* Implementation of GiNaC's symbolic exponentiation (basis^exponent). */
/*
- * GiNaC Copyright (C) 1999-2002 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2003 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
#include <vector>
#include <iostream>
#include <stdexcept>
+#include <limits>
#include "power.h"
#include "expairseq.h"
#include "ncmul.h"
#include "numeric.h"
#include "constant.h"
+#include "operators.h"
#include "inifcns.h" // for log() in power::derivative()
#include "matrix.h"
#include "indexed.h"
#include "symbol.h"
-#include "print.h"
+#include "lst.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;
//////////
-// default ctor, dtor, copy ctor, assignment operator and helpers
+// default constructor
//////////
power::power() : inherited(TINFO_power) { }
-void power::copy(const power & other)
-{
- inherited::copy(other);
- basis = other.basis;
- exponent = other.exponent;
-}
-
-DEFAULT_DESTROY(power)
-
//////////
-// other ctors
+// other constructors
//////////
// all inlined
// archiving
//////////
-power::power(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
+power::power(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
{
n.find_ex("basis", basis, sym_lst);
n.find_ex("exponent", exponent, sym_lst);
// 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_exactly_a<symbol>(basis) || is_exactly_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);
+void power::do_print_python(const print_python & c, unsigned level) const
+{
+ print_power(c, "**", "", "", level);
+}
- if (exponent.is_equal(_ex1_2)) {
- c.s << (is_tex ? "\\sqrt{" : "sqrt(");
- basis.print(c);
- c.s << (is_tex ? '}' : ')');
- } else {
- 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
return inherited::info(inf);
}
-unsigned power::nops() const
+size_t power::nops() const
{
return 2;
}
-ex & power::let_op(int i)
+ex power::op(size_t i) const
{
- GINAC_ASSERT(i>=0);
GINAC_ASSERT(i<2);
return i==0 ? basis : exponent;
{
if (is_equal(ex_to<basic>(s)))
return 1;
- else if (is_ex_exactly_of_type(exponent, numeric) && ex_to<numeric>(exponent).is_integer()) {
+ else if (is_exactly_a<numeric>(exponent) && ex_to<numeric>(exponent).is_integer()) {
if (basis.is_equal(s))
return ex_to<numeric>(exponent).to_int();
else
{
if (is_equal(ex_to<basic>(s)))
return 1;
- else if (is_ex_exactly_of_type(exponent, numeric) && ex_to<numeric>(exponent).is_integer()) {
+ else if (is_exactly_a<numeric>(exponent) && ex_to<numeric>(exponent).is_integer()) {
if (basis.is_equal(s))
return ex_to<numeric>(exponent).to_int();
else
return _ex0;
} else {
// basis equal to s
- if (is_ex_exactly_of_type(exponent, numeric) && ex_to<numeric>(exponent).is_integer()) {
+ if (is_exactly_a<numeric>(exponent) && ex_to<numeric>(exponent).is_integer()) {
// integer exponent
int int_exp = ex_to<numeric>(exponent).to_int();
if (n == int_exp)
const numeric *num_basis;
const numeric *num_exponent;
- if (is_ex_exactly_of_type(ebasis, numeric)) {
+ if (is_exactly_a<numeric>(ebasis)) {
basis_is_numerical = true;
num_basis = &ex_to<numeric>(ebasis);
}
- if (is_ex_exactly_of_type(eexponent, numeric)) {
+ if (is_exactly_a<numeric>(eexponent)) {
exponent_is_numerical = true;
num_exponent = &ex_to<numeric>(eexponent);
}
// ^(^(x,c1),c2) -> ^(x,c1*c2)
// (c1, c2 numeric(), c2 integer or -1 < c1 <= 1,
// case c1==1 should not happen, see below!)
