* computation, square-free factorization and rational function normalization. */
/*
- * GiNaC Copyright (C) 1999-2008 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2018 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;
/** Maximum number of terms of leading coefficient of symbol in both polynomials */
size_t max_lcnops;
- /** Commparison operator for sorting */
+ /** Comparison operator for sorting */
bool operator<(const sym_desc &x) const
{
if (max_deg == x.max_deg)
// 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())
* @param v vector of sym_desc structs (filled in) */
static void get_symbol_stats(const ex &a, const ex &b, sym_desc_vec &v)
{
- 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;
+ collect_symbols(a, v);
+ collect_symbols(b, v);
+ 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());
* @param lcm LCM to multiply in */
static ex multiply_lcm(const ex &e, const numeric &lcm)
{
+ if (lcm.is_equal(*_num1_p))
+ // e * 1 -> e;
+ return e;
+
if (is_exactly_a<mul>(e)) {
+ // (a*b*...)*lcm -> (a*lcma)*(b*lcmb)*...*(lcm/(lcma*lcmb*...))
size_t num = e.nops();
- exvector v; v.reserve(num + 1);
+ exvector v;
+ v.reserve(num + 1);
numeric lcm_accum = *_num1_p;
for (size_t i=0; i<num; i++) {
numeric op_lcm = lcmcoeff(e.op(i), *_num1_p);
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)) {
+ // (a+b+...)*lcm -> a*lcm+b*lcm+...
size_t num = e.nops();
- exvector v; v.reserve(num);
+ 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;
- else
- return pow(multiply_lcm(e.op(0), lcm.power(ex_to<numeric>(e.op(1)).inverse())), e.op(1));
- } else
- return e * lcm;
+ if (!is_a<symbol>(e.op(0))) {
+ // (b^e)*lcm -> (b*lcm^(1/e))^e if lcm^(1/e) ∈ ℚ (i.e. not a float)
+ // but not for symbolic b, as evaluation would undo this again
+ numeric root_of_lcm = lcm.power(ex_to<numeric>(e.op(1)).inverse());
+ if (root_of_lcm.is_rational())
+ return pow(multiply_lcm(e.op(0), root_of_lcm), e.op(1));
+ }
+ }
+ // can't recurse down into e
+ return dynallocate<mul>(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);
+ term *= pow(x, rdeg - bdeg);
v.push_back(term);
r -= (term * b).expand();
if (r.is_zero())
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);
+ term *= pow(x, rdeg - bdeg);
r -= (term * b).expand();
if (r.is_zero())
break;
if (bdeg == 0)
eb = _ex0;
else
- eb -= blcoeff * power(x, bdeg);
+ eb -= blcoeff * pow(x, bdeg);
} else
blcoeff = _ex1;
int delta = rdeg - bdeg + 1, i = 0;
while (rdeg >= bdeg && !r.is_zero()) {
ex rlcoeff = r.coeff(x, rdeg);
- ex term = (power(x, rdeg - bdeg) * eb * rlcoeff).expand();
+ ex term = (pow(x, rdeg - bdeg) * eb * rlcoeff).expand();
if (rdeg == 0)
r = _ex0;
else
- r -= rlcoeff * power(x, rdeg);
+ r -= rlcoeff * pow(x, rdeg);
r = (blcoeff * r).expand() - term;
rdeg = r.degree(x);
i++;
}
- return power(blcoeff, delta - i) * r;
+ return pow(blcoeff, delta - i) * r;
}
if (bdeg == 0)
eb = _ex0;
else
- eb -= blcoeff * power(x, bdeg);
+ eb -= blcoeff * pow(x, bdeg);
} else
blcoeff = _ex1;
while (rdeg >= bdeg && !r.is_zero()) {
ex rlcoeff = r.coeff(x, rdeg);
- ex term = (power(x, rdeg - bdeg) * eb * rlcoeff).expand();
+ ex term = (pow(x, rdeg - bdeg) * eb * rlcoeff).expand();
if (rdeg == 0)
r = _ex0;
else
- r -= rlcoeff * power(x, rdeg);
+ r -= rlcoeff * pow(x, rdeg);
r = (blcoeff * r).expand() - term;
rdeg = r.degree(x);
}
else
resv.push_back(a.op(j));
}
- q = (new mul(resv))->setflag(status_flags::dynallocated);
+ q = dynallocate<mul>(resv);
return true;
}
} else if (is_exactly_a<power>(a)) {
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);
+ q = rem_i * pow(ab, a_exp - 1);
return true;
}
- 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.
