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();
245 int power::ldegree(const ex & s) const
247 if (is_ex_exactly_of_type(exponent, numeric) && ex_to<numeric>(exponent).is_integer()) {
248 if (basis.is_equal(s))
249 return ex_to<numeric>(exponent).to_int();
251 return basis.ldegree(s) * ex_to<numeric>(exponent).to_int();
256 ex power::coeff(const ex & s, int n) const
258 if (!basis.is_equal(s)) {
259 // basis not equal to s
266 if (is_ex_exactly_of_type(exponent, numeric) && ex_to<numeric>(exponent).is_integer()) {
268 int int_exp = ex_to<numeric>(exponent).to_int();
274 // non-integer exponents are treated as zero
283 /** Perform automatic term rewriting rules in this class. In the following
284 * x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
285 * stand for such expressions that contain a plain number.
286 * - ^(x,0) -> 1 (also handles ^(0,0))
288 * - ^(0,c) -> 0 or exception (depending on the real part of c)
290 * - ^(c1,c2) -> *(c1^n,c1^(c2-n)) (so that 0<(c2-n)<1, try to evaluate roots, possibly in numerator and denominator of c1)
291 * - ^(^(x,c1),c2) -> ^(x,c1*c2) (c2 integer or -1 < c1 <= 1, case c1=1 should not happen, see below!)
292 * - ^(*(x,y,z),c) -> *(x^c,y^c,z^c) (if c integer)
293 * - ^(*(x,c1),c2) -> ^(x,c2)*c1^c2 (c1>0)
294 * - ^(*(x,c1),c2) -> ^(-x,c2)*c1^c2 (c1<0)
296 * @param level cut-off in recursive evaluation */
297 ex power::eval(int level) const
299 if ((level==1) && (flags & status_flags::evaluated))
301 else if (level == -max_recursion_level)
302 throw(std::runtime_error("max recursion level reached"));
304 const ex & ebasis = level==1 ? basis : basis.eval(level-1);
305 const ex & eexponent = level==1 ? exponent : exponent.eval(level-1);
307 bool basis_is_numerical = false;
308 bool exponent_is_numerical = false;
309 const numeric *num_basis;
310 const numeric *num_exponent;
312 if (is_ex_exactly_of_type(ebasis, numeric)) {
313 basis_is_numerical = true;
314 num_basis = &ex_to<numeric>(ebasis);
316 if (is_ex_exactly_of_type(eexponent, numeric)) {
317 exponent_is_numerical = true;
318 num_exponent = &ex_to<numeric>(eexponent);
321 // ^(x,0) -> 1 (0^0 also handled here)
322 if (eexponent.is_zero()) {
323 if (ebasis.is_zero())
324 throw (std::domain_error("power::eval(): pow(0,0) is undefined"));
330 if (eexponent.is_equal(_ex1))
333 // ^(0,c1) -> 0 or exception (depending on real value of c1)
334 if (ebasis.is_zero() && exponent_is_numerical) {
335 if ((num_exponent->real()).is_zero())
336 throw (std::domain_error("power::eval(): pow(0,I) is undefined"));
337 else if ((num_exponent->real()).is_negative())
338 throw (pole_error("power::eval(): division by zero",1));
344 if (ebasis.is_equal(_ex1))
347 if (exponent_is_numerical) {
349 // ^(c1,c2) -> c1^c2 (c1, c2 numeric(),
350 // except if c1,c2 are rational, but c1^c2 is not)
351 if (basis_is_numerical) {
352 const bool basis_is_crational = num_basis->is_crational();
353 const bool exponent_is_crational = num_exponent->is_crational();
354 if (!basis_is_crational || !exponent_is_crational) {
355 // return a plain float
356 return (new numeric(num_basis->power(*num_exponent)))->setflag(status_flags::dynallocated |
357 status_flags::evaluated |
358 status_flags::expanded);
361 const numeric res = num_basis->power(*num_exponent);
362 if (res.is_crational()) {
365 GINAC_ASSERT(!num_exponent->is_integer()); // has been handled by now
367 // ^(c1,n/m) -> *(c1^q,c1^(n/m-q)), 0<(n/m-q)<1, q integer
368 if (basis_is_crational && exponent_is_crational
369 && num_exponent->is_real()
370 && !num_exponent->is_integer()) {
371 const numeric n = num_exponent->numer();
372 const numeric m = num_exponent->denom();
374 numeric q = iquo(n, m, r);
375 if (r.is_negative()) {
379 if (q.is_zero()) { // the exponent was in the allowed range 0<(n/m)<1
380 if (num_basis->is_rational() && !num_basis->is_integer()) {
381 // try it for numerator and denominator separately, in order to
382 // partially simplify things like (5/8)^(1/3) -> 1/2*5^(1/3)
383 const numeric bnum = num_basis->numer();
384 const numeric bden = num_basis->denom();
385 const numeric res_bnum = bnum.power(*num_exponent);
386 const numeric res_bden = bden.power(*num_exponent);
387 if (res_bnum.is_integer())
388 return (new mul(power(bden,-*num_exponent),res_bnum))->setflag(status_flags::dynallocated | status_flags::evaluated);
389 if (res_bden.is_integer())
390 return (new mul(power(bnum,*num_exponent),res_bden.inverse()))->setflag(status_flags::dynallocated | status_flags::evaluated);
394 // assemble resulting product, but allowing for a re-evaluation,
395 // because otherwise we'll end up with something like
396 // (7/8)^(4/3) -> 7/8*(1/2*7^(1/3))
397 // instead of 7/16*7^(1/3).
