X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fpower.cpp;h=ba7a66f4bc77cb912947fa06975b2ee801e304d9;hp=2aedc9bfbd28b7af727e7275b75edc30ae28a31b;hb=HEAD;hpb=65f2693a0948d1db0bc68d7656c64e1fed91c158 diff --git a/ginac/power.cpp b/ginac/power.cpp index 2aedc9bf..c30c9547 100644 --- a/ginac/power.cpp +++ b/ginac/power.cpp @@ -3,7 +3,7 @@ * Implementation of GiNaC's symbolic exponentiation (basis^exponent). */ /* - * GiNaC Copyright (C) 1999-2015 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2024 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 @@ -140,7 +140,7 @@ void power::do_print_latex(const print_latex & c, unsigned level) const 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 14882:2011, section 1.9 [intro execution], paragraph 15 + // C.f. ISO/IEC 14882:2011, section 1.9 [intro.execution], paragraph 15 // to learn why such a parenthesation is really necessary. if (exp == 1) { x.print(c); @@ -229,21 +229,18 @@ 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) && - basis.info(inf); + return basis.info(inf) && exponent.info(info_flags::nonnegint); case info_flags::rational_function: - return exponent.info(info_flags::integer) && - basis.info(inf); - case info_flags::algebraic: - return !exponent.info(info_flags::integer) || - basis.info(inf); + return basis.info(inf) && exponent.info(info_flags::integer); + case info_flags::real: + return basis.info(inf) && exponent.info(info_flags::integer); case info_flags::expanded: return (flags & status_flags::expanded); case info_flags::positive: return basis.info(info_flags::positive) && exponent.info(info_flags::real); case info_flags::nonnegative: return (basis.info(info_flags::positive) && exponent.info(info_flags::real)) || - (basis.info(info_flags::real) && exponent.info(info_flags::integer) && exponent.info(info_flags::even)); + (basis.info(info_flags::real) && exponent.info(info_flags::even)); case info_flags::has_indices: { if (flags & status_flags::has_indices) return true; @@ -373,42 +370,36 @@ ex power::coeff(const ex & s, int n) const * - ^(*(x,y,z),c) -> *(x^c,y^c,z^c) (if c integer) * - ^(*(x,c1),c2) -> ^(x,c2)*c1^c2 (c1>0) * - ^(*(x,c1),c2) -> ^(-x,c2)*c1^c2 (c1<0) - * - * @param level cut-off in recursive evaluation */ -ex power::eval(int level) const + */ +ex power::eval() const { - if ((level==1) && (flags & status_flags::evaluated)) + if (flags & status_flags::evaluated) return *this; - else if (level == -max_recursion_level) - throw(std::runtime_error("max recursion level reached")); - - const ex & ebasis = level==1 ? basis : basis.eval(level-1); - const ex & eexponent = level==1 ? exponent : exponent.eval(level-1); - + const numeric *num_basis = nullptr; const numeric *num_exponent = nullptr; - - if (is_exactly_a(ebasis)) { - num_basis = &ex_to(ebasis); + + if (is_exactly_a(basis)) { + num_basis = &ex_to(basis); } - if (is_exactly_a(eexponent)) { - num_exponent = &ex_to(eexponent); + if (is_exactly_a(exponent)) { + num_exponent = &ex_to(exponent); } // ^(x,0) -> 1 (0^0 also handled here) - if (eexponent.is_zero()) { - if (ebasis.is_zero()) + if (exponent.is_zero()) { + if (basis.is_zero()) throw (std::domain_error("power::eval(): pow(0,0) is undefined")); else return _ex1; } // ^(x,1) -> x - if (eexponent.is_equal(_ex1)) - return ebasis; + if (exponent.is_equal(_ex1)) + return basis; // ^(0,c1) -> 0 or exception (depending on real value of c1) - if ( ebasis.is_zero() && num_exponent ) { + if (basis.is_zero() && num_exponent) { if ((num_exponent->real()).is_zero()) throw (std::domain_error("power::eval(): pow(0,I) is undefined")); else if ((num_exponent->real()).is_negative()) @@ -418,16 +409,16 @@ ex power::eval(int level) const } // ^(1,x) -> 