+// 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)
else
if (!divide(rcoeff, blcoeff, term, false))
return false;
- term *= power(x, rdeg - bdeg);
+ term *= pow(x, rdeg - bdeg);
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);
if (is_exactly_a<mul>(b)) {
ex qbar = a;
- for (const_iterator itrb = b.begin(); itrb != b.end(); ++itrb) {
+ for (const auto & it : b) {
sym_desc_vec sym_stats;
- get_symbol_stats(a, *itrb, sym_stats);
- if (!divide_in_z(qbar, *itrb, q, sym_stats.begin()))
+ get_symbol_stats(a, it, sym_stats);
+ if (!divide_in_z(qbar, it, q, sym_stats.begin()))
return false;
qbar = q;
ex term, rcoeff = r.coeff(x, rdeg);
if (!divide_in_z(rcoeff, blcoeff, term, var+1))
break;
- term = (term * power(x, rdeg - bdeg)).expand();
+ term = (term * pow(x, rdeg - bdeg)).expand();
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;
}
numeric rxi = xi.inverse();
for (int i=0; !e.is_zero(); i++) {
ex gi = e.smod(xi);
- g.push_back(gi * power(x, i));
+ g.push_back(gi * pow(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. */
*
* @param a first integer multivariate polynomial (expanded)
* @param b second integer multivariate polynomial (expanded)
- * @param ca cofactor of polynomial a (returned), NULL to suppress
+ * @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
* @param res the GCD (returned)
*
* @param a first rational multivariate polynomial (expanded)
* @param b second rational multivariate polynomial (expanded)
- * @param ca cofactor of polynomial a (returned), NULL to suppress
+ * @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
* @param res the GCD (returned)
}
+// 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 */
}
// 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();
if (ca)
*ca = ex_to<numeric>(aex)/g;
if (cb)
- *cb = bex/g;
+ *cb = bex/g;
return g;
}
// The symbol with least degree which is contained in both polynomials
// is our main variable
- sym_desc_vec::iterator vari = sym_stats.begin();
+ auto 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))))
int ldeg_b = var->ldeg_b;
int min_ldeg = std::min(ldeg_a,ldeg_b);
if (min_ldeg > 0) {
- ex common = power(x, min_ldeg);
+ ex common = pow(x, min_ldeg);
return gcd((aex / common).expand(), (bex / common).expand(), ca, cb, false) * common;
}
// Try heuristic algorithm first, fall back to PRS if that failed
ex g;
- bool found = heur_gcd(g, aex, bex, ca, cb, var);
- if (!found) {
+ 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 = pow(p, exp_b - exp_a);
+ return pow(p, exp_a);
} else {
if (ca)
- divide(aex, g, *ca, false);
+ *ca = pow(p, exp_a - exp_b);
if (cb)
- divide(bex, g, *cb, false);
+ *cb = _ex1;
+ return pow(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(pow(p_co, exp_a), pow(p_gcd, exp_b-exp_a)*pow(pb_co, exp_b), ca, cb, false);
+ return pow(p_gcd, exp_a)*pg;
+ } else {
+ ex pg = gcd(pow(p_gcd, exp_a - exp_b)*pow(p_co, exp_a), pow(pb_co, exp_b), ca, cb, false);
+ return pow(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 = pow(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(pow(p_gcd, exp_a-1)*pow(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].
*
* Yun's algorithm. Used internally by sqrfree().
*
* @param a multivariate polynomial over Z[X], treated here as univariate
- * polynomial in x.
+ * polynomial in x (needs not be expanded).