398 ex prod = power(*num_basis,r.div(m));
399 return prod*power(*num_basis,q);
404 // ^(^(x,c1),c2) -> ^(x,c1*c2)
405 // (c1, c2 numeric(), c2 integer or -1 < c1 <= 1,
406 // case c1==1 should not happen, see below!)
407 if (is_ex_exactly_of_type(ebasis,power)) {
408 const power & sub_power = ex_to<power>(ebasis);
409 const ex & sub_basis = sub_power.basis;
410 const ex & sub_exponent = sub_power.exponent;
411 if (is_ex_exactly_of_type(sub_exponent,numeric)) {
412 const numeric & num_sub_exponent = ex_to<numeric>(sub_exponent);
413 GINAC_ASSERT(num_sub_exponent!=numeric(1));
414 if (num_exponent->is_integer() || (abs(num_sub_exponent) - _num1).is_negative())
415 return power(sub_basis,num_sub_exponent.mul(*num_exponent));
419 // ^(*(x,y,z),c1) -> *(x^c1,y^c1,z^c1) (c1 integer)
420 if (num_exponent->is_integer() && is_ex_exactly_of_type(ebasis,mul)) {
421 return expand_mul(ex_to<mul>(ebasis), *num_exponent);
424 // ^(*(...,x;c1),c2) -> *(^(*(...,x;1),c2),c1^c2) (c1, c2 numeric(), c1>0)
425 // ^(*(...,x;c1),c2) -> *(^(*(...,x;-1),c2),(-c1)^c2) (c1, c2 numeric(), c1<0)
426 if (is_ex_exactly_of_type(ebasis,mul)) {
427 GINAC_ASSERT(!num_exponent->is_integer()); // should have been handled above
428 const mul & mulref = ex_to<mul>(ebasis);
429 if (!mulref.overall_coeff.is_equal(_ex1)) {
430 const numeric & num_coeff = ex_to<numeric>(mulref.overall_coeff);
431 if (num_coeff.is_real()) {
432 if (num_coeff.is_positive()) {
433 mul *mulp = new mul(mulref);
434 mulp->overall_coeff = _ex1;
435 mulp->clearflag(status_flags::evaluated);
436 mulp->clearflag(status_flags::hash_calculated);
437 return (new mul(power(*mulp,exponent),
438 power(num_coeff,*num_exponent)))->setflag(status_flags::dynallocated);
440 GINAC_ASSERT(num_coeff.compare(_num0)<0);
441 if (!num_coeff.is_equal(_num_1)) {
442 mul *mulp = new mul(mulref);
443 mulp->overall_coeff = _ex_1;
444 mulp->clearflag(status_flags::evaluated);
445 mulp->clearflag(status_flags::hash_calculated);
446 return (new mul(power(*mulp,exponent),
447 power(abs(num_coeff),*num_exponent)))->setflag(status_flags::dynallocated);
454 // ^(nc,c1) -> ncmul(nc,nc,...) (c1 positive integer, unless nc is a matrix)
455 if (num_exponent->is_pos_integer() &&
456 ebasis.return_type() != return_types::commutative &&
457 !is_ex_of_type(ebasis,matrix)) {
458 return ncmul(exvector(num_exponent->to_int(), ebasis), true);
462 if (are_ex_trivially_equal(ebasis,basis) &&
463 are_ex_trivially_equal(eexponent,exponent)) {
466 return (new power(ebasis, eexponent))->setflag(status_flags::dynallocated |
467 status_flags::evaluated);
470 ex power::evalf(int level) const
477 eexponent = exponent;
478 } else if (level == -max_recursion_level) {
479 throw(std::runtime_error("max recursion level reached"));
481 ebasis = basis.evalf(level-1);
482 if (!is_exactly_a<numeric>(exponent))
483 eexponent = exponent.evalf(level-1);
485 eexponent = exponent;
488 return power(ebasis,eexponent);
491 ex power::evalm(void) const
493 const ex ebasis = basis.evalm();
494 const ex eexponent = exponent.evalm();
495 if (is_ex_of_type(ebasis,matrix)) {
496 if (is_ex_of_type(eexponent,numeric)) {
497 return (new matrix(ex_to<matrix>(ebasis).pow(eexponent)))->setflag(status_flags::dynallocated);
500 return (new power(ebasis, eexponent))->setflag(status_flags::dynallocated);
503 ex power::subs(const lst & ls, const lst & lr, bool no_pattern) const
505 const ex &subsed_basis = basis.subs(ls, lr, no_pattern);
506 const ex &subsed_exponent = exponent.subs(ls, lr, no_pattern);
508 if (are_ex_trivially_equal(basis, subsed_basis)
509 && are_ex_trivially_equal(exponent, subsed_exponent))
510 return basic::subs(ls, lr, no_pattern);
512 return power(subsed_basis, subsed_exponent).basic::subs(ls, lr, no_pattern);
515 ex power::simplify_ncmul(const exvector & v) const
517 return inherited::simplify_ncmul(v);
522 /** Implementation of ex::diff() for a power.
