/** @file factor.cpp
*
- * Polynomial factorization routines.
- * Only univariate at the moment and completely non-optimized!
+ * Polynomial factorization code (Implementation).
+ *
+ * Algorithms used can be found in
+ * [W1] An Improved Multivariate Polynomial Factoring Algorithm,
+ * P.S.Wang, Mathematics of Computation, Vol. 32, No. 144 (1978) 1215--1231.
+ * [GCL] Algorithms for Computer Algebra,
+ * K.O.Geddes, S.R.Czapor, G.Labahn, Springer Verlag, 1992.
*/
/*
#define DCOUT2(str,var)
#endif
+// forward declaration
+ex factor(const ex& poly, unsigned options);
+
+// anonymous namespace to hide all utility functions
namespace {
typedef vector<cl_MI> Vec;
// assert: poly is in Z[x]
Term t;
for ( int i=poly.degree(x); i>=poly.ldegree(x); --i ) {
- int coeff = ex_to<numeric>(poly.coeff(x,i)).to_int();
- if ( coeff ) {
+ cl_I coeff = the<cl_I>(ex_to<numeric>(poly.coeff(x,i)).to_cl_N());
+ if ( !zerop(coeff) ) {
t.c = R->canonhom(coeff);
if ( !zerop(t.c) ) {
t.exp = i;
maxcoeff += pow(abs(a.coeff(x, i)),2);
}
cl_I normmc = ceiling1(the<cl_R>(cln::sqrt(ex_to<numeric>(maxcoeff).to_cl_N())));
- unsigned int maxdegree = (u1_.degree() > w1_.degree()) ? u1_.degree() : w1_.degree();
- unsigned int B = cl_I_to_uint(normmc * expt_pos(cl_I(2), maxdegree));
+ cl_I maxdegree = (u1_.degree() > w1_.degree()) ? u1_.degree() : w1_.degree();
+ cl_I B = normmc * expt_pos(cl_I(2), maxdegree);
// step 1
ex alpha = a.lcoeff(x);
if ( gamma == 0 ) {
gamma = alpha;
}
- unsigned int gamma_ui = ex_to<numeric>(abs(gamma)).to_int();
+ numeric gamma_ui = ex_to<numeric>(abs(gamma));
a = a * gamma;
UniPoly nu1 = u1_;
nu1.unit_normal();
ex u = replace_lc(u1.to_ex(x), x, gamma);
ex w = replace_lc(w1.to_ex(x), x, alpha);
ex e = expand(a - u * w);
- unsigned int modulus = p;
+ numeric modulus = p;
+ const numeric maxmodulus = 2*numeric(B)*gamma_ui;
// step 4
- while ( !e.is_zero() && modulus < 2*B*gamma_ui ) {
+ while ( !e.is_zero() && modulus < maxmodulus ) {
ex c = e / modulus;
phi = expand(s.to_ex(x)*c);
UniPoly sigmatilde(R, phi, x);
return unit * cont * result;
}
-struct FindSymbolsMap : public map_function {
- exset syms;
- ex operator()(const ex& e)
- {
- if ( is_a<symbol>(e) ) {
- syms.insert(e);
- return e;
- }
- return e.map(*this);
- }
-};
-
struct EvalPoint
{
ex x;
vector<ex> anew = a;
for ( size_t i=0; i<r; ++i ) {
- a[i] = a[i].subs(xnu == alphanu);
+ anew[i] = anew[i].subs(xnu == alphanu);
}
ex cnew = c.subs(xnu == alphanu);
vector<EvalPoint> Inew = I;
Inew.pop_back();
- vector<ex> sigma = multivar_diophant(anew, x, cnew, Inew, d, p, k);
+ sigma = multivar_diophant(anew, x, cnew, Inew, d, p, k);
+ DCOUTVAR(sigma);
ex buf = c;
for ( size_t i=0; i<r; ++i ) {
ex e = buf;
e = make_modular(e, R);
+ e = e.expand();
+ DCOUTVAR(e);
+ DCOUTVAR(d);
ex monomial = 1;
for ( size_t m=1; m<=d; ++m ) {
- while ( !e.is_zero() ) {
+ DCOUTVAR(m);
+ while ( !e.is_zero() && e.has(xnu) ) {
monomial *= (xnu - alphanu);
monomial = expand(monomial);
+ DCOUTVAR(xnu);
+ DCOUTVAR(alphanu);
ex cm = e.diff(ex_to<symbol>(xnu), m).subs(xnu==alphanu) / factorial(m);
+ DCOUTVAR(cm);
if ( !cm.is_zero() ) {
vector<ex> delta_s = multivar_diophant(anew, x, cm, Inew, d, p, k);
+ DCOUTVAR(delta_s);
ex buf = e;
for ( size_t j=0; j<delta_s.size(); ++j ) {
delta_s[j] *= monomial;
sigma[j] += delta_s[j];
buf -= delta_s[j] * b[j];
}
- e = buf;
+ e = buf.expand();
e = make_modular(e, R);
}
}
}
}
else {
+ DCOUT(uniterm left);
UniPolyVec amod;
for ( size_t i=0; i<a.size(); ++i ) {
UniPoly up(R, a[i], x);
DCOUTVAR(j);
vector<ex> U1 = U;
ex monomial = 1;
+ DCOUTVAR(U);
for ( size_t m=0; m<n; ++m) {
if ( lcU[m] != 1 ) {
ex coef = lcU[m];
U[m] = U[m] - U[m].lcoeff(x) * pow(x,deg) + coef * pow(x,deg);
}
}
+ DCOUTVAR(U);
ex Uprod = 1;
for ( size_t i=0; i<n; ++i ) {
Uprod *= U[i];
ex e = expand(A[j-1] - Uprod);
DCOUTVAR(e);
