/*
* $Id$
*/
package edu.jas.poly;
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.Random;
import org.apache.log4j.Logger;
import edu.jas.kern.PrettyPrint;
import edu.jas.kern.Scripting;
import edu.jas.structure.RingElem;
import edu.jas.structure.RingFactory;
/**
* GenSolvablePolynomialRing generic solvable polynomial factory implementing
* RingFactory and extending GenPolynomialRing factory. Factory for n-variate
* ordered solvable polynomials over C. The non-commutative multiplication
* relations are maintained in a relation table. Almost immutable object, except
* variable names and relation table contents.
* @param coefficient type.
* @author Heinz Kredel
*/
public class GenSolvablePolynomialRing> extends GenPolynomialRing {
// implements RingFactory< GenSolvablePolynomial > {
/**
* The solvable multiplication relations.
*/
public final RelationTable table;
/**
* The constant polynomial 0 for this ring. Hides super ZERO.
*/
public final GenSolvablePolynomial ZERO;
/**
* The constant polynomial 1 for this ring. Hides super ONE.
*/
public final GenSolvablePolynomial ONE;
private static final Logger logger = Logger.getLogger(GenSolvablePolynomialRing.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 GenSolvablePolynomialRing(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 GenSolvablePolynomialRing(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 GenSolvablePolynomialRing(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 GenSolvablePolynomialRing(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 GenSolvablePolynomialRing(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 GenSolvablePolynomialRing(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 GenSolvablePolynomialRing(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 GenSolvablePolynomialRing(RingFactory cf, int n, TermOrder t, String[] v, RelationTable rt) {
super(cf, n, t, v);
if (rt == null) {
table = new RelationTable(this);
} else {
table = rt;
}
ZERO = new GenSolvablePolynomial(this);
C coeff = coFac.getONE();
//evzero = ExpVector.create(nvar); // from super
ONE = new GenSolvablePolynomial(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 GenSolvablePolynomialRing(RingFactory cf, GenSolvablePolynomialRing o) {
this(cf, o.nvar, o.tord, o.getVars(), null);
}
/**
* Generate the relation table of the solvable polynomial ring
* from a relation generator.
* @param rg relation generator.
*/
public void addRelations(RelationGenerator rg) {
rg.generate(this);
}
/**
* Generate the relation table of the solvable polynomial ring
* from a polynomial list of relations.
* @param rel polynomial list of relations [..., ei, fj, pij, ... ] with ei * fj = pij.
*/
public void addRelations(List> rel) {
table.addRelations(rel);
}
/**
* Generate the relation table of the solvable polynomial ring
* from a solvable polynomial list of relations.
* @param rel solvable polynomial list of relations [..., ei, fj, pij, ... ] with ei * fj = pij.
*/
public void addSolvRelations(List> rel) {
table.addSolvRelations(rel);
}
/**
* 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);
} else {
res += ", #rel = " + table.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);
}
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 GenSolvablePolynomialRing)) {
return false;
}
GenSolvablePolynomialRing oring = null;
try {
oring = (GenSolvablePolynomialRing) 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)) {
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();
return h;
}
/**
* Get the zero element.
* @return 0 as GenSolvablePolynomial.
*/
@Override
public GenSolvablePolynomial getZERO() {
return ZERO;
}
/**
* Get the one element.
* @return 1 as GenSolvablePolynomial.
*/
@Override
public GenSolvablePolynomial getONE() {
return ONE;
}
/**
* Query if this ring is commutative.
* @return true if this ring is commutative, else false.
*/
@Override
public boolean isCommutative() {
if (table.isEmpty()) {
return super.isCommutative();
}
return false;
}
/**
* Query if this ring is associative. Test if the relations define an
* associative solvable ring.
* @return true, if this ring is associative, else false.
