#include "indexed.h"
#include "symbol.h"
#include "lst.h"
-#include "print.h"
#include "archive.h"
#include "utils.h"
namespace GiNaC {
-GINAC_IMPLEMENT_REGISTERED_CLASS(power, basic)
+GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(power, basic,
+ print_func<print_dflt>(&power::do_print_dflt).
+ print_func<print_latex>(&power::do_print_latex).
+ print_func<print_csrc>(&power::do_print_csrc).
+ print_func<print_python>(&power::do_print_python).
+ print_func<print_python_repr>(&power::do_print_python_repr))
typedef std::vector<int> intvector;
// public
+void power::print_power(const print_context & c, const char *powersymbol, const char *openbrace, const char *closebrace, unsigned level) const
+{
+ // Ordinary output of powers using '^' or '**'
+ if (precedence() <= level)
+ c.s << openbrace << '(';
+ basis.print(c, precedence());
+ c.s << powersymbol;
+ c.s << openbrace;
+ exponent.print(c, precedence());
+ c.s << closebrace;
+ if (precedence() <= level)
+ c.s << ')' << closebrace;
+}
+
+void power::do_print_dflt(const print_dflt & c, unsigned level) const
+{
+ if (exponent.is_equal(_ex1_2)) {
+
+ // Square roots are printed in a special way
+ c.s << "sqrt(";
+ basis.print(c);
+ c.s << ')';
+
+ } else
+ print_power(c, "^", "", "", level);
+}
+
+void power::do_print_latex(const print_latex & c, unsigned level) const
+{
+ if (is_exactly_a<numeric>(exponent) && ex_to<numeric>(exponent).is_negative()) {
+
+ // Powers with negative numeric exponents are printed as fractions
+ c.s << "\\frac{1}{";
+ power(basis, -exponent).eval().print(c);
+ c.s << '}';
+
+ } else if (exponent.is_equal(_ex1_2)) {
+
+ // Square roots are printed in a special way
+ c.s << "\\sqrt{";
+ basis.print(c);
+ c.s << '}';
+
+ } else
+ print_power(c, "^", "{", "}", level);
+}
+
static void print_sym_pow(const print_context & c, const symbol &x, int exp)
{
// Optimal output of integer powers of symbols to aid compiler CSE.
// C.f. ISO/IEC 14882:1998, section 1.9 [intro execution], paragraph 15
- // to learn why such a parenthisation is really necessary.
+ // to learn why such a parenthesation is really necessary.
if (exp == 1) {
x.print(c);
} else if (exp == 2) {
}
}
-void power::print(const print_context & c, unsigned level) const
+void power::do_print_csrc(const print_csrc & c, unsigned level) const
{
- if (is_a<print_tree>(c)) {
-
- inherited::print(c, level);
-
- } else if (is_a<print_csrc>(c)) {
-
- // Integer powers of symbols are printed in a special, optimized way
- if (exponent.info(info_flags::integer)
- && (is_a<symbol>(basis) || is_a<constant>(basis))) {
- int exp = ex_to<numeric>(exponent).to_int();
- if (exp > 0)
- c.s << '(';
- else {
- exp = -exp;
- if (is_a<print_csrc_cl_N>(c))
- c.s << "recip(";
- else
- c.s << "1.0/(";
- }
- print_sym_pow(c, ex_to<symbol>(basis), exp);
- c.s << ')';
-
- // <expr>^-1 is printed as "1.0/<expr>" or with the recip() function of CLN
- } else if (exponent.is_equal(_ex_1)) {
+ // Integer powers of symbols are printed in a special, optimized way
+ if (exponent.info(info_flags::integer)
+ && (is_a<symbol>(basis) || is_a<constant>(basis))) {
+ int exp = ex_to<numeric>(exponent).to_int();
+ if (exp > 0)
+ c.s << '(';
+ else {
+ exp = -exp;
if (is_a<print_csrc_cl_N>(c))
c.s << "recip(";
else
c.s << "1.0/(";
- basis.print(c);
- c.s << ')';
-
- // Otherwise, use the pow() or expt() (CLN) functions
- } else {
- if (is_a<print_csrc_cl_N>(c))
- c.s << "expt(";
- else
- c.s << "pow(";
- basis.print(c);
- c.s << ',';
- exponent.print(c);
- c.s << ')';
}
+ print_sym_pow(c, ex_to<symbol>(basis), exp);
+ c.s << ')';
- } else if (is_a<print_python_repr>(c)) {
+ // <expr>^-1 is printed as "1.0/<expr>" or with the recip() function of CLN
+ } else if (exponent.is_equal(_ex_1)) {
+ if (is_a<print_csrc_cl_N>(c))
+ c.s << "recip(";
+ else
+ c.s << "1.0/(";
+ basis.print(c);
+ c.s << ')';
- c.s << class_name() << '(';
+ // Otherwise, use the pow() or expt() (CLN) functions
+ } else {
+ if (is_a<print_csrc_cl_N>(c))
+ c.s << "expt(";
+ else
+ c.s << "pow(";
basis.print(c);
c.s << ',';
exponent.print(c);
c.s << ')';
+ }
+}
- } else {
-
- bool is_tex = is_a<print_latex>(c);
-
- if (is_tex && is_exactly_a<numeric>(exponent) && ex_to<numeric>(exponent).is_negative()) {
-
