+ DCOUT(put_factors_into_lst);
+ DCOUTVAR(e);
+
+ lst result;
+
+ if ( is_a<numeric>(e) ) {
+ result.append(e);
+ DCOUT(END put_factors_into_lst);
+ DCOUTVAR(result);
+ return result;
+ }
+ if ( is_a<power>(e) ) {
+ result.append(1);
+ result.append(e.op(0));
+ result.append(e.op(1));
+ DCOUT(END put_factors_into_lst);
+ DCOUTVAR(result);
+ return result;
+ }
+ if ( is_a<symbol>(e) || is_a<add>(e) ) {
+ result.append(1);
+ result.append(e);
+ result.append(1);
+ DCOUT(END put_factors_into_lst);
+ DCOUTVAR(result);
+ return result;
+ }
+ if ( is_a<mul>(e) ) {
+ ex nfac = 1;
+ for ( size_t i=0; i<e.nops(); ++i ) {
+ ex op = e.op(i);
+ if ( is_a<numeric>(op) ) {
+ nfac = op;
+ }
+ if ( is_a<power>(op) ) {
+ result.append(op.op(0));
+ result.append(op.op(1));
+ }
+ if ( is_a<symbol>(op) || is_a<add>(op) ) {
+ result.append(op);
+ result.append(1);
+ }
+ }
+ result.prepend(nfac);
+ DCOUT(END put_factors_into_lst);
+ DCOUTVAR(result);
+ return result;
+ }
+ throw runtime_error("put_factors_into_lst: bad term.");
+}
+
+#ifdef DEBUGFACTOR
+ostream& operator<<(ostream& o, const vector<numeric>& v)
+{
+ for ( size_t i=0; i<v.size(); ++i ) {
+ o << v[i] << " ";
+ }
+ return o;
+}
+#endif // def DEBUGFACTOR
+
+static bool checkdivisors(const lst& f, vector<numeric>& d)
+{
+ DCOUT(checkdivisors);
+ const int k = f.nops()-2;
+ DCOUTVAR(k);
+ DCOUTVAR(d.size());
+ numeric q, r;
+ d[0] = ex_to<numeric>(f.op(0) * f.op(f.nops()-1));
+ if ( d[0] == 1 && k == 1 && abs(f.op(1)) != 1 ) {
+ DCOUT(false);
+ DCOUT(END checkdivisors);
+ return false;
+ }
+ DCOUTVAR(d[0]);
+ for ( int i=1; i<=k; ++i ) {
+ DCOUTVAR(i);
+ DCOUTVAR(abs(f.op(i)));
+ q = ex_to<numeric>(abs(f.op(i)));
+ DCOUTVAR(q);
+ for ( int j=i-1; j>=0; --j ) {
+ r = d[j];
+ DCOUTVAR(r);
+ do {
+ r = gcd(r, q);
+ DCOUTVAR(r);
+ q = q/r;
+ DCOUTVAR(q);
+ } while ( r != 1 );
+ if ( q == 1 ) {
+ DCOUT(true);
+ DCOUT(END checkdivisors);
+ return true;
+ }
+ }
+ d[i] = q;
+ }
+ DCOUT(false);
+ DCOUT(END checkdivisors);
+ return false;
+}
+
+static bool generate_set(const ex& u, const ex& vn, const exset& syms, const ex& f, const numeric& modulus, vector<numeric>& a, vector<numeric>& d)
+{
+ // computation of d is actually not necessary
+ DCOUT(generate_set);
+ DCOUTVAR(u);
+ DCOUTVAR(vn);
+ DCOUTVAR(f);
+ DCOUTVAR(modulus);
+ const ex& x = *syms.begin();
+ bool trying = true;
+ do {
+ ex u0 = u;
+ ex vna = vn;
+ ex vnatry;
+ exset::const_iterator s = syms.begin();
+ ++s;
+ for ( size_t i=0; i<a.size(); ++i ) {
+ DCOUTVAR(*s);
+ do {
+ a[i] = mod(numeric(rand()), 2*modulus) - modulus;
+ vnatry = vna.subs(*s == a[i]);
