3 * Implementation of GiNaC's symbolic exponentiation (basis^exponent). */
6 * GiNaC Copyright (C) 1999-2002 Johannes Gutenberg University Mainz, Germany
8 * This program is free software; you can redistribute it and/or modify
9 * it under the terms of the GNU General Public License as published by
10 * the Free Software Foundation; either version 2 of the License, or
11 * (at your option) any later version.
13 * This program is distributed in the hope that it will be useful,
14 * but WITHOUT ANY WARRANTY; without even the implied warranty of
15 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
16 * GNU General Public License for more details.
18 * You should have received a copy of the GNU General Public License
19 * along with this program; if not, write to the Free Software
20 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
28 #include "expairseq.h"
34 #include "inifcns.h" // for log() in power::derivative()
43 GINAC_IMPLEMENT_REGISTERED_CLASS(power, basic)
45 typedef std::vector<int> intvector;
48 // default ctor, dtor, copy ctor, assignment operator and helpers
51 power::power() : inherited(TINFO_power) { }
53 void power::copy(const power & other)
55 inherited::copy(other);
57 exponent = other.exponent;
60 DEFAULT_DESTROY(power)
72 power::power(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
74 n.find_ex("basis", basis, sym_lst);
75 n.find_ex("exponent", exponent, sym_lst);
78 void power::archive(archive_node &n) const
80 inherited::archive(n);
81 n.add_ex("basis", basis);
82 n.add_ex("exponent", exponent);
85 DEFAULT_UNARCHIVE(power)
88 // functions overriding virtual functions from base classes
93 static void print_sym_pow(const print_context & c, const symbol &x, int exp)
95 // Optimal output of integer powers of symbols to aid compiler CSE.
96 // C.f. ISO/IEC 14882:1998, section 1.9 [intro execution], paragraph 15
97 // to learn why such a parenthisation is really necessary.
100 } else if (exp == 2) {
104 } else if (exp & 1) {
107 print_sym_pow(c, x, exp-1);
110 print_sym_pow(c, x, exp >> 1);
112 print_sym_pow(c, x, exp >> 1);
117 void power::print(const print_context & c, unsigned level) const
119 if (is_a<print_tree>(c)) {
121 inherited::print(c, level);
123 } else if (is_a<print_csrc>(c)) {
125 // Integer powers of symbols are printed in a special, optimized way
126 if (exponent.info(info_flags::integer)
127 && (is_exactly_a<symbol>(basis) || is_exactly_a<constant>(basis))) {
128 int exp = ex_to<numeric>(exponent).to_int();
133 if (is_a<print_csrc_cl_N>(c))
138 print_sym_pow(c, ex_to<symbol>(basis), exp);
141 // <expr>^-1 is printed as "1.0/<expr>" or with the recip() function of CLN
142 } else if (exponent.is_equal(_ex_1)) {
143 if (is_a<print_csrc_cl_N>(c))
150 // Otherwise, use the pow() or expt() (CLN) functions
152 if (is_a<print_csrc_cl_N>(c))
162 } else if (is_a<print_python_repr>(c)) {
164 c.s << class_name() << '(';
172 if (exponent.is_equal(_ex1_2)) {
173 if (is_a<print_latex>(c))
178 if (is_a<print_latex>(c))
183 if (precedence() <= level) {
184 if (is_a<print_latex>(c))
189 basis.print(c, precedence());
190 if (is_a<print_python>(c))
194 if (is_a<print_latex>(c))
196 exponent.print(c, precedence());
197 if (is_a<print_latex>(c))
199 if (precedence() <= level) {
200 if (is_a<print_latex>(c))
209 bool power::info(unsigned inf) const
212 case info_flags::polynomial:
213 case info_flags::integer_polynomial:
214 case info_flags::cinteger_polynomial:
215 case info_flags::rational_polynomial:
216 case info_flags::crational_polynomial:
217 return exponent.info(info_flags::nonnegint);
218 case info_flags::rational_function:
219 return exponent.info(info_flags::integer);
220 case info_flags::algebraic:
221 return (!exponent.info(info_flags::integer) ||