1 - if (ebasis.is_equal(_ex1)) + if (basis.is_equal(_ex1)) return _ex1; // power of a function calculated by separate rules defined for this function - if (is_exactly_a(ebasis)) - return ex_to(ebasis).power(eexponent); + if (is_exactly_a(basis)) + return ex_to(basis).power(exponent); // Turn (x^c)^d into x^(c*d) in the case that x is positive and c is real. - if (is_exactly_a(ebasis) && ebasis.op(0).info(info_flags::positive) && ebasis.op(1).info(info_flags::real)) - return power(ebasis.op(0), ebasis.op(1) * eexponent); + if (is_exactly_a(basis) && basis.op(0).info(info_flags::positive) && basis.op(1).info(info_flags::real)) + return dynallocate(basis.op(0), basis.op(1) * exponent); if ( num_exponent ) { @@ -478,8 +469,7 @@ ex power::eval(int level) const // because otherwise we'll end up with something like // (7/8)^(4/3) -> 7/8*(1/2*7^(1/3)) // instead of 7/16*7^(1/3). - ex prod = power(*num_basis,r.div(m)); - return prod*power(*num_basis,q); + return pow(basis, r.div(m)) * pow(basis, q); } } } @@ -487,8 +477,8 @@ ex power::eval(int level) const // ^(^(x,c1),c2) -> ^(x,c1*c2) // (c1, c2 numeric(), c2 integer or -1 < c1 <= 1 or (c1=-1 and c2>0), // case c1==1 should not happen, see below!) - if (is_exactly_a(ebasis)) { - const power & sub_power = ex_to(ebasis); + if (is_exactly_a(basis)) { + const power & sub_power = ex_to(basis); const ex & sub_basis = sub_power.basis; const ex & sub_exponent = sub_power.exponent; if (is_exactly_a(sub_exponent)) { @@ -496,21 +486,21 @@ ex power::eval(int level) const GINAC_ASSERT(num_sub_exponent!=numeric(1)); if (num_exponent->is_integer() || (abs(num_sub_exponent) - (*_num1_p)).is_negative() || (num_sub_exponent == *_num_1_p && num_exponent->is_positive())) { - return power(sub_basis,num_sub_exponent.mul(*num_exponent)); + return dynallocate(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, 0); + if (num_exponent->is_integer() && is_exactly_a(basis)) { + return expand_mul(ex_to(basis), *num_exponent, false); } // (2*x + 6*y)^(-4) -> 1/16*(x + 3*y)^(-4) - if (num_exponent->is_integer() && is_exactly_a(ebasis)) { - numeric icont = ebasis.integer_content(); + if (num_exponent->is_integer() && is_exactly_a(basis)) { + numeric icont = basis.integer_content(); const numeric lead_coeff = - ex_to(ex_to(ebasis).seq.begin()->coeff).div(icont); + ex_to(ex_to(basis).seq.begin()->coeff).div(icont); const bool canonicalizable = lead_coeff.is_integer(); const bool unit_normal = lead_coeff.is_pos_integer(); @@ -518,7 +508,7 @@ ex power::eval(int level) const icont = icont.mul(*_num_1_p); if (canonicalizable && (icont != *_num1_p)) { - const add& addref = ex_to(ebasis); + const add& addref = ex_to(basis); add & addp = dynallocate(addref); addp.clearflag(status_flags::hash_calculated); addp.overall_coeff = ex_to(addp.overall_coeff).div_dyn(icont); @@ -535,9 +525,9 @@ ex power::eval(int level) const // ^(*(...,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_exactly_a(ebasis)) { + if (is_exactly_a(basis)) { GINAC_ASSERT(!num_exponent->is_integer()); // should have been handled above - const mul & mulref = ex_to(ebasis); + const mul & mulref = ex_to(basis); if (!mulref.overall_coeff.is_equal(_ex1)) { const numeric & num_coeff = ex_to(mulref.overall_coeff); if (num_coeff.is_real()) { @@ -563,38 +553,26 @@ ex power::eval(int level) const // ^(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_a(ebasis)) { - return ncmul(exvector(num_exponent->to_int(), ebasis)); + basis.return_type() != return_types::commutative && + !is_a(basis)) { + return ncmul(exvector(num_exponent->to_int(), basis)); } } - - if (are_ex_trivially_equal(ebasis,basis) && - are_ex_trivially_equal(eexponent,exponent)) { - return