Ejemplo n.º 1
0
 static Polynomial polynomial(Polynomial s, Monomial monomial[]) {
   Polynomial p = s.valueOf(JsclInteger.valueOf(0));
   Iterator it = monomial[1].iterator(monomial[0]);
   for (int i = 0; it.hasNext(); i++) {
     Monomial m = (Monomial) it.next();
     Variable t =
         it.hasNext() ? new TechnicalVariable(ter, new int[] {i}) : new TechnicalVariable(ter);
     p = p.add(p.valueOf(m).multiply(t.expressionValue()));
   }
   return p;
 }
Ejemplo n.º 2
0
 public static Generic compute(Generic generic) {
   try {
     return GenericVariable.content(factorize(generic.integerValue()));
   } catch (NotIntegerException e) {
     Factorization f =
         new Factorization(Polynomial.factory(generic.variables(), Monomial.iteratorOrdering, -1));
     f.computeValue(generic);
     return f.getValue();
   }
 }
Ejemplo n.º 3
0
 static Polynomial[] remainder(Polynomial s, Polynomial p, Generic t[]) {
   Polynomial zero = s.valueOf(JsclInteger.valueOf(0));
   Generic a[] = Basis.augment(t, s.remainderUpToCoefficient(p).elements());
   Variable unk[] = Basis.augmentUnknown(new Variable[] {}, p.elements());
   {
     Variable u = unk[unk.length - 1];
     System.arraycopy(unk, 0, unk, 1, unk.length - 1);
     unk[0] = u;
   }
   Generic be[][] =
       Linearization.compute(
           Basis.compute(a, unk, Monomial.lexicographic, 0, Basis.DEGREE).elements(), unk);
   for (int i = 0; i < be.length; i++) {
     Polynomial r = substitute(p, be[i], unk);
     try {
       return new Polynomial[] {zero, r, s.divide(r)};
     } catch (NotDivisibleException e) {
     }
   }
   return new Polynomial[] {s, zero, zero};
 }
Ejemplo n.º 4
0
 void process(Generic generic[]) {
   boolean flag = true;
   for (int i = 0; i < generic.length; i++) {
     Generic s = generic[i];
     Variable va[] = s.variables();
     if (va.length == 1) {
       Variable t = va[0];
       Polynomial p = Polynomial.factory(t).valueOf(s);
       if (p.degree() > 1) {
         flag = false;
         Polynomial r[] = linearize(p, t);
         for (int j = 0; j < r.length; j++) {
           process(
               Basis.compute(Basis.augment(new Generic[] {r[j].genericValue()}, generic), unknown)
                   .elements());
         }
       }
     } else flag = false;
   }
   if (flag) result.add(generic);
 }
Ejemplo n.º 5
0
 void computeValue(Generic generic) {
   Debug.println("factorization");
   Polynomial n[] = factory.valueOf(generic).gcdAndNormalize();
   Monomial m = n[1].monomialGcd();
   Polynomial s = n[1].divide(m);
   Generic a = JsclInteger.valueOf(1);
   Divisor d[] = new Divisor[2];
   Monomial p[] = new Monomial[2];
   Monomial q[] = new Monomial[2];
   d[1] = new Divisor(s.head().monomial());
   loop:
   while (d[1].hasNext()) {
     p[1] = (Monomial) d[1].next();
     q[1] = d[1].complementary();
     d[0] = new Divisor(s.tail().monomial());
     while (d[0].hasNext()) {
       p[0] = (Monomial) d[0].next();
       q[0] = d[0].complementary();
       if (p[1].compareTo(p[0]) <= 0) continue loop;
       Debug.println(toString(p) + " * " + toString(q) + " = " + s);
       if (ArrayComparator.comparator.compare(q, p) < 0) {
         a = a.multiply(expression(s.genericValue()));
         break loop;
       } else {
         Debug.increment();
         Polynomial r[] = remainder(s, polynomial(s, p), terminator(s));
         Debug.decrement();
         if (r[0].signum() == 0) {
           a = a.multiply(expression(r[1].genericValue()));
           s = r[2];
           d[1].divide();
           d[0].divide();
           continue loop;
         }
       }
     }
   }
   result = a.multiply(n[0].multiply(m).genericValue());
 }
Ejemplo n.º 6
0
 static Polynomial[] linearize(Polynomial polynomial, Variable variable) {
   List l = new ArrayList();
   Generic x = variable.expressionValue();
   Polynomial s = polynomial;
   try {
     Polynomial r = s.valueOf(x);
     s = s.divide(r);
     l.add(r);
     while (true) s = s.divide(r);
   } catch (NotDivisibleException e) {
   }
   IntegerDivisor d[] = new IntegerDivisor[2];
   Generic p[] = new Generic[2];
   Generic q[] = new Generic[2];
   d[1] = IntegerDivisor.create(JsclInteger.valueOf(1));
   loop:
   while (d[1].hasNext()) {
     p[1] = (Generic) d[1].next();
     q[1] = d[1].integer(d[1].complementary());
     d[0] = IntegerDivisor.create(s.tail().coef().integerValue());
     while (d[0].hasNext()) {
       p[0] = (Generic) d[0].next();
       q[0] = d[0].integer(d[0].complementary());
       if (ArrayComparator.comparator.compare(q, p) < 0) break loop;
       for (int i = 0; i < 2; i++) {
         Polynomial r =
             s.valueOf(i == 0 ? p[1].multiply(x).subtract(p[0]) : p[1].multiply(x).add(p[0]));
         for (boolean flag = true; true; flag = false) {
           try {
             s = s.divide(r);
           } catch (NotDivisibleException e) {
             break;
           }
           d[1].divide();
           d[0].divide();
           if (flag) l.add(r);
         }
       }
     }
   }
   return (Polynomial[]) ArrayUtils.toArray(l, new Polynomial[l.size()]);
 }
Ejemplo n.º 7
0
 static Generic[] terminator(Polynomial polynomial) {
   Generic t[] = new Generic[2];
   t[1] = terminator(polynomial.head().coef().abs(), new TechnicalVariable(ter), false);
   t[0] = terminator(polynomial.tail().coef(), new TechnicalVariable(ter, new int[] {0}), true);
   return t;
 }
Ejemplo n.º 8
0
 static Polynomial substitute(Polynomial p, Generic a[], Variable unk[]) {
   Generic s[] = new Generic[] {p.genericValue()};
   return p.valueOf(
       Basis.compute(Basis.augment(a, s), Basis.augmentUnknown(unk, s)).elements()[0]);
 }
Ejemplo n.º 9
0
 IntegerDivisor(Generic generic, Variable unknown[], Ordering ordering) {
   super(Polynomial.factory(unknown, ordering).valueOf(generic).head().monomial());
 }