224 return inherited::info(inf);
227 unsigned power::nops() const
232 ex & power::let_op(int i)
237 return i==0 ? basis : exponent;
240 ex power::map(map_function & f) const
242 return (new power(f(basis), f(exponent)))->setflag(status_flags::dynallocated);
245 int power::degree(const ex & s) const
247 if (is_equal(ex_to<basic>(s)))
249 else if (is_exactly_a<numeric>(exponent) && ex_to<numeric>(exponent).is_integer()) {
250 if (basis.is_equal(s))
251 return ex_to<numeric>(exponent).to_int();
253 return basis.degree(s) * ex_to<numeric>(exponent).to_int();
254 } else if (basis.has(s))
255 throw(std::runtime_error("power::degree(): undefined degree because of non-integer exponent"));
260 int power::ldegree(const ex & s) const
262 if (is_equal(ex_to<basic>(s)))
264 else if (is_exactly_a<numeric>(exponent) && ex_to<numeric>(exponent).is_integer()) {
265 if (basis.is_equal(s))
266 return ex_to<numeric>(exponent).to_int();
268 return basis.ldegree(s) * ex_to<numeric>(exponent).to_int();
269 } else if (basis.has(s))
270 throw(std::runtime_error("power::ldegree(): undefined degree because of non-integer exponent"));
275 ex power::coeff(const ex & s, int n) const
277 if (is_equal(ex_to<basic>(s)))
278 return n==1 ? _ex1 : _ex0;
279 else if (!basis.is_equal(s)) {
280 // basis not equal to s
287 if (is_exactly_a<numeric>(exponent) && ex_to<numeric>(exponent).is_integer()) {
289 int int_exp = ex_to<numeric>(exponent).to_int();
295 // non-integer exponents are treated as zero
304 /** Perform automatic term rewriting rules in this class. In the following
305 * x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
306 * stand for such expressions that contain a plain number.
307 * - ^(x,0) -> 1 (also handles ^(0,0))
309 * - ^(0,c) -> 0 or exception (depending on the real part of c)
311 * - ^(c1,c2) -> *(c1^n,c1^(c2-n)) (so that 0<(c2-n)<1, try to evaluate roots, possibly in numerator and denominator of c1)
312 * - ^(^(x,c1),c2) -> ^(x,c1*c2) (c2 integer or -1 < c1 <= 1, case c1=1 should not happen, see below!)
313 * - ^(*(x,y,z),c) -> *(x^c,y^c,z^c) (if c integer)
314 * - ^(*(x,c1),c2) -> ^(x,c2)*c1^c2 (c1>0)
315 * - ^(*(x,c1),c2) -> ^(-x,c2)*c1^c2 (c1<0)
317 * @param level cut-off in recursive evaluation */
318 ex power::eval(int level) const
320 if ((level==1) && (flags & status_flags::evaluated))
322 else if (level == -max_recursion_level)
323 throw(std::runtime_error("max recursion level reached"));
325 const ex & ebasis = level==1 ? basis : basis.eval(level-1);
326 const ex & eexponent = level==1 ? exponent : exponent.eval(level-1);
328 bool basis_is_numerical = false;
329 bool exponent_is_numerical = false;
330 const numeric *num_basis;
331 const numeric *num_exponent;
333 if (is_exactly_a<numeric>(ebasis)) {
334 basis_is_numerical = true;
335 num_basis = &ex_to<numeric>(ebasis);
337 if (is_exactly_a<numeric>(eexponent)) {
338 exponent_is_numerical = true;
339 num_exponent = &ex_to<numeric>(eexponent);
342 // ^(x,0) -> 1 (0^0 also handled here)
343 if (eexponent.is_zero()) {
344 if (ebasis.is_zero())
345 throw (std::domain_error("power::eval(): pow(0,0) is undefined"));
351 if (eexponent.is_equal(_ex1))
354 // ^(0,c1) -> 0 or exception (depending on real value of c1)
355 if (ebasis.is_zero() && exponent_is_numerical) {
356 if ((num_exponent->real()).is_zero())
357 throw (std::domain_error("power::eval(): pow(0,I) is undefined"));
358 else if ((num_exponent->real()).is_negative())
359 throw (pole_error("power::eval(): division by zero",1));
365 if (ebasis.is_equal(_ex1))
368 if (exponent_is_numerical) {
370 // ^(c1,c2) -> c1^c2 (c1, c2 numeric(),
371 // except if c1,c2 are rational, but c1^c2 is not)
372 if (basis_is_numerical) {
