3 * Implementation of GiNaC's symbolic exponentiation (basis^exponent). */
6 * GiNaC Copyright (C) 1999-2001 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.compare(_num_1) == 0) {
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))
164 if (exponent.is_equal(_ex1_2)) {
165 if (is_a<print_latex>(c))
170 if (is_a<print_latex>(c))
175 if (precedence() <= level) {
176 if (is_a<print_latex>(c))
181 basis.print(c, precedence());
183 if (is_a<print_latex>(c))
185 exponent.print(c, precedence());
186 if (is_a<print_latex>(c))
188 if (precedence() <= level) {
189 if (is_a<print_latex>(c))
198 bool power::info(unsigned inf) const
201 case info_flags::polynomial:
202 case info_flags::integer_polynomial:
203 case info_flags::cinteger_polynomial:
204 case info_flags::rational_polynomial:
205 case info_flags::crational_polynomial:
206 return exponent.info(info_flags::nonnegint);
207 case info_flags::rational_function:
208 return exponent.info(info_flags::integer);
209 case info_flags::algebraic:
210 return (!exponent.info(info_flags::integer) ||
213 return inherited::info(inf);
216 unsigned power::nops() const
221 ex & power::let_op(int i)
226 return i==0 ? basis : exponent;
229 ex power::map(map_function & f) const
231 return (new power(f(basis), f(exponent)))->setflag(status_flags::dynallocated);
234 int power::degree(const ex & s) const
236 if (is_ex_exactly_of_type(exponent, numeric) && ex_to<numeric>(exponent).is_integer()) {
237 if (basis.is_equal(s))
238 return ex_to<numeric>(exponent).to_int();
240 return basis.degree(s) * ex_to<numeric>(exponent).to_int();
241 } else if (basis.has(s))
242 throw(std::runtime_error("power::degree(): undefined degree because of non-integer exponent"));
247 int power::ldegree(const ex & s) const
249 if (is_ex_exactly_of_type(exponent, numeric) && ex_to<numeric>(exponent).is_integer()) {
250 if (basis.is_equal(s))
251 return ex_to<numeric>(exponent).to_int();
253 return basis.ldegree(s) * ex_to<numeric>(exponent).to_int();
254 } else if (basis.has(s))
255 throw(std::runtime_error("power::ldegree(): undefined degree because of non-integer exponent"));
260 ex power::coeff(const ex & s, int n) const
262 if (!basis.is_equal(s)) {
263 // basis not equal to s
270 if (is_ex_exactly_of_type(exponent, numeric) && ex_to<numeric>(exponent).is_integer()) {
272 int int_exp = ex_to<numeric>(exponent).to_int();
278 // non-integer exponents are treated as zero
287 /** Perform automatic term rewriting rules in this class. In the following
288 * x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
289 * stand for such expressions that contain a plain number.
290 * - ^(x,0) -> 1 (also handles ^(0,0))
292 * - ^(0,c) -> 0 or exception (depending on the real part of c)
294 * - ^(c1,c2) -> *(c1^n,c1^(c2-n)) (so that 0<(c2-n)<1, try to evaluate roots, possibly in numerator and denominator of c1)
295 * - ^(^(x,c1),c2) -> ^(x,c1*c2) (c2 integer or -1 < c1 <= 1, case c1=1 should not happen, see below!)
