* computation, square-free factorization and rational function normalization. */
/*
- * GiNaC Copyright (C) 1999-2005 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2015 Johannes Gutenberg University Mainz, Germany
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
-#include <algorithm>
-#include <map>
-
#include "normal.h"
#include "basic.h"
#include "ex.h"
#include "pseries.h"
#include "symbol.h"
#include "utils.h"
+#include "polynomial/chinrem_gcd.h"
+
+#include <algorithm>
+#include <map>
namespace GiNaC {
*
* @see get_symbol_stats */
struct sym_desc {
+ /** Initialize symbol, leave other variables uninitialized */
+ sym_desc(const ex& s)
+ : sym(s), deg_a(0), deg_b(0), ldeg_a(0), ldeg_b(0), max_deg(0), max_lcnops(0)
+ { }
+
/** Reference to symbol */
ex sym;
// Add symbol the sym_desc_vec (used internally by get_symbol_stats())
static void add_symbol(const ex &s, sym_desc_vec &v)
{
- sym_desc_vec::const_iterator it = v.begin(), itend = v.end();
- while (it != itend) {
- if (it->sym.is_equal(s)) // If it's already in there, don't add it a second time
+ for (auto & it : v)
+ if (it.sym.is_equal(s)) // If it's already in there, don't add it a second time
return;
- ++it;
- }
- sym_desc d;
- d.sym = s;
- v.push_back(d);
+
+ v.push_back(sym_desc(s));
}
// Collect all symbols of an expression (used internally by get_symbol_stats())
{
collect_symbols(a.eval(), v); // eval() to expand assigned symbols
collect_symbols(b.eval(), v);
- sym_desc_vec::iterator it = v.begin(), itend = v.end();
- while (it != itend) {
- int deg_a = a.degree(it->sym);
- int deg_b = b.degree(it->sym);
- it->deg_a = deg_a;
- it->deg_b = deg_b;
- it->max_deg = std::max(deg_a, deg_b);
- it->max_lcnops = std::max(a.lcoeff(it->sym).nops(), b.lcoeff(it->sym).nops());
- it->ldeg_a = a.ldegree(it->sym);
- it->ldeg_b = b.ldegree(it->sym);
- ++it;
+ for (auto & it : v) {
+ int deg_a = a.degree(it.sym);
+ int deg_b = b.degree(it.sym);
+ it.deg_a = deg_a;
+ it.deg_b = deg_b;
+ it.max_deg = std::max(deg_a, deg_b);
+ it.max_lcnops = std::max(a.lcoeff(it.sym).nops(), b.lcoeff(it.sym).nops());
+ it.ldeg_a = a.ldegree(it.sym);
+ it.ldeg_b = b.ldegree(it.sym);
}
std::sort(v.begin(), v.end());
lcm_accum *= op_lcm;
}
v.push_back(lcm / lcm_accum);
- return (new mul(v))->setflag(status_flags::dynallocated);
+ return dynallocate<mul>(v);
} else if (is_exactly_a<add>(e)) {
size_t num = e.nops();
exvector v; v.reserve(num);
for (size_t i=0; i<num; i++)
v.push_back(multiply_lcm(e.op(i), lcm));
- return (new add(v))->setflag(status_flags::dynallocated);
+ return dynallocate<add>(v);
} else if (is_exactly_a<power>(e)) {
if (is_a<symbol>(e.op(0)))
return e * lcm;
numeric add::integer_content() const
{
- epvector::const_iterator it = seq.begin();
- epvector::const_iterator itend = seq.end();
numeric c = *_num0_p, l = *_num1_p;
- while (it != itend) {
- GINAC_ASSERT(!is_exactly_a<numeric>(it->rest));
- GINAC_ASSERT(is_exactly_a<numeric>(it->coeff));
- c = gcd(ex_to<numeric>(it->coeff).numer(), c);
- l = lcm(ex_to<numeric>(it->coeff).denom(), l);
- it++;
+ for (auto & it : seq) {
+ GINAC_ASSERT(!is_exactly_a<numeric>(it.rest));
+ GINAC_ASSERT(is_exactly_a<numeric>(it.coeff));
+ c = gcd(ex_to<numeric>(it.coeff).numer(), c);
+ l = lcm(ex_to<numeric>(it.coeff).denom(), l);
}
GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
c = gcd(ex_to<numeric>(overall_coeff).numer(), c);
numeric mul::integer_content() const
{
#ifdef DO_GINAC_ASSERT
- epvector::const_iterator it = seq.begin();
- epvector::const_iterator itend = seq.end();
- while (it != itend) {
- GINAC_ASSERT(!is_exactly_a<numeric>(recombine_pair_to_ex(*it)));
- ++it;
+ for (auto & it : seq) {
+ GINAC_ASSERT(!is_exactly_a<numeric>(recombine_pair_to_ex(it)));
}
#endif // def DO_GINAC_ASSERT
GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
term = rcoeff / blcoeff;
else {
if (!divide(rcoeff, blcoeff, term, false))
- return (new fail())->setflag(status_flags::dynallocated);
+ return dynallocate<fail>();
}
term *= power(x, rdeg - bdeg);
v.push_back(term);
break;
rdeg = r.degree(x);
}
- return (new add(v))->setflag(status_flags::dynallocated);
+ return dynallocate<add>(v);
}
term = rcoeff / blcoeff;
else {
if (!divide(rcoeff, blcoeff, term, false))
- return (new fail())->setflag(status_flags::dynallocated);
+ return dynallocate<fail>();
}
term *= power(x, rdeg - bdeg);
r -= (term * b).expand();
if (!get_first_symbol(a, x) && !get_first_symbol(b, x))
throw(std::invalid_argument("invalid expression in divide()"));
+ // Try to avoid expanding partially factored expressions.
+ if (is_exactly_a<mul>(b)) {
+ // Divide sequentially by each term
+ ex rem_new, rem_old = a;
+ for (size_t i=0; i < b.nops(); i++) {
+ if (! divide(rem_old, b.op(i), rem_new, false))
+ return false;
+ rem_old = rem_new;
+ }
+ q = rem_new;
+ return true;
+ } else if (is_exactly_a<power>(b)) {
+ const ex& bb(b.op(0));
+ int exp_b = ex_to<numeric>(b.op(1)).to_int();
+ ex rem_new, rem_old = a;
+ for (int i=exp_b; i>0; i--) {
+ if (! divide(rem_old, bb, rem_new, false))
+ return false;
+ rem_old = rem_new;
+ }
+ q = rem_new;
+ return true;
+ }
+
+ if (is_exactly_a<mul>(a)) {
+ // Divide sequentially each term. If some term in a is divisible
+ // by b we are done... and if not, we can't really say anything.