373 const bool basis_is_crational = num_basis->is_crational();
374 const bool exponent_is_crational = num_exponent->is_crational();
375 if (!basis_is_crational || !exponent_is_crational) {
376 // return a plain float
377 return (new numeric(num_basis->power(*num_exponent)))->setflag(status_flags::dynallocated |
378 status_flags::evaluated |
379 status_flags::expanded);
382 const numeric res = num_basis->power(*num_exponent);
383 if (res.is_crational()) {
386 GINAC_ASSERT(!num_exponent->is_integer()); // has been handled by now
388 // ^(c1,n/m) -> *(c1^q,c1^(n/m-q)), 0<(n/m-q)<1, q integer
389 if (basis_is_crational && exponent_is_crational
390 && num_exponent->is_real()
391 && !num_exponent->is_integer()) {
392 const numeric n = num_exponent->numer();
393 const numeric m = num_exponent->denom();
395 numeric q = iquo(n, m, r);
396 if (r.is_negative()) {
400 if (q.is_zero()) { // the exponent was in the allowed range 0<(n/m)<1
401 if (num_basis->is_rational() && !num_basis->is_integer()) {
402 // try it for numerator and denominator separately, in order to
403 // partially simplify things like (5/8)^(1/3) -> 1/2*5^(1/3)
404 const numeric bnum = num_basis->numer();
405 const numeric bden = num_basis->denom();
406 const numeric res_bnum = bnum.power(*num_exponent);
407 const numeric res_bden = bden.power(*num_exponent);
408 if (res_bnum.is_integer())
409 return (new mul(power(bden,-*num_exponent),res_bnum))->setflag(status_flags::dynallocated | status_flags::evaluated);
410 if (res_bden.is_integer())
411 return (new mul(power(bnum,*num_exponent),res_bden.inverse()))->setflag(status_flags::dynallocated | status_flags::evaluated);
415 // assemble resulting product, but allowing for a re-evaluation,
416 // because otherwise we'll end up with something like
417 // (7/8)^(4/3) -> 7/8*(1/2*7^(1/3))
418 // instead of 7/16*7^(1/3).
419 ex prod = power(*num_basis,r.div(m));
420 return prod*power(*num_basis,q);
425 // ^(^(x,c1),c2) -> ^(x,c1*c2)
426 // (c1, c2 numeric(), c2 integer or -1 < c1 <= 1,
427 // case c1==1 should not happen, see below!)
428 if (is_exactly_a<power>(ebasis)) {
429 const power & sub_power = ex_to<power>(ebasis);
430 const ex & sub_basis = sub_power.basis;
431 const ex & sub_exponent = sub_power.exponent;
432 if (is_exactly_a<numeric>(sub_exponent)) {
433 const numeric & num_sub_exponent = ex_to<numeric>(sub_exponent);
434 GINAC_ASSERT(num_sub_exponent!=numeric(1));
435 if (num_exponent->is_integer() || (abs(num_sub_exponent) - _num1).is_negative())
436 return power(sub_basis,num_sub_exponent.mul(*num_exponent));
440 // ^(*(x,y,z),c1) -> *(x^c1,y^c1,z^c1) (c1 integer)
441 if (num_exponent->is_integer() && is_exactly_a<mul>(ebasis)) {
442 return expand_mul(ex_to<mul>(ebasis), *num_exponent);
445 // ^(*(...,x;c1),c2) -> *(^(*(...,x;1),c2),c1^c2) (c1, c2 numeric(), c1>0)
446 // ^(*(...,x;c1),c2) -> *(^(*(...,x;-1),c2),(-c1)^c2) (c1, c2 numeric(), c1<0)
447 if (is_exactly_a<mul>(ebasis)) {
448 GINAC_ASSERT(!num_exponent->is_integer()); // should have been handled above
449 const mul & mulref = ex_to<mul>(ebasis);
450 if (!mulref.overall_coeff.is_equal(_ex1)) {
451 const numeric & num_coeff = ex_to<numeric>(mulref.overall_coeff);
452 if (num_coeff.is_real()) {
453 if (num_coeff.is_positive()) {
454 mul *mulp = new mul(mulref);
455 mulp->overall_coeff = _ex1;
456 mulp->clearflag(status_flags::evaluated);
457 mulp->clearflag(status_flags::hash_calculated);
458 return (new mul(power(*mulp,exponent),
459 power(num_coeff,*num_exponent)))->setflag(status_flags::dynallocated);
461 GINAC_ASSERT(num_coeff.compare(_num0)<0);
462 if (!num_coeff.is_equal(_num_1)) {
463 mul *mulp = new mul(mulref);
464 mulp->overall_coeff = _ex_1;
465 mulp->clearflag(status_flags::evaluated);