296 * - ^(*(x,y,z),c) -> *(x^c,y^c,z^c) (if c integer)
297 * - ^(*(x,c1),c2) -> ^(x,c2)*c1^c2 (c1>0)
298 * - ^(*(x,c1),c2) -> ^(-x,c2)*c1^c2 (c1<0)
300 * @param level cut-off in recursive evaluation */
301 ex power::eval(int level) const
303 if ((level==1) && (flags & status_flags::evaluated))
305 else if (level == -max_recursion_level)
306 throw(std::runtime_error("max recursion level reached"));
308 const ex & ebasis = level==1 ? basis : basis.eval(level-1);
309 const ex & eexponent = level==1 ? exponent : exponent.eval(level-1);
311 bool basis_is_numerical = false;
312 bool exponent_is_numerical = false;
313 const numeric *num_basis;
314 const numeric *num_exponent;
316 if (is_ex_exactly_of_type(ebasis, numeric)) {
317 basis_is_numerical = true;
318 num_basis = &ex_to<numeric>(ebasis);
320 if (is_ex_exactly_of_type(eexponent, numeric)) {
321 exponent_is_numerical = true;
322 num_exponent = &ex_to<numeric>(eexponent);
325 // ^(x,0) -> 1 (0^0 also handled here)
326 if (eexponent.is_zero()) {
327 if (ebasis.is_zero())
328 throw (std::domain_error("power::eval(): pow(0,0) is undefined"));
334 if (eexponent.is_equal(_ex1))
337 // ^(0,c1) -> 0 or exception (depending on real value of c1)
338 if (ebasis.is_zero() && exponent_is_numerical) {
339 if ((num_exponent->real()).is_zero())
340 throw (std::domain_error("power::eval(): pow(0,I) is undefined"));
341 else if ((num_exponent->real()).is_negative())
342 throw (pole_error("power::eval(): division by zero",1));
348 if (ebasis.is_equal(_ex1))
351 if (exponent_is_numerical) {
353 // ^(c1,c2) -> c1^c2 (c1, c2 numeric(),
354 // except if c1,c2 are rational, but c1^c2 is not)
355 if (basis_is_numerical) {
356 const bool basis_is_crational = num_basis->is_crational();
357 const bool exponent_is_crational = num_exponent->is_crational();
358 if (!basis_is_crational || !exponent_is_crational) {
359 // return a plain float
360 return (new numeric(num_basis->power(*num_exponent)))->setflag(status_flags::dynallocated |
361 status_flags::evaluated |
362 status_flags::expanded);
365 const numeric res = num_basis->power(*num_exponent);
366 if (res.is_crational()) {
369 GINAC_ASSERT(!num_exponent->is_integer()); // has been handled by now
371 // ^(c1,n/m) -> *(c1^q,c1^(n/m-q)), 0<(n/m-q)<1, q integer
372 if (basis_is_crational && exponent_is_crational
373 && num_exponent->is_real()
374 && !num_exponent->is_integer()) {
375 const numeric n = num_exponent->numer();
376 const numeric m = num_exponent->denom();
378 numeric q = iquo(n, m, r);
379 if (r.is_negative()) {
383 if (q.is_zero()) { // the exponent was in the allowed range 0<(n/m)<1
384 if (num_basis->is_rational() && !num_basis->is_integer()) {
385 // try it for numerator and denominator separately, in order to
386 // partially simplify things like (5/8)^(1/3) -> 1/2*5^(1/3)
387 const numeric bnum = num_basis->numer();
388 const numeric bden = num_basis->denom();
389 const numeric res_bnum = bnum.power(*num_exponent);
390 const numeric res_bden = bden.power(*num_exponent);
391 if (res_bnum.is_integer())
392 return (new mul(power(bden,-*num_exponent),res_bnum))->setflag(status_flags::dynallocated | status_flags::evaluated);
393 if (res_bden.is_integer())
394 return (new mul(power(bnum,*num_exponent),res_bden.inverse()))->setflag(status_flags::dynallocated | status_flags::evaluated);
398 // assemble resulting product, but allowing for a re-evaluation,
399 // because otherwise we'll end up with something like
400 // (7/8)^(4/3) -> 7/8*(1/2*7^(1/3))
401 // instead of 7/16*7^(1/3).
402 ex prod = power(*num_basis,r.div(m));
403 return prod*power(*num_basis,q);
408 // ^(^(x,c1),c2) -> ^(x,c1*c2)
409 // (c1, c2 numeric(), c2 integer or -1 < c1 <= 1,
410 // case c1==1 should not happen, see below!)
