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/*
* $Id: Product.java 4125 2012-08-19 19:05:22Z kredel $
*/
package edu.jas.arith;
import java.util.Iterator;
import java.util.Map;
import java.util.SortedMap;
import java.util.TreeMap;
import org.apache.log4j.Logger;
import edu.jas.structure.NotInvertibleException;
import edu.jas.structure.RegularRingElem;
import edu.jas.structure.RingElem;
import edu.jas.structure.RingFactory;
/**
* Direct product element based on RingElem. Objects of this class are (nearly)
* immutable.
* @author Heinz Kredel
*/
public class Product> implements RegularRingElem> {
private static final Logger logger = Logger.getLogger(Product.class);
//private final boolean debug = logger.isDebugEnabled();
/**
* Product class factory data structure.
*/
public final ProductRing ring;
/**
* Value part of the element data structure.
*/
public final SortedMap val;
/**
* Flag to remember if this product element is a unit in each cmponent. -1
* is unknown, 1 is unit, 0 not a unit.
*/
protected int isunit = -1; // initially unknown
/**
* The constructor creates a Product object from a ring factory.
* @param r ring factory.
*/
public Product(ProductRing r) {
this(r, new TreeMap(), 0);
}
/**
* The constructor creates a Product object from a ring factory and a ring
* element.
* @param r ring factory.
* @param a ring element.
*/
public Product(ProductRing r, SortedMap a) {
this(r, a, -1);
}
/**
* The constructor creates a Product object from a ring factory, a ring
* element and an indicator if a is a unit.
* @param r ring factory.
* @param a ring element.
* @param u isunit indicator, -1, 0, 1.
*/
public Product(ProductRing r, SortedMap a, int u) {
ring = r;
val = a;
isunit = u;
}
/**
* Get component.
* @param i index of component.
* @return val(i).
*/
public C get(int i) {
return val.get(i); // auto-boxing
}
/**
* Get the corresponding element factory.
* @return factory for this Element.
* @see edu.jas.structure.Element#factory()
*/
public ProductRing factory() {
return ring;
}
/**
* Clone this.
* @see java.lang.Object#clone()
*/
@Override
public Product copy() {
return new Product(ring, val, isunit);
}
/**
* Is Product zero.
* @return If this is 0 then true is returned, else false.
* @see edu.jas.structure.RingElem#isZERO()
*/
public boolean isZERO() {
return val.size() == 0;
}
/**
* Is Product one.
* @return If this is 1 then true is returned, else false.
* @see edu.jas.structure.RingElem#isONE()
*/
public boolean isONE() {
if (val.size() != ring.length()) {
return false;
}
for (C e : val.values()) {
if (!e.isONE()) {
return false;
}
}
return true;
}
/**
* Is Product full.
* @return If every component is non-zero, then true is returned, else
* false.
*/
public boolean isFull() {
if (val.size() != ring.length()) {
return false;
}
return true;
}
/**
* Is Product 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;
}
if (isZERO()) {
isunit = 0;
return false;
}
for (C e : val.values()) {
if (!e.isUnit()) {
isunit = 0;
return false;
}
}
isunit = 1;
return true;
}
/**
* Is Product idempotent.
* @return If this is a idempotent element then true is returned, else
* false.
*/
public boolean isIdempotent() {
for (C e : val.values()) {
if (!e.isONE()) {
return false;
}
}
return true;
}
/**
* Get the String representation as RingElem.
* @see java.lang.Object#toString()
*/
@Override
public String toString() {
return val.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
StringBuffer s = new StringBuffer("( ");
boolean first = true;
for (Integer i : val.keySet()) {
C v = val.get(i);
if (first) {
first = false;
} else {
if (v.signum() < 0) {
s.append(" - ");
v = v.negate();
} else {
s.append(" + ");
}
}
if (!v.isONE()) {
s.append(v.toScript() + "*");
}
s.append("pg" + i);
}
s.append(" )");
return s.toString();
}
/**
* 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();
}
/**
* Product comparison.