- if (is_ex_exactly_of_type(ebasis,power)) {
+ if (is_exactly_a<power>(ebasis)) {
const power & sub_power = ex_to<power>(ebasis);
const ex & sub_basis = sub_power.basis;
const ex & sub_exponent = sub_power.exponent;
- if (is_ex_exactly_of_type(sub_exponent,numeric)) {
+ if (is_exactly_a<numeric>(sub_exponent)) {
const numeric & num_sub_exponent = ex_to<numeric>(sub_exponent);
GINAC_ASSERT(num_sub_exponent!=numeric(1));
if (num_exponent->is_integer() || (abs(num_sub_exponent) - _num1).is_negative())
}
// ^(*(x,y,z),c1) -> *(x^c1,y^c1,z^c1) (c1 integer)
- if (num_exponent->is_integer() && is_ex_exactly_of_type(ebasis,mul)) {
+ if (num_exponent->is_integer() && is_exactly_a<mul>(ebasis)) {
return expand_mul(ex_to<mul>(ebasis), *num_exponent);
}
// ^(*(...,x;c1),c2) -> *(^(*(...,x;1),c2),c1^c2) (c1, c2 numeric(), c1>0)
// ^(*(...,x;c1),c2) -> *(^(*(...,x;-1),c2),(-c1)^c2) (c1, c2 numeric(), c1<0)
- if (is_ex_exactly_of_type(ebasis,mul)) {
+ if (is_exactly_a<mul>(ebasis)) {
GINAC_ASSERT(!num_exponent->is_integer()); // should have been handled above
const mul & mulref = ex_to<mul>(ebasis);
if (!mulref.overall_coeff.is_equal(_ex1)) {
// ^(nc,c1) -> ncmul(nc,nc,...) (c1 positive integer, unless nc is a matrix)
if (num_exponent->is_pos_integer() &&
ebasis.return_type() != return_types::commutative &&
- !is_ex_of_type(ebasis,matrix)) {
+ !is_a<matrix>(ebasis)) {
return ncmul(exvector(num_exponent->to_int(), ebasis), true);
}
}
return power(ebasis,eexponent);
}
-ex power::evalm(void) const
+ex power::evalm() const
{
const ex ebasis = basis.evalm();
const ex eexponent = exponent.evalm();
- if (is_ex_of_type(ebasis,matrix)) {
- if (is_ex_of_type(eexponent,numeric)) {
+ if (is_a<matrix>(ebasis)) {
+ if (is_exactly_a<numeric>(eexponent)) {
return (new matrix(ex_to<matrix>(ebasis).pow(eexponent)))->setflag(status_flags::dynallocated);
}
}
return (new power(ebasis, eexponent))->setflag(status_flags::dynallocated);
}
-ex power::subs(const lst & ls, const lst & lr, bool no_pattern) const
-{
- const ex &subsed_basis = basis.subs(ls, lr, no_pattern);
- const ex &subsed_exponent = exponent.subs(ls, lr, no_pattern);
+// from mul.cpp
+extern bool tryfactsubs(const ex &, const ex &, int &, lst &);
- if (are_ex_trivially_equal(basis, subsed_basis)
- && are_ex_trivially_equal(exponent, subsed_exponent))
- return basic::subs(ls, lr, no_pattern);
- else
- return power(subsed_basis, subsed_exponent).basic::subs(ls, lr, no_pattern);
+ex power::subs(const exmap & m, unsigned options) const
+{
+ 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(m, options);
+
+ if (!(options & subs_options::algebraic))
+ return subs_one_level(m, options);
+
+ for (exmap::const_iterator it = m.begin(); it != m.end(); ++it) {
+ int nummatches = std::numeric_limits<int>::max();
+ lst repls;
+ 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(m, options);
}
-ex power::simplify_ncmul(const exvector & v) const
+ex power::eval_ncmul(const exvector & v) const
{
- return inherited::simplify_ncmul(v);
+ return inherited::eval_ncmul(v);
}
// protected
return exponent.compare(o.exponent);
}
-unsigned power::return_type(void) const
+unsigned power::return_type() const
{
return basis.return_type();
}
-unsigned power::return_type_tinfo(void) const
+unsigned power::return_type_tinfo() const
{
return basis.return_type_tinfo();
}
const ex expanded_exponent = exponent.expand(options);
// x^(a+b) -> x^a * x^b
- if (is_ex_exactly_of_type(expanded_exponent, add)) {
+ if (is_exactly_a<add>(expanded_exponent)) {
const add &a = ex_to<add>(expanded_exponent);
exvector distrseq;
distrseq.reserve(a.seq.size() + 1);
if (ex_to<numeric>(a.overall_coeff).is_integer()) {