411 if (is_ex_exactly_of_type(ebasis,power)) {
412 const power & sub_power = ex_to<power>(ebasis);
413 const ex & sub_basis = sub_power.basis;
414 const ex & sub_exponent = sub_power.exponent;
415 if (is_ex_exactly_of_type(sub_exponent,numeric)) {
416 const numeric & num_sub_exponent = ex_to<numeric>(sub_exponent);
417 GINAC_ASSERT(num_sub_exponent!=numeric(1));
418 if (num_exponent->is_integer() || (abs(num_sub_exponent) - _num1).is_negative())
419 return power(sub_basis,num_sub_exponent.mul(*num_exponent));
423 // ^(*(x,y,z),c1) -> *(x^c1,y^c1,z^c1) (c1 integer)
424 if (num_exponent->is_integer() && is_ex_exactly_of_type(ebasis,mul)) {
425 return expand_mul(ex_to<mul>(ebasis), *num_exponent);
428 // ^(*(...,x;c1),c2) -> *(^(*(...,x;1),c2),c1^c2) (c1, c2 numeric(), c1>0)
429 // ^(*(...,x;c1),c2) -> *(^(*(...,x;-1),c2),(-c1)^c2) (c1, c2 numeric(), c1<0)
430 if (is_ex_exactly_of_type(ebasis,mul)) {
431 GINAC_ASSERT(!num_exponent->is_integer()); // should have been handled above
432 const mul & mulref = ex_to<mul>(ebasis);
433 if (!mulref.overall_coeff.is_equal(_ex1)) {
434 const numeric & num_coeff = ex_to<numeric>(mulref.overall_coeff);
435 if (num_coeff.is_real()) {
436 if (num_coeff.is_positive()) {
437 mul *mulp = new mul(mulref);
438 mulp->overall_coeff = _ex1;
439 mulp->clearflag(status_flags::evaluated);
440 mulp->clearflag(status_flags::hash_calculated);
441 return (new mul(power(*mulp,exponent),
442 power(num_coeff,*num_exponent)))->setflag(status_flags::dynallocated);
444 GINAC_ASSERT(num_coeff.compare(_num0)<0);
445 if (!num_coeff.is_equal(_num_1)) {
446 mul *mulp = new mul(mulref);
447 mulp->overall_coeff = _ex_1;
448 mulp->clearflag(status_flags::evaluated);
449 mulp->clearflag(status_flags::hash_calculated);
450 return (new mul(power(*mulp,exponent),
451 power(abs(num_coeff),*num_exponent)))->setflag(status_flags::dynallocated);
458 // ^(nc,c1) -> ncmul(nc,nc,...) (c1 positive integer, unless nc is a matrix)
459 if (num_exponent->is_pos_integer() &&
460 ebasis.return_type() != return_types::commutative &&
461 !is_ex_of_type(ebasis,matrix)) {
462 return ncmul(exvector(num_exponent->to_int(), ebasis), true);
466 if (are_ex_trivially_equal(ebasis,basis) &&
467 are_ex_trivially_equal(eexponent,exponent)) {
470 return (new power(ebasis, eexponent))->setflag(status_flags::dynallocated |
471 status_flags::evaluated);
474 ex power::evalf(int level) const
481 eexponent = exponent;
482 } else if (level == -max_recursion_level) {
483 throw(std::runtime_error("max recursion level reached"));
485 ebasis = basis.evalf(level-1);
486 if (!is_exactly_a<numeric>(exponent))
487 eexponent = exponent.evalf(level-1);
489 eexponent = exponent;
492 return power(ebasis,eexponent);
495 ex power::evalm(void) const
497 const ex ebasis = basis.evalm();
498 const ex eexponent = exponent.evalm();
499 if (is_ex_of_type(ebasis,matrix)) {
500 if (is_ex_of_type(eexponent,numeric)) {
501 return (new matrix(ex_to<matrix>(ebasis).pow(eexponent)))->setflag(status_flags::dynallocated);
504 return (new power(ebasis, eexponent))->setflag(status_flags::dynallocated);
507 ex power::subs(const lst & ls, const lst & lr, bool no_pattern) const
509 const ex &subsed_basis = basis.subs(ls, lr, no_pattern);
510 const ex &subsed_exponent = exponent.subs(ls, lr, no_pattern);
512 if (are_ex_trivially_equal(basis, subsed_basis)
513 && are_ex_trivially_equal(exponent, subsed_exponent))
514 return basic::subs(ls, lr, no_pattern);
516 return power(subsed_basis, subsed_exponent).basic::subs(ls, lr, no_pattern);
519 ex power::simplify_ncmul(const exvector & v) const
521 return inherited::simplify_ncmul(v);
526 /** Implementation of ex::diff() for a power.
