X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fpower.cpp;h=815c59306accc437a9234707919af9e855e77fe2;hp=b38b733cb575667e0047fdad10383ccd3b53af0d;hb=7e8f4f43bc25f9231680c128c8e38612b0dbdc88;hpb=f5e84af31b20c7f732bee375bacc152e7fb01e56 diff --git a/ginac/power.cpp b/ginac/power.cpp index b38b733c..815c5930 100644 --- a/ginac/power.cpp +++ b/ginac/power.cpp @@ -3,7 +3,7 @@ * 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 @@ -17,7 +17,7 @@ * * 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 @@ -222,12 +222,14 @@ bool power::info(unsigned inf) const 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); } @@ -246,7 +248,14 @@ ex power::op(size_t i) const 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 @@ -439,14 +448,14 @@ ex power::eval(int level) const if (is_exactly_a(sub_exponent)) { const numeric & num_sub_exponent = ex_to(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)); } } // ^(*(x,y,z),c1) -> *(x^c1,y^c1,z^c1) (c1 integer) if (num_exponent->is_integer() && is_exactly_a(ebasis)) { - return expand_mul(ex_to(ebasis), *num_exponent); + return expand_mul(ex_to(ebasis), *num_exponent, 0); } // ^(*(...,x;c1),c2) -> *(^(*(...,x;1),c2),c1^c2) (c1, c2 numeric(), c1>0) @@ -465,8 +474,8 @@ ex power::eval(int level) const 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); @@ -558,6 +567,16 @@ ex power::eval_ncmul(const exvector & v) const 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. @@ -595,7 +614,7 @@ unsigned power::return_type() const { return basis.return_type(); } - + unsigned power::return_type_tinfo() const { return basis.return_type_tinfo(); @@ -626,7 +645,7 @@ ex power::expand(unsigned options) const const numeric &num_exponent = ex_to(a.overall_coeff); int int_exponent = num_exponent.to_int(); if (int_exponent > 0 && is_exactly_a(expanded_basis)) - distrseq.push_back(expand_add(ex_to(expanded_basis), int_exponent)); + distrseq.push_back(expand_add(ex_to(expanded_basis), int_exponent, options)); else distrseq.push_back(power(expanded_basis, a.overall_coeff)); } else @@ -634,7 +653,7 @@ ex power::expand(unsigned options) const // 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(expanded_exponent) || @@ -652,11 +671,11 @@ ex power::expand(unsigned options) const // (x+y)^n, n>0 if (int_exponent > 0 && is_exactly_a(expanded_basis)) - return expand_add(ex_to(expanded_basis), int_exponent); + return expand_add(ex_to(expanded_basis), int_exponent, options); // (x*y)^n -> x^n * y^n if (is_exactly_a(expanded_basis)) - return expand_mul(ex_to(expanded_basis), num_exponent); + return expand_mul(ex_to(expanded_basis), num_exponent, options, true); // cannot expand further if (are_ex_trivially_equal(basis,expanded_basis) && are_ex_trivially_equal(exponent,expanded_exponent)) @@ -677,10 +696,10 @@ ex power::expand(unsigned options) const /** 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; @@ -713,7 +732,7 @@ ex power::expand_add(const add & a, int n) const !is_exactly_a(ex_to(b).basis) || !is_exactly_a(ex_to(b).basis)); if (is_exactly_a(b)) - term.push_back(expand_mul(ex_to(b),numeric(k[l]))); + term.push_back(expand_mul(ex_to(b), numeric(k[l]), options, true)); else term.push_back(power(b,k[l])); } @@ -727,7 +746,7 @@ ex power::expand_add(const add & a, int n) const !is_exactly_a(ex_to(b).basis) || !is_exactly_a(ex_to(b).basis)); if (is_exactly_a(b)) - term.push_back(expand_mul(ex_to(b),numeric(n-k_cum[m-2]))); + term.push_back(expand_mul(ex_to(b), numeric(n-k_cum[m-2]), options, true)); else term.push_back(power(b,n-k_cum[m-2])); @@ -737,7 +756,7 @@ ex power::expand_add(const add & a, int n) const 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; @@ -764,7 +783,7 @@ ex power::expand_add(const add & a, int n) const /** 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(); @@ -787,7 +806,7 @@ ex power::expand_add_2(const add & a) const if (c.is_equal(_ex1)) { if (is_exactly_a(r)) { - sum.push_back(expair(expand_mul(ex_to(r),_num2), + sum.push_back(expair(expand_mul(ex_to(r), *_num2_p, options, true), _ex1)); } else { sum.push_back(expair((new power(r,_ex2))->setflag(status_flags::dynallocated), @@ -795,11 +814,11 @@ ex power::expand_add_2(const add & a) const } } else { if (is_exactly_a(r)) { - sum.push_back(a.combine_ex_with_coeff_to_pair(expand_mul(ex_to(r),_num2), - ex_to(c).power_dyn(_num2))); + sum.push_back(a.combine_ex_with_coeff_to_pair(expand_mul(ex_to(r), *_num2_p, options, true), + ex_to(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(c).power_dyn(_num2))); + ex_to(c).power_dyn(*_num2_p))); } } @@ -807,7 +826,7 @@ ex power::expand_add_2(const add & a) const 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(c)).mul_dyn(ex_to(c1)))); + _num2_p->mul(ex_to(c)).mul_dyn(ex_to(c1)))); } } @@ -817,10 +836,10 @@ ex power::expand_add_2(const add & a) const 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(a.overall_coeff).mul_dyn(_num2))); + sum.push_back(a.combine_pair_with_coeff_to_pair(*i, ex_to(a.overall_coeff).mul_dyn(*_num2_p))); ++i; } - sum.push_back(expair(ex_to(a.overall_coeff).power_dyn(_num2),_ex1)); + sum.push_back(expair(ex_to(a.overall_coeff).power_dyn(*_num2_p),_ex1)); } GINAC_ASSERT(sum.size()==(a_nops*(a_nops+1))/2); @@ -830,15 +849,26 @@ ex power::expand_add_2(const add & a) const /** 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, 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) { + 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()); + bool need_reexpand = false; + epvector::const_iterator last = m.seq.end(); epvector::const_iterator cit = m.seq.begin(); while (cit!=last) { @@ -847,11 +877,23 @@ ex power::expand_mul(const mul & m, const numeric & n) const } 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(cit->coeff).mul(n))); + numeric new_coeff = ex_to(cit->coeff).mul(n); + if (from_expand && is_exactly_a(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(m.overall_coeff).power_dyn(n)))->setflag(status_flags::dynallocated); + + const mul & result = static_cast((new mul(distrseq, ex_to(m.overall_coeff).power_dyn(n)))->setflag(status_flags::dynallocated)); + if (need_reexpand) + return ex(result).expand(options); + if (from_expand) + return result.setflag(status_flags::expanded); + return result; } } // namespace GiNaC