コード例 #1
0
  /** Test scalar multiplication. */
  public void testPolynomialMultiplication() {
    BigRational cfac = new BigRational(1);
    GenPolynomialRing<BigRational> pfac = new GenPolynomialRing<BigRational>(cfac, rl);

    GenVectorModul<GenPolynomial<BigRational>> mfac =
        new GenVectorModul<GenPolynomial<BigRational>>(pfac, ll);

    GenPolynomial<BigRational> r, s, t;
    GenVector<GenPolynomial<BigRational>> a, b, c, d, e;

    r = pfac.random(kl);
    // System.out.println("r = " + r);
    s = r.negate();
    // System.out.println("s = " + s);

    a = mfac.random(kl, q);
    // System.out.println("a = " + a);

    c = a.scalarMultiply(r);
    d = a.scalarMultiply(s);
    e = c.sum(d);
    // System.out.println("c = " + c);
    // System.out.println("d = " + d);
    // System.out.println("e = " + e);
    assertEquals("a*b + a*(-b) = 0", e, mfac.getZERO());

    b = mfac.random(kl, q);
    // System.out.println("b = " + b);

    t = pfac.getONE();
    // System.out.println("t = " + t);
    c = a.linearCombination(b, t);
    d = b.linearCombination(a, t);
    // System.out.println("c = " + c);
    // System.out.println("d = " + d);
    assertEquals("a+1*b = b+1*a", c, d);

    c = a.linearCombination(b, t);
    d = a.sum(b);
    // System.out.println("c = " + c);
    // System.out.println("d = " + d);
    assertEquals("a+1*b = b+1*a", c, d);

    s = t.negate();
    // System.out.println("s = " + s);
    c = a.linearCombination(b, t);
    d = c.linearCombination(b, s);
    // System.out.println("c = " + c);
    // System.out.println("d = " + d);
    assertEquals("a+1*b+(-1)*b = a", a, d);

    c = a.linearCombination(t, b, t);
    d = c.linearCombination(t, b, s);
    // System.out.println("c = " + c);
    // System.out.println("d = " + d);
    assertEquals("a+1*b+(-1)*b = a", a, d);

    t = pfac.getZERO();
    // System.out.println("t = " + t);
    c = a.linearCombination(b, t);
    // System.out.println("c = " + c);
    assertEquals("a+0*b = a", a, c);

    d = a.linearCombination(t, b, t);
    // System.out.println("d = " + d);
    assertEquals("0*a+0*b = 0", mfac.getZERO(), d);