528 ex power::derivative(const symbol & s) const
530 if (exponent.info(info_flags::real)) {
531 // D(b^r) = r * b^(r-1) * D(b) (faster than the formula below)
534 newseq.push_back(expair(basis, exponent - _ex1));
535 newseq.push_back(expair(basis.diff(s), _ex1));
536 return mul(newseq, exponent);
538 // D(b^e) = b^e * (D(e)*ln(b) + e*D(b)/b)
540 add(mul(exponent.diff(s), log(basis)),
541 mul(mul(exponent, basis.diff(s)), power(basis, _ex_1))));
545 int power::compare_same_type(const basic & other) const
547 GINAC_ASSERT(is_exactly_a<power>(other));
548 const power &o = static_cast<const power &>(other);
550 int cmpval = basis.compare(o.basis);
554 return exponent.compare(o.exponent);
557 unsigned power::return_type(void) const
559 return basis.return_type();
562 unsigned power::return_type_tinfo(void) const
564 return basis.return_type_tinfo();
567 ex power::expand(unsigned options) const
569 if (options == 0 && (flags & status_flags::expanded))
572 const ex expanded_basis = basis.expand(options);
573 const ex expanded_exponent = exponent.expand(options);
575 // x^(a+b) -> x^a * x^b
576 if (is_ex_exactly_of_type(expanded_exponent, add)) {
577 const add &a = ex_to<add>(expanded_exponent);
579 distrseq.reserve(a.seq.size() + 1);
580 epvector::const_iterator last = a.seq.end();
581 epvector::const_iterator cit = a.seq.begin();
583 distrseq.push_back(power(expanded_basis, a.recombine_pair_to_ex(*cit)));
587 // Make sure that e.g. (x+y)^(2+a) expands the (x+y)^2 factor
588 if (ex_to<numeric>(a.overall_coeff).is_integer()) {
589 const numeric &num_exponent = ex_to<numeric>(a.overall_coeff);
590 int int_exponent = num_exponent.to_int();
591 if (int_exponent > 0 && is_ex_exactly_of_type(expanded_basis, add))
592 distrseq.push_back(expand_add(ex_to<add>(expanded_basis), int_exponent));
594 distrseq.push_back(power(expanded_basis, a.overall_coeff));
596 distrseq.push_back(power(expanded_basis, a.overall_coeff));
598 // Make sure that e.g. (x+y)^(1+a) -> x*(x+y)^a + y*(x+y)^a
599 ex r = (new mul(distrseq))->setflag(status_flags::dynallocated);
603 if (!is_ex_exactly_of_type(expanded_exponent, numeric) ||
604 !ex_to<numeric>(expanded_exponent).is_integer()) {
605 if (are_ex_trivially_equal(basis,expanded_basis) && are_ex_trivially_equal(exponent,expanded_exponent)) {
608 return (new power(expanded_basis,expanded_exponent))->setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
612 // integer numeric exponent
613 const numeric & num_exponent = ex_to<numeric>(expanded_exponent);
614 int int_exponent = num_exponent.to_int();
617 if (int_exponent > 0 && is_ex_exactly_of_type(expanded_basis,add))
618 return expand_add(ex_to<add>(expanded_basis), int_exponent);
620 // (x*y)^n -> x^n * y^n
621 if (is_ex_exactly_of_type(expanded_basis,mul))
622 return expand_mul(ex_to<mul>(expanded_basis), num_exponent);
624 // cannot expand further
625 if (are_ex_trivially_equal(basis,expanded_basis) && are_ex_trivially_equal(exponent,expanded_exponent))
628 return (new power(expanded_basis,expanded_exponent))->setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
632 // new virtual functions which can be overridden by derived classes
638 // non-virtual functions in this class
641 /** expand a^n where a is an add and n is an integer.