this->hold(); - } - return dynallocate(ebasis, eexponent).setflag(status_flags::evaluated); + + return this->hold(); } -ex power::evalf(int level) const +ex power::evalf() const { - ex ebasis; + ex ebasis = basis.evalf(); ex eexponent; - if (level==1) { - ebasis = basis; + if (!is_exactly_a(exponent)) + eexponent = exponent.evalf(); + else eexponent = exponent; - } else if (level == -max_recursion_level) { - throw(std::runtime_error("max recursion level reached")); - } else { - ebasis = basis.evalf(level-1); - if (!is_exactly_a(exponent)) - eexponent = exponent.evalf(level-1); - else - eexponent = exponent; - } - return power(ebasis,eexponent); + return dynallocate(ebasis, eexponent); } ex power::evalm() const @@ -641,7 +619,7 @@ ex power::subs(const exmap & m, unsigned options) const 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); + return dynallocate(subsed_basis, subsed_exponent); if (!(options & subs_options::algebraic)) return subs_one_level(m, options); @@ -652,7 +630,7 @@ ex power::subs(const exmap & m, unsigned options) const if (tryfactsubs(*this, it.first, nummatches, repls)) { ex anum = it.second.subs(repls, subs_options::no_pattern); ex aden = it.first.subs(repls, subs_options::no_pattern); - ex result = (*this)*power(anum/aden, nummatches); + ex result = (*this) * pow(anum/aden, nummatches); return (ex_to(result)).subs_one_level(m, options); } } @@ -691,7 +669,8 @@ ex power::real_part() const // basis == a+I*b, exponent == c+I*d const ex a = basis.real_part(); const ex c = exponent.real_part(); - if (basis.is_equal(a) && exponent.is_equal(c)) { + if (basis.is_equal(a) && exponent.is_equal(c) && + (a.info(info_flags::nonnegative) || c.info(info_flags::integer))) { // Re(a^c) return *this; } @@ -701,12 +680,12 @@ ex power::real_part() const // Re((a+I*b)^c) w/ c ∈ ℤ long N = ex_to(c).to_long(); // Use real terms in Binomial expansion to construct - // Re(expand(power(a+I*b, N))). + // Re(expand(pow(a+I*b, N))). long NN = N > 0 ? N : -N; - ex numer = N > 0 ? _ex1 : power(power(a,2) + power(b,2), NN); + ex numer = N > 0 ? _ex1 : pow(pow(a,2) + pow(b,2), NN); ex result = 0; for (long n = 0; n <= NN; n += 2) { - ex term = binomial(NN, n) * power(a, NN-n) * power(b, n) / numer; + ex term = binomial(NN, n) * pow(a, NN-n) * pow(b, n) / numer; if (n % 4 == 0) { result += term; // sign: I^n w/ n == 4*m } else { @@ -718,14 +697,16 @@ ex power::real_part() const // Re((a+I*b)^(c+I*d)) const ex d = exponent.imag_part(); - return power(abs(basis),c)*exp(-d*atan2(b,a))*cos(c*atan2(b,a)+d*log(abs(basis))); + return pow(abs(basis),c) * exp(-d*atan2(b,a)) * cos(c*atan2(b,a)+d*log(abs(basis))); } ex power::imag_part() const { + // basis == a+I*b, exponent == c+I*d const ex a = basis.real_part(); const ex c = exponent.real_part(); - if (basis.is_equal(a) && exponent.is_equal(c)) { + if (basis.is_equal(a) && exponent.is_equal(c) && + (a.info(info_flags::nonnegative) || c.info(info_flags::integer))) { // Im(a^c) return 0; } @@ -735,13 +716,13 @@ ex power::imag_part() const // Im((a+I*b)^c) w/ c ∈ ℤ long N = ex_to(c).to_long(); // Use imaginary terms in Binomial expansion to construct - // Im(expand(power(a+I*b, N))). + // Im(expand(pow(a+I*b, N))). long p = N > 0 ? 