+ size_t i;
+ ex rem_i;
+ bool divisible_p = false;
+ for (i=0; i < a.nops(); ++i) {
+ if (divide(a.op(i), b, rem_i, false)) {
+ divisible_p = true;
+ break;
+ }
+ }
+ if (divisible_p) {
+ exvector resv;
+ resv.reserve(a.nops());
+ for (size_t j=0; j < a.nops(); j++) {
+ if (j==i)
+ resv.push_back(rem_i);
+ else
+ resv.push_back(a.op(j));
+ }
+ q = dynallocate<mul>(resv);
+ return true;
+ }
+ } else if (is_exactly_a<power>(a)) {
+ // The base itself might be divisible by b, in that case we don't
+ // need to expand a
+ const ex& ab(a.op(0));
+ int a_exp = ex_to<numeric>(a.op(1)).to_int();
+ ex rem_i;
+ if (divide(ab, b, rem_i, false)) {
+ q = rem_i*power(ab, a_exp - 1);
+ return true;
+ }
+// code below is commented-out because it leads to a significant slowdown
+// for (int i=2; i < a_exp; i++) {
+// if (divide(power(ab, i), b, rem_i, false)) {
+// q = rem_i*power(ab, a_exp - i);
+// return true;
+// }
+// } // ... so we *really* need to expand expression.
+ }
+
// Polynomial long division (recursive)
ex r = a.expand();
if (r.is_zero()) {
v.push_back(term);
r -= (term * b).expand();
if (r.is_zero()) {
- q = (new add(v))->setflag(status_flags::dynallocated);
+ q = dynallocate<add>(v);
return true;
}
rdeg = r.degree(x);
}
#endif
+ if (is_exactly_a<power>(b)) {
+ const ex& bb(b.op(0));
+ ex qbar = a;
+ int exp_b = ex_to<numeric>(b.op(1)).to_int();
+ for (int i=exp_b; i>0; i--) {
+ if (!divide_in_z(qbar, bb, q, var))
+ return false;
+ qbar = q;
+ }
+ return true;
+ }
+
+ if (is_exactly_a<mul>(b)) {
+ ex qbar = a;
+ for (const auto & it : b) {
+ sym_desc_vec sym_stats;
+ get_symbol_stats(a, it, sym_stats);
+ if (!divide_in_z(qbar, it, q, sym_stats.begin()))
+ return false;
+
+ qbar = q;
+ }
+ return true;
+ }
+
// Main symbol
const ex &x = var->sym;
v.push_back(term);
r -= (term * eb).expand();
if (r.is_zero()) {
- q = (new add(v))->setflag(status_flags::dynallocated);
+ q = dynallocate<add>(v);
#if USE_REMEMBER
dr_remember[ex2(a, b)] = exbool(q, true);
#endif
return lcoeff * c / lcoeff.unit(x);
ex cont = _ex0;
for (int i=ldeg; i<=deg; i++)
- cont = gcd(r.coeff(x, i), cont, NULL, NULL, false);
+ cont = gcd(r.coeff(x, i), cont, nullptr, nullptr, false);
return cont * c;
}
// Remove content from c and d, to be attached to GCD later
ex cont_c = c.content(x);
ex cont_d = d.content(x);
- ex gamma = gcd(cont_c, cont_d, NULL, NULL, false);
+ ex gamma = gcd(cont_c, cont_d, nullptr, nullptr, false);
if (ddeg == 0)
return gamma;
c = c.primpart(x, cont_c);
numeric add::max_coefficient() const
{
- epvector::const_iterator it = seq.begin();
- epvector::const_iterator itend = seq.end();
GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
numeric cur_max = abs(ex_to<numeric>(overall_coeff));
- while (it != itend) {
+ for (auto & it : seq) {
numeric a;
- GINAC_ASSERT(!is_exactly_a<numeric>(it->rest));
- a = abs(ex_to<numeric>(it->coeff));
+ GINAC_ASSERT(!is_exactly_a<numeric>(it.rest));
+ a = abs(ex_to<numeric>(it.coeff));
if (a > cur_max)
cur_max = a;
- it++;
}
return cur_max;
}
numeric mul::max_coefficient() const
{
#ifdef DO_GINAC_ASSERT
- epvector::const_iterator it = seq.begin();
- epvector::const_iterator itend = seq.end();
- while (it != itend) {
- GINAC_ASSERT(!is_exactly_a<numeric>(recombine_pair_to_ex(*it)));
- it++;
+ for (auto & it : seq) {
+ GINAC_ASSERT(!is_exactly_a<numeric>(recombine_pair_to_ex(it)));
}
#endif // def DO_GINAC_ASSERT
GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
{
epvector newseq;
newseq.reserve(seq.size()+1);
- epvector::const_iterator it = seq.begin();
- epvector::const_iterator itend = seq.end();
- while (it != itend) {
- GINAC_ASSERT(!is_exactly_a<numeric>(it->rest));
- numeric coeff = GiNaC::smod(ex_to<numeric>(it->coeff), xi);
+ for (auto & it : seq) {
+ GINAC_ASSERT(!is_exactly_a<numeric>(it.rest));
+ numeric coeff = GiNaC::smod(ex_to<numeric>(it.coeff), xi);
if (!coeff.is_zero())
- newseq.push_back(expair(it->rest, coeff));
- it++;
+ newseq.push_back(expair(it.rest, coeff));
}
GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
numeric coeff = GiNaC::smod(ex_to<numeric>(overall_coeff), xi);
- return (new add(newseq,coeff))->setflag(status_flags::dynallocated);
+ return dynallocate<add>(std::move(newseq), coeff);
}
ex mul::smod(const numeric &xi) const
{
#ifdef DO_GINAC_ASSERT
- epvector::const_iterator it = seq.begin();
- epvector::const_iterator itend = seq.end();
- while (it != itend) {
- GINAC_ASSERT(!is_exactly_a<numeric>(recombine_pair_to_ex(*it)));
- it++;
+ for (auto & it : seq) {
+ GINAC_ASSERT(!is_exactly_a<numeric>(recombine_pair_to_ex(it)));
}
#endif // def DO_GINAC_ASSERT
- mul * mulcopyp = new mul(*this);
+ mul & mulcopy = dynallocate<mul>(*this);
GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
- mulcopyp->overall_coeff = GiNaC::smod(ex_to<numeric>(overall_coeff),xi);
- mulcopyp->clearflag(status_flags::evaluated);
- mulcopyp->clearflag(status_flags::hash_calculated);
- return mulcopyp->setflag(status_flags::dynallocated);
+ mulcopy.overall_coeff = GiNaC::smod(ex_to<numeric>(overall_coeff),xi);
+ mulcopy.clearflag(status_flags::evaluated);
+ mulcopy.clearflag(status_flags::hash_calculated);
+ return mulcopy;
}
g.push_back(gi * power(x, i));
e = (e - gi) * rxi;
}
- return (new add(g))->setflag(status_flags::dynallocated);
+ return dynallocate<add>(g);
}
/** Exception thrown by heur_gcd() to signal failure. */
* polynomials and an iterator to the first element of the sym_desc vector
* passed in. This function is used internally by gcd().