642 * @see power::expand */
643 ex power::expand_add(const add & a, int n) const
646 return expand_add_2(a);
650 sum.reserve((n+1)*(m-1));
652 intvector k_cum(m-1); // k_cum[l]:=sum(i=0,l,k[l]);
653 intvector upper_limit(m-1);
656 for (int l=0; l<m-1; l++) {
665 for (l=0; l<m-1; l++) {
666 const ex & b = a.op(l);
667 GINAC_ASSERT(!is_exactly_a<add>(b));
668 GINAC_ASSERT(!is_exactly_a<power>(b) ||
669 !is_exactly_a<numeric>(ex_to<power>(b).exponent) ||
670 !ex_to<numeric>(ex_to<power>(b).exponent).is_pos_integer() ||
671 !is_exactly_a<add>(ex_to<power>(b).basis) ||
672 !is_exactly_a<mul>(ex_to<power>(b).basis) ||
673 !is_exactly_a<power>(ex_to<power>(b).basis));
674 if (is_ex_exactly_of_type(b,mul))
675 term.push_back(expand_mul(ex_to<mul>(b),numeric(k[l])));
677 term.push_back(power(b,k[l]));
680 const ex & b = a.op(l);
681 GINAC_ASSERT(!is_exactly_a<add>(b));
682 GINAC_ASSERT(!is_exactly_a<power>(b) ||
683 !is_exactly_a<numeric>(ex_to<power>(b).exponent) ||
684 !ex_to<numeric>(ex_to<power>(b).exponent).is_pos_integer() ||
685 !is_exactly_a<add>(ex_to<power>(b).basis) ||
686 !is_exactly_a<mul>(ex_to<power>(b).basis) ||
687 !is_exactly_a<power>(ex_to<power>(b).basis));
688 if (is_ex_exactly_of_type(b,mul))
689 term.push_back(expand_mul(ex_to<mul>(b),numeric(n-k_cum[m-2])));
691 term.push_back(power(b,n-k_cum[m-2]));
693 numeric f = binomial(numeric(n),numeric(k[0]));
694 for (l=1; l<m-1; l++)
695 f *= binomial(numeric(n-k_cum[l-1]),numeric(k[l]));
699 // TODO: Can we optimize this? Alex seemed to think so...
700 sum.push_back((new mul(term))->setflag(status_flags::dynallocated));
704 while ((l>=0) && ((++k[l])>upper_limit[l])) {
710 // recalc k_cum[] and upper_limit[]
714 k_cum[l] = k_cum[l-1]+k[l];
716 for (int i=l+1; i<m-1; i++)
717 k_cum[i] = k_cum[i-1]+k[i];
719 for (int i=l+1; i<m-1; i++)
720 upper_limit[i] = n-k_cum[i-1];
722 return (new add(sum))->setflag(status_flags::dynallocated |
723 status_flags::expanded );
727 /** Special case of power::expand_add. Expands a^2 where a is an add.