1 : 3; // modulus for positive sign long NN = N > 0 ? N : -N; - ex numer = N > 0 ? _ex1 : power(power(a,2) + power(b,2), NN); + ex numer = N > 0 ? _ex1 : pow(pow(a,2) + pow(b,2), NN); ex result = 0; for (long n = 1; n <= NN; n += 2) { - ex term = binomial(NN, n) * power(a, NN-n) * power(b, n) / numer; + ex term = binomial(NN, n) * pow(a, NN-n) * pow(b, n) / numer; if (n % 4 == p) { result += term; // sign: I^n w/ n == 4*m+p } else { @@ -753,7 +734,7 @@ ex power::imag_part() const // Im((a+I*b)^(c+I*d)) const ex d = exponent.imag_part(); - return power(abs(basis),c)*exp(-d*atan2(b,a))*sin(c*atan2(b,a)+d*log(abs(basis))); + return pow(abs(basis),c) * exp(-d*atan2(b,a)) * sin(c*atan2(b,a)+d*log(abs(basis))); } // protected @@ -764,16 +745,11 @@ ex power::derivative(const symbol & s) const { if (is_a(exponent)) { // D(b^r) = r * b^(r-1) * D(b) (faster than the formula below) - epvector newseq; - newseq.reserve(2); - newseq.push_back(expair(basis, exponent - _ex1)); - newseq.push_back(expair(basis.diff(s), _ex1)); - return mul(std::move(newseq), exponent); + const epvector newseq = {expair(basis, exponent - _ex1), expair(basis.diff(s), _ex1)}; + return dynallocate(std::move(newseq), exponent); } else { // D(b^e) = b^e * (D(e)*ln(b) + e*D(b)/b) - return mul(*this, - add(mul(exponent.diff(s), log(basis)), - mul(mul(exponent, basis.diff(s)), power(basis, _ex_1)))); + return *this * (exponent.diff(s)*log(basis) + exponent*basis.diff(s)*pow(basis, _ex_1)); } } @@ -832,17 +808,18 @@ ex power::expand(unsigned options) const // take care on the numeric coefficient ex coeff=(possign? _ex1 : _ex_1); if (m.overall_coeff.info(info_flags::positive) && m.overall_coeff != _ex1) - prodseq.push_back(power(m.overall_coeff, exponent)); - else if (m.overall_coeff.info(info_flags::negative) && m.overall_coeff != _ex_1) - prodseq.push_back(power(-m.overall_coeff, exponent)); - else + prodseq.push_back(pow(m.overall_coeff, exponent)); + else if (m.overall_coeff.info(info_flags::negative) && m.overall_coeff != _ex_1) { + prodseq.push_back(pow(-m.overall_coeff, exponent)); + coeff = -coeff; + } else coeff *= m.overall_coeff; // If positive/negative factors are found, then extract them. // In either case we set a flag to avoid the second run on a part // which does not have positive/negative terms. if (prodseq.size() > 0) { - ex newbasis = coeff*mul(std::move(powseq)); + ex newbasis = dynallocate(std::move(powseq), coeff); ex_to(newbasis).setflag(status_flags::purely_indefinite); return dynallocate(std::move(prodseq)) * pow(newbasis, exponent); } else @@ -858,7 +835,7 @@ ex power::expand(unsigned options) const exvector distrseq; distrseq.reserve(a.seq.size() + 1); for (auto & cit : a.seq) { - distrseq.push_back(power(expanded_basis, a.recombine_pair_to_ex(cit))); + distrseq.push_back(pow(expanded_basis, a.recombine_pair_to_ex(cit))); } // Make sure that e.g. (x+y)^(2+a) expands the (x+y)^2 factor @@ -868,9 +845,9 @@ ex power::expand(unsigned options) const if (int_exponent > 0 && is_exactly_a(expanded_basis)) distrseq.push_back(expand_add(ex_to(expanded_basis), int_exponent, options)); else - distrseq.push_back(power(expanded_basis, a.overall_coeff)); + distrseq.push_back(pow(expanded_basis, a.overall_coeff)); } else - distrseq.push_back(power(expanded_basis, a.overall_coeff)); + distrseq.push_back(pow(expanded_basis, a.overall_coeff)); // Make sure that e.g. (x+y)^(1+a) -> x*(x+y)^a + y*(x+y)^a ex r = dynallocate(distrseq); @@ -915,188 +892,6 @@ ex power::expand(unsigned options) const // non-virtual functions in this class ////////// -namespace { // anonymous namespace for power::expand_add() helpers - -/** Helper class to generate all bounded combinatorial partitions of an integer - * n with exactly m parts (including zero parts) in non-decreasing order. - */ -class partition_generator { -private: - // Partitions n into m parts, not including zero parts. - // (Cf. OEIS sequence A008284; implementation adapted from Jörg Arndt's - // FXT library) - struct mpartition2 - { - // partition: x[1] + x[2] + ... + x[m] = n and sentinel x[0] == 0 - std::vector x; - int n; // n>0 - int m; // 0 partition; // current partition -public: - partition_generator(unsigned n_, unsigned m_) - : mpgen(n_, 1), m(m_), partition(m_) - { } - // returns current partition in non-decreasing order, padded with zeros - const std::vector& current() const - { - for (int i = 0; i < m - mpgen.m; ++i) - partition[i] = 0; // pad with zeros - - for (int i = m - mpgen.m; i < m; ++i) - partition[i] = mpgen.x[i - m + mpgen.m + 1]; - - return partition; - } - bool next() - { - if (!mpgen.next_partition()) { - if (mpgen.m == m || mpgen.m == mpgen.n) - return false; // current is last - // increment number of parts - mpgen = mpartition2(mpgen.n, mpgen.m + 1); - } - return true; - } -}; - -/** Helper class to generate all compositions of a partition of an integer n, - * starting with the compositions which has non-decreasing order. - */ -class composition_generator { -private: - // Generates all distinct permutations of a multiset. - // (Based on Aaron Williams' algorithm 1 from "Loopless Generation of - // Multiset Permutations using a Constant Number of Variables by Prefix - // Shifts." ) - struct coolmulti { - // element of singly linked list - struct element { - int value; - element* next; - element(int val, element* n) - : value(val), next(n) {} - ~element() - { // recurses down to the end of the singly linked list - delete next; - } - }; - element *head, *i, *after_i; - // NB: Partition must be sorted in non-decreasing order. - explicit coolmulti(const std::vector& partition) - : head(nullptr), i(nullptr), after_i(nullptr) - { - for (unsigned n = 0; n < partition.size(); ++n) { - head = new element(partition[n], head); - if (n <= 1) - i = head; - } - after_i = i->next; - } - ~coolmulti() - { // deletes singly linked list - delete head; - } - void next_permutation() - { - element *before_k; - if (after_i->next != nullptr && i->value >= after_i->next->value) - before_k = after_i; - else - before_k = i; - element *k = before_k->next; - before_k->next = k->next; - k->next = head; - if (k->value < head->value) - i = k; - after_i = i->next; - head = k; - } - bool finished() const - { - return after_i->next == nullptr && after_i->value >= head->value; - } - } cmgen; - bool atend; // needed for simplifying iteration over permutations - bool trivial; // likewise, true if all elements are equal - mutable std::vector composition; // current compositions -public: - explicit composition_generator(const std::vector& partition) - : cmgen(partition), atend(false), trivial(true), composition(partition.size()) - { - for (unsigned i=1; i& current() const - { - coolmulti::element* it = cmgen.head; - size_t i = 0; - while (it != nullptr) { - composition[i] = it->value; - it = it->next; - ++i; - } - return composition; - } - bool next() - { - // This ugly contortion is needed because the original coolmulti - // algorithm requires code duplication of the payload procedure, - // one before the loop and one inside it. - if (trivial || atend) - return false; - cmgen.next_permutation(); - atend = cmgen.finished(); - return true; - } -}; - -/** Helper function to compute the multinomial coefficient n!/(p1!*p2!*...*pk!) - * where n = p1+p2+...+pk, i.e. p is a partition of n. - */ -const numeric -multinomial_coefficient(const std::vector & p) -{ - numeric n = 0, d = 1; - for (auto & it : p) { - n += numeric(it); - d *= factorial(numeric(it)); - } - return factorial(numeric(n)) / d; -} - -} // anonymous namespace - - /** expand a^n where a is an add and n is a positive integer. * @see power::expand */ ex power::expand_add(const add & a, long n, unsigned options) @@ -1187,9 +982,9 @@ ex power::expand_add(const add & a, long n, unsigned options) // Multinomial expansion of power(+(x,...,z;0),k)*c^(n-k): // Iterate over all