Monomial.java

package jscl.math.polynomial;

import jscl.math.Literal;
import jscl.math.NotDivisibleException;
import jscl.math.Variable;
import jscl.math.function.Fraction;
import jscl.math.function.Pow;
import jscl.mathml.MathML;

import java.util.Iterator;

public class Monomial implements Comparable {
    public static final Ordering lexicographic = Lexicographic.ordering;
    public static final Ordering totalDegreeLexicographic = TotalDegreeLexicographic.ordering;
    public static final Ordering degreeReverseLexicographic = DegreeReverseLexicographic.ordering;
    public static final Ordering iteratorOrdering = totalDegreeLexicographic;
    final Variable unknown[];
    final Ordering ordering;
    final int element[];
    int degree;

    Monomial(Variable unknown[], Ordering ordering) {
        this(unknown.length, unknown, ordering);
    }

    Monomial(int length, Variable unknown[], Ordering ordering) {
        this.unknown = unknown;
        this.ordering = ordering;
        element = new int[length];
    }

    public static Ordering kthElimination(int k) {
        return new KthElimination(k, 1);
    }

    static Monomial factory(Variable unknown[]) {
        return factory(unknown, lexicographic);
    }

    static Monomial factory(Variable unknown[], Ordering ordering) {
        return factory(unknown, ordering, 0);
    }

    static Monomial factory(Variable unknown[], Ordering ordering, int power_size) {
        switch (power_size) {
            case Basis.POWER_8:
                return new SmallMonomial(unknown, small(ordering));
            case Basis.POWER_2:
                return new BooleanMonomial(unknown, small(ordering));
            case Basis.POWER_2_DEFINED:
                return new DefinedBooleanMonomial(unknown, small(ordering));
            default:
                return new Monomial(unknown, ordering);
        }
    }

    static Ordering small(Ordering ordering) {
        if (ordering == lexicographic) return SmallMonomial.lexicographic;
        else if (ordering == totalDegreeLexicographic) return SmallMonomial.totalDegreeLexicographic;
        else if (ordering == degreeReverseLexicographic) return SmallMonomial.degreeReverseLexicographic;
        else throw new UnsupportedOperationException();
    }

    static int variable(Variable v, Variable unknown[]) {
        int i = 0;
        for (; i < unknown.length; i++) if (unknown[i].equals(v)) break;
        return i;
    }

    public Variable[] unknown() {
        return unknown;
    }

    public Ordering ordering() {
        return ordering;
    }

    public Monomial multiply(Monomial monomial) {
        Monomial m = newinstance();
        for (int i = 0; i < unknown.length; i++) {
            m.element[i] = element[i] + monomial.element[i];
        }
        m.degree = degree + monomial.degree;
        return m;
    }

    public boolean multiple(Monomial monomial) {
        return multiple(monomial, false);
    }

    public boolean multiple(Monomial monomial, boolean strict) {
        boolean equal = true;
        for (int i = 0; i < unknown.length; i++) {
            if (element[i] < monomial.element[i]) return false;
            equal &= element[i] == monomial.element[i];
        }
        return strict ? !equal : true;
    }

    public Monomial divide(Monomial monomial) throws ArithmeticException {
        Monomial m = newinstance();
        for (int i = 0; i < unknown.length; i++) {
            int n = element[i] - monomial.element[i];
            if (n < 0) throw new NotDivisibleException();
            m.element[i] = n;
        }
        m.degree = degree - monomial.degree;
        return m;
    }

    public Monomial gcd(Monomial monomial) {
        Monomial m = newinstance();
        for (int i = 0; i < unknown.length; i++) {
            int n = Math.min(element[i], monomial.element[i]);
            m.element[i] = n;
            m.degree += n;
        }
        return m;
    }

    public Monomial scm(Monomial monomial) {
        Monomial m = newinstance();
        for (int i = 0; i < unknown.length; i++) {
            int n = Math.max(element[i], monomial.element[i]);
            m.element[i] = n;
            m.degree += n;
        }
        return m;
    }

    public int degree() {
        return degree;
    }

    public Monomial valueof(Monomial monomial) {
        Monomial m = newinstance();
        System.arraycopy(monomial.element, 0, m.element, 0, m.element.length);
        m.degree = monomial.degree;
        return m;
    }

    public Monomial valueof(Literal literal) {
        Monomial m = newinstance();
        m.init(literal);
        return m;
    }

    public Literal literalValue() {
        return Literal.valueOf(this);
    }

    public int element(int n) {
        return element[n];
    }

    public Iterator iterator() {
        return iterator(newinstance());
    }

    public Iterator iterator(Monomial beginning) {
        return new MonomialIterator(beginning, this);
    }

    public Iterator divisor() {
        return divisor(newinstance());
    }

    public Iterator divisor(Monomial beginning) {
        return new MonomialDivisor(beginning, this);
    }

    public int compareTo(Monomial monomial) {
        return ordering.compare(this, monomial);
    }

    public int compareTo(Object o) {
        return compareTo((Monomial) o);
    }

    void init(Literal literal) {
        int s = literal.size();
        for (int i = 0; i < s; i++) {
            Variable v = literal.getVariable(i);
            int c = literal.getPower(i);
            int n = variable(v, unknown);
            if (n < unknown.length) put(n, c);
        }
    }

    void put(int n, int integer) {
        element[n] += integer;
        degree += integer;
    }