+ vector<EvalPoint> newI;
+ for ( size_t i=1; i<=j-2; ++i ) {
+ newI.push_back(I[i-1]);
+ }
+ DCOUTVAR(newI);
+
ex xj = I[j-2].x;
int alphaj = I[j-2].evalpoint;
size_t deg = A[j-1].degree(xj);
ex c = dif.subs(xj==alphaj) / factorial(k);
DCOUTVAR(c);
if ( !c.is_zero() ) {
- vector<EvalPoint> newI = I;
- newI.pop_back();
vector<ex> deltaU = multivar_diophant(U1, x, c, newI, maxdeg, p, cl_I_to_uint(l));
for ( size_t i=0; i<n; ++i ) {
DCOUTVAR(i);
deltaU[i] *= monomial;
U[i] += deltaU[i];
U[i] = make_modular(U[i], R);
+ U[i] = U[i].expand();
+ DCOUTVAR(U[i]);
}
ex Uprod = 1;
for ( size_t i=0; i<n; ++i ) {
Uprod *= U[i];
}
+ DCOUTVAR(Uprod.expand());
+ DCOUTVAR(A[j-1]);
e = expand(A[j-1] - Uprod);
e = make_modular(e, R);
DCOUTVAR(e);
DCOUTVAR(result);
return result;
}
- if ( is_a<symbol>(e) ) {
+ if ( is_a<symbol>(e) || is_a<add>(e) ) {
result.append(1);
result.append(e);
result.append(1);
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 ) {
- q = ex_to<numeric>(abs(f.op(i-1)));
+ 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 void generate_set(const ex& u, const ex& vn, const exset& syms, const ex& f, const numeric& modulus, vector<numeric>& a, vector<numeric>& d)
+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 {
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) ) {
- d = a;
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;
- s = syms.begin();
- ++s;
- for ( size_t j=0; j<a.size(); ++j ) {
- fs = fs.subs(*s == a[j]);
+ 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
-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 ex factor_multivariate(const ex& poly, const exset& syms)
{
DCOUT(factor_multivariate);
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 = p.lcoeff(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);
- vector<numeric> d(syms.size()-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;
- UniPolyVec uvec;
+ size_t factor_count;
+ ex ufac;
+ ex ufaclst;
while ( trialcount < maxtrials ) {
- uvec.clear();
- generate_set(pp, vn, syms, vnlst, modulus, a, d);
+ bool problem = generate_set(pp, vn, syms, vnlst, modulus, a, d);
+ DCOUTVAR(problem);
+ if ( problem ) {
+ ++modulus;
+ continue;
+ }
DCOUTVAR(a);
DCOUTVAR(d);
u = pp;
++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);
}
- UniPoly umod(R, u, x);
- DCOUTVAR(u);
- factor_modular(umod, uvec);
- DCOUTVAR(uvec);
+#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 ( uvec.size() == 1 ) {
+ if ( factor_count <= 1 ) {
DCOUTVAR(poly);
DCOUT(END factor_multivariate);
return poly;
}
if ( minimalr < 0 ) {
- minimalr = uvec.size();
+ minimalr = factor_count;
}
- else if ( minimalr == uvec.size() ) {
+ else if ( minimalr == factor_count ) {
++trialcount;
++modulus;
}
- else if ( minimalr > uvec.size() ) {
- minimalr = uvec.size();
+ else if ( minimalr > factor_count ) {
+ minimalr = factor_count;
trialcount = 0;
}
DCOUTVAR(trialcount);
DCOUTVAR(minimalr);
- if ( minimalr == 0 ) {
+ if ( minimalr <= 1 ) {
DCOUTVAR(poly);
DCOUT(END factor_multivariate);
return poly;
}
}
- vector<ex> C;
- if ( vnlst.nops() == 1 ) {
- C.resize(uvec.size(), 1);
+ 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);
}
- else {
+ DCOUTVAR(ftilde);
- vector<numeric> ftilde((vnlst.nops()-1)/2);
- for ( size_t i=0; i<ftilde.size(); ++i ) {
- ex ft = vnlst.op(i*2+1);
- s = syms.begin();
- ++s;
- for ( size_t j=0; j<a.size(); ++j ) {
- ft = ft.subs(*s == a[j]);
- ++s;
+ 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;
}
- ftilde[i] = ex_to<numeric>(ft);
- }
- DCOUTVAR(ftilde);
-
- vector<ex> D;
- vector<bool> fflag(ftilde.size(), false);
- for ( size_t i=0; i<uvec.size(); ++i ) {
- ex ui = uvec[i].to_ex(x);
- ex Di = 1;
- numeric coeff = ex_to<numeric>(ui.lcoeff(x));
- for ( size_t j=0; j<ftilde.size(); ++j ) {
- if ( numeric(coeff / ftilde[j]).is_integer() ) {
- coeff = coeff / ftilde[j];