* @param x variable to factor in
- * @return vector of factors sorted in ascending degree */
-static exvector sqrfree_yun(const ex &a, const symbol &x)
+ * @return vector of expairs (factor, exponent), sorted by exponents */
+static epvector sqrfree_yun(const ex &a, const symbol &x)
{
- exvector res;
ex w = a;
ex z = w.diff(x);
ex g = gcd(w, z);
+ if (g.is_zero()) {
+ return epvector{};
+ }
if (g.is_equal(_ex1)) {
- res.push_back(a);
- return res;
+ return epvector{expair(a, _ex1)};
}
- ex y;
+ epvector results;
+ ex exponent = _ex0;
do {
w = quo(w, g, x);
- y = quo(z, g, x);
- z = y - w.diff(x);
+ if (w.is_zero()) {
+ return res;
+ }
+ z = quo(z, g, x) - w.diff(x);
+ exponent = exponent + 1;
+ if (w.is_equal(x)) {
+ // shortcut for x^n with n ∈ ℕ
+ exponent += quo(z, w.diff(x), x);
+ results.push_back(expair(w, exponent));
+ break;
+ }
g = gcd(w, z);
- res.push_back(g);
+ if (!g.is_equal(_ex1)) {
+ results.push_back(expair(g, exponent));
+ }
} while (!z.is_zero());
- return res;
+ return results;
}
/** Compute a square-free factorization of a multivariate polynomial in Q[X].
*
- * @param a multivariate polynomial over Q[X]
+ * @param a multivariate polynomial over Q[X] (needs not be expanded)
* @param l lst of variables to factor in, may be left empty for autodetection
* @return a square-free factorization of \p a.
*
*/
ex sqrfree(const ex &a, const lst &l)
{
- if (is_exactly_a<numeric>(a) || // algorithm does not trap a==0
- is_a<symbol>(a)) // shortcut
+ if (is_exactly_a<numeric>(a) ||
+ is_a<symbol>(a)) // shortcuts
return a;
// If no lst of variables to factorize in was specified we have to
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;
}
const ex tmp = multiply_lcm(a,lcm);
// find the factors
- exvector factors = sqrfree_yun(tmp, x);
+ epvector factors = sqrfree_yun(tmp, x);
- // construct the next list of symbols with the first element popped
- lst newargs = args;
- newargs.remove_first();
+ // remove symbol x and proceed recursively with the remaining symbols
+ args.remove_first();
// 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;
- }
+ if (args.nops()>0) {
+ for (auto & it : factors)
+ it.rest = sqrfree(it.rest, args);
}
// 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);
+ for (auto & it : factors)
+ result *= pow(it.rest, it.coeff);
// Yun's algorithm does not account for constant factors. (For univariate
// polynomials it works only in the monic case.) We can correct this by
// inserting what has been lost back into the result. For completeness
// we'll also have to recurse down that factor in the remaining variables.
- if (newargs.nops()>0)
- result *= sqrfree(quo(tmp, result, x), newargs);
+ if (args.nops()>0)
+ result *= sqrfree(quo(tmp, result, x), args);
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();
}
//clog << "red_poly = " << red_poly << ", red_numer = " << red_numer << endl;
// Factorize denominator and compute cofactors
- exvector yun = sqrfree_yun(denom, x);
-//clog << "yun factors: " << exprseq(yun) << endl;
- size_t num_yun = yun.size();
- exvector factor; factor.reserve(num_yun);
- exvector cofac; cofac.reserve(num_yun);
- for (size_t i=0; i<num_yun; i++) {
- if (!yun[i].is_equal(_ex1)) {
- for (size_t j=0; j<=i; j++) {
- factor.push_back(pow(yun[i], j+1));
- ex prod = _ex1;
- for (size_t k=0; k<num_yun; k++) {
- if (k == i)
- prod *= pow(yun[k], i-j);
- else
- prod *= pow(yun[k], k+1);
- }
- cofac.push_back(prod.expand());
+ epvector yun = sqrfree_yun(denom, x);
+ size_t yun_max_exponent = yun.empty() ? 0 : ex_to<numeric>(yun.back().coeff).to_int();
+ exvector factor, cofac;
+ for (size_t i=0; i<yun.size(); i++) {
+ numeric i_exponent = ex_to<numeric>(yun[i].coeff);
+ for (size_t j=0; j<i_exponent; j++) {
+ factor.push_back(pow(yun[i].rest, j+1));
+ ex prod = _ex1;
+ for (size_t k=0; k<yun.size(); k++) {
+ if (yun[k].coeff == i_exponent)
+ prod *= pow(yun[k].rest, i_exponent-1-j);
+ else
+ prod *= pow(yun[k].rest, yun[k].coeff);
}
+ cofac.push_back(prod.expand());
}
}
size_t num_factors = factor.size();
* @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;
}
/** Function object to be applied by basic::normal(). */
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); }
};
/** Default implementation of ex::normal(). It normalizes the children and
* replaces the object with a temporary symbol.