+ } while ( vnatry == 0 );
+ vna = vnatry;
+ u0 = u0.subs(*s == a[i]);
+ ++s;
+ }
+ DCOUTVAR(a);
+ DCOUTVAR(u0);
+ if ( gcd(u0,u0.diff(ex_to<symbol>(x))) != 1 ) {
+ continue;
+ }
+ if ( is_a<numeric>(vn) ) {
+ trying = false;
+ }
+ else {
+ DCOUT(do substitution);
+ lst fnum;
+ lst::const_iterator i = ex_to<lst>(f).begin();
+ fnum.append(*i++);
+ bool problem = false;
+ while ( i!=ex_to<lst>(f).end() ) {
+ ex fs = *i;
+ if ( !is_a<numeric>(fs) ) {
+ s = syms.begin();
+ ++s;
+ for ( size_t j=0; j<a.size(); ++j ) {
+ fs = fs.subs(*s == a[j]);
+ ++s;
+ }
+ if ( abs(fs) == 1 ) {
+ problem = true;
+ break;
+ }
+ }
+ fnum.append(fs);
+ ++i; ++i;
+ }
+ if ( problem ) {
+ return true;
+ }
+ ex con = u0.content(x);
+ fnum.append(con);
+ DCOUTVAR(fnum);
+ trying = checkdivisors(fnum, d);
+ }
+ } while ( trying );
+ DCOUT(END generate_set);
+ return false;
+}
+
+#ifdef DEBUGFACTOR
+ex factor(const ex&);
+#endif
+
+static ex factor_multivariate(const ex& poly, const exset& syms)
+{
+ DCOUT(factor_multivariate);
+ DCOUTVAR(poly);
+
+ exset::const_iterator s;
+ const ex& x = *syms.begin();
+ DCOUTVAR(x);
+
+ /* make polynomial primitive */
+ ex p = poly.expand().collect(x);
+ DCOUTVAR(p);
+ ex cont = p.lcoeff(x);
+ for ( numeric i=p.degree(x)-1; i>=p.ldegree(x); --i ) {
+ cont = gcd(cont, p.coeff(x,ex_to<numeric>(i).to_int()));
+ if ( cont == 1 ) break;
+ }
+ DCOUTVAR(cont);
+ ex pp = expand(normal(p / cont));
+ DCOUTVAR(pp);
+ if ( !is_a<numeric>(cont) ) {
+#ifdef DEBUGFACTOR
+ return ::factor(cont) * ::factor(pp);
+#else
+ return factor(cont) * factor(pp);
+#endif
+ }
+
+ /* factor leading coefficient */
+ pp = pp.collect(x);
+ ex vn = pp.lcoeff(x);
+ pp = pp.expand();
+ ex vnlst;
+ if ( is_a<numeric>(vn) ) {
+ vnlst = lst(vn);
+ }
+ else {
+#ifdef DEBUGFACTOR
+ ex vnfactors = ::factor(vn);
+#else
+ ex vnfactors = factor(vn);
+#endif
+ vnlst = put_factors_into_lst(vnfactors);
+ }
+ DCOUTVAR(vnlst);
+
+ const numeric maxtrials = 3;
+ numeric modulus = (vnlst.nops()-1 > 3) ? vnlst.nops()-1 : 3;
+ DCOUTVAR(modulus);
+ numeric minimalr = -1;
+ vector<numeric> a(syms.size()-1, 0);
+ vector<numeric> d((vnlst.nops()-1)/2+1, 0);
+
+ while ( true ) {
+ numeric trialcount = 0;
+ ex u, delta;
+ unsigned int prime;
+ size_t factor_count;
+ ex ufac;
+ ex ufaclst;
+ while ( trialcount < maxtrials ) {
+ bool problem = generate_set(pp, vn, syms, vnlst, modulus, a, d);
+ DCOUTVAR(problem);
+ if ( problem ) {
+ ++modulus;
+ continue;
+ }
+ DCOUTVAR(a);
+ DCOUTVAR(d);
+ u = pp;
+ s = syms.begin();
+ ++s;
+ for ( size_t i=0; i<a.size(); ++i ) {
+ u = u.subs(*s == a[i]);