*
- * @param a first multivariate polynomial (expanded)
- * @param b second multivariate polynomial (expanded)
- * @param ca cofactor of polynomial a (returned), NULL to suppress
+ * @param a first integer multivariate polynomial (expanded)
+ * @param b second integer multivariate polynomial (expanded)
+ * @param ca cofactor of polynomial a (returned), nullptr to suppress
* calculation of cofactor
- * @param cb cofactor of polynomial b (returned), NULL to suppress
+ * @param cb cofactor of polynomial b (returned), nullptr to suppress
* calculation of cofactor
* @param var iterator to first element of vector of sym_desc structs
- * @return the GCD as a new expression
+ * @param res the GCD (returned)
+ * @return true if GCD was computed, false otherwise.
* @see gcd
* @exception gcdheu_failed() */
-static ex heur_gcd(const ex &a, const ex &b, ex *ca, ex *cb, sym_desc_vec::const_iterator var)
+static bool heur_gcd_z(ex& res, const ex &a, const ex &b, ex *ca, ex *cb,
+ sym_desc_vec::const_iterator var)
{
#if STATISTICS
heur_gcd_called++;
// Algorithm only works for non-vanishing input polynomials
if (a.is_zero() || b.is_zero())
- return (new fail())->setflag(status_flags::dynallocated);
+ return false;
// GCD of two numeric values -> CLN
if (is_exactly_a<numeric>(a) && is_exactly_a<numeric>(b)) {
*ca = ex_to<numeric>(a) / g;
if (cb)
*cb = ex_to<numeric>(b) / g;
- return g;
+ res = g;
+ return true;
}
// The first symbol is our main variable
// Apply evaluation homomorphism and calculate GCD
ex cp, cq;
- ex gamma = heur_gcd(p.subs(x == xi, subs_options::no_pattern), q.subs(x == xi, subs_options::no_pattern), &cp, &cq, var+1).expand();
- if (!is_exactly_a<fail>(gamma)) {
-
+ ex gamma;
+ bool found = heur_gcd_z(gamma,
+ p.subs(x == xi, subs_options::no_pattern),
+ q.subs(x == xi, subs_options::no_pattern),
+ &cp, &cq, var+1);
+ if (found) {
+ gamma = gamma.expand();
// Reconstruct polynomial from GCD of mapped polynomials
ex g = interpolate(gamma, xi, x, maxdeg);
ex dummy;
if (divide_in_z(p, g, ca ? *ca : dummy, var) && divide_in_z(q, g, cb ? *cb : dummy, var)) {
g *= gc;
- return g;
+ res = g;
+ return true;
}
}
// Next evaluation point
xi = iquo(xi * isqrt(isqrt(xi)) * numeric(73794), numeric(27011));
}
- return (new fail())->setflag(status_flags::dynallocated);
+ return false;
+}
+
+/** Compute GCD of multivariate polynomials using the heuristic GCD algorithm.
+ * get_symbol_stats() must have been called previously with the input
+ * polynomials and an iterator to the first element of the sym_desc vector
+ * passed in. This function is used internally by gcd().
+ *
+ * @param a first rational multivariate polynomial (expanded)
+ * @param b second rational multivariate polynomial (expanded)
+ * @param ca cofactor of polynomial a (returned), nullptr to suppress
+ * calculation of cofactor
+ * @param cb cofactor of polynomial b (returned), nullptr to suppress
+ * calculation of cofactor
+ * @param var iterator to first element of vector of sym_desc structs
+ * @param res the GCD (returned)
+ * @return true if GCD was computed, false otherwise.
+ * @see heur_gcd_z
+ * @see gcd
+ */
+static bool heur_gcd(ex& res, const ex& a, const ex& b, ex *ca, ex *cb,
+ sym_desc_vec::const_iterator var)
+{
+ if (a.info(info_flags::integer_polynomial) &&
+ b.info(info_flags::integer_polynomial)) {
+ try {
+ return heur_gcd_z(res, a, b, ca, cb, var);
+ } catch (gcdheu_failed) {
+ return false;
+ }
+ }
+
+ // convert polynomials to Z[X]
+ const numeric a_lcm = lcm_of_coefficients_denominators(a);
+ const numeric ab_lcm = lcmcoeff(b, a_lcm);
+
+ const ex ai = a*ab_lcm;
+ const ex bi = b*ab_lcm;
+ if (!ai.info(info_flags::integer_polynomial))
+ throw std::logic_error("heur_gcd: not an integer polynomial [1]");
+
+ if (!bi.info(info_flags::integer_polynomial))
+ throw std::logic_error("heur_gcd: not an integer polynomial [2]");
+
+ bool found = false;
+ try {
+ found = heur_gcd_z(res, ai, bi, ca, cb, var);
+ } catch (gcdheu_failed) {
+ return false;
+ }
+
+ // GCD is not unique, it's defined up to a unit (i.e. invertible
+ // element). If the coefficient ring is a field, every its element is
+ // invertible, so one can multiply the polynomial GCD with any element
+ // of the coefficient field. We use this ambiguity to make cofactors
+ // integer polynomials.
+ if (found)
+ res /= ab_lcm;
+ return found;
}
+// gcd helper to handle partially factored polynomials (to avoid expanding
+// large expressions). At least one of the arguments should be a power.
+static ex gcd_pf_pow(const ex& a, const ex& b, ex* ca, ex* cb);
+
+// gcd helper to handle partially factored polynomials (to avoid expanding
+// large expressions). At least one of the arguments should be a product.
+static ex gcd_pf_mul(const ex& a, const ex& b, ex* ca, ex* cb);
+
/** Compute GCD (Greatest Common Divisor) of multivariate polynomials a(X)
* and b(X) in Z[X]. Optionally also compute the cofactors of a and b,
* defined by a = ca * gcd(a, b) and b = cb * gcd(a, b).