466 mulp->clearflag(status_flags::hash_calculated);
467 return (new mul(power(*mulp,exponent),
468 power(abs(num_coeff),*num_exponent)))->setflag(status_flags::dynallocated);
475 // ^(nc,c1) -> ncmul(nc,nc,...) (c1 positive integer, unless nc is a matrix)
476 if (num_exponent->is_pos_integer() &&
477 ebasis.return_type() != return_types::commutative &&
478 !is_a<matrix>(ebasis)) {
479 return ncmul(exvector(num_exponent->to_int(), ebasis), true);
483 if (are_ex_trivially_equal(ebasis,basis) &&
484 are_ex_trivially_equal(eexponent,exponent)) {
487 return (new power(ebasis, eexponent))->setflag(status_flags::dynallocated |
488 status_flags::evaluated);
491 ex power::evalf(int level) const
498 eexponent = exponent;
499 } else if (level == -max_recursion_level) {
500 throw(std::runtime_error("max recursion level reached"));
502 ebasis = basis.evalf(level-1);
503 if (!is_exactly_a<numeric>(exponent))
504 eexponent = exponent.evalf(level-1);
506 eexponent = exponent;
509 return power(ebasis,eexponent);
512 ex power::evalm(void) const
514 const ex ebasis = basis.evalm();
515 const ex eexponent = exponent.evalm();
516 if (is_a<matrix>(ebasis)) {
517 if (is_a<numeric>(eexponent)) {
518 return (new matrix(ex_to<matrix>(ebasis).pow(eexponent)))->setflag(status_flags::dynallocated);
521 return (new power(ebasis, eexponent))->setflag(status_flags::dynallocated);
524 ex power::subs(const lst & ls, const lst & lr, bool no_pattern) const
526 const ex &subsed_basis = basis.subs(ls, lr, no_pattern);
527 const ex &subsed_exponent = exponent.subs(ls, lr, no_pattern);
529 if (are_ex_trivially_equal(basis, subsed_basis)
530 && are_ex_trivially_equal(exponent, subsed_exponent))
531 return basic::subs(ls, lr, no_pattern);
533 return power(subsed_basis, subsed_exponent).basic::subs(ls, lr, no_pattern);
536 ex power::simplify_ncmul(const exvector & v) const
538 return inherited::simplify_ncmul(v);
543 /** Implementation of ex::diff() for a power.
545 ex power::derivative(const symbol & s) const
547 if (exponent.info(info_flags::real)) {
548 // D(b^r) = r * b^(r-1) * D(b) (faster than the formula below)
551 newseq.push_back(expair(basis, exponent - _ex1));
552 newseq.push_back(expair(basis.diff(s), _ex1));
553 return mul(newseq, exponent);
555 // D(b^e) = b^e * (D(e)*ln(b) + e*D(b)/b)
557 add(mul(exponent.diff(s), log(basis)),
558 mul(mul(exponent, basis.diff(s)), power(basis, _ex_1))));
562 int power::compare_same_type(const basic & other) const
564 GINAC_ASSERT(is_exactly_a<power>(other));
565 const power &o = static_cast<const power &>(other);
567 int cmpval = basis.compare(o.basis);
571 return exponent.compare(o.exponent);
574 unsigned power::return_type(void) const
576 return basis.return_type();
579 unsigned power::return_type_tinfo(void) const
581 return basis.return_type_tinfo();
584 ex power::expand(unsigned options) const
586 if (options == 0 && (flags & status_flags::expanded))
589 const ex expanded_basis = basis.expand(options);
590 const ex expanded_exponent = exponent.expand(options);
592 // x^(a+b) -> x^a * x^b
593 if (is_exactly_a<add>(expanded_exponent)) {
594 const add &a = ex_to<add>(expanded_exponent);
596 distrseq.reserve(a.seq.size() + 1);
597 epvector::const_iterator last = a.seq.end();
598 epvector::const_iterator cit = a.seq.begin();
600 distrseq.push_back(power(expanded_basis, a.recombine_pair_to_ex(*cit)));
604 // Make sure that e.g. (x+y)^(2+a) expands the (x+y)^2 factor
605 if (ex_to<numeric>(a.overall_coeff).is_integer()) {
606 const numeric &num_exponent = ex_to<numeric>(a.overall_coeff);
607 int int_exponent = num_exponent.to_int();
608 if (int_exponent > 0 && is_exactly_a<add>(expanded_basis))
609 distrseq.push_back(expand_add(ex_to<add>(expanded_basis), int_exponent));