728 * @see power::expand_add */
729 ex power::expand_add_2(const add & a) const
732 unsigned a_nops = a.nops();
733 sum.reserve((a_nops*(a_nops+1))/2);
734 epvector::const_iterator last = a.seq.end();
736 // power(+(x,...,z;c),2)=power(+(x,...,z;0),2)+2*c*+(x,...,z;0)+c*c
737 // first part: ignore overall_coeff and expand other terms
738 for (epvector::const_iterator cit0=a.seq.begin(); cit0!=last; ++cit0) {
739 const ex & r = cit0->rest;
740 const ex & c = cit0->coeff;
742 GINAC_ASSERT(!is_exactly_a<add>(r));
743 GINAC_ASSERT(!is_exactly_a<power>(r) ||
744 !is_exactly_a<numeric>(ex_to<power>(r).exponent) ||
745 !ex_to<numeric>(ex_to<power>(r).exponent).is_pos_integer() ||
746 !is_exactly_a<add>(ex_to<power>(r).basis) ||
747 !is_exactly_a<mul>(ex_to<power>(r).basis) ||
748 !is_exactly_a<power>(ex_to<power>(r).basis));
750 if (are_ex_trivially_equal(c,_ex1)) {
751 if (is_ex_exactly_of_type(r,mul)) {
752 sum.push_back(expair(expand_mul(ex_to<mul>(r),_num2),
755 sum.push_back(expair((new power(r,_ex2))->setflag(status_flags::dynallocated),
759 if (is_ex_exactly_of_type(r,mul)) {
760 sum.push_back(expair(expand_mul(ex_to<mul>(r),_num2),
761 ex_to<numeric>(c).power_dyn(_num2)));
763 sum.push_back(expair((new power(r,_ex2))->setflag(status_flags::dynallocated),
764 ex_to<numeric>(c).power_dyn(_num2)));
768 for (epvector::const_iterator cit1=cit0+1; cit1!=last; ++cit1) {
769 const ex & r1 = cit1->rest;
770 const ex & c1 = cit1->coeff;
771 sum.push_back(a.combine_ex_with_coeff_to_pair((new mul(r,r1))->setflag(status_flags::dynallocated),
772 _num2.mul(ex_to<numeric>(c)).mul_dyn(ex_to<numeric>(c1))));
776 GINAC_ASSERT(sum.size()==(a.seq.size()*(a.seq.size()+1))/2);
778 // second part: add terms coming from overall_factor (if != 0)
779 if (!a.overall_coeff.is_zero()) {
780 epvector::const_iterator i = a.seq.begin(), end = a.seq.end();
782 sum.push_back(a.combine_pair_with_coeff_to_pair(*i, ex_to<numeric>(a.overall_coeff).mul_dyn(_num2)));
785 sum.push_back(expair(ex_to<numeric>(a.overall_coeff).power_dyn(_num2),_ex1));
788 GINAC_ASSERT(sum.size()==(a_nops*(a_nops+1))/2);
790 return (new add(sum))->setflag(status_flags::dynallocated | status_flags::expanded);
793 /** Expand factors of m in m^n where m is a mul and n is and integer
794 * @see power::expand */
795 ex power::expand_mul(const mul & m, const numeric & n) const
801 distrseq.reserve(m.seq.size());
802 epvector::const_iterator last = m.seq.end();
803 epvector::const_iterator cit = m.seq.begin();
805 if (is_ex_exactly_of_type((*cit).rest,numeric)) {
806 distrseq.push_back(m.combine_pair_with_coeff_to_pair(*cit,n));
808 // it is safe not to call mul::combine_pair_with_coeff_to_pair()
809 // since n is an integer
810 distrseq.push_back(expair((*cit).rest, ex_to<numeric>((*cit).coeff).mul(n)));
814 return (new mul(distrseq,ex_to<numeric>(m.overall_coeff).power_dyn(n)))->setflag(status_flags::dynallocated);