* Implementation of GiNaC's symbolic exponentiation (basis^exponent). */
/*
- * GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2005 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
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
- * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
#include <vector>
case info_flags::cinteger_polynomial:
case info_flags::rational_polynomial:
case info_flags::crational_polynomial:
- return exponent.info(info_flags::nonnegint);
+ return exponent.info(info_flags::nonnegint) &&
+ basis.info(inf);
case info_flags::rational_function:
- return exponent.info(info_flags::integer);
+ return exponent.info(info_flags::integer) &&
+ basis.info(inf);
case info_flags::algebraic:
- return (!exponent.info(info_flags::integer) ||
- basis.info(inf));
+ return !exponent.info(info_flags::integer) ||
+ basis.info(inf);
}
return inherited::info(inf);
}
ex power::map(map_function & f) const
{
- return (new power(f(basis), f(exponent)))->setflag(status_flags::dynallocated);
+ const ex &mapped_basis = f(basis);
+ const ex &mapped_exponent = f(exponent);
+
+ if (!are_ex_trivially_equal(basis, mapped_basis)
+ || !are_ex_trivially_equal(exponent, mapped_exponent))
+ return (new power(mapped_basis, mapped_exponent))->setflag(status_flags::dynallocated);
+ else
+ return *this;
}
int power::degree(const ex & s) const
if (ebasis.is_equal(_ex1))
return _ex1;
+ // power of a function calculated by separate rules defined for this function
+ if (is_exactly_a<function>(ebasis))
+ return ex_to<function>(ebasis).power(eexponent);
+
if (exponent_is_numerical) {
// ^(c1,c2) -> c1^c2 (c1, c2 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())
+ if (num_exponent->is_integer() || (abs(num_sub_exponent) - (*_num1_p)).is_negative())
return power(sub_basis,num_sub_exponent.mul(*num_exponent));
}
}
return (new mul(power(*mulp,exponent),
power(num_coeff,*num_exponent)))->setflag(status_flags::dynallocated);
} else {
- GINAC_ASSERT(num_coeff.compare(_num0)<0);
- if (!num_coeff.is_equal(_num_1)) {
+ GINAC_ASSERT(num_coeff.compare(*_num0_p)<0);
+ if (!num_coeff.is_equal(*_num_1_p)) {
mul *mulp = new mul(mulref);
mulp->overall_coeff = _ex_1;
mulp->clearflag(status_flags::evaluated);
return inherited::eval_ncmul(v);
}
+ex power::conjugate() const
+{
+ ex newbasis = basis.conjugate();
+ ex newexponent = exponent.conjugate();
+ if (are_ex_trivially_equal(basis, newbasis) && are_ex_trivially_equal(exponent, newexponent)) {
+ return *this;
+ }
+ return (new power(newbasis, newexponent))->setflag(status_flags::dynallocated);
+}
+
// protected
/** Implementation of ex::diff() for a power.
{
return basis.return_type();
}
-
+
unsigned power::return_type_tinfo() const
{
return basis.return_type_tinfo();
// (x*y)^n -> x^n * y^n
if (is_exactly_a<mul>(expanded_basis))
- return expand_mul(ex_to<mul>(expanded_basis), num_exponent, options);
+ return expand_mul(ex_to<mul>(expanded_basis), num_exponent, options, true);
// cannot expand further
if (are_ex_trivially_equal(basis,expanded_basis) && are_ex_trivially_equal(exponent,expanded_exponent))
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
+ // i.e. the number of unordered arrangements of m nonnegative integers
// which sum up to n. It is frequently written as C_n(m) and directly
// related with binomial coefficients:
result.reserve(binomial(numeric(n+m-1), numeric(m-1)).to_int());
!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]), options));
+ term.push_back(expand_mul(ex_to<mul>(b), numeric(k[l]), options, true));
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]), options));
+ term.push_back(expand_mul(ex_to<mul>(b), numeric(n-k_cum[m-2]), options, true));
else
term.push_back(power(b,n-k_cum[m-2]));
if (c.is_equal(_ex1)) {
if (is_exactly_a<mul>(r)) {
- sum.push_back(expair(expand_mul(ex_to<mul>(r), _num2, options),
+ sum.push_back(expair(expand_mul(ex_to<mul>(r), *_num2_p, options, true),
_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, options),
- ex_to<numeric>(c).power_dyn(_num2)));
+ sum.push_back(a.combine_ex_with_coeff_to_pair(expand_mul(ex_to<mul>(r), *_num2_p, options, true),
+ ex_to<numeric>(c).power_dyn(*_num2_p)));
} else {
sum.push_back(a.combine_ex_with_coeff_to_pair((new power(r,_ex2))->setflag(status_flags::dynallocated),
- ex_to<numeric>(c).power_dyn(_num2)));
+ ex_to<numeric>(c).power_dyn(*_num2_p)));
}
}
const ex & r1 = cit1->rest;
const ex & c1 = cit1->coeff;
sum.push_back(a.combine_ex_with_coeff_to_pair((new mul(r,r1))->setflag(status_flags::dynallocated),
- _num2.mul(ex_to<numeric>(c)).mul_dyn(ex_to<numeric>(c1))));
+ _num2_p->mul(ex_to<numeric>(c)).mul_dyn(ex_to<numeric>(c1))));
}
}
if (!a.overall_coeff.is_zero()) {
epvector::const_iterator i = a.seq.begin(), end = a.seq.end();
while (i != end) {
- sum.push_back(a.combine_pair_with_coeff_to_pair(*i, ex_to<numeric>(a.overall_coeff).mul_dyn(_num2)));
+ sum.push_back(a.combine_pair_with_coeff_to_pair(*i, ex_to<numeric>(a.overall_coeff).mul_dyn(*_num2_p)));
++i;
}
- sum.push_back(expair(ex_to<numeric>(a.overall_coeff).power_dyn(_num2),_ex1));
+ sum.push_back(expair(ex_to<numeric>(a.overall_coeff).power_dyn(*_num2_p),_ex1));
}
GINAC_ASSERT(sum.size()==(a_nops*(a_nops+1))/2);
/** 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, unsigned options) const
+ex power::expand_mul(const mul & m, const numeric & n, unsigned options, bool from_expand) const
{
GINAC_ASSERT(n.is_integer());
- if (n.is_zero())
+ if (n.is_zero()) {
return _ex1;
+ }
+
+ // Leave it to multiplication since dummy indices have to be renamed
+ if (get_all_dummy_indices(m).size() > 0 && n.is_positive()) {
+ ex result = m;
+ for (int i=1; i < n.to_int(); i++)
+ result *= rename_dummy_indices_uniquely(m,m);
+ return result;
+ }
epvector distrseq;
distrseq.reserve(m.seq.size());
// it is safe not to call mul::combine_pair_with_coeff_to_pair()
// since n is an integer
numeric new_coeff = ex_to<numeric>(cit->coeff).mul(n);
- if (is_exactly_a<add>(cit->rest) && new_coeff.is_pos_integer()) {
+ if (from_expand && 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;
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
+ if (from_expand)
return result.setflag(status_flags::expanded);
+ return result;
}
} // namespace GiNaC