- // Powers with negative numeric exponents are printed as fractions in TeX
- c.s << "\\frac{1}{";
- power(basis, -exponent).eval().print(c);
- c.s << "}";
-
- } else if (exponent.is_equal(_ex1_2)) {
-
- // Square roots are printed in a special way
- c.s << (is_tex ? "\\sqrt{" : "sqrt(");
- basis.print(c);
- c.s << (is_tex ? '}' : ')');
-
- } else {
+void power::do_print_python(const print_python & c, unsigned level) const
+{
+ print_power(c, "**", "", "", level);
+}
- // Ordinary output of powers using '^' or '**'
- if (precedence() <= level)
- c.s << (is_tex ? "{(" : "(");
- basis.print(c, precedence());
- if (is_a<print_python>(c))
- c.s << "**";
- else
- c.s << '^';
- if (is_tex)
- c.s << '{';
- exponent.print(c, precedence());
- if (is_tex)
- c.s << '}';
- if (precedence() <= level)
- c.s << (is_tex ? ")}" : ")");
- }
- }
+void power::do_print_python_repr(const print_python_repr & c, unsigned level) const
+{
+ c.s << class_name() << '(';
+ basis.print(c);
+ c.s << ',';
+ exponent.print(c);
+ c.s << ')';
}
bool power::info(unsigned inf) const
// ^(*(x,y,z),c1) -> *(x^c1,y^c1,z^c1) (c1 integer)
if (num_exponent->is_integer() && is_exactly_a<mul>(ebasis)) {
- return expand_mul(ex_to<mul>(ebasis), *num_exponent);
+ return expand_mul(ex_to<mul>(ebasis), *num_exponent, 0);
}
// ^(*(...,x;c1),c2) -> *(^(*(...,x;1),c2),c1^c2) (c1, c2 numeric(), c1>0)
// from mul.cpp
extern bool tryfactsubs(const ex &, const ex &, int &, lst &);
-ex power::subs(const lst & ls, const lst & lr, unsigned options) const
+ex power::subs(const exmap & m, unsigned options) const
{
- const ex &subsed_basis = basis.subs(ls, lr, options);
- const ex &subsed_exponent = exponent.subs(ls, lr, options);
+ const ex &subsed_basis = basis.subs(m, options);
+ const ex &subsed_exponent = exponent.subs(m, options);
if (!are_ex_trivially_equal(basis, subsed_basis)
|| !are_ex_trivially_equal(exponent, subsed_exponent))
- return power(subsed_basis, subsed_exponent).subs_one_level(ls, lr, options);
+ return power(subsed_basis, subsed_exponent).subs_one_level(m, options);
- if (!(options & subs_options::subs_algebraic))
- return subs_one_level(ls, lr, options);
+ if (!(options & subs_options::algebraic))
+ return subs_one_level(m, options);
- lst::const_iterator its, itr;
- for (its = ls.begin(), itr = lr.begin(); its != ls.end(); ++its, ++itr) {
+ for (exmap::const_iterator it = m.begin(); it != m.end(); ++it) {
int nummatches = std::numeric_limits<int>::max();
lst repls;
- if (tryfactsubs(*this, *its, nummatches, repls))
- return (ex_to<basic>((*this) * power(itr->subs(ex(repls), subs_options::subs_no_pattern) / its->subs(ex(repls), subs_options::subs_no_pattern), nummatches))).subs_one_level(ls, lr, options);
+ if (tryfactsubs(*this, it->first, nummatches, repls))
+ return (ex_to<basic>((*this) * power(it->second.subs(ex(repls), subs_options::no_pattern) / it->first.subs(ex(repls), subs_options::no_pattern), nummatches))).subs_one_level(m, options);
}
- return subs_one_level(ls, lr, options);
+ return subs_one_level(m, options);
}
ex power::eval_ncmul(const exvector & v) const
const numeric &num_exponent = ex_to<numeric>(a.overall_coeff);
int int_exponent = num_exponent.to_int();
if (int_exponent > 0 && is_exactly_a<add>(expanded_basis))
- distrseq.push_back(expand_add(ex_to<add>(expanded_basis), int_exponent));
+ distrseq.push_back(expand_add(ex_to<add>(expanded_basis), int_exponent, options));
else
distrseq.push_back(power(expanded_basis, a.overall_coeff));
} else
// Make sure that e.g. (x+y)^(1+a) -> x*(x+y)^a + y*(x+y)^a
ex r = (new mul(distrseq))->setflag(status_flags::dynallocated);
- return r.expand();
+ return r.expand(options);
}
if (!is_exactly_a<numeric>(expanded_exponent) ||
// (x+y)^n, n>0
if (int_exponent > 0 && is_exactly_a<add>(expanded_basis))
- return expand_add(ex_to<add>(expanded_basis), int_exponent);
+ return expand_add(ex_to<add>(expanded_basis), int_exponent, options);
// (x*y)^n -> x^n * y^n
if (is_exactly_a<mul>(expanded_basis))
- return expand_mul(ex_to<mul>(expanded_basis), num_exponent);
+ return expand_mul(ex_to<mul>(expanded_basis), num_exponent, options);
// cannot expand further
if (are_ex_trivially_equal(basis,expanded_basis) && are_ex_trivially_equal(exponent,expanded_exponent))
/** expand a^n where a is an add and n is a positive integer.