partitions of k with exactly as many parts as // there are symbolic terms in the basis (including zero parts). - partition_generator partitions(k, a.seq.size()); + partition_with_zero_parts_generator partitions(k, a.seq.size()); do { - const std::vector& partition = partitions.current(); + const std::vector& partition = partitions.get(); // All monomials of this partition have the same number of terms and the same coefficient. const unsigned msize = std::count_if(partition.begin(), partition.end(), [](int i) { return i > 0; }); const numeric coeff = multinomial_coefficient(partition) * binomial_coefficient; @@ -1197,8 +992,8 @@ ex power::expand_add(const add & a, long n, unsigned options) // Iterate over all compositions of the current partition. composition_generator compositions(partition); do { - const std::vector& exponent = compositions.current(); - exvector monomial; + const std::vector& exponent = compositions.get(); + epvector monomial; monomial.reserve(msize); numeric factor = coeff; for (unsigned i = 0; i < exponent.size(); ++i) { @@ -1216,22 +1011,21 @@ ex power::expand_add(const add & a, long n, unsigned options) // optimize away } else if (exponent[i] == 1) { // optimized - monomial.push_back(r); + monomial.emplace_back(expair(r, _ex1)); if (c != *_num1_p) factor = factor.mul(c); } else { // general case exponent[i] > 1 - monomial.push_back(dynallocate(r, exponent[i])); + monomial.emplace_back(expair(r, exponent[i])); if (c != *_num1_p) factor = factor.mul(c.power(exponent[i])); } } - result.push_back(a.combine_ex_with_coeff_to_pair(mul(monomial).expand(options), factor)); + result.emplace_back(expair(mul(std::move(monomial)).expand(options), factor)); } while (compositions.next()); } while (partitions.next()); } GINAC_ASSERT(result.size() == result_size); - if (a.overall_coeff.is_zero()) { return dynallocate(std::move(result)).setflag(status_flags::expanded); } else { @@ -1252,11 +1046,11 @@ ex power::expand_add_2(const add & a, unsigned options) } result.reserve(result_size); - epvector::const_iterator last = a.seq.end(); + auto last = a.seq.end(); // power(+(x,...,z;c),2)=power(+(x,...,z;0),2)+2*c*+(x,...,z;0)+c*c // first part: ignore overall_coeff and expand other terms - for (epvector::const_iterator cit0=a.seq.begin(); cit0!=last; ++cit0) { + for (auto cit0=a.seq.begin(); cit0!=last; ++cit0) { const ex & r = cit0->rest; const ex & c = cit0->coeff; @@ -1270,27 +1064,27 @@ ex power::expand_add_2(const add & a, unsigned options) if (c.is_equal(_ex1)) { if (is_exactly_a(r)) { - result.push_back(a.combine_ex_with_coeff_to_pair(expand_mul(ex_to(r), *_num2_p, options, true), - _ex1)); + result.emplace_back(expair(expand_mul(ex_to(r), *_num2_p, options, true), + _ex1)); } else { - result.push_back(a.combine_ex_with_coeff_to_pair(dynallocate(r, _ex2), - _ex1)); + result.emplace_back(expair(dynallocate(r, _ex2), + _ex1)); } } else { if (is_exactly_a(r)) { - result.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))); + result.emplace_back(expair(expand_mul(ex_to(r), *_num2_p, options, true), + ex_to(c).power_dyn(*_num2_p))); } else { - result.push_back(a.combine_ex_with_coeff_to_pair(dynallocate(r, _ex2), - ex_to(c).power_dyn(*_num2_p))); + result.emplace_back(expair(dynallocate(r, _ex2), + ex_to(c).power_dyn(*_num2_p))); } } - for (epvector::const_iterator cit1=cit0+1; cit1!=last; ++cit1) { + for (auto cit1=cit0+1; cit1!=last; ++cit1) { const ex & r1 = cit1->rest; const ex & c1 = cit1->coeff; - result.push_back(a.combine_ex_with_coeff_to_pair(mul(r,r1).expand(options), - _num2_p->mul(ex_to(c)).mul_dyn(ex_to(c1)))); + result.emplace_back(expair(mul(r,r1).expand(options), + _num2_p->mul(ex_to(c)).mul_dyn(ex_to(c1)))); } }