+ ++s;
+ }
+ delta = u.content(x);
+ DCOUTVAR(u);
+
+ // determine proper prime
+ prime = 3;
+ DCOUTVAR(prime);
+ cl_modint_ring R = find_modint_ring(prime);
+ DCOUTVAR(u.lcoeff(x));
+ while ( true ) {
+ if ( irem(ex_to<numeric>(u.lcoeff(x)), prime) != 0 ) {
+ UniPoly modpoly(R, u, x);
+ UniFactorVec sqrfree_ufv;
+ squarefree(modpoly, sqrfree_ufv);
+ DCOUTVAR(sqrfree_ufv);
+ if ( sqrfree_ufv.factors.size() == 1 && sqrfree_ufv.factors.front().exp == 1 ) break;
+ }
+ prime = next_prime(prime);
+ DCOUTVAR(prime);
+ R = find_modint_ring(prime);
+ }
+
+#ifdef DEBUGFACTOR
+ ufac = ::factor(u);
+#else
+ ufac = factor(u);
+#endif
+ DCOUTVAR(ufac);
+ ufaclst = put_factors_into_lst(ufac);
+ DCOUTVAR(ufaclst);
+ factor_count = (ufaclst.nops()-1)/2;
+ DCOUTVAR(factor_count);
+
+ if ( factor_count <= 1 ) {
+ DCOUTVAR(poly);
+ DCOUT(END factor_multivariate);
+ return poly;
+ }
+
+ if ( minimalr < 0 ) {
+ minimalr = factor_count;
+ }
+ else if ( minimalr == factor_count ) {
+ ++trialcount;
+ ++modulus;
+ }
+ else if ( minimalr > factor_count ) {
+ minimalr = factor_count;
+ trialcount = 0;
+ }
+ DCOUTVAR(trialcount);
+ DCOUTVAR(minimalr);
+ if ( minimalr <= 1 ) {
+ DCOUTVAR(poly);
+ DCOUT(END factor_multivariate);
+ return poly;
+ }
+ }
+
+ vector<numeric> ftilde((vnlst.nops()-1)/2+1);
+ ftilde[0] = ex_to<numeric>(vnlst.op(0));
+ for ( size_t i=1; i<ftilde.size(); ++i ) {
+ ex ft = vnlst.op((i-1)*2+1);
+ s = syms.begin();
+ ++s;
+ for ( size_t j=0; j<a.size(); ++j ) {
+ ft = ft.subs(*s == a[j]);
+ ++s;
+ }
+ ftilde[i] = ex_to<numeric>(ft);
+ }
+ DCOUTVAR(ftilde);
+
+ vector<bool> used_flag((vnlst.nops()-1)/2+1, false);
+ vector<ex> D(factor_count, 1);
+ for ( size_t i=0; i<=factor_count; ++i ) {
+ DCOUTVAR(i);
+ numeric prefac;
+ if ( i == 0 ) {
+ prefac = ex_to<numeric>(ufaclst.op(0));
+ ftilde[0] = ftilde[0] / prefac;
+ vnlst.let_op(0) = vnlst.op(0) / prefac;
+ continue;
+ }
+ else {
+ prefac = ex_to<numeric>(ufaclst.op(2*(i-1)+1).lcoeff(x));
+ }
+ DCOUTVAR(prefac);
+ for ( size_t j=(vnlst.nops()-1)/2+1; j>0; --j ) {
+ DCOUTVAR(j);
+ DCOUTVAR(prefac);
+ DCOUTVAR(ftilde[j-1]);
+ if ( abs(ftilde[j-1]) == 1 ) {
+ used_flag[j-1] = true;
+ continue;
+ }
+ numeric g = gcd(prefac, ftilde[j-1]);
+ DCOUTVAR(g);
+ if ( g != 1 ) {
+ DCOUT(has_common_prime);
+ prefac = prefac / g;
+ numeric count = abs(iquo(g, ftilde[j-1]));
+ DCOUTVAR(count);
+ used_flag[j-1] = true;
+ if ( i > 0 ) {
+ if ( j == 1 ) {
+ D[i-1] = D[i-1] * pow(vnlst.op(0), count);
+ }
+ else {
+ D[i-1] = D[i-1] * pow(vnlst.op(2*(j-2)+1), count);
+ }
+ }
+ else {
+ ftilde[j-1] = ftilde[j-1] / prefac;
