예제 #1
0
  /**
   * Univariate GenPolynomial algebraic partial fraction decomposition, Absolute factorization or
   * Rothstein-Trager algorithm.
   *
   * @param A univariate GenPolynomial, deg(A) < deg(P).
   * @param P univariate squarefree GenPolynomial, gcd(A,P) == 1.
   * @return partial fraction container.
   */
  public PartialFraction<C> baseAlgebraicPartialFraction(GenPolynomial<C> A, GenPolynomial<C> P) {
    if (P == null || P.isZERO()) {
      throw new RuntimeException(" P == null or P == 0");
    }
    if (A == null || A.isZERO()) {
      throw new RuntimeException(" A == null or A == 0");
      // PartialFraction(A,P,al,pl,empty,empty)
    }
    // System.out.println("\nP_base_algeb_part = " + P);
    GenPolynomialRing<C> pfac = P.ring; // K[x]
    if (pfac.nvar > 1) {
      // System.out.println("facs_base_irred: univ");
      throw new RuntimeException("only for univariate polynomials");
    }
    if (!pfac.coFac.isField()) {
      // System.out.println("facs_base_irred: field");
      throw new RuntimeException("only for field coefficients");
    }
    List<C> cfactors = new ArrayList<C>();
    List<GenPolynomial<C>> cdenom = new ArrayList<GenPolynomial<C>>();
    List<AlgebraicNumber<C>> afactors = new ArrayList<AlgebraicNumber<C>>();
    List<GenPolynomial<AlgebraicNumber<C>>> adenom =
        new ArrayList<GenPolynomial<AlgebraicNumber<C>>>();

    // P linear
    if (P.degree(0) <= 1) {
      cfactors.add(A.leadingBaseCoefficient());
      cdenom.add(P);
      return new PartialFraction<C>(A, P, cfactors, cdenom, afactors, adenom);
    }
    List<GenPolynomial<C>> Pfac = baseFactorsSquarefree(P);
    // System.out.println("\nPfac = " + Pfac);

    List<GenPolynomial<C>> Afac = engine.basePartialFraction(A, Pfac);

    GenPolynomial<C> A0 = Afac.remove(0);
    if (!A0.isZERO()) {
      throw new RuntimeException(" A0 != 0: deg(A)>= deg(P)");
    }

    // algebraic and linear factors
    int i = 0;
    for (GenPolynomial<C> pi : Pfac) {
      GenPolynomial<C> ai = Afac.get(i++);
      if (pi.degree(0) <= 1) {
        cfactors.add(ai.leadingBaseCoefficient());
        cdenom.add(pi);
        continue;
      }
      PartialFraction<C> pf = baseAlgebraicPartialFractionIrreducibleAbsolute(ai, pi);
      // PartialFraction<C> pf = baseAlgebraicPartialFractionIrreducible(ai,pi);
      cfactors.addAll(pf.cfactors);
      cdenom.addAll(pf.cdenom);
      afactors.addAll(pf.afactors);
      adenom.addAll(pf.adenom);
    }
    return new PartialFraction<C>(A, P, cfactors, cdenom, afactors, adenom);
  }
  /** Test object multiplication. */
  public void testMultiplication() {

    a = fac.random(ll);
    assertTrue("not isZERO( a )", !a.isZERO());

    b = fac.random(ll);
    assertTrue("not isZERO( b )", !b.isZERO());

    c = b.multiply(a);
    d = a.multiply(b);
    assertTrue("not isZERO( c )", !c.isZERO());
    assertTrue("not isZERO( d )", !d.isZERO());

    // System.out.println("a = " + a);
    // System.out.println("b = " + b);
    e = d.subtract(c);
    assertTrue("isZERO( a*b-b*a ) " + e, e.isZERO());

    assertTrue("a*b = b*a", c.equals(d));
    assertEquals("a*b = b*a", c, d);

    c = fac.random(ll);
    // System.out.println("c = " + c);
    d = a.multiply(b.multiply(c));
    e = (a.multiply(b)).multiply(c);

    // System.out.println("d = " + d);
    // System.out.println("e = " + e);

    // System.out.println("d-e = " + d.subtract(c) );

    assertEquals("a(bc) = (ab)c", d, e);
    assertTrue("a(bc) = (ab)c", d.equals(e));

    BigComplex x = a.leadingBaseCoefficient().inverse();
    c = a.monic();
    d = a.multiply(x);
    assertEquals("a.monic() = a(1/ldcf(a))", c, d);