*/
@Override
public boolean isAssociative() {
GenSolvablePolynomial Xi, Xj, Xk, p, q;
for (int i = 0; i < nvar; i++) {
Xi = univariate(i);
for (int j = i + 1; j < nvar; j++) {
Xj = univariate(j);
for (int k = j + 1; k < nvar; k++) {
Xk = univariate(k);
p = Xk.multiply(Xj).multiply(Xi);
q = Xk.multiply(Xj.multiply(Xi));
if (!p.equals(q)) {
if (true||debug) {
logger.info("Xi = " + Xi + ", Xj = " + Xj + ", Xk = " + Xk);
logger.info("p = ( Xk * Xj ) * Xi = " + p);
logger.info("q = Xk * ( Xj * Xi ) = " + q);
}
return false;
}
}
}
}
return coFac.isAssociative();
}
/**
* Get a (constant) GenSolvablePolynomial<C> element from a long
* value.
* @param a long.
* @return a GenSolvablePolynomial<C>.
*/
@Override
public GenSolvablePolynomial fromInteger(long a) {
return new GenSolvablePolynomial(this, coFac.fromInteger(a), evzero);
}
/**
* Get a (constant) GenSolvablePolynomial<C> element from a BigInteger
* value.
* @param a BigInteger.
* @return a GenSolvablePolynomial<C>.
*/
@Override
public GenSolvablePolynomial fromInteger(BigInteger a) {
return new GenSolvablePolynomial(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 GenSolvablePolynomial 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 GenSolvablePolynomial 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 GenSolvablePolynomial 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 GenSolvablePolynomial random(int k, int l, int d, float q, Random rnd) {
GenSolvablePolynomial r = getZERO(); //.clone();
// copy( ZERO );
// new GenPolynomial( this, getZERO().val );
ExpVector e;
C 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 = (GenSolvablePolynomial) r.sum(a, e);
// somewhat inefficient but clean
}
return r;
}
/**
* Copy polynomial c.
* @param c
* @return a copy of c.
*/
public GenSolvablePolynomial copy(GenSolvablePolynomial c) {
return new GenSolvablePolynomial(this, c.val);
}
/**
* Parse a solvable polynomial with the use of GenPolynomialTokenizer
* @param s String.
* @return GenSolvablePolynomial from s.
*/
@Override
public GenSolvablePolynomial parse(String s) {
//return getZERO();
return parse(new StringReader(s));
}
/**
* Parse a solvable polynomial with the use of GenPolynomialTokenizer
* @param r Reader.
* @return next GenSolvablePolynomial from r.
*/
@Override
@SuppressWarnings("unchecked")
public GenSolvablePolynomial parse(Reader r) {
GenPolynomialTokenizer pt = new GenPolynomialTokenizer(this, r);
GenSolvablePolynomial p = null;
try {
p = (GenSolvablePolynomial) pt.nextSolvablePolynomial();
} 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 GenSolvablePolynomial univariate(int i) {
return (GenSolvablePolynomial) 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 GenSolvablePolynomial univariate(int i, long e) {
return (GenSolvablePolynomial) 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 GenSolvablePolynomial univariate(int modv, int i, long e) {
return (GenSolvablePolynomial) super.univariate(modv, i, e);
}
/**
* Generate list of univariate polynomials in all variables.
* @return List(X_1,...,X_n) a list of univariate polynomials.
*/
@Override
public List> univariateList() {
//return castToSolvableList( super.univariateList() );
return 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.
*/
@Override
public List> univariateList(int modv) {
return 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.
*/
@Override
public List> univariateList(int modv, long e) {
List> pols = new ArrayList>(nvar);
int nm = nvar - modv;
for (int i = 0; i < nm; i++) {
GenSolvablePolynomial p = univariate(modv, nm - 1 - i, e);
pols.add(p);
}
return pols;
}
/**
* Extend variables. Used e.g. in module embedding. Extend number of
* variables by i. New variables commute with the exiting variables.
* @param i number of variables to extend.
* @return extended solvable polynomial ring factory.
*/
@Override
public GenSolvablePolynomialRing extend(int i) {
GenPolynomialRing pfac = super.extend(i);
GenSolvablePolynomialRing spfac = new GenSolvablePolynomialRing(pfac.coFac, pfac.nvar,
pfac.tord, pfac.vars);
spfac.table.extend(this.table);
return spfac;
}
/**
* Extend variables. Used e.g. in module embedding. Extend number of
* variables by length(vn). New variables commute with the exiting variables.