*
* @param a first multivariate polynomial
* @param b second multivariate polynomial
- * @param ca pointer to expression that will receive the cofactor of a, or NULL
- * @param cb pointer to expression that will receive the cofactor of b, or NULL
+ * @param ca pointer to expression that will receive the cofactor of a, or nullptr
+ * @param cb pointer to expression that will receive the cofactor of b, or nullptr
* @param check_args check whether a and b are polynomials with rational
* coefficients (defaults to "true")
* @return the GCD as a new expression */
-ex gcd(const ex &a, const ex &b, ex *ca, ex *cb, bool check_args)
+ex gcd(const ex &a, const ex &b, ex *ca, ex *cb, bool check_args, unsigned options)
{
#if STATISTICS
gcd_called++;
}
// Partially factored cases (to avoid expanding large expressions)
- if (is_exactly_a<mul>(a)) {
- if (is_exactly_a<mul>(b) && b.nops() > a.nops())
- goto factored_b;
-factored_a:
- size_t num = a.nops();
- exvector g; g.reserve(num);
- exvector acc_ca; acc_ca.reserve(num);
- ex part_b = b;
- for (size_t i=0; i<num; i++) {
- ex part_ca, part_cb;
- g.push_back(gcd(a.op(i), part_b, &part_ca, &part_cb, check_args));
- acc_ca.push_back(part_ca);
- part_b = part_cb;
- }
- if (ca)
- *ca = (new mul(acc_ca))->setflag(status_flags::dynallocated);
- if (cb)
- *cb = part_b;
- return (new mul(g))->setflag(status_flags::dynallocated);
- } else if (is_exactly_a<mul>(b)) {
- if (is_exactly_a<mul>(a) && a.nops() > b.nops())
- goto factored_a;
-factored_b:
- size_t num = b.nops();
- exvector g; g.reserve(num);
- exvector acc_cb; acc_cb.reserve(num);
- ex part_a = a;
- for (size_t i=0; i<num; i++) {
- ex part_ca, part_cb;
- g.push_back(gcd(part_a, b.op(i), &part_ca, &part_cb, check_args));
- acc_cb.push_back(part_cb);
- part_a = part_ca;
- }
- if (ca)
- *ca = part_a;
- if (cb)
- *cb = (new mul(acc_cb))->setflag(status_flags::dynallocated);
- return (new mul(g))->setflag(status_flags::dynallocated);
- }
-
+ if (!(options & gcd_options::no_part_factored)) {
+ if (is_exactly_a<mul>(a) || is_exactly_a<mul>(b))
+ return gcd_pf_mul(a, b, ca, cb);
#if FAST_COMPARE
- // Input polynomials of the form poly^n are sometimes also trivial
- if (is_exactly_a<power>(a)) {
- ex p = a.op(0);
- const ex& exp_a = a.op(1);
- if (is_exactly_a<power>(b)) {
- ex pb = b.op(0);
- const ex& exp_b = b.op(1);
- if (p.is_equal(pb)) {
- // a = p^n, b = p^m, gcd = p^min(n, m)
- if (exp_a < exp_b) {
- if (ca)
- *ca = _ex1;
- if (cb)
- *cb = power(p, exp_b - exp_a);
- return power(p, exp_a);
- } else {
- if (ca)
- *ca = power(p, exp_a - exp_b);
- if (cb)
- *cb = _ex1;
- return power(p, exp_b);
- }
- } else {
- ex p_co, pb_co;
- ex p_gcd = gcd(p, pb, &p_co, &pb_co, check_args);
- if (p_gcd.is_equal(_ex1)) {
- // a(x) = p(x)^n, b(x) = p_b(x)^m, gcd (p, p_b) = 1 ==>
- // gcd(a,b) = 1
- if (ca)
- *ca = a;
- if (cb)
- *cb = b;
- return _ex1;
- // XXX: do I need to check for p_gcd = -1?
- } else {
- // there are common factors:
- // a(x) = g(x)^n A(x)^n, b(x) = g(x)^m B(x)^m ==>
- // gcd(a, b) = g(x)^n gcd(A(x)^n, g(x)^(n-m) B(x)^m
- if (exp_a < exp_b) {
- return power(p_gcd, exp_a)*
- gcd(power(p_co, exp_a), power(p_gcd, exp_b-exp_a)*power(pb_co, exp_b), ca, cb, false);
- } else {
- return power(p_gcd, exp_b)*
- gcd(power(p_gcd, exp_a - exp_b)*power(p_co, exp_a), power(pb_co, exp_b), ca, cb, false);
- }
- } // p_gcd.is_equal(_ex1)
- } // p.is_equal(pb)
-
- } else {
- if (p.is_equal(b)) {
- // a = p^n, b = p, gcd = p
- if (ca)
- *ca = power(p, a.op(1) - 1);
- if (cb)
- *cb = _ex1;
- return p;
- }
-
- ex p_co, bpart_co;
- ex p_gcd = gcd(p, b, &p_co, &bpart_co, false);
-
- if (p_gcd.is_equal(_ex1)) {
- // a(x) = p(x)^n, gcd(p, b) = 1 ==> gcd(a, b) = 1
- if (ca)
- *ca = a;
- if (cb)
- *cb = b;
- return _ex1;
- } else {
- // a(x) = g(x)^n A(x)^n, b(x) = g(x) B(x) ==> gcd(a, b) = g(x) gcd(g(x)^(n-1) A(x)^n, B(x))
- return p_gcd*gcd(power(p_gcd, exp_a-1)*power(p_co, exp_a), bpart_co, ca, cb, false);
- }
- } // is_exactly_a<power>(b)
-
- } else if (is_exactly_a<power>(b)) {
- ex p = b.op(0);
- if (p.is_equal(a)) {
- // a = p, b = p^n, gcd = p
- if (ca)
- *ca = _ex1;
- if (cb)
- *cb = power(p, b.op(1) - 1);
- return p;
- }
-
- ex p_co, apart_co;
- const ex& exp_b(b.op(1));
- ex p_gcd = gcd(a, p, &apart_co, &p_co, false);
- if (p_gcd.is_equal(_ex1)) {
- // b=p(x)^n, gcd(a, p) = 1 ==> gcd(a, b) == 1
- if (ca)
- *ca = a;
- if (cb)
- *cb = b;
- return _ex1;
- } else {
- // there are common factors:
- // a(x) = g(x) A(x), b(x) = g(x)^n B(x)^n ==> gcd = g(x) gcd(g(x)^(n-1) A(x)^n, B(x))
-
- return p_gcd*gcd(apart_co, power(p_gcd, exp_b-1)*power(p_co, exp_b), ca, cb, false);
- } // p_gcd.is_equal(_ex1)
- }
+ if (is_exactly_a<power>(a) || is_exactly_a<power>(b))
+ return gcd_pf_pow(a, b, ca, cb);
#endif
+ }
// Some trivial cases
ex aex = a.expand(), bex = b.expand();
}
#endif
+ if (is_a<symbol>(aex)) {
+ if (! bex.subs(aex==_ex0, subs_options::no_pattern).is_zero()) {
+ if (ca)
+ *ca = a;
+ if (cb)
+ *cb = b;
+ return _ex1;
+ }
+ }
+
+ if (is_a<symbol>(bex)) {
+ if (! aex.subs(bex==_ex0, subs_options::no_pattern).is_zero()) {
+ if (ca)
+ *ca = a;
+ if (cb)
+ *cb = b;
+ return _ex1;
+ }
+ }
+
+ if (is_exactly_a<numeric>(aex)) {
+ numeric bcont = bex.integer_content();
+ numeric g = gcd(ex_to<numeric>(aex), bcont);
+ if (ca)
+ *ca = ex_to<numeric>(aex)/g;
+ if (cb)
+ *cb = bex/g;
+ return g;
+ }
+
+ if (is_exactly_a<numeric>(bex)) {
+ numeric acont = aex.integer_content();
+ numeric g = gcd(ex_to<numeric>(bex), acont);
+ if (ca)
+ *ca = aex/g;
+ if (cb)
+ *cb = ex_to<numeric>(bex)/g;
+ return g;
+ }
+
// Gather symbol statistics
sym_desc_vec sym_stats;
get_symbol_stats(a, b, sym_stats);
- // The symbol with least degree is our main variable
+ // The symbol with least degree which is contained in both polynomials
+ // is our main variable
+ sym_desc_vec::iterator vari = sym_stats.begin();
+ while ((vari != sym_stats.end()) &&
+ (((vari->ldeg_b == 0) && (vari->deg_b == 0)) ||
+ ((vari->ldeg_a == 0) && (vari->deg_a == 0))))
+ vari++;
+
+ // No common symbols at all, just return 1:
+ if (vari == sym_stats.end()) {
+ // N.B: keep cofactors factored
+ if (ca)
+ *ca = a;
+ if (cb)
+ *cb = b;
+ return _ex1;
+ }
+ // move symbols which contained only in one of the polynomials
+ // to the end:
+ rotate(sym_stats.begin(), vari, sym_stats.end());
+
sym_desc_vec::const_iterator var = sym_stats.begin();
const ex &x = var->sym;
}
// Try to eliminate variables
- if (var->deg_a == 0) {
+ if (var->deg_a == 0 && var->deg_b != 0 ) {
ex bex_u, bex_c, bex_p;
bex.unitcontprim(x, bex_u, bex_c, bex_p);
ex g = gcd(aex, bex_c, ca, cb, false);
if (cb)
*cb *= bex_u * bex_p;
return g;
- } else if (var->deg_b == 0) {
+ } else if (var->deg_b == 0 && var->deg_a != 0) {
ex aex_u, aex_c, aex_p;
aex.unitcontprim(x, aex_u, aex_c, aex_p);
ex g = gcd(aex_c, bex, ca, cb, false);
// Try heuristic algorithm first, fall back to PRS if that failed
ex g;
- try {
- g = heur_gcd(aex, bex, ca, cb, var);
- } catch (gcdheu_failed) {
- g = fail();
- }
- if (is_exactly_a<fail>(g)) {
+ if (!(options & gcd_options::no_heur_gcd)) {
+ bool found = heur_gcd(g, aex, bex, ca, cb, var);
+ if (found) {
+ // heur_gcd have already computed cofactors...
+ if (g.is_equal(_ex1)) {
+ // ... but we want to keep them factored if possible.
+ if (ca)
+ *ca = a;
+ if (cb)
+ *cb = b;
+ }
+ return g;
+ }
#if STATISTICS
- heur_gcd_failed++;
+ else {
+ heur_gcd_failed++;
+ }
#endif
+ }
+ if (options & gcd_options::use_sr_gcd) {
g = sr_gcd(aex, bex, var);
- if (g.is_equal(_ex1)) {
- // Keep cofactors factored if possible
+ } else {
+ exvector vars;
+ for (std::size_t n = sym_stats.size(); n-- != 0; )
+ vars.push_back(sym_stats[n].sym);
+ g = chinrem_gcd(aex, bex, vars);
+ }
+
+ if (g.is_equal(_ex1)) {
+ // Keep cofactors factored if possible
+ if (ca)
+ *ca = a;
+ if (cb)
+ *cb = b;
+ } else {
+ if (ca)
+ divide(aex, g, *ca, false);
+ if (cb)
+ divide(bex, g, *cb, false);
+ }
+ return g;
+}
+
+// gcd helper to handle partially factored polynomials (to avoid expanding
+// large expressions). Both arguments should be powers.
+static ex gcd_pf_pow_pow(const ex& a, const ex& b, ex* ca, ex* cb)
+{
+ ex p = a.op(0);
+ const ex& exp_a = a.op(1);
+ ex pb = b.op(0);
+ const ex& exp_b = b.op(1);
+
+ // a = p^n, b = p^m, gcd = p^min(n, m)
+ if (p.is_equal(pb)) {
+ if (exp_a < exp_b) {
if (ca)
- *ca = a;
+ *ca = _ex1;
if (cb)
- *cb = b;
+ *cb = power(p, exp_b - exp_a);
+ return power(p, exp_a);
} else {
if (ca)
- divide(aex, g, *ca, false);
+ *ca = power(p, exp_a - exp_b);
if (cb)
- divide(bex, g, *cb, false);
+ *cb = _ex1;
+ return power(p, exp_b);
}
- } else {
- if (g.is_equal(_ex1)) {
- // Keep cofactors factored if possible
+ }
+
+ ex p_co, pb_co;
+ ex p_gcd = gcd(p, pb, &p_co, &pb_co, false);
+ // a(x) = p(x)^n, b(x) = p_b(x)^m, gcd (p, p_b) = 1 ==> gcd(a,b) = 1
+ if (p_gcd.is_equal(_ex1)) {
if (ca)
*ca = a;
if (cb)
*cb = b;
- }
+ return _ex1;
+ // XXX: do I need to check for p_gcd = -1?