    BigComplex y = b.leadingBaseCoefficient().inverse();
    c = b.monic();
    d = b.multiply(y);
    assertEquals("b.monic() = b(1/ldcf(b))", c, d);

    e = new GenPolynomial<BigComplex>(fac, y);
    d = b.multiply(e);
    assertEquals("b.monic() = b(1/ldcf(b))", c, d);

    d = e.multiply(b);
    assertEquals("b.monic() = (1/ldcf(b) (0))*b", c, d);
  }
예제 #3
0
 /**
  * Real algebraic number magnitude.
  *
  * @param iv root isolating interval for f, with f(left) * f(right) &lt; 0.
  * @param f univariate polynomial, non-zero.
  * @param g univariate polynomial, gcd(f,g) == 1.
  * @param eps length limit for interval length.
  * @return g(iv) .
  */
 public C realMagnitude(Interval<C> iv, GenPolynomial<C> f, GenPolynomial<C> g, C eps) {
   if (g.isZERO() || g.isConstant()) {
     return g.leadingBaseCoefficient();
   }
   Interval<C> v = invariantMagnitudeInterval(iv, f, g, eps);
   return realIntervalMagnitude(v, f, g, eps);
 }
예제 #4
0
 /**
  * Real root bound. With f(M) * f(-M) != 0.
  *
  * @param f univariate polynomial.
  * @return M such that -M &lt; root(f) &lt; M.
  */
 public C realRootBound(GenPolynomial<C> f) {
   if (f == null) {
     return null;
   }
   RingFactory<C> cfac = f.ring.coFac;
   C M = cfac.getONE();
   if (f.isZERO() || f.isConstant()) {
     return M;
   }
   C a = f.leadingBaseCoefficient().abs();
   for (C c : f.getMap().values()) {
     C d = c.abs().divide(a);
     if (M.compareTo(d) < 0) {
       M = d;
     }
   }
   // works also without this case, only for optimization
   // to use rational number interval end points
   // can fail if real root is in interval [r,r+1]
   // for too low precision or too big r, since r is approximation
   if ((Object) M instanceof RealAlgebraicNumber) {
     RealAlgebraicNumber Mr = (RealAlgebraicNumber) M;
     BigRational r = Mr.magnitude();
     M = cfac.fromInteger(r.numerator()).divide(cfac.fromInteger(r.denominator()));
   }
   M = M.sum(f.ring.coFac.getONE());
   // System.out.println("M = " + M);
   return M;
 }
예제 #5
0
 /**
  * Real algebraic number magnitude.
  *
  * @param iv root isolating interval for f, with f(left) * f(right) &lt; 0, with iv such that
  *     |g(a) - g(b)| &lt; eps for a, b in iv.
  * @param f univariate polynomial, non-zero.
  * @param g univariate polynomial, gcd(f,g) == 1.
  * @param eps length limit for interval length.
  * @return g(iv) .
  */
 public C realIntervalMagnitude(Interval<C> iv, GenPolynomial<C> f, GenPolynomial<C> g, C eps) {
   if (g.isZERO() || g.isConstant()) {
     return g.leadingBaseCoefficient();
   }
   RingFactory<C> cfac = g.ring.coFac;
   C c = iv.left.sum(iv.right);
   c = c.divide(cfac.fromInteger(2));
   C ev = PolyUtil.<C>evaluateMain(cfac, g, c);
   // System.out.println("ev = " + ev);
   return ev;
 }
예제 #6
0
  /**
   * Magnitude bound.
   *
   * @param iv interval.
   * @param f univariate polynomial.
   * @return B such that |f(c)| &lt; B for c in iv.
   */
  public C magnitudeBound(Interval<C> iv, GenPolynomial<C> f) {
    if (f == null) {
      return null;
    }
    if (f.isZERO()) {
      return f.ring.coFac.getONE();
    }
    if (f.isConstant()) {
      return f.leadingBaseCoefficient().abs();
    }
    GenPolynomial<C> fa =
        f.map(
            new UnaryFunctor<C, C>() {

