/*
* $Id$
*/
package edu.jas.application;
import java.io.Reader;
import java.util.ArrayList;
import java.util.List;
import java.util.Random;
import org.apache.log4j.Logger;
import edu.jas.gb.SolvableGroebnerBaseAbstract;
import edu.jas.gb.SolvableGroebnerBaseSeq;
import edu.jas.gbmod.SolvableSyzygyAbstract;
import edu.jas.kern.StringUtil;
import edu.jas.poly.GenPolynomial;
import edu.jas.poly.GenSolvablePolynomial;
import edu.jas.poly.GenSolvablePolynomialRing;
import edu.jas.poly.PolynomialList;
import edu.jas.structure.GcdRingElem;
import edu.jas.structure.RingFactory;
import edu.jas.structure.QuotPairFactory;
// import edu.jas.ufd.GreatestCommonDivisor;
// import edu.jas.ufd.GCDFactory;
/**
* SolvableLocal ring class based on GenSolvablePolynomial with RingElem
* interface. Objects of this class are effective immutable.
* @author Heinz Kredel
*/
public class SolvableLocalRing>
implements RingFactory>, QuotPairFactory,SolvableLocal> {
// Can not extend SolvableQuotientRing
// because of different constructor semantics.
private static final Logger logger = Logger.getLogger(SolvableLocalRing.class);
private final boolean debug = logger.isDebugEnabled();
/**
* Solvable polynomial ideal for localization.
*/
public final SolvableIdeal ideal;
/**
* Solvable polynomial ring of the factory.
*/
public final GenSolvablePolynomialRing ring;
/**
* Syzygy engine of the factory.
*/
public final SolvableSyzygyAbstract engine;
/**
* Groebner base engine.
*/
protected final SolvableGroebnerBaseAbstract bb;
/**
* Indicator if this ring is a field.
*/
protected int isField = -1; // initially unknown
/**
* The constructor creates a SolvableLocalRing object from a SolvableIdeal.
* @param i solvable localization polynomial ideal.
*/
public SolvableLocalRing(SolvableIdeal i) {
if (i == null) {
throw new IllegalArgumentException("ideal may not be null");
}
ring = i.getRing();
ideal = i.GB(); // cheap if isGB
if (ideal.isONE()) {
throw new IllegalArgumentException("ideal may not be 1");
}
if (ideal.isMaximal()) {
isField = 1;
} else {
isField = 0;
logger.warn("ideal not maximal");
//throw new IllegalArgumentException("ideal must be maximal");
}
engine = new SolvableSyzygyAbstract();
bb = new SolvableGroebnerBaseSeq();
logger.debug("solvable local ring constructed");
}
/**
* Factory for base elements.
*/
public GenSolvablePolynomialRing pairFactory() {
return ring;
}
/**
* Create from numerator.
*/
public SolvableLocal create(GenPolynomial n) {
return new SolvableLocal(this,(GenSolvablePolynomial)n);
}
/**
* Create from numerator, denominator pair.
*/
public SolvableLocal create(GenPolynomial n, GenPolynomial d) {
return new SolvableLocal(this,(GenSolvablePolynomial)n,(GenSolvablePolynomial)d);
}
/**
* Is this structure finite or infinite.
* @return true if this structure is finite, else false.
*/
public boolean isFinite() {
return ring.isFinite() && bb.commonZeroTest(ideal.getList()) <= 0;
}
/**
* Copy SolvableLocal element c.
* @param c element to copy
* @return a copy of c.
*/
public SolvableLocal copy(SolvableLocal c) {
return new SolvableLocal(c.ring, c.num, c.den, true);
}
/**
* Get the zero element.
* @return 0 as SolvableLocal.
*/
public SolvableLocal getZERO() {
return new SolvableLocal(this, ring.getZERO());
}
/**
* Get the one element.
* @return 1 as SolvableLocal.
*/
public SolvableLocal getONE() {
return new SolvableLocal(this, ring.getONE());
}
/**
* Get a list of the generating elements.
* @return list of generators for the algebraic structure.
*/
public List> generators() {
List> pgens = PolynomialList. castToSolvableList(ring.generators());
List> gens = new ArrayList>(pgens.size() * 2 - 1);
GenSolvablePolynomial one = ring.getONE();
for (GenSolvablePolynomial p : pgens) {
SolvableLocal q = new SolvableLocal(this, p);
gens.add(q);
if (!p.isONE() && !ideal.contains(p)) { // q.isUnit()
q = new SolvableLocal(this, one, p);
gens.add(q);
}
}
return gens;
}
/**
* Query if this ring is commutative.
* @return true if this ring is commutative, else false.
*/
public boolean isCommutative() {
return ring.isCommutative();
}
/**
* Query if this ring is associative.
* @return true if this ring is associative, else false.