* @see ex::normal */
-ex basic::normal(exmap & repl, exmap & rev_lookup, int level) const
+ex basic::normal(exmap & repl, exmap & rev_lookup) const
{
if (nops() == 0)
- return (new lst(replace_with_symbol(*this, repl, rev_lookup), _ex1))->setflag(status_flags::dynallocated);
- else {
- if (level == 1)
- return (new lst(replace_with_symbol(*this, repl, rev_lookup), _ex1))->setflag(status_flags::dynallocated);
- 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(*this, repl, rev_lookup), _ex1});
+
+ normal_map_function map_normal;
+ return dynallocate<lst>({replace_with_symbol(map(map_normal), repl, rev_lookup), _ex1});
}
/** Implementation of ex::normal() for symbols. This returns the unmodified symbol.
* @see ex::normal */
-ex symbol::normal(exmap & repl, exmap & rev_lookup, int level) const
+ex symbol::normal(exmap & repl, exmap & rev_lookup) const
{
- return (new lst(*this, _ex1))->setflag(status_flags::dynallocated);
+ return dynallocate<lst>({*this, _ex1});
}
* into re+I*im and replaces I and non-rational real numbers with a temporary
* symbol.
* @see ex::normal */
-ex numeric::normal(exmap & repl, exmap & rev_lookup, int level) const
+ex numeric::normal(exmap & repl, exmap & rev_lookup) const
{
numeric num = numer();
ex numex = num;
}
// 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()});
}
/** Implementation of ex::normal() for a sum. It expands terms and performs
* fractional addition.
* @see ex::normal */
-ex add::normal(exmap & repl, exmap & rev_lookup, int level) const
+ex add::normal(exmap & repl, exmap & rev_lookup) const
{
- if (level == 1)
- return (new lst(replace_with_symbol(*this, repl, rev_lookup), _ex1))->setflag(status_flags::dynallocated);
- else if (level == -max_recursion_level)
- throw(std::runtime_error("max recursion level reached"));
-
// Normalize children and split each one into numerator and denominator
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);
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);
+ ex n = ex_to<numeric>(overall_coeff).normal(repl, rev_lookup);
nums.push_back(n.op(0));
dens.push_back(n.op(1));
GINAC_ASSERT(nums.size() == dens.size());
//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);
/** Implementation of ex::normal() for a product. It cancels common factors
* from fractions.
* @see ex::normal() */
-ex mul::normal(exmap & repl, exmap & rev_lookup, int level) const
+ex mul::normal(exmap & repl, exmap & rev_lookup) const
{
- if (level == 1)
- return (new lst(replace_with_symbol(*this, repl, rev_lookup), _ex1))->setflag(status_flags::dynallocated);
- else if (level == -max_recursion_level)
- throw(std::runtime_error("max recursion level reached"));
-
// Normalize children, separate into numerator and denominator
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);
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);
+ n = ex_to<numeric>(overall_coeff).normal(repl, rev_lookup);
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));
}
* distributes integer exponents to numerator and denominator, and replaces
* non-integer powers by temporary symbols.
