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/*
* $Id: Residue.java 4407 2013-04-30 10:34:27Z kredel $
*/
package edu.jas.application;
import edu.jas.kern.PrettyPrint;
import edu.jas.poly.GenPolynomial;
import edu.jas.poly.PolyUtil;
import edu.jas.structure.GcdRingElem;
/**
* Residue ring element based on GenPolynomial with RingElem interface. Objects
* of this class are (nearly) immutable.
* @author Heinz Kredel
*/
public class Residue> implements GcdRingElem> {
/**
* Residue class factory data structure.
*/
public final ResidueRing ring;
/**
* Value part of the element data structure.
*/
public final GenPolynomial val;
/**
* Flag to remember if this residue element is a unit. -1 is unknown, 1 is
* unit, 0 not a unit.
*/
protected int isunit = -1; // initially unknown
/**
* The constructor creates a Residue object from a ring factory.
* @param r residue ring factory.
*/
public Residue(ResidueRing r) {
this(r, r.ring.getZERO(), 0);
}
/**
* The constructor creates a Residue object from a ring factory and a
* polynomial.
* @param r residue ring factory.
* @param a polynomial.
*/
public Residue(ResidueRing r, GenPolynomial a) {
this(r, a, -1);
}
/**
* The constructor creates a Residue object from a ring factory, a
* polynomial and an indicator if a is a unit.
* @param r residue ring factory.
* @param a polynomial.
* @param u isunit indicator, -1, 0, 1.
*/
public Residue(ResidueRing r, GenPolynomial a, int u) {
ring = r;
val = ring.ideal.normalform(a); //.monic() no go
if ( u == 0 || u == 1 ) {
isunit = u;
return;
}
if (val.isZERO()) {
isunit = 0;
return;
}
if ( val.isUnit() ) {
isunit = 1;
//} else { // not possible
//isunit = 0;
}
isunit = -1;
}
/**
* Get the corresponding element factory.
* @return factory for this Element.
* @see edu.jas.structure.Element#factory()
*/
public ResidueRing factory() {
return ring;
}
/**
* Clone this.
* @see java.lang.Object#clone()
*/
@Override
public Residue copy() {
return new Residue(ring, val, isunit);
}
/**
* Is Residue zero.
* @return If this is 0 then true is returned, else false.
* @see edu.jas.structure.RingElem#isZERO()
*/
public boolean isZERO() {
return val.isZERO();
}
/**
* Is Residue one.
* @return If this is 1 then true is returned, else false.
* @see edu.jas.structure.RingElem#isONE()
*/
public boolean isONE() {
return val.isONE();
}
/**
* Is Residue unit.
* @return If this is a unit then true is returned, else false.
* @see edu.jas.structure.RingElem#isUnit()
*/
public boolean isUnit() {
if (isunit > 0) {
return true;
}
if (isunit == 0) {
return false;
}
// not jet known
boolean u = ring.ideal.isUnit(val);
if (u) {
isunit = 1;
} else {
isunit = 0;
}
return (u);
}
/**
* Is Residue a constant.
* @return true if this.val is a constant polynomial, else false.
*/
public boolean isConstant() {
return val.isConstant();
}
/**
* Get the String representation as RingElem.
* @see java.lang.Object#toString()
*/
@Override
public String toString() {
if (PrettyPrint.isTrue()) {
return val.toString(ring.ring.getVars());
}
return "Residue[ " + val.toString() + " mod " + ring.toString() + " ]";
}
/**
* Get a scripting compatible string representation.
* @return script compatible representation for this Element.
* @see edu.jas.structure.Element#toScript()
*/
//JAVA6only: @Override
public String toScript() {
// Python case
return val.toScript();
// return "PolyResidue( " + val.toScript()
// + ", " + ring.toScript() + " )";
}
/**
* Get a scripting compatible string representation of the factory.
* @return script compatible representation for this ElemFactory.
* @see edu.jas.structure.Element#toScriptFactory()
*/
//JAVA6only: @Override
public String toScriptFactory() {
// Python case
return factory().toScript();
}
/**
* Residue comparison.