              public C eval(C a) {
                return a.abs();
              }
            });
    // System.out.println("fa = " + fa);
    C M = iv.left.abs();
    if (M.compareTo(iv.right.abs()) < 0) {
      M = iv.right.abs();
    }
    // System.out.println("M = " + M);
    RingFactory<C> cfac = f.ring.coFac;
    C B = PolyUtil.<C>evaluateMain(cfac, fa, M);
    // works also without this case, only for optimization
    // to use rational number interval end points
    // can fail if real root is in interval [r,r+1]
    // for too low precision or too big r, since r is approximation
    if ((Object) B instanceof RealAlgebraicNumber) {
      RealAlgebraicNumber Br = (RealAlgebraicNumber) B;
      BigRational r = Br.magnitude();
      B = cfac.fromInteger(r.numerator()).divide(cfac.fromInteger(r.denominator()));
    }
    // System.out.println("B = " + B);
    return B;
  }
예제 #7
0
  /**
   * Univariate GenPolynomial algebraic partial fraction decomposition, via absolute factorization
   * to linear factors.
   *
   * @param A univariate GenPolynomial, deg(A) < deg(P).
   * @param P univariate squarefree GenPolynomial, gcd(A,P) == 1.
   * @return partial fraction container.
   */
  public PartialFraction<C> baseAlgebraicPartialFractionIrreducibleAbsolute(
      GenPolynomial<C> A, GenPolynomial<C> P) {
    if (P == null || P.isZERO()) {
      throw new RuntimeException(" P == null or P == 0");
    }
    // System.out.println("\nP_base_algeb_part = " + P);
    GenPolynomialRing<C> pfac = P.ring; // K[x]
    if (pfac.nvar > 1) {
      // System.out.println("facs_base_irred: univ");
      throw new RuntimeException("only for univariate polynomials");
    }
    if (!pfac.coFac.isField()) {
      // System.out.println("facs_base_irred: field");
      throw new RuntimeException("only for field coefficients");
    }
    List<C> cfactors = new ArrayList<C>();
    List<GenPolynomial<C>> cdenom = new ArrayList<GenPolynomial<C>>();
    List<AlgebraicNumber<C>> afactors = new ArrayList<AlgebraicNumber<C>>();
    List<GenPolynomial<AlgebraicNumber<C>>> adenom =
        new ArrayList<GenPolynomial<AlgebraicNumber<C>>>();

    // P linear
    if (P.degree(0) <= 1) {
      cfactors.add(A.leadingBaseCoefficient());
      cdenom.add(P);
      return new PartialFraction<C>(A, P, cfactors, cdenom, afactors, adenom);
    }

    // non linear case
    Factors<C> afacs = factorsAbsoluteIrreducible(P);
    // System.out.println("linear algebraic factors = " + afacs);

    // System.out.println("afactors      = " + afacs.afactors);
    // System.out.println("arfactors     = " + afacs.arfactors);
    // System.out.println("arfactors pol = " + afacs.arfactors.get(0).poly);
    // System.out.println("arfactors2    = " + afacs.arfactors.get(0).afactors);

    List<GenPolynomial<AlgebraicNumber<C>>> fact = afacs.getFactors();
    // System.out.println("factors       = " + fact);
    GenPolynomial<AlgebraicNumber<C>> Pa = afacs.apoly;

    GenPolynomial<AlgebraicNumber<C>> Aa =
        PolyUtil.<C>convertToRecAlgebraicCoefficients(1, Pa.ring, A);

    GreatestCommonDivisorAbstract<AlgebraicNumber<C>> aengine = GCDFactory.getProxy(afacs.afac);

    // System.out.println("denom         = " + Pa);
    // System.out.println("numer         = " + Aa);

    List<GenPolynomial<AlgebraicNumber<C>>> numers = aengine.basePartialFraction(Aa, fact);
    // System.out.println("part frac     = " + numers);
    GenPolynomial<AlgebraicNumber<C>> A0 = numers.remove(0);
    if (!A0.isZERO()) {
      throw new RuntimeException(" A0 != 0: deg(A)>= deg(P)");
    }
    int i = 0;
    for (GenPolynomial<AlgebraicNumber<C>> fa : fact) {
      GenPolynomial<AlgebraicNumber<C>> an = numers.get(i++);
      if (fa.degree(0) <= 1) {
        afactors.add(an.leadingBaseCoefficient());
        adenom.add(fa);
        continue;
      }
      System.out.println("fa = " + fa);
      Factors<AlgebraicNumber<C>> faf = afacs.getFactor(fa);
      System.out.println("faf = " + faf);
      List<GenPolynomial<AlgebraicNumber<AlgebraicNumber<C>>>> fafact = faf.getFactors();
      GenPolynomial<AlgebraicNumber<AlgebraicNumber<C>>> Aaa =
          PolyUtil.<AlgebraicNumber<C>>convertToRecAlgebraicCoefficients(1, faf.apoly.ring, an);

      GreatestCommonDivisorAbstract<AlgebraicNumber<AlgebraicNumber<C>>> aaengine =
          GCDFactory.getImplementation(faf.afac);