* @see ex::normal */
-ex power::normal(exmap & repl, exmap & rev_lookup, int level) const
+ex power::normal(exmap & repl, exmap & rev_lookup) const
{
- if (level == 1)
- return (new lst(replace_with_symbol(*this, repl, rev_lookup), _ex1))->setflag(status_flags::dynallocated);
- else if (level == -max_recursion_level)
- throw(std::runtime_error("max recursion level reached"));
-
// Normalize basis and exponent (exponent gets reassembled)
- ex n_basis = ex_to<basic>(basis).normal(repl, rev_lookup, level-1);
- ex n_exponent = ex_to<basic>(exponent).normal(repl, rev_lookup, level-1);
+ ex n_basis = ex_to<basic>(basis).normal(repl, rev_lookup);
+ ex n_exponent = ex_to<basic>(exponent).normal(repl, rev_lookup);
n_exponent = n_exponent.op(0) / n_exponent.op(1);
if (n_exponent.info(info_flags::integer)) {
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>({pow(n_basis.op(0), n_exponent), pow(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>({pow(n_basis.op(1), -n_exponent), pow(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(pow(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(pow(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(pow(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(pow(n_basis.op(0) / n_basis.op(1), n_exponent), repl, rev_lookup), _ex1});
}
/** Implementation of ex::normal() for pseries. It normalizes each coefficient
* and replaces the series by a temporary symbol.
* @see ex::normal */
-ex pseries::normal(exmap & repl, exmap & rev_lookup, int level) const
+ex pseries::normal(exmap & repl, exmap & rev_lookup) 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});
}
* expression can be treated as a rational function). normal() is applied
* recursively to arguments of functions etc.
*
- * @param level maximum depth of recursion
* @return normalized expression */
-ex ex::normal(int level) const
+ex ex::normal() const
{
exmap repl, rev_lookup;
- ex e = bp->normal(repl, rev_lookup, level);
+ ex e = bp->normal(repl, rev_lookup);
GINAC_ASSERT(is_a<lst>(e));
// Re-insert replaced symbols
{
exmap repl, rev_lookup;
- ex e = bp->normal(repl, rev_lookup, 0);
+ ex e = bp->normal(repl, rev_lookup);
GINAC_ASSERT(is_a<lst>(e));
// Re-insert replaced symbols
{
exmap repl, rev_lookup;
- ex e = bp->normal(repl, rev_lookup, 0);
+ ex e = bp->normal(repl, rev_lookup);
GINAC_ASSERT(is_a<lst>(e));
// Re-insert replaced symbols
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.
*
{
exmap repl, rev_lookup;
- ex e = bp->normal(repl, rev_lookup, 0);
+ ex e = bp->normal(repl, rev_lookup);
GINAC_ASSERT(is_a<lst>(e));
// Re-insert replaced symbols
return bp->to_rational(repl);
}
-// GiNaC 1.1 compatibility function
-ex ex::to_rational(lst & repl_lst) const
-{
- // 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)));
-
- 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);
-
- return ret;
-}
-
ex ex::to_polynomial(exmap & repl) const
{
return bp->to_polynomial(repl);
}
-// GiNaC 1.1 compatibility function
-ex ex::to_polynomial(lst & repl_lst) const
-{
- // 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)));
-
- 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);
-
- return ret;
-}
-
/** Default implementation of ex::to_rational(). This replaces the object with
* a temporary symbol. */
ex basic::to_rational(exmap & repl) const
ex power::to_rational(exmap & repl) const
{
if (exponent.info(info_flags::integer))
- return power(basis.to_rational(repl), exponent);
+ return pow(basis.to_rational(repl), exponent);
else
return replace_with_symbol(*this, repl);
}
ex power::to_polynomial(exmap & repl) const
{
if (exponent.info(info_flags::posint))
- return power(basis.to_rational(repl), exponent);
+ return pow(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);
+ ex t = pow(basis_pref, exponent);
return t.to_polynomial(repl);
}
else
- return power(replace_with_symbol(power(basis, _ex_1), repl), -exponent);
+ return pow(replace_with_symbol(pow(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());
}
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)) {
const ex e_exp(e.op(1));
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);
+ factor *= pow(factor_local, e_exp);
+ return pow(pre_res, e_exp);
} else
return e.to_polynomial(repl);
git://www.ginac.de / ginac.git / blobdiff