* @see power::expand */
-ex power::expand_add(const add & a, int n) const
+ex power::expand_add(const add & a, int n, unsigned options) const
{
if (n==2)
- return expand_add_2(a);
+ return expand_add_2(a, options);
const size_t m = a.nops();
exvector result;
!is_exactly_a<mul>(ex_to<power>(b).basis) ||
!is_exactly_a<power>(ex_to<power>(b).basis));
if (is_exactly_a<mul>(b))
- term.push_back(expand_mul(ex_to<mul>(b),numeric(k[l])));
+ term.push_back(expand_mul(ex_to<mul>(b), numeric(k[l]), options));
else
term.push_back(power(b,k[l]));
}
!is_exactly_a<mul>(ex_to<power>(b).basis) ||
!is_exactly_a<power>(ex_to<power>(b).basis));
if (is_exactly_a<mul>(b))
- term.push_back(expand_mul(ex_to<mul>(b),numeric(n-k_cum[m-2])));
+ term.push_back(expand_mul(ex_to<mul>(b), numeric(n-k_cum[m-2]), options));
else
term.push_back(power(b,n-k_cum[m-2]));
term.push_back(f);
- result.push_back((new mul(term))->setflag(status_flags::dynallocated));
+ result.push_back(ex((new mul(term))->setflag(status_flags::dynallocated)).expand(options));
// increment k[]
l = m-2;
/** Special case of power::expand_add. Expands a^2 where a is an add.
* @see power::expand_add */
-ex power::expand_add_2(const add & a) const
+ex power::expand_add_2(const add & a, unsigned options) const
{
epvector sum;
size_t a_nops = a.nops();
if (c.is_equal(_ex1)) {
if (is_exactly_a<mul>(r)) {
- sum.push_back(expair(expand_mul(ex_to<mul>(r),_num2),
+ sum.push_back(expair(expand_mul(ex_to<mul>(r), _num2, options),
_ex1));
} else {
sum.push_back(expair((new power(r,_ex2))->setflag(status_flags::dynallocated),
}
} else {
if (is_exactly_a<mul>(r)) {
- sum.push_back(a.combine_ex_with_coeff_to_pair(expand_mul(ex_to<mul>(r),_num2),
+ sum.push_back(a.combine_ex_with_coeff_to_pair(expand_mul(ex_to<mul>(r), _num2, options),
ex_to<numeric>(c).power_dyn(_num2)));
} else {
sum.push_back(a.combine_ex_with_coeff_to_pair((new power(r,_ex2))->setflag(status_flags::dynallocated),
/** Expand factors of m in m^n where m is a mul and n is and integer.
* @see power::expand */
-ex power::expand_mul(const mul & m, const numeric & n) const
+ex power::expand_mul(const mul & m, const numeric & n, unsigned options) const
{
GINAC_ASSERT(n.is_integer());
epvector distrseq;
distrseq.reserve(m.seq.size());
+ bool need_reexpand = false;
+
epvector::const_iterator last = m.seq.end();
epvector::const_iterator cit = m.seq.begin();
while (cit!=last) {
} else {
// it is safe not to call mul::combine_pair_with_coeff_to_pair()
// since n is an integer
- distrseq.push_back(expair(cit->rest, ex_to<numeric>(cit->coeff).mul(n)));
+ numeric new_coeff = ex_to<numeric>(cit->coeff).mul(n);
+ if (is_exactly_a<add>(cit->rest) && new_coeff.is_pos_integer()) {
+ // this happens when e.g. (a+b)^(1/2) gets squared and
+ // the resulting product needs to be reexpanded
+ need_reexpand = true;
+ }
+ distrseq.push_back(expair(cit->rest, new_coeff));
}
++cit;
}
- return (new mul(distrseq, ex_to<numeric>(m.overall_coeff).power_dyn(n)))->setflag(status_flags::dynallocated);
+
+ const mul & result = static_cast<const mul &>((new mul(distrseq, ex_to<numeric>(m.overall_coeff).power_dyn(n)))->setflag(status_flags::dynallocated));
+ if (need_reexpand)
+ return ex(result).expand(options);
+ else
+ return result.setflag(status_flags::expanded);
}
} // namespace GiNaC
git://www.ginac.de / ginac.git / blobdiff