611 distrseq.push_back(power(expanded_basis, a.overall_coeff));
613 distrseq.push_back(power(expanded_basis, a.overall_coeff));
615 // Make sure that e.g. (x+y)^(1+a) -> x*(x+y)^a + y*(x+y)^a
616 ex r = (new mul(distrseq))->setflag(status_flags::dynallocated);
620 if (!is_exactly_a<numeric>(expanded_exponent) ||
621 !ex_to<numeric>(expanded_exponent).is_integer()) {
622 if (are_ex_trivially_equal(basis,expanded_basis) && are_ex_trivially_equal(exponent,expanded_exponent)) {
625 return (new power(expanded_basis,expanded_exponent))->setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
629 // integer numeric exponent
630 const numeric & num_exponent = ex_to<numeric>(expanded_exponent);
631 int int_exponent = num_exponent.to_int();
634 if (int_exponent > 0 && is_exactly_a<add>(expanded_basis))
635 return expand_add(ex_to<add>(expanded_basis), int_exponent);
637 // (x*y)^n -> x^n * y^n
638 if (is_exactly_a<mul>(expanded_basis))
639 return expand_mul(ex_to<mul>(expanded_basis), num_exponent);
641 // cannot expand further
642 if (are_ex_trivially_equal(basis,expanded_basis) && are_ex_trivially_equal(exponent,expanded_exponent))
645 return (new power(expanded_basis,expanded_exponent))->setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
649 // new virtual functions which can be overridden by derived classes
655 // non-virtual functions in this class
658 /** expand a^n where a is an add and n is a positive integer.
659 * @see power::expand */
660 ex power::expand_add(const add & a, int n) const
663 return expand_add_2(a);
665 const int m = a.nops();
667 // The number of terms will be the number of combinatorial compositions,
668 // i.e. the number of unordered arrangement of m nonnegative integers
669 // which sum up to n. It is frequently written as C_n(m) and directly
670 // related with binomial coefficients:
671 result.reserve(binomial(numeric(n+m-1), numeric(m-1)).to_int());
673 intvector k_cum(m-1); // k_cum[l]:=sum(i=0,l,k[l]);
674 intvector upper_limit(m-1);
677 for (int l=0; l<m-1; ++l) {
686 for (l=0; l<m-1; ++l) {
687 const ex & b = a.op(l);
688 GINAC_ASSERT(!is_exactly_a<add>(b));
689 GINAC_ASSERT(!is_exactly_a<power>(b) ||
690 !is_exactly_a<numeric>(ex_to<power>(b).exponent) ||
691 !ex_to<numeric>(ex_to<power>(b).exponent).is_pos_integer() ||
692 !is_exactly_a<add>(ex_to<power>(b).basis) ||
693 !is_exactly_a<mul>(ex_to<power>(b).basis) ||
694 !is_exactly_a<power>(ex_to<power>(b).basis));
695 if (is_exactly_a<mul>(b))
696 term.push_back(expand_mul(ex_to<mul>(b),numeric(k[l])));
698 term.push_back(power(b,k[l]));
701 const ex & b = a.op(l);
702 GINAC_ASSERT(!is_exactly_a<add>(b));
703 GINAC_ASSERT(!is_exactly_a<power>(b) ||
704 !is_exactly_a<numeric>(ex_to<power>(b).exponent) ||
705 !ex_to<numeric>(ex_to<power>(b).exponent).is_pos_integer() ||
706 !is_exactly_a<add>(ex_to<power>(b).basis) ||
707 !is_exactly_a<mul>(ex_to<power>(b).basis) ||
708 !is_exactly_a<power>(ex_to<power>(b).basis));
709 if (is_exactly_a<mul>(b))
710 term.push_back(expand_mul(ex_to<mul>(b),numeric(n-k_cum[m-2])));
712 term.push_back(power(b,n-k_cum[m-2]));
714 numeric f = binomial(numeric(n),numeric(k[0]));
715 for (l=1; l<m-1; ++l)
716 f *= binomial(numeric(n-k_cum[l-1]),numeric(k[l]));
720 result.push_back((new mul(term))->setflag(status_flags::dynallocated));
724 while ((l>=0) && ((++k[l])>upper_limit[l])) {
730 // recalc k_cum[] and upper_limit[]
731 k_cum[l] = (l==0 ? k[0] : k_cum[l-1]+k[l]);
733 for (int i=l+1; i<m-1; ++i)
734 k_cum[i] = k_cum[i-1]+k[i];
736 for (int i=l+1; i<m-1; ++i)
737 upper_limit[i] = n-k_cum[i-1];
740 return (new add(result))->setflag(status_flags::dynallocated |
741 status_flags::expanded);
745 /** Special case of power::expand_add. Expands a^2 where a is an add.