* @param vn names for extended variables.
* @return extended polynomial ring factory.
*/
@Override
public GenSolvablePolynomialRing extend(String[] vn) {
GenPolynomialRing pfac = super.extend(vn);
GenSolvablePolynomialRing spfac = new GenSolvablePolynomialRing(pfac.coFac, pfac.nvar,
pfac.tord, pfac.vars);
//GenSolvablePolynomialRing spfac = new GenSolvablePolynomialRing(pfac.coFac, pfac);
spfac.table.extend(this.table);
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 GenSolvablePolynomialRing contract(int i) {
GenPolynomialRing pfac = super.contract(i);
GenSolvablePolynomialRing spfac = new GenSolvablePolynomialRing(pfac.coFac, pfac.nvar,
pfac.tord, pfac.vars);
spfac.table.contract(this.table);
return spfac;
}
/**
* Reverse variables. Used e.g. in opposite rings.
* @return solvable polynomial ring factory with reversed variables.
*/
@Override
public GenSolvablePolynomialRing 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 GenSolvablePolynomialRing reverse(boolean partial) {
GenPolynomialRing pfac = super.reverse(partial);
GenSolvablePolynomialRing spfac = new GenSolvablePolynomialRing(pfac.coFac, pfac.nvar,
pfac.tord, pfac.vars);
spfac.partial = partial;
spfac.table.reverse(this.table);
return spfac;
}
/**
* Recursive representation as polynomial ring with i main variables.
* @param i number of main variables.
* @return recursive polynomial ring factory.
*/
@Override
public GenSolvablePolynomialRing> recursive(int i) {
if (i <= 0 || i >= nvar) {
throw new IllegalArgumentException("wrong: 0 < " + i + " < " + nvar);
}
GenSolvablePolynomialRing cfac = contract(i);
//System.out.println("cvars = " + Arrays.toString(cfac.vars));
//System.out.println("vars = " + Arrays.toString(vars));
String[] v = null;
if (vars != null) {
v = new String[i];
int k = 0;
for (int j = nvar - i; j < nvar; j++) {
v[k++] = vars[j];
}
}
//System.out.println("v = " + Arrays.toString(v));
TermOrder to = tord.contract(0, i); // ??
RecSolvablePolynomialRing pfac = new RecSolvablePolynomialRing(cfac, i, to, v);
//System.out.println("pfac = " + pfac.toScript());
pfac.table.recursive(table);
pfac.coeffTable.recursive(table);
return pfac;
}
/**
* Distributive representation as polynomial with all main variables.
* @return distributive polynomial ring factory.
*/
@Override
public GenSolvablePolynomialRing distribute() {
if ( !(coFac instanceof GenPolynomialRing) ) {
return this;
}
RingFactory cf = coFac;
RingFactory> cfp = (RingFactory>) cf;
GenPolynomialRing cr = (GenPolynomialRing) cfp;
//System.out.println("cr = " + cr.toScript());
GenPolynomialRing fac;
if ( cr.vars != null ) {
fac = cr.extend(vars);
} else {
fac = cr.extend(nvar);
}
//System.out.println("fac = " + fac.toScript());
// fac could be a commutative polynomial ring, coefficient relations
GenSolvablePolynomialRing pfac
= new GenSolvablePolynomialRing(fac.coFac, fac.nvar, this.tord, fac.vars);
//System.out.println("pfac = " + pfac.toScript());
if (fac instanceof GenSolvablePolynomialRing) {
GenSolvablePolynomialRing sfac = (GenSolvablePolynomialRing) fac;
List> rlc = sfac.table.relationList();
pfac.table.addSolvRelations(rlc);
//System.out.println("pfac = " + pfac.toScript());
}
// main relations
List>> rl = (List>>) (List)
PolynomialList.castToList( table.relationList() );
List> rld = PolyUtil. distribute(pfac,rl);
pfac.table.addRelations(rld);
//System.out.println("pfac = " + pfac.toScript());
// coeffTable not avaliable here
return pfac;
}
}
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