}
- return g;
+ // there are common factors:
+ // a(x) = g(x)^n A(x)^n, b(x) = g(x)^m B(x)^m ==>
+ // gcd(a, b) = g(x)^n gcd(A(x)^n, g(x)^(n-m) B(x)^m
+ if (exp_a < exp_b) {
+ ex pg = gcd(power(p_co, exp_a), power(p_gcd, exp_b-exp_a)*power(pb_co, exp_b), ca, cb, false);
+ return power(p_gcd, exp_a)*pg;
+ } else {
+ ex pg = gcd(power(p_gcd, exp_a - exp_b)*power(p_co, exp_a), power(pb_co, exp_b), ca, cb, false);
+ return power(p_gcd, exp_b)*pg;
+ }
+}
+
+static ex gcd_pf_pow(const ex& a, const ex& b, ex* ca, ex* cb)
+{
+ if (is_exactly_a<power>(a) && is_exactly_a<power>(b))
+ return gcd_pf_pow_pow(a, b, ca, cb);
+
+ if (is_exactly_a<power>(b) && (! is_exactly_a<power>(a)))
+ return gcd_pf_pow(b, a, cb, ca);
+
+ GINAC_ASSERT(is_exactly_a<power>(a));
+
+ ex p = a.op(0);
+ const ex& exp_a = a.op(1);
+ if (p.is_equal(b)) {
+ // a = p^n, b = p, gcd = p
+ if (ca)
+ *ca = power(p, a.op(1) - 1);
+ if (cb)
+ *cb = _ex1;
+ return p;
+ }
+
+ ex p_co, bpart_co;
+ ex p_gcd = gcd(p, b, &p_co, &bpart_co, false);
+
+ // a(x) = p(x)^n, gcd(p, b) = 1 ==> gcd(a, b) = 1
+ if (p_gcd.is_equal(_ex1)) {
+ if (ca)
+ *ca = a;
+ if (cb)
+ *cb = b;
+ return _ex1;
+ }
+ // a(x) = g(x)^n A(x)^n, b(x) = g(x) B(x) ==> gcd(a, b) = g(x) gcd(g(x)^(n-1) A(x)^n, B(x))
+ ex rg = gcd(power(p_gcd, exp_a-1)*power(p_co, exp_a), bpart_co, ca, cb, false);
+ return p_gcd*rg;
}
+static ex gcd_pf_mul(const ex& a, const ex& b, ex* ca, ex* cb)
+{
+ if (is_exactly_a<mul>(a) && is_exactly_a<mul>(b)
+ && (b.nops() > a.nops()))
+ return gcd_pf_mul(b, a, cb, ca);
+
+ if (is_exactly_a<mul>(b) && (!is_exactly_a<mul>(a)))
+ return gcd_pf_mul(b, a, cb, ca);
+
+ GINAC_ASSERT(is_exactly_a<mul>(a));
+ size_t num = a.nops();
+ exvector g; g.reserve(num);
+ exvector acc_ca; acc_ca.reserve(num);
+ ex part_b = b;
+ for (size_t i=0; i<num; i++) {
+ ex part_ca, part_cb;
+ g.push_back(gcd(a.op(i), part_b, &part_ca, &part_cb, false));
+ acc_ca.push_back(part_ca);
+ part_b = part_cb;
+ }
+ if (ca)
+ *ca = dynallocate<mul>(acc_ca);
+ if (cb)
+ *cb = part_b;
+ return dynallocate<mul>(g);
+}
/** Compute LCM (Least Common Multiple) of multivariate polynomials in Z[X].
*
if (l.nops()==0) {
sym_desc_vec sdv;
get_symbol_stats(a, _ex0, sdv);
- sym_desc_vec::const_iterator it = sdv.begin(), itend = sdv.end();
- while (it != itend) {
- args.append(it->sym);
- ++it;
- }
+ for (auto & it : sdv)
+ args.append(it.sym);
} else {
args = l;
}
// recurse down the factors in remaining variables
if (newargs.nops()>0) {
- exvector::iterator i = factors.begin();
- while (i != factors.end()) {
- *i = sqrfree(*i, newargs);
- ++i;
- }
+ for (auto & it : factors)
+ it = sqrfree(it, newargs);
}
// Done with recursion, now construct the final result
ex result = _ex1;
- exvector::const_iterator it = factors.begin(), itend = factors.end();
- for (int p = 1; it!=itend; ++it, ++p)
- result *= power(*it, p);
+ int p = 1;
+ for (auto & it : factors)
+ result *= power(it, p++);
// Yun's algorithm does not account for constant factors. (For univariate
// polynomials it works only in the monic case.) We can correct this by
else
result *= quo(tmp, result, x);
- // Put in the reational overall factor again and return
+ // Put in the rational overall factor again and return
return result * lcm.inverse();
}
* @see ex::normal */
static ex replace_with_symbol(const ex & e, exmap & repl, exmap & rev_lookup)
{
+ // Since the repl contains replaced expressions we should search for them
+ ex e_replaced = e.subs(repl, subs_options::no_pattern);
+
// Expression already replaced? Then return the assigned symbol
- exmap::const_iterator it = rev_lookup.find(e);
+ auto it = rev_lookup.find(e_replaced);
if (it != rev_lookup.end())
return it->second;
-
+
// Otherwise create new symbol and add to list, taking care that the
// replacement expression doesn't itself contain symbols from repl,
// because subs() is not recursive
- ex es = (new symbol)->setflag(status_flags::dynallocated);
- ex e_replaced = e.subs(repl, subs_options::no_pattern);
+ ex es = dynallocate<symbol>();
repl.insert(std::make_pair(es, e_replaced));
rev_lookup.insert(std::make_pair(e_replaced, es));
return es;
* @see basic::to_polynomial */
static ex replace_with_symbol(const ex & e, exmap & repl)
{
+ // Since the repl contains replaced expressions we should search for them
+ ex e_replaced = e.subs(repl, subs_options::no_pattern);
+
// Expression already replaced? Then return the assigned symbol
- for (exmap::const_iterator it = repl.begin(); it != repl.end(); ++it)
- if (it->second.is_equal(e))
- return it->first;
-
+ for (auto & it : repl)
+ if (it.second.is_equal(e_replaced))
+ return it.first;
+
// Otherwise create new symbol and add to list, taking care that the
// replacement expression doesn't itself contain symbols from repl,
// because subs() is not recursive
- ex es = (new symbol)->setflag(status_flags::dynallocated);
- ex e_replaced = e.subs(repl, subs_options::no_pattern);
+ ex es = dynallocate<symbol>();
repl.insert(std::make_pair(es, e_replaced));
return es;
}
struct normal_map_function : public map_function {
int level;
normal_map_function(int l) : level(l) {}
- ex operator()(const ex & e) { return normal(e, level); }
+ ex operator()(const ex & e) override { return normal(e, level); }
};
/** Default implementation of ex::normal(). It normalizes the children and
ex basic::normal(exmap & repl, exmap & rev_lookup, int level) const
{
if (nops() == 0)
- return (new lst(replace_with_symbol(*this, repl, rev_lookup), _ex1))->setflag(status_flags::dynallocated);
+ return dynallocate<lst>({replace_with_symbol(*this, repl, rev_lookup), _ex1});
else {
if (level == 1)
- return (new lst(replace_with_symbol(*this, repl, rev_lookup), _ex1))->setflag(status_flags::dynallocated);
+ return dynallocate<lst>({replace_with_symbol(*this, repl, rev_lookup), _ex1});
else if (level == -max_recursion_level)
throw(std::runtime_error("max recursion level reached"));
else {
normal_map_function map_normal(level - 1);
- return (new lst(replace_with_symbol(map(map_normal), repl, rev_lookup), _ex1))->setflag(status_flags::dynallocated);
+ return dynallocate<lst>({replace_with_symbol(map(map_normal), repl, rev_lookup), _ex1});
}
}
}
* @see ex::normal */
ex symbol::normal(exmap & repl, exmap & rev_lookup, int level) const
{
- return (new lst(*this, _ex1))->setflag(status_flags::dynallocated);
+ return dynallocate<lst>({*this, _ex1});
}
}
// Denominator is always a real integer (see numeric::denom())
- return (new lst(numex, denom()))->setflag(status_flags::dynallocated);
+ return dynallocate<lst>({numex, denom()});
}
// Handle trivial case where denominator is 1
if (den.is_equal(_ex1))
- return (new lst(num, den))->setflag(status_flags::dynallocated);
+ return dynallocate<lst>({num, den});
// Handle special cases where numerator or denominator is 0
