Java ExpVector.signum方法代码示例

import edu.jas.poly.ExpVector; //导入方法依赖的package包/类
/**
 * Prepend a new leading coefficient.
 * @param r variable for the direction.
 * @param h new coefficient.
 * @return new power series.
 */
public MultiVarPowerSeries<C> prepend(final C h, final int r) {
    if (r < 0 || ring.nvar < r) {
        throw new IllegalArgumentException("variable index out of bound");
    }
    return new MultiVarPowerSeries<C>(ring, new MultiVarCoefficients<C>(ring) {


        @Override
        public C generate(ExpVector i) {
            if (i.isZERO()) {
                return h;
            }
            ExpVector e = i.subst(r, i.getVal(r) - 1);
            if (e.signum() < 0) {
                return pfac.coFac.getZERO();
            }
            return coefficient(e);
        }
    });
}
 

import edu.jas.poly.ExpVector; //导入方法依赖的package包/类
/**
 * Shift coefficients. Multiply by exponent vector.
 * @param k shift ExpVector.
 * @return new power series with coefficient(i) = old.coefficient(i-k).
 */
public MultiVarPowerSeries<C> shift(final ExpVector k) {
    if (k == null) {
        throw new IllegalArgumentException("null ExpVector not allowed");
    }
    if (k.signum() == 0) {
        return this;
    }
    int nt = Math.min(truncate + (int) k.totalDeg(), ring.truncate);
    return new MultiVarPowerSeries<C>(ring, new MultiVarCoefficients<C>(ring) {


        @Override
        public C generate(ExpVector i) {
            ExpVector d = i.subtract(k);
            if (d.signum() < 0) {
                return ring.coFac.getZERO();
            }
            return coefficient(d);
        }
    }, nt);
}
 

import edu.jas.poly.ExpVector; //导入方法依赖的package包/类
/**
 * GB criterion 4. Use only for commutative power series rings.
 * @param A power series.
 * @param B power series.
 * @param e = lcm(ht(A),ht(B))
 * @return true if the S-power-series(i,j) is required, else false.
 */
public boolean criterion4(MultiVarPowerSeries<C> A, MultiVarPowerSeries<C> B, ExpVector e) {
    if (logger.isInfoEnabled()) {
        if (!A.ring.equals(B.ring)) {
            logger.error("rings not equal " + A.ring + ", " + B.ring);
        }
        if (!A.ring.isCommutative()) {
            logger.error("GBCriterion4 not applicabable to non-commutative power series");
            return true;
        }
    }
    ExpVector ei = A.orderExpVector();
    ExpVector ej = B.orderExpVector();
    ExpVector g = ei.sum(ej);
    // boolean t =  g == e ;
    ExpVector h = g.subtract(e);
    int s = h.signum();
    return !(s == 0);
}
 

import edu.jas.poly.ExpVector; //导入方法依赖的package包/类
/**
 * Multi-partial deriviative.
 * @param i exponent vector.
 * @return partial deriviative of this with respect to all variables.
 */
public TaylorFunction<C> deriviative(ExpVector i) {
    GenPolynomial<C> p = pol;
    long f = 1L;
    if (i.signum() == 0 || pol.isZERO()) {
        return new PolynomialTaylorFunction<C>(p, f);
    }
    for (int j = 0; j < i.length(); j++) {
        long e = i.getVal(j);
        if (e == 0) {
            continue;
        }
        int jl = i.length() - 1 - j;
        for (long k = 0; k < e; k++) {
            p = PolyUtil.<C> baseDeriviative(p, jl);
            f *= (k + 1);
            if (p.isZERO()) {
                return new PolynomialTaylorFunction<C>(p, f);
            }
        }
    }
    //System.out.println("i = " + i + ", f = " + f + ", der = " + p);
    return new PolynomialTaylorFunction<C>(p, f);
}
 

import edu.jas.poly.ExpVector; //导入方法依赖的package包/类
/**
 * GB criterium 4. Use only for commutative polynomial rings. <b>Note:</b>
 * Experimental version for r-Groebner bases.
 * @param A polynomial.
 * @param B polynomial.
 * @return true if the S-polynomial(i,j) is required, else false.
 */
@Override
public boolean criterion4(GenPolynomial<C> A, GenPolynomial<C> B) {
    if (logger.isInfoEnabled()) {
        if (A instanceof GenSolvablePolynomial || B instanceof GenSolvablePolynomial) {
            logger.error("GBCriterion4 not applicabable to SolvablePolynomials");
            return true;
        }
    }
    ExpVector ei = A.leadingExpVector();
    ExpVector ej = B.leadingExpVector();
    ExpVector g = ei.sum(ej);
    ExpVector e = ei.lcm(ej);
    //        boolean t =  g == e ;
    ExpVector h = g.subtract(e);
    int s = h.signum();
    if (s == 0) { // disjoint ht
        C a = A.leadingBaseCoefficient();
        C b = B.leadingBaseCoefficient();
        C d = a.multiply(b);
        if (d.isZERO()) { // a guess
            return false; // can skip pair
        }
    }
    return true; //! ( s == 0 );
}
 