746 * @see power::expand_add */
747 ex power::expand_add_2(const add & a) const
750 unsigned a_nops = a.nops();
751 sum.reserve((a_nops*(a_nops+1))/2);
752 epvector::const_iterator last = a.seq.end();
754 // power(+(x,...,z;c),2)=power(+(x,...,z;0),2)+2*c*+(x,...,z;0)+c*c
755 // first part: ignore overall_coeff and expand other terms
756 for (epvector::const_iterator cit0=a.seq.begin(); cit0!=last; ++cit0) {
757 const ex & r = cit0->rest;
758 const ex & c = cit0->coeff;
760 GINAC_ASSERT(!is_exactly_a<add>(r));
761 GINAC_ASSERT(!is_exactly_a<power>(r) ||
762 !is_exactly_a<numeric>(ex_to<power>(r).exponent) ||
763 !ex_to<numeric>(ex_to<power>(r).exponent).is_pos_integer() ||
764 !is_exactly_a<add>(ex_to<power>(r).basis) ||
765 !is_exactly_a<mul>(ex_to<power>(r).basis) ||
766 !is_exactly_a<power>(ex_to<power>(r).basis));
768 if (are_ex_trivially_equal(c,_ex1)) {
769 if (is_exactly_a<mul>(r)) {
770 sum.push_back(expair(expand_mul(ex_to<mul>(r),_num2),
773 sum.push_back(expair((new power(r,_ex2))->setflag(status_flags::dynallocated),
777 if (is_exactly_a<mul>(r)) {
778 sum.push_back(expair(expand_mul(ex_to<mul>(r),_num2),
779 ex_to<numeric>(c).power_dyn(_num2)));
781 sum.push_back(expair((new power(r,_ex2))->setflag(status_flags::dynallocated),
782 ex_to<numeric>(c).power_dyn(_num2)));
786 for (epvector::const_iterator cit1=cit0+1; cit1!=last; ++cit1) {
787 const ex & r1 = cit1->rest;
788 const ex & c1 = cit1->coeff;
789 sum.push_back(a.combine_ex_with_coeff_to_pair((new mul(r,r1))->setflag(status_flags::dynallocated),
790 _num2.mul(ex_to<numeric>(c)).mul_dyn(ex_to<numeric>(c1))));
794 GINAC_ASSERT(sum.size()==(a.seq.size()*(a.seq.size()+1))/2);
796 // second part: add terms coming from overall_factor (if != 0)
797 if (!a.overall_coeff.is_zero()) {
798 epvector::const_iterator i = a.seq.begin(), end = a.seq.end();
800 sum.push_back(a.combine_pair_with_coeff_to_pair(*i, ex_to<numeric>(a.overall_coeff).mul_dyn(_num2)));
803 sum.push_back(expair(ex_to<numeric>(a.overall_coeff).power_dyn(_num2),_ex1));
806 GINAC_ASSERT(sum.size()==(a_nops*(a_nops+1))/2);
808 return (new add(sum))->setflag(status_flags::dynallocated | status_flags::expanded);
811 /** Expand factors of m in m^n where m is a mul and n is and integer.
812 * @see power::expand */
813 ex power::expand_mul(const mul & m, const numeric & n) const
815 GINAC_ASSERT(n.is_integer());
821 distrseq.reserve(m.seq.size());
822 epvector::const_iterator last = m.seq.end();
823 epvector::const_iterator cit = m.seq.begin();
825 if (is_exactly_a<numeric>((*cit).rest)) {
826 distrseq.push_back(m.combine_pair_with_coeff_to_pair(*cit,n));
828 // it is safe not to call mul::combine_pair_with_coeff_to_pair()
829 // since n is an integer
830 distrseq.push_back(expair((*cit).rest, ex_to<numeric>((*cit).coeff).mul(n)));
834 return (new mul(distrseq,ex_to<numeric>(m.overall_coeff).power_dyn(n)))->setflag(status_flags::dynallocated);