
GenPolynomialTokenizer pt = new GenPolynomialTokenizer(this, r);
ResidueSolvablePolynomial p = null;
try {
GenSolvablePolynomial> s = pt.nextSolvablePolynomial();
p = new ResidueSolvablePolynomial(this, s);
} catch (IOException e) {
logger.error(e.toString() + " parse " + this);
p = ZERO;
}
return p;
}
/**
* Generate univariate solvable polynomial in a given variable.
* @param i the index of the variable.
* @return X_i as solvable univariate polynomial.
*/
@Override
public ResidueSolvablePolynomial univariate(int i) {
return (ResidueSolvablePolynomial) super.univariate(i);
}
/**
* Generate univariate solvable polynomial in a given variable with given
* exponent.
* @param i the index of the variable.
* @param e the exponent of the variable.
* @return X_i^e as solvable univariate polynomial.
*/
@Override
public ResidueSolvablePolynomial univariate(int i, long e) {
return (ResidueSolvablePolynomial) super.univariate(i, e);
}
/**
* Generate univariate solvable polynomial in a given variable with given
* exponent.
* @param modv number of module variables.
* @param i the index of the variable.
* @param e the exponent of the variable.
* @return X_i^e as solvable univariate polynomial.
*/
@Override
public ResidueSolvablePolynomial univariate(int modv, int i, long e) {
return (ResidueSolvablePolynomial) super.univariate(modv, i, e);
}
/**
* Generate list of univariate polynomials in all variables.
* @return List(X_1,...,X_n) a list of univariate polynomials.
*/
//todo Override
@SuppressWarnings("unchecked")
public List> recUnivariateList() {
//return castToSolvableList( super.univariateList() );
return (List>) (Object) univariateList(0, 1L);
}
/**
* Generate list of univariate polynomials in all variables.
* @param modv number of module variables.
* @return List(X_1,...,X_n) a list of univariate polynomials.
*/
//todo Override
@SuppressWarnings("unchecked")
public List> recUnivariateList(int modv) {
return (List>) (Object) univariateList(modv, 1L);
}
/**
* Generate list of univariate polynomials in all variables with given
* exponent.
* @param modv number of module variables.
* @param e the exponent of the variables.
* @return List(X_1^e,...,X_n^e) a list of univariate polynomials.
*/
//todo Override
public List> recUnivariateList(int modv, long e) {
List> pols = new ArrayList>(nvar);
int nm = nvar - modv;
for (int i = 0; i < nm; i++) {
ResidueSolvablePolynomial p = univariate(modv, nm - 1 - i, e);
pols.add(p);
}
return pols;
}
/*
* Generate list of univariate polynomials in all variables with given exponent.
* @param modv number of module variables.
* @param e the exponent of the variables.
* @return List(X_1^e,...,X_n^e) a list of univariate polynomials.
@Override
public List> univariateList(int modv, long e) {
List> pol = super.univariateList(modv,e);
UnaryFunctor,ResidueSolvablePolynomial> fc
= new UnaryFunctor,ResidueSolvablePolynomial>() {
public ResidueSolvablePolynomial eval(GenPolynomial p) {
if ( ! (p instanceof ResidueSolvablePolynomial) ) {
throw new RuntimeException("no solvable polynomial "+p);
}
return (ResidueSolvablePolynomial) p;
}
};
List> pols
= ListUtil.,ResidueSolvablePolynomial>map(this,pol,fc);
return pols;
}
*/
/**
* Extend variables. Used e.g. in module embedding. Extend number of
* variables by i.
* @param i number of variables to extend.
* @return extended solvable polynomial ring factory.
*/
@Override
public ResidueSolvablePolynomialRing extend(int i) {
GenPolynomialRing> pfac = super.extend(i);
ResidueSolvablePolynomialRing spfac = new ResidueSolvablePolynomialRing(pfac.coFac, pfac.nvar,
pfac.tord, pfac.getVars());
spfac.table.extend(this.table);
spfac.polCoeff.coeffTable.extend(this.polCoeff.coeffTable);
return spfac;
}
/**
* Contract variables. Used e.g. in module embedding. Contract number of
* variables by i.