* @param b Product.
* @return sign(this-b).
*/
//JAVA6only: @Override
public int compareTo(Product b) {
if (!ring.equals(b.ring)) {
logger.info("other ring " + b.ring);
throw new IllegalArgumentException("rings not comparable " + this);
}
SortedMap v = b.val;
Iterator> ti = val.entrySet().iterator();
Iterator> bi = v.entrySet().iterator();
int s;
while (ti.hasNext() && bi.hasNext()) {
Map.Entry te = ti.next();
Map.Entry be = bi.next();
s = te.getKey().compareTo(be.getKey());
if (s != 0) {
return s;
}
s = te.getValue().compareTo(be.getValue());
if (s != 0) {
return s;
}
}
if (ti.hasNext()) {
return -1;
}
if (bi.hasNext()) {
return 1;
}
return 0;
}
/**
* Comparison with any other object.
* @see java.lang.Object#equals(java.lang.Object)
*/
@SuppressWarnings("unchecked")
@Override
public boolean equals(Object b) {
if (!(b instanceof Product)) {
return false;
}
Product a = null;
try {
a = (Product) b;
} catch (ClassCastException e) {
}
if (a == null) {
return false;
}
return (0 == compareTo(a));
}
/**
* Hash code for this local.
* @see java.lang.Object#hashCode()
*/
@Override
public int hashCode() {
int h = ring.hashCode();
h = 37 * h + val.hashCode();
return h;
}
/**
* Product extend. Add new component j with value of component i.
* @param i from index.
* @param j to index.
* @return the extended value of this.
*/
public Product extend(int i, int j) {
RingFactory rf = ring.getFactory(j);
SortedMap elem = new TreeMap(val);
C v = val.get(i);
C w = rf.copy(v); // valueOf
if (!w.isZERO()) {
elem.put(j, w);
}
return new Product(ring, elem, isunit);
}
/**
* Product absolute value.
* @return the absolute value of this.
* @see edu.jas.structure.RingElem#abs()
*/
public Product abs() {
SortedMap elem = new TreeMap();
for (Integer i : val.keySet()) {
C v = val.get(i).abs();
elem.put(i, v);
}
return new Product(ring, elem, isunit);
}
/**
* Product summation.
* @param S Product.
* @return this+S.
*/
public Product sum(Product S) {
if (S == null || S.isZERO()) {
return this;
}
if (this.isZERO()) {
return S;
}
SortedMap elem = new TreeMap(val); // clone
SortedMap sel = S.val;
for (Map.Entry is : sel.entrySet()) {
Integer i = is.getKey();
C x = elem.get(i);
C y = is.getValue(); //sel.get( i ); // assert y != null
if (x != null) {
x = x.sum(y);
if (!x.isZERO()) {
elem.put(i, x);
} else {
elem.remove(i);
}
} else {
elem.put(i, y);
}
}
return new Product(ring, elem);
}
/**
* Product negate.
* @return -this.
* @see edu.jas.structure.RingElem#negate()
*/
public Product negate() {
SortedMap elem = new TreeMap();
for (Integer i : val.keySet()) {
C v = val.get(i).negate();
elem.put(i, v);
}
return new Product(ring, elem, isunit);
}
/**
* Product signum.
* @see edu.jas.structure.RingElem#signum()
* @return signum of first non-zero component.
*/
public int signum() {
if (val.size() == 0) {
return 0;
}
C v = val.get(val.firstKey());
return v.signum();
}
/**
* Product subtraction.
* @param S Product.
* @return this-S.
*/
public Product subtract(Product S) {
return sum(S.negate());
}
/**
* Product quasi-inverse.
* @see edu.jas.structure.RingElem#inverse()
* @return S with S = 1/this if defined.