const numeric &num_exponent = ex_to<numeric>(a.overall_coeff);
int int_exponent = num_exponent.to_int();
- if (int_exponent > 0 && is_ex_exactly_of_type(expanded_basis, add))
+ if (int_exponent > 0 && is_exactly_a<add>(expanded_basis))
distrseq.push_back(expand_add(ex_to<add>(expanded_basis), int_exponent));
else
distrseq.push_back(power(expanded_basis, a.overall_coeff));
return r.expand();
}
- if (!is_ex_exactly_of_type(expanded_exponent, numeric) ||
+ if (!is_exactly_a<numeric>(expanded_exponent) ||
!ex_to<numeric>(expanded_exponent).is_integer()) {
if (are_ex_trivially_equal(basis,expanded_basis) && are_ex_trivially_equal(exponent,expanded_exponent)) {
return this->hold();
int int_exponent = num_exponent.to_int();
// (x+y)^n, n>0
- if (int_exponent > 0 && is_ex_exactly_of_type(expanded_basis,add))
+ if (int_exponent > 0 && is_exactly_a<add>(expanded_basis))
return expand_add(ex_to<add>(expanded_basis), int_exponent);
// (x*y)^n -> x^n * y^n
- if (is_ex_exactly_of_type(expanded_basis,mul))
+ if (is_exactly_a<mul>(expanded_basis))
return expand_mul(ex_to<mul>(expanded_basis), num_exponent);
// cannot expand further
if (n==2)
return expand_add_2(a);
- const int m = a.nops();
+ const size_t m = a.nops();
exvector result;
// The number of terms will be the number of combinatorial compositions,
// i.e. the number of unordered arrangement of m nonnegative integers
intvector upper_limit(m-1);
int l;
- for (int l=0; l<m-1; ++l) {
+ for (size_t l=0; l<m-1; ++l) {
k[l] = 0;
k_cum[l] = 0;
upper_limit[l] = n;
!is_exactly_a<add>(ex_to<power>(b).basis) ||
!is_exactly_a<mul>(ex_to<power>(b).basis) ||
!is_exactly_a<power>(ex_to<power>(b).basis));
- if (is_ex_exactly_of_type(b,mul))
+ if (is_exactly_a<mul>(b))
term.push_back(expand_mul(ex_to<mul>(b),numeric(k[l])));
else
term.push_back(power(b,k[l]));
!is_exactly_a<add>(ex_to<power>(b).basis) ||
!is_exactly_a<mul>(ex_to<power>(b).basis) ||
!is_exactly_a<power>(ex_to<power>(b).basis));
- if (is_ex_exactly_of_type(b,mul))
+ if (is_exactly_a<mul>(b))
term.push_back(expand_mul(ex_to<mul>(b),numeric(n-k_cum[m-2])));
else
term.push_back(power(b,n-k_cum[m-2]));
// recalc k_cum[] and upper_limit[]
k_cum[l] = (l==0 ? k[0] : k_cum[l-1]+k[l]);
- for (int i=l+1; i<m-1; ++i)
+ for (size_t i=l+1; i<m-1; ++i)
k_cum[i] = k_cum[i-1]+k[i];
- for (int i=l+1; i<m-1; ++i)
+ for (size_t i=l+1; i<m-1; ++i)
upper_limit[i] = n-k_cum[i-1];
}
ex power::expand_add_2(const add & a) const
{
epvector sum;
- unsigned a_nops = a.nops();
+ size_t a_nops = a.nops();
sum.reserve((a_nops*(a_nops+1))/2);
epvector::const_iterator last = a.seq.end();
!is_exactly_a<mul>(ex_to<power>(r).basis) ||
!is_exactly_a<power>(ex_to<power>(r).basis));
- if (are_ex_trivially_equal(c,_ex1)) {
- if (is_ex_exactly_of_type(r,mul)) {
+ if (c.is_equal(_ex1)) {
+ if (is_exactly_a<mul>(r)) {
sum.push_back(expair(expand_mul(ex_to<mul>(r),_num2),
_ex1));
} else {
_ex1));
}
} else {
- if (is_ex_exactly_of_type(r,mul)) {
+ if (is_exactly_a<mul>(r)) {
sum.push_back(a.combine_ex_with_coeff_to_pair(expand_mul(ex_to<mul>(r),_num2),
ex_to<numeric>(c).power_dyn(_num2)));
} else {
ex_to<numeric>(c).power_dyn(_num2)));
}
}
-
+
for (epvector::const_iterator cit1=cit0+1; cit1!=last; ++cit1) {
const ex & r1 = cit1->rest;
const ex & c1 = cit1->coeff;
epvector::const_iterator last = m.seq.end();
epvector::const_iterator cit = m.seq.begin();
while (cit!=last) {
- if (is_ex_exactly_of_type(cit->rest,numeric)) {
+ if (is_exactly_a<numeric>(cit->rest)) {
distrseq.push_back(m.combine_pair_with_coeff_to_pair(*cit, n));
} else {
// it is safe not to call mul::combine_pair_with_coeff_to_pair()
git://www.ginac.de / ginac.git / blobdiff