* @param b Residue.
* @return sign(this-b), 0 means that this and b are equivalent in this
* residue class ring.
*/
//JAVA6only: @Override
public int compareTo(Residue b) {
GenPolynomial v = b.val;
if (!ring.equals(b.ring)) {
v = ring.ideal.normalform(v);
}
return val.compareTo(v);
}
/**
* Comparison with any other object.
* @see java.lang.Object#equals(java.lang.Object)
* @return true means that this and b are equivalent in this residue class
* ring.
*/
@Override
@SuppressWarnings("unchecked")
public boolean equals(Object b) {
if (!(b instanceof Residue)) {
return false;
}
Residue a = null;
try {
a = (Residue) b;
} catch (ClassCastException e) {
}
if (a == null) {
return false;
}
return compareTo(a) == 0;
}
/**
* Hash code for this residue.
* @see java.lang.Object#hashCode()
*/
@Override
public int hashCode() {
int h;
h = ring.hashCode();
h = 37 * h + val.hashCode();
return h;
}
/**
* Residue absolute value.
* @return the absolute value of this.
* @see edu.jas.structure.RingElem#abs()
*/
public Residue abs() {
return new Residue(ring, val.abs(), isunit);
}
/**
* Residue summation.
* @param S Residue.
* @return this+S.
*/
public Residue sum(Residue S) {
return new Residue(ring, val.sum(S.val));
}
/**
* Residue negate.
* @return -this.
* @see edu.jas.structure.RingElem#negate()
*/
public Residue negate() {
return new Residue(ring, val.negate(), isunit);
}
/**
* Residue signum.
* @see edu.jas.structure.RingElem#signum()
* @return signum(this).
*/
public int signum() {
return val.signum();
}
/**
* Residue subtraction.
* @param S Residue.
* @return this-S.
*/
public Residue subtract(Residue S) {
return new Residue(ring, val.subtract(S.val));
}
/**
* Residue division.
* @param S Residue.
* @return this/S.
*/
public Residue divide(Residue S) {
if (ring.isField()) {
return multiply(S.inverse());
}
GenPolynomial x = PolyUtil. basePseudoDivide(val, S.val);
return new Residue(ring, x);
}
/**
* Residue inverse.
* @see edu.jas.structure.RingElem#inverse()
* @return S with S = 1/this if defined.
*/
public Residue inverse() {
GenPolynomial x = ring.ideal.inverse(val);
return new Residue(ring, x, 1);
}
/**
* Residue remainder.
* @param S Residue.
* @return this - (this/S)*S.
*/
public Residue remainder(Residue S) {
//GenPolynomial x = val.remainder( S.val );
GenPolynomial x = PolyUtil. baseSparsePseudoRemainder(val, S.val);
return new Residue(ring, x);
}
/**
* Residue multiplication.
* @param S Residue.
* @return this*S.
*/
public Residue multiply(Residue S) {
GenPolynomial x = val.multiply(S.val);
int i = -1;
if (isunit == 1 && S.isunit == 1) {
i = 1;
} else if (isunit == 0 || S.isunit == 0) {
i = 0;
}
return new Residue(ring, x, i);
}
/**
* Residue monic.
* @return this with monic value part.
*/
public Residue monic() {
return new Residue(ring, val.monic(), isunit);
}
/**
* Greatest common divisor.
* @param b other element.
* @return gcd(this,b).
*/
public Residue gcd(Residue b) {
GenPolynomial x = ring.engine.gcd(val, b.val);
int i = -1; // gcd might become a unit
if (x.isONE()) {
i = 1;
} else {
System.out.println("Residue gcd = " + x);
}
if (isunit == 1 && b.isunit == 1) {
i = 1;
}
return new Residue(ring, x, i);
}
/**
* Extended greatest common divisor. Note: Not implemented, throws
* UnsupportedOperationException.
* @param b other element.
* @return [ gcd(this,b), c1, c2 ] with c1*this + c2*b = gcd(this,b).
*/
public Residue[] egcd(Residue b) {
throw new UnsupportedOperationException("egcd not implemented");
}
}
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