if (num.is_zero())
- return (new lst(num, _ex1))->setflag(status_flags::dynallocated);
+ return dynallocate<lst>({num, _ex1});
if (den.expand().is_zero())
throw(std::overflow_error("frac_cancel: division by zero in frac_cancel"));
// Return result as list
//std::clog << " returns num = " << num << ", den = " << den << ", pre_factor = " << pre_factor << std::endl;
- return (new lst(num * pre_factor.numer(), den * pre_factor.denom()))->setflag(status_flags::dynallocated);
+ return dynallocate<lst>({num * pre_factor.numer(), den * pre_factor.denom()});
}
ex add::normal(exmap & repl, exmap & rev_lookup, int level) const
{
if (level == 1)
- return (new lst(replace_with_symbol(*this, repl, rev_lookup), _ex1))->setflag(status_flags::dynallocated);
+ return dynallocate<lst>({replace_with_symbol(*this, repl, rev_lookup), _ex1});
else if (level == -max_recursion_level)
throw(std::runtime_error("max recursion level reached"));
exvector nums, dens;
nums.reserve(seq.size()+1);
dens.reserve(seq.size()+1);
- epvector::const_iterator it = seq.begin(), itend = seq.end();
- while (it != itend) {
- ex n = ex_to<basic>(recombine_pair_to_ex(*it)).normal(repl, rev_lookup, level-1);
+ for (auto & it : seq) {
+ ex n = ex_to<basic>(recombine_pair_to_ex(it)).normal(repl, rev_lookup, level-1);
nums.push_back(n.op(0));
dens.push_back(n.op(1));
- it++;
}
ex n = ex_to<numeric>(overall_coeff).normal(repl, rev_lookup, level-1);
nums.push_back(n.op(0));
//std::clog << "add::normal uses " << nums.size() << " summands:\n";
// Add fractions sequentially
- exvector::const_iterator num_it = nums.begin(), num_itend = nums.end();
- exvector::const_iterator den_it = dens.begin(), den_itend = dens.end();
+ auto num_it = nums.begin(), num_itend = nums.end();
+ auto den_it = dens.begin(), den_itend = dens.end();
//std::clog << " num = " << *num_it << ", den = " << *den_it << std::endl;
ex num = *num_it++, den = *den_it++;
while (num_it != num_itend) {
num_it++; den_it++;
}
- // Additiion of two fractions, taking advantage of the fact that
+ // Addition of two fractions, taking advantage of the fact that
// the heuristic GCD algorithm computes the cofactors at no extra cost
ex co_den1, co_den2;
ex g = gcd(den, next_den, &co_den1, &co_den2, false);
ex mul::normal(exmap & repl, exmap & rev_lookup, int level) const
{
if (level == 1)
- return (new lst(replace_with_symbol(*this, repl, rev_lookup), _ex1))->setflag(status_flags::dynallocated);
+ return dynallocate<lst>({replace_with_symbol(*this, repl, rev_lookup), _ex1});
else if (level == -max_recursion_level)
throw(std::runtime_error("max recursion level reached"));
exvector num; num.reserve(seq.size());
exvector den; den.reserve(seq.size());
ex n;
- epvector::const_iterator it = seq.begin(), itend = seq.end();
- while (it != itend) {
- n = ex_to<basic>(recombine_pair_to_ex(*it)).normal(repl, rev_lookup, level-1);
+ for (auto & it : seq) {
+ n = ex_to<basic>(recombine_pair_to_ex(it)).normal(repl, rev_lookup, level-1);
num.push_back(n.op(0));
den.push_back(n.op(1));
- it++;
}
n = ex_to<numeric>(overall_coeff).normal(repl, rev_lookup, level-1);
num.push_back(n.op(0));
den.push_back(n.op(1));
// Perform fraction cancellation
- return frac_cancel((new mul(num))->setflag(status_flags::dynallocated),
- (new mul(den))->setflag(status_flags::dynallocated));
+ return frac_cancel(dynallocate<mul>(num), dynallocate<mul>(den));
}
ex power::normal(exmap & repl, exmap & rev_lookup, int level) const
{
if (level == 1)
- return (new lst(replace_with_symbol(*this, repl, rev_lookup), _ex1))->setflag(status_flags::dynallocated);
+ return dynallocate<lst>({replace_with_symbol(*this, repl, rev_lookup), _ex1});
else if (level == -max_recursion_level)
throw(std::runtime_error("max recursion level reached"));
if (n_exponent.info(info_flags::positive)) {
// (a/b)^n -> {a^n, b^n}
- return (new lst(power(n_basis.op(0), n_exponent), power(n_basis.op(1), n_exponent)))->setflag(status_flags::dynallocated);
+ return dynallocate<lst>({power(n_basis.op(0), n_exponent), power(n_basis.op(1), n_exponent)});
} else if (n_exponent.info(info_flags::negative)) {
// (a/b)^-n -> {b^n, a^n}
- return (new lst(power(n_basis.op(1), -n_exponent), power(n_basis.op(0), -n_exponent)))->setflag(status_flags::dynallocated);
+ return dynallocate<lst>({power(n_basis.op(1), -n_exponent), power(n_basis.op(0), -n_exponent)});
}
} else {
if (n_exponent.info(info_flags::positive)) {
// (a/b)^x -> {sym((a/b)^x), 1}
- return (new lst(replace_with_symbol(power(n_basis.op(0) / n_basis.op(1), n_exponent), repl, rev_lookup), _ex1))->setflag(status_flags::dynallocated);
+ return dynallocate<lst>({replace_with_symbol(power(n_basis.op(0) / n_basis.op(1), n_exponent), repl, rev_lookup), _ex1});
} else if (n_exponent.info(info_flags::negative)) {
if (n_basis.op(1).is_equal(_ex1)) {
// a^-x -> {1, sym(a^x)}
- return (new lst(_ex1, replace_with_symbol(power(n_basis.op(0), -n_exponent), repl, rev_lookup)))->setflag(status_flags::dynallocated);
+ return dynallocate<lst>({_ex1, replace_with_symbol(power(n_basis.op(0), -n_exponent), repl, rev_lookup)});
} else {
// (a/b)^-x -> {sym((b/a)^x), 1}
- return (new lst(replace_with_symbol(power(n_basis.op(1) / n_basis.op(0), -n_exponent), repl, rev_lookup), _ex1))->setflag(status_flags::dynallocated);
+ return dynallocate<lst>({replace_with_symbol(power(n_basis.op(1) / n_basis.op(0), -n_exponent), repl, rev_lookup), _ex1});
}
}
}
// (a/b)^x -> {sym((a/b)^x, 1}
- return (new lst(replace_with_symbol(power(n_basis.op(0) / n_basis.op(1), n_exponent), repl, rev_lookup), _ex1))->setflag(status_flags::dynallocated);
+ return dynallocate<lst>({replace_with_symbol(power(n_basis.op(0) / n_basis.op(1), n_exponent), repl, rev_lookup), _ex1});
}
ex pseries::normal(exmap & repl, exmap & rev_lookup, int level) const
{
epvector newseq;
- epvector::const_iterator i = seq.begin(), end = seq.end();
- while (i != end) {
- ex restexp = i->rest.normal();
+ for (auto & it : seq) {
+ ex restexp = it.rest.normal();
if (!restexp.is_zero())
- newseq.push_back(expair(restexp, i->coeff));
- ++i;
+ newseq.push_back(expair(restexp, it.coeff));
}
- ex n = pseries(relational(var,point), newseq);
- return (new lst(replace_with_symbol(n, repl, rev_lookup), _ex1))->setflag(status_flags::dynallocated);
+ ex n = pseries(relational(var,point), std::move(newseq));
+ return dynallocate<lst>({replace_with_symbol(n, repl, rev_lookup), _ex1});
}
return e.op(1).subs(repl, subs_options::no_pattern);
}
-/** Get numerator and denominator of an expression. If the expresison is not
+/** Get numerator and denominator of an expression. If the expression is not
* of the normal form "numerator/denominator", it is first converted to this
* form and then a list [numerator, denominator] is returned.