+ DCOUT(BREAK);
+ DCOUTVAR(ftilde[j-1]);
+ break;
+ }
+ ++j;
+ }
+ }
+ }
+ DCOUTVAR(D);
+
+ bool some_factor_unused = false;
+ for ( size_t i=0; i<used_flag.size(); ++i ) {
+ if ( !used_flag[i] ) {
+ some_factor_unused = true;
+ break;
+ }
+ }
+ if ( some_factor_unused ) {
+ DCOUT(some factor unused!);
+ continue;
+ }
+
+ vector<ex> C(factor_count);
+ DCOUTVAR(C);
+ DCOUTVAR(delta);
+ if ( delta == 1 ) {
+ for ( size_t i=0; i<D.size(); ++i ) {
+ ex Dtilde = D[i];
+ s = syms.begin();
+ ++s;
+ for ( size_t j=0; j<a.size(); ++j ) {
+ Dtilde = Dtilde.subs(*s == a[j]);
+ ++s;
+ }
+ DCOUTVAR(Dtilde);
+ C[i] = D[i] * (ufaclst.op(2*i+1).lcoeff(x) / Dtilde);
+ }
+ }
+ else {
+ for ( size_t i=0; i<D.size(); ++i ) {
+ ex Dtilde = D[i];
+ s = syms.begin();
+ ++s;
+ for ( size_t j=0; j<a.size(); ++j ) {
+ Dtilde = Dtilde.subs(*s == a[j]);
+ ++s;
+ }
+ ex ui;
+ if ( i == 0 ) {
+ ui = ufaclst.op(0);
+ }
+ else {
+ ui = ufaclst.op(2*(i-1)+1);
+ }
+ while ( true ) {
+ ex d = gcd(ui.lcoeff(x), Dtilde);
+ C[i] = D[i] * ( ui.lcoeff(x) / d );
+ ui = ui * ( Dtilde[i] / d );
+ delta = delta / ( Dtilde[i] / d );
+ if ( delta == 1 ) break;
+ ui = delta * ui;
+ C[i] = delta * C[i];
+ pp = pp * pow(delta, D.size()-1);
+ }
+ }
+ }
+ DCOUTVAR(C);
+
+ EvalPoint ep;
+ vector<EvalPoint> epv;
+ s = syms.begin();
+ ++s;
+ for ( size_t i=0; i<a.size(); ++i ) {
+ ep.x = *s++;
+ ep.evalpoint = a[i].to_int();
+ epv.push_back(ep);
+ }
+ DCOUTVAR(epv);
+
+ // calc bound B
+ ex maxcoeff;
+ for ( int i=u.degree(x); i>=u.ldegree(x); --i ) {
+ maxcoeff += pow(abs(u.coeff(x, i)),2);
+ }
+ cl_I normmc = ceiling1(the<cl_R>(cln::sqrt(ex_to<numeric>(maxcoeff).to_cl_N())));
+ unsigned int maxdegree = 0;
+ for ( size_t i=0; i<factor_count; ++i ) {
+ if ( ufaclst[2*i+1].degree(x) > (int)maxdegree ) {
+ maxdegree = ufaclst[2*i+1].degree(x);
+ }
+ }
+ cl_I B = normmc * expt_pos(cl_I(2), maxdegree);
+ cl_I l = 1;
+ cl_I pl = prime;
+ while ( pl < B ) {
+ l = l + 1;
+ pl = pl * prime;
+ }
+
+ UniPolyVec uvec;
+ cl_modint_ring R = find_modint_ring(expt_pos(cl_I(prime),l));
+ for ( size_t i=0; i<(ufaclst.nops()-1)/2; ++i ) {
+ UniPoly newu(R, ufaclst.op(i*2+1), x);
+ uvec.push_back(newu);
+ }
+ DCOUTVAR(uvec);
+
+ ex res = hensel_multivar(ufaclst.op(0)*pp, x, epv, prime, l, uvec, C);
+ if ( res != lst() ) {
+ ex result = cont * ufaclst.op(0);
+ for ( size_t i=0; i<res.nops(); ++i ) {
+ result *= res.op(i).content(x) * res.op(i).unit(x);
+ result *= res.op(i).primpart(x);
+ }
+ DCOUTVAR(result);
+ DCOUT(END factor_multivariate);
+ return result;
+ }
+ }
git://www.ginac.de / ginac.git / blobdiff