import edu.jas.poly.ExpVector; //导入方法依赖的package包/类
/**
 * GB criterium 4. Use only for commutative polynomial rings. This version
 * works also for d-Groebner bases.
 * @param A polynomial.
 * @param B polynomial.
 * @return true if the S-polynomial(i,j) is required, else false.
 */
@Override
public boolean criterion4(GenPolynomial<C> A, GenPolynomial<C> B) {
    if (logger.isInfoEnabled()) {
        if (A instanceof GenSolvablePolynomial || B instanceof GenSolvablePolynomial) {
            logger.error("GBCriterion4 not applicabable to SolvablePolynomials");
            return true;
        }
    }
    ExpVector ei = A.leadingExpVector();
    ExpVector ej = B.leadingExpVector();
    ExpVector g = ei.sum(ej);
    ExpVector e = ei.lcm(ej);
    //        boolean t =  g == e ;
    ExpVector h = g.subtract(e);
    int s = h.signum();
    if (s == 0) { // disjoint ht
        C a = A.leadingBaseCoefficient();
        C b = B.leadingBaseCoefficient();
        C d = a.gcd(b);
        if (d.isONE()) { // disjoint hc
            return false; // can skip pair
        }
    }
    return true; //! ( s == 0 );
}
 

import edu.jas.poly.ExpVector; //导入方法依赖的package包/类
/**
 * Multiply by exponent vector and coefficient.
 * @param k shift ExpVector.
 * @param c coefficient multiplier.
 * @return new power series with coefficient(i) = old.coefficient(i-k)*c.
 */
public MultiVarPowerSeries<C> multiply(final C c, final ExpVector k) {
    if (k == null) {
        throw new IllegalArgumentException("null ExpVector not allowed");
    }
    if (k.signum() == 0) {
        return this.multiply(c);
    }
    if (c.signum() == 0) {
        return ring.getZERO();
    }
    int nt = Math.min(ring.truncate, truncate + (int) k.totalDeg());

    return new MultiVarPowerSeries<C>(ring, new MultiVarCoefficients<C>(ring) {


        @Override
        public C generate(ExpVector i) {
            ExpVector d = i.subtract(k);
            if (d.signum() < 0) {
                return ring.coFac.getZERO();
            }
            long tdegd = d.totalDeg();
            if (lazyCoeffs.homCheck.get((int) tdegd)) {
                GenPolynomial<C> p = homogeneousPart(tdegd).multiply(c, k);
                long tdegi = i.totalDeg();
                coeffCache.put(tdegi, p); // overwrite
                homCheck.set((int) tdegi);
                C b = p.coefficient(i);
                //System.out.println("b = " + b + ", i = " + i + ", tdegi = " + tdegi+ ", tdegd = " + tdegd);
                //System.out.println("p = " + p + ", i = " + i);
                return b;
            }
            return coefficient(d).multiply(c);
        }
    }, nt);
}
 

import edu.jas.poly.ExpVector; //导入方法依赖的package包/类
/**
 * Shift select coefficients. Not selected coefficients are removed from the
 * result series.
 * @param sel selector functor.
 * @return new power series with shifted selected coefficients.
 */
public MultiVarPowerSeries<C> shiftSelect(final Selector<? super C> sel) {
    return new MultiVarPowerSeries<C>(ring, new MultiVarCoefficients<C>(ring) {


        ExpVectorIterable ib = new ExpVectorIterable(ring.nvar, true, truncate);


        Iterator<ExpVector> pos = ib.iterator();


        @Override
        public C generate(ExpVector i) {
            C c;
            if (i.signum() > 0) {
                int[] deps = i.dependencyOnVariables();
                ExpVector x = i.subst(deps[0], i.getVal(deps[0]) - 1L);
                c = get(x); // ensure all coefficients are generated
            }
            do {
                c = null;
                if (pos.hasNext()) {
                    ExpVector e = pos.next();
                    c = coefficient(e);
                } else {
                    break;
                }
            } while (!sel.select(c));
            if (c == null) { // not correct because not known
                c = ring.coFac.getZERO();
            }
            return c;
        }
    });
}
 

import edu.jas.poly.ExpVector; //导入方法依赖的package包/类
/**
 * GB criterium 4. Use only for commutative polynomial rings.
 * @param ei exponent vector.
 * @param ej exponent vector.
 * @param e = lcm(ei,ej)
 * @return true if the S-polynomial(i,j) is required, else false.
 */
public boolean criterion4(ExpVector ei, ExpVector ej, ExpVector e) {
    ExpVector g = ei.sum(ej);
    ExpVector h = g.subtract(e);
    int s = h.signum();
    return s != 0;
}