*
{
// Convert lst to exmap
exmap m;
- for (lst::const_iterator it = repl_lst.begin(); it != repl_lst.end(); ++it)
- m.insert(std::make_pair(it->op(0), it->op(1)));
+ for (auto & it : repl_lst)
+ m.insert(std::make_pair(it.op(0), it.op(1)));
ex ret = bp->to_rational(m);
// Convert exmap back to lst
repl_lst.remove_all();
- for (exmap::const_iterator it = m.begin(); it != m.end(); ++it)
- repl_lst.append(it->first == it->second);
+ for (auto & it : m)
+ repl_lst.append(it.first == it.second);
return ret;
}
{
// Convert lst to exmap
exmap m;
- for (lst::const_iterator it = repl_lst.begin(); it != repl_lst.end(); ++it)
- m.insert(std::make_pair(it->op(0), it->op(1)));
+ for (auto & it : repl_lst)
+ m.insert(std::make_pair(it.op(0), it.op(1)));
ex ret = bp->to_polynomial(m);
// Convert exmap back to lst
repl_lst.remove_all();
- for (exmap::const_iterator it = m.begin(); it != m.end(); ++it)
- repl_lst.append(it->first == it->second);
+ for (auto & it : m)
+ repl_lst.append(it.first == it.second);
return ret;
}
{
if (exponent.info(info_flags::posint))
return power(basis.to_rational(repl), exponent);
+ else if (exponent.info(info_flags::negint))
+ {
+ ex basis_pref = collect_common_factors(basis);
+ if (is_exactly_a<mul>(basis_pref) || is_exactly_a<power>(basis_pref)) {
+ // (A*B)^n will be automagically transformed to A^n*B^n
+ ex t = power(basis_pref, exponent);
+ return t.to_polynomial(repl);
+ }
+ else
+ return power(replace_with_symbol(power(basis, _ex_1), repl), -exponent);
+ }
else
return replace_with_symbol(*this, repl);
}
{
epvector s;
s.reserve(seq.size());
- epvector::const_iterator i = seq.begin(), end = seq.end();
- while (i != end) {
- s.push_back(split_ex_to_pair(recombine_pair_to_ex(*i).to_rational(repl)));
- ++i;
- }
+ for (auto & it : seq)
+ s.push_back(split_ex_to_pair(recombine_pair_to_ex(it).to_rational(repl)));
+
ex oc = overall_coeff.to_rational(repl);
if (oc.info(info_flags::numeric))
- return thisexpairseq(s, overall_coeff);
+ return thisexpairseq(std::move(s), overall_coeff);
else
- s.push_back(combine_ex_with_coeff_to_pair(oc, _ex1));
- return thisexpairseq(s, default_overall_coeff());
+ s.push_back(expair(oc, _ex1));
+ return thisexpairseq(std::move(s), default_overall_coeff());
}
/** Implementation of ex::to_polynomial() for expairseqs. */
{
epvector s;
s.reserve(seq.size());
- epvector::const_iterator i = seq.begin(), end = seq.end();
- while (i != end) {
- s.push_back(split_ex_to_pair(recombine_pair_to_ex(*i).to_polynomial(repl)));
- ++i;
- }
+ for (auto & it : seq)
+ s.push_back(split_ex_to_pair(recombine_pair_to_ex(it).to_polynomial(repl)));
+
ex oc = overall_coeff.to_polynomial(repl);
if (oc.info(info_flags::numeric))
- return thisexpairseq(s, overall_coeff);
+ return thisexpairseq(std::move(s), overall_coeff);
else
- s.push_back(combine_ex_with_coeff_to_pair(oc, _ex1));
- return thisexpairseq(s, default_overall_coeff());
+ s.push_back(expair(oc, _ex1));
+ return thisexpairseq(std::move(s), default_overall_coeff());
}
for (size_t i=0; i<num; i++) {
ex x = e.op(i).to_polynomial(repl);
- if (is_exactly_a<add>(x) || is_exactly_a<mul>(x)) {
+ if (is_exactly_a<add>(x) || is_exactly_a<mul>(x) || is_a<power>(x)) {
ex f = 1;
x = find_common_factor(x, f, repl);
x *= f;
else
v.push_back(t.op(k));
}
- t = (new mul(v))->setflag(status_flags::dynallocated);
+ t = dynallocate<mul>(v);
goto term_done;
}
}
t = x;
term_done: ;
}
- return (new add(terms))->setflag(status_flags::dynallocated);
+ return dynallocate<add>(terms);
} else if (is_exactly_a<mul>(e)) {
for (size_t i=0; i<num; i++)
v.push_back(find_common_factor(e.op(i), factor, repl));
- return (new mul(v))->setflag(status_flags::dynallocated);
+ return dynallocate<mul>(v);
} else if (is_exactly_a<power>(e)) {
-
- return e.to_polynomial(repl);
+ const ex e_exp(e.op(1));
+ if (e_exp.info(info_flags::integer)) {
+ ex eb = e.op(0).to_polynomial(repl);
+ ex factor_local(_ex1);
+ ex pre_res = find_common_factor(eb, factor_local, repl);
+ factor *= power(factor_local, e_exp);
+ return power(pre_res, e_exp);
+
+ } else
+ return e.to_polynomial(repl);
} else
return e;
* 'a*(b*x+b*y)' to 'a*b*(x+y)'. */
ex collect_common_factors(const ex & e)
{
- if (is_exactly_a<add>(e) || is_exactly_a<mul>(e)) {
+ if (is_exactly_a<add>(e) || is_exactly_a<mul>(e) || is_exactly_a<power>(e)) {
exmap repl;
ex factor = 1;
git://www.ginac.de / ginac.git / blobdiff