*/
public Product inverse() {
if (this.isZERO()) {
return this;
}
int isu = 0;
SortedMap elem = new TreeMap();
for (Integer i : val.keySet()) {
C x = val.get(i); // is non zero
try {
x = x.inverse();
} catch (NotInvertibleException e) {
// could happen for e.g. ModInteger or AlgebraicNumber
x = null; //ring.getFactory(i).getZERO();
}
if (x != null && !x.isZERO()) { // can happen
elem.put(i, x);
isu = 1;
}
}
return new Product(ring, elem, isu);
}
/**
* Product idempotent.
* @return smallest S with this*S = this.
*/
public Product idempotent() {
if (this.isZERO()) {
return this;
}
SortedMap elem = new TreeMap();
for (Integer i : val.keySet()) {
RingFactory f = ring.getFactory(i);
C x = f.getONE();
elem.put(i, x);
}
return new Product(ring, elem, 1);
}
/**
* Product idempotent complement.
* @return 1-this.idempotent().
*/
public Product idemComplement() {
if (this.isZERO()) {
return ring.getONE();
}
int isu = 0;
SortedMap elem = new TreeMap();
for (int i = 0; i < ring.length(); i++) {
C v = val.get(i);
if (v == null) {
RingFactory f = ring.getFactory(i);
C x = f.getONE();
elem.put(i, x);
isu = 1;
}
}
return new Product(ring, elem, isu);
}
/**
* Product idempotent and.
* @param S Product.
* @return this.idempotent() and S.idempotent().
*/
public Product idempotentAnd(Product S) {
if (this.isZERO() && S.isZERO()) {
return this;
}
int isu = 0;
SortedMap elem = new TreeMap();
for (int i = 0; i < ring.length(); i++) {
C v = val.get(i);
C w = S.val.get(i);
if (v != null && w != null) {
RingFactory f = ring.getFactory(i);
C x = f.getONE();
elem.put(i, x);
isu = 1;
}
}
return new Product(ring, elem, isu);
}
/**
* Product idempotent or.
* @param S Product.
* @return this.idempotent() or S.idempotent().
*/
public Product idempotentOr(Product S) {
if (this.isZERO() && S.isZERO()) {
return this;
}
int isu = 0;
SortedMap elem = new TreeMap();
for (int i = 0; i < ring.length(); i++) {
C v = val.get(i);
C w = S.val.get(i);
if (v != null || w != null) {
RingFactory f = ring.getFactory(i);
C x = f.getONE();
elem.put(i, x);
isu = 1;
}
}
return new Product(ring, elem, isu);
}
/**
* Product fill with idempotent.
* @param S Product.
* @return fill this with S.idempotent().
*/
public Product fillIdempotent(Product S) {
if (S.isZERO()) {
return this;
}
SortedMap elem = new TreeMap(val);
for (int i = 0; i < ring.length(); i++) {
C v = elem.get(i);
if (v != null) {
continue;
}
C w = S.val.get(i);
if (w != null) {
RingFactory f = ring.getFactory(i);
C x = f.getONE();
elem.put(i, x);
}
}
return new Product(ring, elem, isunit);
}
/**
* Product fill with one.
* @return fill this with one.
*/
public Product fillOne() {
if (this.isFull()) {
return this;
}
if (this.isZERO()) {
return ring.getONE();
}
SortedMap elem = new TreeMap(val);
for (int i = 0; i < ring.length(); i++) {
C v = elem.get(i);
if (v != null) {
continue;
}
RingFactory f = ring.getFactory(i);
C x = f.getONE();
elem.put(i, x);
}
return new Product(ring, elem, isunit);
}
/**
* Product quasi-division.
* @param S Product.
* @return this/S.
*/
public Product divide(Product S) {
if (S == null) {
return ring.getZERO();
}
if (S.isZERO()) {
return S;
}
if (this.isZERO()) {
return this;
}
SortedMap elem = new TreeMap();
SortedMap sel = S.val;
for (Integer i : val.keySet()) {
C y = sel.get(i);
if (y != null) {
C x = val.get(i);
try {
x = x.divide(y);
} catch (NotInvertibleException e) {
// should not happen any more
System.out.println("product divide error: x = " + x + ", y = " + y);
// could happen for e.g. ModInteger or AlgebraicNumber
x = null; //ring.getFactory(i).getZERO();
}
if (x != null && !x.isZERO()) { // can happen
elem.put(i, x);
}
}
}
return new Product(ring, elem);
}
/**
* Product quasi-remainder.