* @param i number of variables to remove.
* @return contracted solvable polynomial ring factory.
*/
@Override
public ResidueSolvablePolynomialRing contract(int i) {
GenPolynomialRing> pfac = super.contract(i);
ResidueSolvablePolynomialRing spfac = new ResidueSolvablePolynomialRing(pfac.coFac, pfac.nvar,
pfac.tord, pfac.getVars());
spfac.table.contract(this.table);
spfac.polCoeff.coeffTable.contract(this.polCoeff.coeffTable);
return spfac;
}
/**
* Reverse variables. Used e.g. in opposite rings.
* @return solvable polynomial ring factory with reversed variables.
*/
@Override
public ResidueSolvablePolynomialRing reverse() {
return reverse(false);
}
/**
* Reverse variables. Used e.g. in opposite rings.
* @param partial true for partialy reversed term orders.
* @return solvable polynomial ring factory with reversed variables.
*/
@Override
public ResidueSolvablePolynomialRing reverse(boolean partial) {
GenPolynomialRing> pfac = super.reverse(partial);
ResidueSolvablePolynomialRing spfac = new ResidueSolvablePolynomialRing(pfac.coFac, pfac.nvar,
pfac.tord, pfac.getVars());
spfac.partial = partial;
spfac.table.reverse(this.table);
spfac.polCoeff.coeffTable.reverse(this.polCoeff.coeffTable);
return spfac;
}
/**
* Solvable residue coefficients from integral polynomial coefficients.
* Represent as polynomial with type SolvableResidue coefficients.
* @param A polynomial with integral polynomial coefficients to be
* converted.
* @return polynomial with type SolvableResidue coefficients.
*/
public ResidueSolvablePolynomial fromPolyCoefficients(GenSolvablePolynomial> A) {
ResidueSolvablePolynomial B = getZERO().copy();
if (A == null || A.isZERO()) {
return B;
}
RingFactory> cfac = coFac;
SolvableResidueRing qfac = (SolvableResidueRing) cfac;
for (Map.Entry> y : A.getMap().entrySet()) {
ExpVector e = y.getKey();
GenSolvablePolynomial a = (GenSolvablePolynomial) y.getValue();
SolvableResidue p = new SolvableResidue(qfac, a); // can be zero
if (!p.isZERO()) {
//B = B.sum( p, e ); // inefficient
B.doPutToMap(e, p);
}
}
return B;
}
/**
* Integral function from solvable residue coefficients. Represent as
* polynomial with type GenSolvablePolynomial coefficients.
* @param A polynomial with solvable residue coefficients to be converted.
* @return polynomial with type GenSolvablePolynomial coefficients.
*/
public RecSolvablePolynomial toPolyCoefficients(ResidueSolvablePolynomial A) {
RecSolvablePolynomial B = polCoeff.getZERO().copy();
if (A == null || A.isZERO()) {
return B;
}
for (Map.Entry> y : A.getMap().entrySet()) {
ExpVector e = y.getKey();
SolvableResidue a = y.getValue();
GenPolynomial p = a.val; // can not be zero
if (!p.isZERO()) {
//B = B.sum( p, e ); // inefficient
B.doPutToMap(e, p);
}
}
return B;
}
/**
* Integral function from solvable residue coefficients. Represent as
* polynomial with type GenSolvablePolynomial coefficients.
* @param A polynomial with solvable residue coefficients to be converted.
* @return polynomial with type GenSolvablePolynomial coefficients.
*/
public RecSolvablePolynomial toPolyCoefficients(GenPolynomial> A) {
RecSolvablePolynomial B = polCoeff.getZERO().copy();
if (A == null || A.isZERO()) {
return B;
}
for (Map.Entry> y : A.getMap().entrySet()) {
ExpVector e = y.getKey();
SolvableResidue a = y.getValue();
GenPolynomial p = a.val; // can not be zero
if (!p.isZERO()) {
//B = B.sum( p, e ); // inefficient
B.doPutToMap(e, p);
}
}
return B;
}
}
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