* computation, square-free factorization and rational function normalization. */
/*
- * GiNaC Copyright (C) 1999-2015 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2019 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
/** 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)
* @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);
+ 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);
#if 0
std::clog << "Symbols:\n";
- it = v.begin(); itend = v.end();
+ auto it = v.begin(), itend = v.end();
while (it != itend) {
- std::clog << " " << it->sym << ": deg_a=" << it->deg_a << ", deg_b=" << it->deg_b << ", ldeg_a=" << it->ldeg_a << ", ldeg_b=" << it->ldeg_b << ", max_deg=" << it->max_deg << ", max_lcnops=" << it->max_lcnops << endl;
- std::clog << " lcoeff_a=" << a.lcoeff(it->sym) << ", lcoeff_b=" << b.lcoeff(it->sym) << endl;
+ std::clog << " " << it->sym << ": deg_a=" << it->deg_a << ", deg_b=" << it->deg_b << ", ldeg_a=" << it->ldeg_a << ", ldeg_b=" << it->ldeg_b << ", max_deg=" << it->max_deg << ", max_lcnops=" << it->max_lcnops << std::endl;
+ std::clog << " lcoeff_a=" << a.lcoeff(it->sym) << ", lcoeff_b=" << b.lcoeff(it->sym) << std::endl;
++it;
}
#endif
* @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);
v.push_back(lcm / lcm_accum);
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 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);
}
if (!divide(rcoeff, blcoeff, term, false))
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())
if (!divide(rcoeff, blcoeff, term, false))
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);
}
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;
}
// code below is commented-out because it leads to a significant slowdown
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()) {
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()) {
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 dynallocate<add>(g);
}
// Some trivial cases
- ex aex = a.expand(), bex = b.expand();
+ ex aex = a.expand();
if (aex.is_zero()) {
if (ca)
*ca = _ex0;
*cb = _ex1;
return b;
}
+ ex bex = b.expand();
if (bex.is_zero()) {
if (ca)
*ca = _ex1;
// 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))))
*cb = b;
return _ex1;
}
- // move symbols which contained only in one of the polynomials
- // to the end:
+ // move symbol 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();
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;
}
if (ca)
*ca = _ex1;
if (cb)
- *cb = power(p, exp_b - exp_a);
- return power(p, exp_a);
+ *cb = pow(p, exp_b - exp_a);
+ return pow(p, exp_a);
} else {
if (ca)
- *ca = power(p, exp_a - exp_b);
+ *ca = pow(p, exp_a - exp_b);
if (cb)
*cb = _ex1;
- return power(p, exp_b);
+ return pow(p, exp_b);
}
}
if (cb)
*cb = b;
return _ex1;
- // XXX: do I need to check for p_gcd = -1?
}
// 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;
+ 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(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;
+ 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;
}
}
if (p.is_equal(b)) {
// a = p^n, b = p, gcd = p
if (ca)
- *ca = power(p, a.op(1) - 1);
+ *ca = pow(p, exp_a - 1);
if (cb)
*cb = _ex1;
return p;
- }
+ }
+ if (is_a<symbol>(p)) {
+ // Cancel trivial common factor
+ int ldeg_a = ex_to<numeric>(exp_a).to_int();
+ int ldeg_b = b.ldegree(p);
+ int min_ldeg = std::min(ldeg_a, ldeg_b);
+ if (min_ldeg > 0) {
+ ex common = pow(p, min_ldeg);
+ return gcd(pow(p, ldeg_a - min_ldeg), (b / common).expand(), ca, cb, false) * common;
+ }
+ }
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)) {
+ // a(x) = p(x)^n, gcd(p, b) = 1 ==> gcd(a, b) = 1
if (ca)
*ca = a;
if (cb)
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);
+ ex rg = gcd(pow(p_gcd, exp_a-1)*pow(p_co, exp_a), bpart_co, ca, cb, false);
return p_gcd*rg;
}
* 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 results;
+ }
+ 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
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) {
+ if (args.nops()>0) {
for (auto & it : factors)
- it = sqrfree(it, newargs);
+ it.rest = sqrfree(it.rest, args);
}
// Done with recursion, now construct the final result
ex result = _ex1;
- int p = 1;
for (auto & it : factors)
- result *= power(it, p++);
+ 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);
//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();
/** 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) override { 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 dynallocate<lst>({replace_with_symbol(*this, repl, rev_lookup), _ex1});
- else {
- if (level == 1)
- 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 dynallocate<lst>({replace_with_symbol(map(map_normal), 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 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;
/** 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 dynallocate<lst>({replace_with_symbol(*this, repl, rev_lookup), _ex1});
- 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);
for (auto & it : seq) {
- ex n = ex_to<basic>(recombine_pair_to_ex(it)).normal(repl, rev_lookup, level-1);
+ 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));
}
- 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());
/** 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 dynallocate<lst>({replace_with_symbol(*this, repl, rev_lookup), _ex1});
- 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;
for (auto & it : seq) {
- n = ex_to<basic>(recombine_pair_to_ex(it)).normal(repl, rev_lookup, level-1);
+ 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));
}
- 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));
* 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 dynallocate<lst>({replace_with_symbol(*this, repl, rev_lookup), _ex1});
- 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 dynallocate<lst>({power(n_basis.op(0), n_exponent), power(n_basis.op(1), n_exponent)});
+ 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 dynallocate<lst>({power(n_basis.op(1), -n_exponent), power(n_basis.op(0), -n_exponent)});
+ 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 dynallocate<lst>({replace_with_symbol(power(n_basis.op(0) / n_basis.op(1), n_exponent), repl, rev_lookup), _ex1});
+ 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 dynallocate<lst>({_ex1, replace_with_symbol(power(n_basis.op(0), -n_exponent), repl, rev_lookup)});
+ 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 dynallocate<lst>({replace_with_symbol(power(n_basis.op(1) / n_basis.op(0), -n_exponent), repl, rev_lookup), _ex1});
+ 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 dynallocate<lst>({replace_with_symbol(power(n_basis.op(0) / n_basis.op(1), n_exponent), repl, rev_lookup), _ex1});
+ 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;
for (auto & it : seq) {
* 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
{
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 (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 (auto & it : m)
- 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 (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 (auto & it : m)
- 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);
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