    r = a.scalarProduct(b);
    s = b.scalarProduct(a);
    // System.out.println("r = " + r);
    // System.out.println("s = " + s);
    assertEquals("a.b = b.a", r, s);
  }
コード例 #2
0
ファイル: SquarefreeFieldCharP.java プロジェクト: rjolly/jas
 /**
  * GenPolynomial polynomial squarefree factorization.
  *
  * @param A GenPolynomial.
  * @return [p_1 -&gt; e_1, ..., p_k -&gt; e_k] with P = prod_{i=1,...,k} p_i^{e_i} and p_i
  *     squarefree.
  */
 @Override
 public SortedMap<GenPolynomial<C>, Long> baseSquarefreeFactors(GenPolynomial<C> A) {
   SortedMap<GenPolynomial<C>, Long> sfactors = new TreeMap<GenPolynomial<C>, Long>();
   if (A == null || A.isZERO()) {
     return sfactors;
   }
   GenPolynomialRing<C> pfac = A.ring;
   if (A.isConstant()) {
     C coeff = A.leadingBaseCoefficient();
     // System.out.println("coeff = " + coeff + " @ " + coeff.factory());
     SortedMap<C, Long> rfactors = squarefreeFactors(coeff);
     // System.out.println("rfactors,const = " + rfactors);
     if (rfactors != null && rfactors.size() > 0) {
       for (Map.Entry<C, Long> me : rfactors.entrySet()) {
         C c = me.getKey();
         if (!c.isONE()) {
           GenPolynomial<C> cr = pfac.getONE().multiply(c);
           Long rk = me.getValue(); // rfactors.get(c);
           sfactors.put(cr, rk);
         }
       }
     } else {
       sfactors.put(A, 1L);
     }
     return sfactors;
   }
   if (pfac.nvar > 1) {
     throw new IllegalArgumentException(
         this.getClass().getName() + " only for univariate polynomials");
   }
   C ldbcf = A.leadingBaseCoefficient();
   if (!ldbcf.isONE()) {
     A = A.divide(ldbcf);
     SortedMap<C, Long> rfactors = squarefreeFactors(ldbcf);
     // System.out.println("rfactors,ldbcf = " + rfactors);
     if (rfactors != null && rfactors.size() > 0) {
       for (Map.Entry<C, Long> me : rfactors.entrySet()) {
         C c = me.getKey();
         if (!c.isONE()) {
           GenPolynomial<C> cr = pfac.getONE().multiply(c);
           Long rk = me.getValue(); // rfactors.get(c);
           sfactors.put(cr, rk);
         }
       }
     } else {
       GenPolynomial<C> f1 = pfac.getONE().multiply(ldbcf);
       // System.out.println("gcda sqf f1 = " + f1);
       sfactors.put(f1, 1L);
     }
     ldbcf = pfac.coFac.getONE();
   }
   GenPolynomial<C> T0 = A;
   long e = 1L;
   GenPolynomial<C> Tp;
   GenPolynomial<C> T = null;
   GenPolynomial<C> V = null;
   long k = 0L;
   long mp = 0L;
   boolean init = true;
   while (true) {
     // System.out.println("T0 = " + T0);
     if (init) {
       if (T0.isConstant() || T0.isZERO()) {
         break;
       }
       Tp = PolyUtil.<C>baseDeriviative(T0);
       T = engine.baseGcd(T0, Tp);
       T = T.monic();
       V = PolyUtil.<C>basePseudoDivide(T0, T);
       // System.out.println("iT0 = " + T0);
       // System.out.println("iTp = " + Tp);
       // System.out.println("iT  = " + T);
       // System.out.println("iV  = " + V);
       // System.out.println("const(iV)  = " + V.isConstant());
       k = 0L;
       mp = 0L;
       init = false;
     }
     if (V.isConstant()) {
       mp = pfac.characteristic().longValue(); // assert != 0
       // T0 = PolyUtil.<C> baseModRoot(T,mp);
       T0 = baseRootCharacteristic(T);
       logger.info("char root: T0 = " + T0 + ", T = " + T);
       if (T0 == null) {
         // break;
         T0 = pfac.getZERO();
       }
       e = e * mp;
       init = true;
       continue;
     }
     k++;
     if (mp != 0L && k % mp == 0L) {
       T = PolyUtil.<C>basePseudoDivide(T, V);
       System.out.println("k = " + k);
       // System.out.println("T = " + T);
       k++;
     }
     GenPolynomial<C> W = engine.baseGcd(T, V);
     W = W.monic();
     GenPolynomial<C> z = PolyUtil.<C>basePseudoDivide(V, W);
     // System.out.println("W = " + W);
     // System.out.println("z = " + z);
     V = W;
     T = PolyUtil.<C>basePseudoDivide(T, V);
     // System.out.println("V = " + V);
     // System.out.println("T = " + T);
     if (z.degree(0) > 0) {
       if (ldbcf.isONE() && !z.leadingBaseCoefficient().isONE()) {
         z = z.monic();
         logger.info("z,monic = " + z);
       }
       sfactors.put(z, (e * k));
     }
   }
   //      look, a stupid error:
   //         if ( !ldbcf.isONE() ) {
   //             GenPolynomial<C> f1 = sfactors.firstKey();
   //             long e1 = sfactors.remove(f1);
   //             System.out.println("gcda sqf c = " + c);
   //             f1 = f1.multiply(c);
   //             //System.out.println("gcda sqf f1e = " + f1);
   //             sfactors.put(f1,e1);
   //         }
   logger.info("exit char root: T0 = " + T0 + ", T = " + T);
   return sfactors;
 }