Implement sparse Hensel lifting

[PoslavskySV]

In some cases (typically for huge and sparse polynomials) we can reconstruct either the whole factorization or some of the factors using sparse (Zippel, Luks) lifting with precomputed bivariate factors and leading coefficients.

Test case which takes too long with ordinary lifting and is solvable with sparse:

lIntegersModulo domain = new lIntegersModulo(33554467);
String[] vars = {"a", "b", "c", "d", "e", "f", "g"};
lMultivariatePolynomialZp
        factors[] =
        {
                lMultivariatePolynomialZp.parse("25078271*b^5*c*d^2*e^2*f^6*g^3+22985334*a*b*c^2*d*e^7*f^3*g^7+19249719*a*b^7*d^5*e^6*g^2+6865506*a^2*b^5*c^3*d^6*e^6*f^3*g^5+20943085*a^2*b^5*c^8*d^3*e^3*f^7+733087*a^3*c^3*d^4*f^4*g^2+24327652*a^3*b^2*c^2*d^2*e^2*f^3*g^5+2508535*a^3*b^3*c*d^3*e^5*f^2*g^2+9991244*a^3*b^4*c^5*e^5*f^5*g^3+22044750*a^3*b^7*c*d^8*e*f^6+8526153*a^4*c^8*d*e^8*f^4*g^6+15162335*a^4*b^8*c^3*d^4*f^4*g^6+21943911*a^5*b*c^3*d^2*e^5*g^2+7268253*a^5*b^8*c^4*d^4*e*f*g^5+11265450*a^6*b^3*c^5*d^5*e+1307471*a^6*b^5*c^4*d^3*e*f^7+27352310*a^7*b^2*c^2*d^6*e^3*f^3*g+18596343*a^8*b^3*e^4*f^2*g+477464*a^8*b^4*c^3*d*e^3*f^5*g^3+20723946*a^8*b^4*c^8*d^3*e^2*g^3", domain, vars),
                lMultivariatePolynomialZp.parse("24999489*c^6*d^5*g^7+31605719*b^5*c^5*d^4*e^3*g^6+33475465*b^8*c^5*d^6*f^7+21150942*a*c^4*d^4*e^3*f^3*g+30544835*a*b^3*d^7*e*f^8*g^5+8725705*a*b^8*c^6*d^5*e^4*f*g+3830207*a^2*d^2*e*f^7*g^8+31725230*a^2*b^8*c*e*f^8*g^2+5924640*a^3*c*d^4*e^8+14191319*a^3*b*c^3*e^7*f^3*g^8+5482302*a^3*b^2*c^2*d^5*f^8*g^2+350050*a^4*b^3*c^6*d^6*e^7*f^6+246147*a^4*b^4*c^3*d^7*e^5*g^8+27052604*a^5*c^4*d^4*f+2073523*a^5*b^4*c^4*d^7*e^4*f^2*g^5+21322895*a^5*b^5*c*d^3*e^5*f^5*g^4+19375356*a^5*b^6*c^7*e^3*f^2*g^6+15676776*a^6*b^7*c^3*d^8*e^3*f^6*g^6+9971731*a^7*b^4*c^3*d*e^5*f*g^5+16734963*a^8*b^8*c^7*d^4*e*g^7", domain, vars),
                lMultivariatePolynomialZp.parse("21113415*b^5*c^6*d^4*e^4*f^2*g^3+20864231*b^8*c*d^6*e^5*f^8*g^5+33448448*a*b^3*c^6*d*e^4*f^7*g^2+31133965*a*b^4*c^2*d^2*e^7*f^6*g^2+27612593*a*b^5*d^5*e^2*f^7*g^4+17128197*a*b^7*c^3*d^6*e^2+4469686*a^2*b^5*c^4*d^8*e^4*f^4*g^7+1374035*a^3*c^8*e^7*f*g^5+10414621*a^3*b^6*c^5*d^7*e^7*f^6*g^6+10872067*a^3*b^8*c^3*d*e^4*f^8*g^4+6381772*a^4*b^2*c^6*d^6*e^6*f^3*g^3+26978581*a^4*b^5*d^6*e^5*f^7+30602413*a^4*b^8*c^8*d^4*e^5*f^3*g^3+13372094*a^5*b^3*c^3*d^7*e^5*f^8*g^3+25263857*a^5*b^5*c*d^7*e^6*g^5+4204332*a^6*c^2*d^2*e*f^6*g^2+13228578*a^6*b^2*c^5*d^7*e^6*f^8*g^6+17934510*a^6*b^8*c^4*d^5*e^3*f^4+17371834*a^7*b^4*c^2*d^8*e^4*f^2*g+8745908*a^8*b*c^4*d^7*e^5*f*g^6", domain, vars)
        };
lMultivariatePolynomialZp base = factors[0].createOne().multiply(factors);

FactorDecomposition<lMultivariatePolynomialZp> decomposition = MultivariateFactorization.factorInField(base);
Assert.assertEquals(3, decomposition.size());

[PoslavskySV]

Implemented via #13