- Di *= ftilde[j];
- fflag[j] = true;
- --j;
+ 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;
}
- D.push_back(Di.expand());
}
- for ( size_t i=0; i<fflag.size(); ++i ) {
- if ( !fflag[i] ) {
- --minimalr;
- continue;
- }
+ }
+ 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;
}
- DCOUTVAR(D);
+ }
+ if ( some_factor_unused ) {
+ DCOUT(some factor unused!);
+ continue;
+ }
- C.resize(D.size());
- if ( delta == 1 ) {
- for ( size_t i=0; i<D.size(); ++i ) {
- ex Dtilde = D[i];
- s = syms.begin();
+ 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;
- for ( size_t j=0; j<a.size(); ++j ) {
- Dtilde = Dtilde.subs(*s == a[j]);
- ++s;
- }
- ex Ci = D[i] * (uvec[i].to_ex(x).lcoeff(x) / Dtilde);
- C.push_back(Ci);
}
+ 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();
+ }
+ 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;
- for ( size_t j=0; j<a.size(); ++j ) {
- Dtilde = Dtilde.subs(*s == a[j]);
- ++s;
- }
- ex ui = uvec[i].to_ex(x);
- ex Ci;
- while ( true ) {
- ex d = gcd(ui.lcoeff(x), Dtilde);
- Ci = D[i] * ( ui.lcoeff(x) / d );
- ui = ui * ( Dtilde[i] / d );
- delta = delta / ( Dtilde[i] / d );
- if ( delta == 1 ) break;
- ui = delta * ui;
- Ci = delta * Ci;
- pp = pp * pow(delta, D.size()-1);
- }
+ }
+ 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;
ep.evalpoint = a[i].to_int();
epv.push_back(ep);
}
+ DCOUTVAR(epv);
// calc bound B
ex maxcoeff;
}
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<uvec.size(); ++i ) {
- if ( uvec[i].degree() > maxdegree ) {
- maxdegree = uvec[i].degree();
+ 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);
}
}
- unsigned int B = cl_I_to_uint(normmc * expt_pos(cl_I(2), maxdegree));
+ 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;
+ }
- ex res = hensel_multivar(poly, x, epv, prime, B, uvec, C);
+ 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;
+ 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);
}
}
+struct find_symbols_map : public map_function {
+ exset syms;
+ ex operator()(const ex& e)
+ {
+ if ( is_a<symbol>(e) ) {
+ syms.insert(e);
+ return e;
+ }
+ return e.map(*this);
+ }
+};
+
static ex factor_sqrfree(const ex& poly)
{
// determine all symbols in poly
- FindSymbolsMap findsymbols;
+ find_symbols_map findsymbols;
findsymbols(poly);
if ( findsymbols.syms.size() == 0 ) {
return poly;
return res;
}
+struct apply_factor_map : public map_function {
+ unsigned options;
+ apply_factor_map(unsigned options_) : options(options_) { }
+ ex operator()(const ex& e)
+ {
+ if ( e.info(info_flags::polynomial) ) {
+#ifdef DEBUGFACTOR
+ return ::factor(e, options);
+#else
+ return factor(e, options);
+#endif
+ }
+ if ( is_a<add>(e) ) {
+ ex s1, s2;
+ for ( size_t i=0; i<e.nops(); ++i ) {
+ if ( e.op(i).info(info_flags::polynomial) ) {
+ s1 += e.op(i);
+ }
+ else {
+ s2 += e.op(i);
+ }
+ }
+ s1 = s1.eval();
+ s2 = s2.eval();
+#ifdef DEBUGFACTOR
+ return ::factor(s1, options) + s2.map(*this);
+#else
+ return factor(s1, options) + s2.map(*this);
+#endif
+ }
+ return e.map(*this);
+ }
+};
+
} // anonymous namespace
-ex factor(const ex& poly)
+#ifdef DEBUGFACTOR
+ex factor(const ex& poly, unsigned options = 0)
+#else
+ex factor(const ex& poly, unsigned options)
+#endif
{
+ // check arguments
+ if ( !poly.info(info_flags::polynomial) ) {
+ if ( options & factor_options::all ) {
+ options &= ~factor_options::all;
+ apply_factor_map factor_map(options);
+ return factor_map(poly);
+ }
+ return poly;
+ }
+
// determine all symbols in poly
- FindSymbolsMap findsymbols;
+ find_symbols_map findsymbols;
findsymbols(poly);
if ( findsymbols.syms.size() == 0 ) {
return poly;
return pow(f, sfpoly.op(1));
}
if ( is_a<mul>(sfpoly) ) {
+ // case: multiple factors
ex res = 1;
for ( size_t i=0; i<sfpoly.nops(); ++i ) {
const ex& t = sfpoly.op(i);
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