*/
public boolean isAssociative() {
if (!ring.isAssociative()) {
return false;
}
SolvableLocal Xi, Xj, Xk, p, q;
List> gens = generators();
int ngen = gens.size();
for (int i = 0; i < ngen; i++) {
Xi = gens.get(i);
for (int j = i + 1; j < ngen; j++) {
Xj = gens.get(j);
for (int k = j + 1; k < ngen; k++) {
Xk = gens.get(k);
try {
p = Xk.multiply(Xj).multiply(Xi);
q = Xk.multiply(Xj.multiply(Xi));
} catch (IllegalArgumentException e) {
//e.printStackTrace();
continue; // ignore undefined multiplication
}
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 true;
}
/**
* Query if this ring is a field.
* @return false.
*/
public boolean isField() {
if (isField > 0) {
return true;
}
if (isField == 0) {
return false;
}
// not reached
return false;
}
/**
* Characteristic of this ring.
* @return characteristic of this ring.
*/
public java.math.BigInteger characteristic() {
return ring.characteristic();
}
/**
* Get a SolvableLocal element from a BigInteger value.
* @param a BigInteger.
* @return a SolvableLocal.
*/
public SolvableLocal fromInteger(java.math.BigInteger a) {
return new SolvableLocal(this, ring.fromInteger(a));
}
/**
* Get a SolvableLocal element from a long value.
* @param a long.
* @return a SolvableLocal.
*/
public SolvableLocal fromInteger(long a) {
return new SolvableLocal(this, ring.fromInteger(a));
}
/**
* Get the String representation as RingFactory.
*/
@Override
public String toString() {
return "SolvableLocalRing[ " + ideal.toString() + " ]";
}
/**
* Get a scripting compatible string representation.
* @return script compatible representation for this ElemFactory.
*/
@Override
public String toScript() {
// Python case
return "SLC(" + ideal.list.toScript() + ")";
}
/**
* Comparison with any other object.
*/
@Override
@SuppressWarnings("unchecked")
public boolean equals(Object b) {
if (!(b instanceof SolvableLocalRing)) {
return false;
}
SolvableLocalRing a = null;
try {
a = (SolvableLocalRing) b;
} catch (ClassCastException e) {
}
if (a == null) {
return false;
}
if (!ring.equals(a.ring)) {
return false;
}
return ideal.equals(a.ideal);
}
/**
* Hash code for this local ring.
*/
@Override
public int hashCode() {
int h;
h = ideal.hashCode();
return h;
}
/**
* SolvableLocal random.
* @param n such that 0 ≤ v ≤ (2n-1).
* @return a random residue element.
*/
public SolvableLocal random(int n) {
GenSolvablePolynomial r = ring.random(n).monic();
r = ideal.normalform(r);
GenSolvablePolynomial s;
do {
s = ring.random(n).monic();
s = ideal.normalform(s);
} while (s.isZERO());
return new SolvableLocal(this, r, s, false);
}
/**
* Generate a random residum 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 residue polynomial.
*/
public SolvableLocal random(int k, int l, int d, float q) {
GenSolvablePolynomial r = ring.random(k, l, d, q).monic();
r = ideal.normalform(r);
GenSolvablePolynomial s;
do {
s = ring.random(k, l, d, q).monic();
s = ideal.normalform(s);
} while (s.isZERO());
return new SolvableLocal(this, r, s, false);
}
/**
* SolvableLocal random.
* @param n such that 0 ≤ v ≤ (2n-1).
* @param rnd is a source for random bits.
* @return a random residue element.
*/
public SolvableLocal random(int n, Random rnd) {
GenSolvablePolynomial r = ring.random(n, rnd).monic();
r = ideal.normalform(r);
GenSolvablePolynomial s;
do {
s = ring.random(n).monic();
s = ideal.normalform(s);
} while (s.isZERO());
return new SolvableLocal(this, r, s, false);
}
/**
* Parse SolvableLocal from String.
* @param s String.
* @return SolvableLocal from s.
*/
public SolvableLocal parse(String s) {
int i = s.indexOf("{");
if (i >= 0) {
s = s.substring(i + 1);
}
i = s.lastIndexOf("}");
if (i >= 0) {
s = s.substring(0, i);
}
i = s.indexOf("|");
if (i < 0) {
GenSolvablePolynomial n = ring.parse(s);
return new SolvableLocal(this, n);
}
String s1 = s.substring(0, i);
String s2 = s.substring(i + 1);
GenSolvablePolynomial n = ring.parse(s1);
GenSolvablePolynomial d = ring.parse(s2);
return new SolvableLocal(this, n, d);
}
/**
* Parse SolvableLocal from Reader.
* @param r Reader.
* @return next SolvableLocal from r.
*/
public SolvableLocal parse(Reader r) {
String s = StringUtil.nextPairedString(r, '{', '}');
return parse(s);
}
}
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