      List<GenPolynomial<AlgebraicNumber<AlgebraicNumber<C>>>> anumers =
          aaengine.basePartialFraction(Aaa, fafact);
      System.out.println("algeb part frac = " + anumers);
      GenPolynomial<AlgebraicNumber<AlgebraicNumber<C>>> A0a = anumers.remove(0);
      if (!A0a.isZERO()) {
        throw new RuntimeException(" A0 != 0: deg(A)>= deg(P)");
      }
      int k = 0;
      for (GenPolynomial<AlgebraicNumber<AlgebraicNumber<C>>> faa : fafact) {
        GenPolynomial<AlgebraicNumber<AlgebraicNumber<C>>> ana = anumers.get(k++);
        System.out.println("faa = " + faa);
        System.out.println("ana = " + ana);
        if (faa.degree(0) > 1) {
          throw new RuntimeException(" faa not linear");
        }
        GenPolynomial<AlgebraicNumber<C>> ana1 =
            (GenPolynomial<AlgebraicNumber<C>>) (GenPolynomial) ana;
        GenPolynomial<AlgebraicNumber<C>> faa1 =
            (GenPolynomial<AlgebraicNumber<C>>) (GenPolynomial) faa;

        afactors.add(ana1.leadingBaseCoefficient());
        adenom.add(faa1);
      }
    }
    return new PartialFraction<C>(A, P, cfactors, cdenom, afactors, adenom);
  }
예제 #8
0
  /**
   * Univariate GenPolynomial algebraic partial fraction decomposition, Rothstein-Trager algorithm.
   *
   * @param A univariate GenPolynomial, deg(A) < deg(P).
   * @param P univariate squarefree GenPolynomial, gcd(A,P) == 1.
   * @return partial fraction container.
   */
  @Deprecated
  public PartialFraction<C> baseAlgebraicPartialFractionIrreducible(
      GenPolynomial<C> A, GenPolynomial<C> P) {
    if (P == null || P.isZERO()) {
      throw new RuntimeException(" P == null or P == 0");
    }
    // System.out.println("\nP_base_algeb_part = " + P);
    GenPolynomialRing<C> pfac = P.ring; // K[x]
    if (pfac.nvar > 1) {
      // System.out.println("facs_base_irred: univ");
      throw new RuntimeException("only for univariate polynomials");
    }
    if (!pfac.coFac.isField()) {
      // System.out.println("facs_base_irred: field");
      throw new RuntimeException("only for field coefficients");
    }
    List<C> cfactors = new ArrayList<C>();
    List<GenPolynomial<C>> cdenom = new ArrayList<GenPolynomial<C>>();
    List<AlgebraicNumber<C>> afactors = new ArrayList<AlgebraicNumber<C>>();
    List<GenPolynomial<AlgebraicNumber<C>>> adenom =
        new ArrayList<GenPolynomial<AlgebraicNumber<C>>>();

    // P linear
    if (P.degree(0) <= 1) {
      cfactors.add(A.leadingBaseCoefficient());
      cdenom.add(P);
      return new PartialFraction<C>(A, P, cfactors, cdenom, afactors, adenom);
    }

    // deriviative
    GenPolynomial<C> Pp = PolyUtil.<C>baseDeriviative(P);
    // no: Pp = Pp.monic();
    // System.out.println("\nP  = " + P);
    // System.out.println("Pp = " + Pp);

    // Q[t]
    String[] vars = new String[] {"t"};
    GenPolynomialRing<C> cfac = new GenPolynomialRing<C>(pfac.coFac, 1, pfac.tord, vars);
    GenPolynomial<C> t = cfac.univariate(0);
    // System.out.println("t = " + t);

    // Q[x][t]
    GenPolynomialRing<GenPolynomial<C>> rfac =
        new GenPolynomialRing<GenPolynomial<C>>(pfac, cfac); // sic
    // System.out.println("rfac = " + rfac.toScript());

    // transform polynomials to bi-variate polynomial
    GenPolynomial<GenPolynomial<C>> Ac = PolyUfdUtil.<C>introduceLowerVariable(rfac, A);
    // System.out.println("Ac = " + Ac);
    GenPolynomial<GenPolynomial<C>> Pc = PolyUfdUtil.<C>introduceLowerVariable(rfac, P);
    // System.out.println("Pc = " + Pc);
    GenPolynomial<GenPolynomial<C>> Pcp = PolyUfdUtil.<C>introduceLowerVariable(rfac, Pp);
    // System.out.println("Pcp = " + Pcp);

    // Q[t][x]
    GenPolynomialRing<GenPolynomial<C>> rfac1 = Pc.ring;
    // System.out.println("rfac1 = " + rfac1.toScript());

    // A - t P'
    GenPolynomial<GenPolynomial<C>> tc = rfac1.getONE().multiply(t);
    // System.out.println("tc = " + tc);
    GenPolynomial<GenPolynomial<C>> At = Ac.subtract(tc.multiply(Pcp));
    // System.out.println("At = " + At);