* @param S Product.
* @return this - (this/S)*S.
*/
public Product remainder(Product S) {
if (S == null) {
return this; //ring.getZERO();
}
if (S.isZERO()) {
return this;
}
if (this.isZERO()) {
return this;
}
SortedMap elem = new TreeMap();
SortedMap sel = S.val;
for (Integer i : val.keySet()) {
C y = sel.get(i);
if (y != null) {
C x = val.get(i);
x = x.remainder(y);
if (x != null && !x.isZERO()) { // can happen
elem.put(i, x);
}
}
}
return new Product(ring, elem);
}
/**
* Product multiplication.
* @param S Product.
* @return this*S.
*/
public Product multiply(Product S) {
if (S == null) {
return ring.getZERO();
}
if (S.isZERO()) {
return S;
}
if (this.isZERO()) {
return this;
}
SortedMap elem = new TreeMap();
SortedMap sel = S.val;
for (Integer i : val.keySet()) {
C y = sel.get(i);
if (y != null) {
C x = val.get(i);
x = x.multiply(y);
if (x != null && !x.isZERO()) {
elem.put(i, x);
}
}
}
return new Product(ring, elem);
}
/**
* Product multiply by coefficient.
* @param c coefficient.
* @return this*c.
*/
public Product multiply(C c) {
SortedMap elem = new TreeMap();
for (Integer i : val.keySet()) {
C v = val.get(i).multiply(c);
if (v != null && !v.isZERO()) {
elem.put(i, v);
}
}
return new Product(ring, elem);
}
/**
* Greatest common divisor.
* @param S other element.
* @return gcd(this,S).
*/
public Product gcd(Product S) {
if (S == null || S.isZERO()) {
return this;
}
if (this.isZERO()) {
return S;
}
SortedMap elem = new TreeMap(val); // clone
SortedMap sel = S.val;
for (Map.Entry is : sel.entrySet()) {
Integer i = is.getKey();
C x = elem.get(i);
C y = is.getValue(); //sel.get( i ); // assert y != null
if (x != null) {
x = x.gcd(y);
if (x != null && !x.isZERO()) {
elem.put(i, x);
} else {
elem.remove(i);
}
} else {
elem.put(i, y);
}
}
return new Product(ring, elem);
}
/**
* Extended greatest common divisor.
* @param S other element.
* @return [ gcd(this,S), c1, c2 ] with c1*this + c2*b = gcd(this,S).
*/
@SuppressWarnings("unchecked")
public Product[] egcd(Product S) {
Product[] ret = (Product[]) new Product[3];
ret[0] = null;
ret[1] = null;
ret[2] = null;
if (S == null || S.isZERO()) {
ret[0] = this;
return ret;
}
if (this.isZERO()) {
ret[0] = S;
return ret;
}
SortedMap elem = new TreeMap(val); // clone
SortedMap elem1 = this.idempotent().val; // init with 1
SortedMap elem2 = new TreeMap(); // zero
SortedMap sel = S.val;
for (Map.Entry is : sel.entrySet()) {
Integer i = is.getKey();
C x = elem.get(i);
C y = is.getValue(); //sel.get( i ); // assert y != null
if (x != null) {
C[] g = x.egcd(y);
if (!g[0].isZERO()) {
elem.put(i, g[0]);
elem1.put(i, g[1]);
elem2.put(i, g[2]);
} else {
elem.remove(i);
}
} else {
elem.put(i, y);
elem2.put(i, ring.getFactory(i).getONE());
}
}
ret[0] = new Product(ring, elem);
ret[1] = new Product(ring, elem1);
ret[2] = new Product(ring, elem2);
return ret;
}
}
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