    public String toString() {
        StringBuffer buffer = new StringBuffer();
        if (degree == 0) buffer.append("1");
        boolean b = false;
        for (int i = 0; i < unknown.length; i++) {
            int c = element(i);
            if (c > 0) {
                if (b) buffer.append("*");
                else b = true;
                Variable v = unknown[i];
                if (c == 1) buffer.append(v);
                else {
                    if (v instanceof Fraction || v instanceof Pow) {
                        buffer.append("(").append(v).append(")");
                    } else buffer.append(v);
                    buffer.append("^").append(c);
                }
            }
        }
        return buffer.toString();
    }

    public void toMathML(MathML element, Object data) {
        if (degree == 0) {
            MathML e1 = element.element("mn");
            e1.appendChild(element.text("1"));
            element.appendChild(e1);
        }
        for (int i = 0; i < unknown.length; i++) {
            int c = element(i);
            if (c > 0) {
                unknown[i].toMathML(element, new Integer(c));
            }
        }
    }

    protected Monomial newinstance() {
        return new Monomial(element.length, unknown, ordering);
    }
}

class MonomialIterator implements Iterator {
    static final Ordering ordering = Monomial.iteratorOrdering;
    Monomial monomial;
    Monomial current;
    boolean carry;

    MonomialIterator(Monomial beginning, Monomial monomial) {
        this.monomial = monomial;
        current = monomial.valueof(beginning);
        if (ordering.compare(current, monomial) > 0) carry = true;
    }

    public boolean hasNext() {
        return !carry;
    }

    public Object next() {
        Monomial m = monomial.valueof(current);
        if (ordering.compare(current, monomial) < 0) increment();
        else carry = true;
        return m;
    }

    void increment() {
        int s = 0;
        int n = 0;
        while (n < current.element.length && current.element[n] == 0) n++;
        if (n < current.element.length) {
            s = current.element[n];
            current.element[n] = 0;
            n++;
        }
        if (n < current.element.length) {
            current.element[n]++;
            fill(s - 1);
        } else {
            current.degree++;
            fill(s + 1);
        }
    }

    private void fill(int s) {
        current.element[0] = s;
    }

    public void remove() {
        throw new UnsupportedOperationException();
    }
}

class MonomialDivisor extends MonomialIterator {
    MonomialDivisor(Monomial beginning, Monomial monomial) {
        super(beginning, monomial);
        if (hasNext()) seek();
    }

    void seek() {
        int n = current.element.length;
        while (n > 0) {
            n--;
            if (current.element[n] > monomial.element[n]) break;
        }
        int p = n;
        while (n > 0) {
            n--;
            current.element[p] += current.element[n];
            current.element[n] = 0;
        }
        if (p < current.element.length && current.element[p] > monomial.element[p]) increment();
    }

    void increment() {
        int s = 0;
        int n = 0;
        while (n < current.element.length && current.element[n] == 0) n++;
        if (n < current.element.length) {
            s = current.element[n];
            current.element[n] = 0;
            n++;
        }
        while (n < current.element.length && current.element[n] == monomial.element[n]) {
            s += current.element[n];
            current.element[n] = 0;
            n++;
        }
        if (n < current.element.length) {
            current.element[n]++;
            fill(s - 1);
        } else {
            current.degree++;
            fill(s + 1);
        }
    }

    private void fill(int s) {
        for (int i = 0; i < current.element.length; i++) {
            int d = Math.min(monomial.element[i] - current.element[i], s);
            current.element[i] += d;
            s -= d;
        }
    }
}

class Lexicographic extends Ordering {
    public static final Ordering ordering = new Lexicographic();

    Lexicographic() {
    }

    public int compare(Monomial m1, Monomial m2) {
        int c1[] = m1.element;
        int c2[] = m2.element;
        int n = c1.length;
        for (int i = n - 1; i >= 0; i--) {
            if (c1[i] < c2[i]) return -1;
            else if (c1[i] > c2[i]) return 1;
        }
        return 0;
    }
}

class TotalDegreeLexicographic extends Lexicographic implements DegreeOrdering {
    public static final Ordering ordering = new TotalDegreeLexicographic();

    TotalDegreeLexicographic() {
    }

    public int compare(Monomial m1, Monomial m2) {
        if (m1.degree < m2.degree) return -1;
        else if (m1.degree > m2.degree) return 1;
        else return super.compare(m1, m2);
    }
}

class DegreeReverseLexicographic extends Ordering implements DegreeOrdering {
    public static final Ordering ordering = new DegreeReverseLexicographic();

    DegreeReverseLexicographic() {
    }

    public int compare(Monomial m1, Monomial m2) {
        if (m1.degree < m2.degree) return -1;
        else if (m1.degree > m2.degree) return 1;
        else {
            int c1[] = m1.element;
            int c2[] = m2.element;
            int n = c1.length;
            for (int i = 0; i < n; i++) {
                if (c1[i] > c2[i]) return -1;
                else if (c1[i] < c2[i]) return 1;
            }
            return 0;
        }
    }
}

class KthElimination extends Ordering {
    final int k;

    KthElimination(int k, int direction) {
        this.k = k;
    }

    public int compare(Monomial m1, Monomial m2) {
        int c1[] = m1.element;
        int c2[] = m2.element;
        int n = c1.length;
        int k = n - this.k;
        for (int i = n - 1; i >= k; i--) {
            if (c1[i] < c2[i]) return -1;
            else if (c1[i] > c2[i]) return 1;
        }
        return DegreeReverseLexicographic.ordering.compare(m1, m2);
    }
}