    GreatestCommonDivisorSubres<C> engine = new GreatestCommonDivisorSubres<C>();
    // = GCDFactory.<C>getImplementation( cfac.coFac );
    GreatestCommonDivisorAbstract<AlgebraicNumber<C>> aengine = null;

    GenPolynomial<GenPolynomial<C>> Rc = engine.recursiveResultant(Pc, At);
    // System.out.println("Rc = " + Rc);
    GenPolynomial<C> res = Rc.leadingBaseCoefficient();
    // no: res = res.monic();
    // System.out.println("\nres = " + res);

    SortedMap<GenPolynomial<C>, Long> resfac = baseFactors(res);
    // System.out.println("resfac = " + resfac + "\n");

    for (GenPolynomial<C> r : resfac.keySet()) {
      // System.out.println("\nr(t) = " + r);
      if (r.isConstant()) {
        continue;
      }
      //             if ( r.degree(0) <= 1L ) {
      //                 System.out.println("warning linear factor in resultant ignored");
      //                 continue;
      //                 //throw new RuntimeException("input not irreducible");
      //             }
      // vars = new String[] { "z_" + Math.abs(r.hashCode() % 1000) };
      vars = pfac.newVars("z_");
      pfac = pfac.clone();
      vars = pfac.setVars(vars);
      r = pfac.copy(r); // hack to exchange the variables
      // System.out.println("r(z_) = " + r);
      AlgebraicNumberRing<C> afac = new AlgebraicNumberRing<C>(r, true); // since irreducible
      logger.debug("afac = " + afac.toScript());
      AlgebraicNumber<C> a = afac.getGenerator();
      // no: a = a.negate();
      // System.out.println("a = " + a);

      // K(alpha)[x]
      GenPolynomialRing<AlgebraicNumber<C>> pafac =
          new GenPolynomialRing<AlgebraicNumber<C>>(afac, Pc.ring);
      // System.out.println("pafac = " + pafac.toScript());

      // convert to K(alpha)[x]
      GenPolynomial<AlgebraicNumber<C>> Pa = PolyUtil.<C>convertToAlgebraicCoefficients(pafac, P);
      // System.out.println("Pa = " + Pa);
      GenPolynomial<AlgebraicNumber<C>> Pap = PolyUtil.<C>convertToAlgebraicCoefficients(pafac, Pp);
      // System.out.println("Pap = " + Pap);
      GenPolynomial<AlgebraicNumber<C>> Aa = PolyUtil.<C>convertToAlgebraicCoefficients(pafac, A);
      // System.out.println("Aa = " + Aa);

      // A - a P'
      GenPolynomial<AlgebraicNumber<C>> Ap = Aa.subtract(Pap.multiply(a));
      // System.out.println("Ap = " + Ap);

      if (aengine == null) {
        aengine = GCDFactory.<AlgebraicNumber<C>>getImplementation(afac);
        // System.out.println("aengine = " + aengine);
      }
      GenPolynomial<AlgebraicNumber<C>> Ga = aengine.baseGcd(Pa, Ap);
      // System.out.println("Ga = " + Ga);
      if (Ga.isConstant()) {
        // System.out.println("warning constant gcd ignored");
        continue;
      }
      afactors.add(a);
      adenom.add(Ga);
      // quadratic case
      if (P.degree(0) == 2 && Ga.degree(0) == 1) {
        GenPolynomial<AlgebraicNumber<C>>[] qra =
            PolyUtil.<AlgebraicNumber<C>>basePseudoQuotientRemainder(Pa, Ga);
        GenPolynomial<AlgebraicNumber<C>> Qa = qra[0];
        if (!qra[1].isZERO()) {
          throw new RuntimeException("remainder not zero");
        }
        // System.out.println("Qa = " + Qa);
        afactors.add(a.negate());
        adenom.add(Qa);
      }
      if (false && P.degree(0) == 3 && Ga.degree(0) == 1) {
        GenPolynomial<AlgebraicNumber<C>>[] qra =
            PolyUtil.<AlgebraicNumber<C>>basePseudoQuotientRemainder(Pa, Ga);
        GenPolynomial<AlgebraicNumber<C>> Qa = qra[0];
        if (!qra[1].isZERO()) {
          throw new RuntimeException("remainder not zero");
        }
        System.out.println("Qa3 = " + Qa);
        // afactors.add( a.negate() );
        // adenom.add( Qa );
      }
    }
    return new PartialFraction<C>(A, P, cfactors, cdenom, afactors, adenom);
  }
예제 #9
0
 /**
  * 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;
 }