524 ex power::derivative(const symbol & s) const
526 if (exponent.info(info_flags::real)) {
527 // D(b^r) = r * b^(r-1) * D(b) (faster than the formula below)
530 newseq.push_back(expair(basis, exponent - _ex1));
531 newseq.push_back(expair(basis.diff(s), _ex1));
532 return mul(newseq, exponent);
534 // D(b^e) = b^e * (D(e)*ln(b) + e*D(b)/b)
536 add(mul(exponent.diff(s), log(basis)),
537 mul(mul(exponent, basis.diff(s)), power(basis, _ex_1))));
541 int power::compare_same_type(const basic & other) const
543 GINAC_ASSERT(is_exactly_a<power>(other));
544 const power &o = static_cast<const power &>(other);
546 int cmpval = basis.compare(o.basis);
550 return exponent.compare(o.exponent);
553 unsigned power::return_type(void) const
555 return basis.return_type();
558 unsigned power::return_type_tinfo(void) const
560 return basis.return_type_tinfo();
563 ex power::expand(unsigned options) const
565 if (options == 0 && (flags & status_flags::expanded))
568 const ex expanded_basis = basis.expand(options);
569 const ex expanded_exponent = exponent.expand(options);
571 // x^(a+b) -> x^a * x^b
572 if (is_ex_exactly_of_type(expanded_exponent, add)) {
573 const add &a = ex_to<add>(expanded_exponent);
575 distrseq.reserve(a.seq.size() + 1);
576 epvector::const_iterator last = a.seq.end();
577 epvector::const_iterator cit = a.seq.begin();
579 distrseq.push_back(power(expanded_basis, a.recombine_pair_to_ex(*cit)));
583 // Make sure that e.g. (x+y)^(2+a) expands the (x+y)^2 factor
584 if (ex_to<numeric>(a.overall_coeff).is_integer()) {
585 const numeric &num_exponent = ex_to<numeric>(a.overall_coeff);
586 int int_exponent = num_exponent.to_int();
587 if (int_exponent > 0 && is_ex_exactly_of_type(expanded_basis, add))
588 distrseq.push_back(expand_add(ex_to<add>(expanded_basis), int_exponent));
590 distrseq.push_back(power(expanded_basis, a.overall_coeff));
592 distrseq.push_back(power(expanded_basis, a.overall_coeff));
594 // Make sure that e.g. (x+y)^(1+a) -> x*(x+y)^a + y*(x+y)^a
595 ex r = (new mul(distrseq))->setflag(status_flags::dynallocated);
599 if (!is_ex_exactly_of_type(expanded_exponent, numeric) ||
600 !ex_to<numeric>(expanded_exponent).is_integer()) {
601 if (are_ex_trivially_equal(basis,expanded_basis) && are_ex_trivially_equal(exponent,expanded_exponent)) {
604 return (new power(expanded_basis,expanded_exponent))->setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
608 // integer numeric exponent
609 const numeric & num_exponent = ex_to<numeric>(expanded_exponent);
610 int int_exponent = num_exponent.to_int();
613 if (int_exponent > 0 && is_ex_exactly_of_type(expanded_basis,add))
614 return expand_add(ex_to<add>(expanded_basis), int_exponent);
616 // (x*y)^n -> x^n * y^n
617 if (is_ex_exactly_of_type(expanded_basis,mul))
618 return expand_mul(ex_to<mul>(expanded_basis), num_exponent);
620 // cannot expand further
621 if (are_ex_trivially_equal(basis,expanded_basis) && are_ex_trivially_equal(exponent,expanded_exponent))
624 return (new power(expanded_basis,expanded_exponent))->setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
628 // new virtual functions which can be overridden by derived classes
634 // non-virtual functions in this class
637 /** expand a^n where a is an add and n is an integer.
638 * @see power::expand */
639 ex power::expand_add(const add & a, int n) const
642 return expand_add_2(a);
646 sum.reserve((n+1)*(m-1));
648 intvector k_cum(m-1); // k_cum[l]:=sum(i=0,l,k[l]);
649 intvector upper_limit(m-1);
652 for (int l=0; l<m-1; l++) {
661 for (l=0; l<m-1; l++) {
662 const ex & b = a.op(l);
663 GINAC_ASSERT(!is_exactly_a<add>(b));
664 GINAC_ASSERT(!is_exactly_a<power>(b) ||
665 !is_exactly_a<numeric>(ex_to<power>(b).exponent) ||
666 !ex_to<numeric>(ex_to<power>(b).exponent).is_pos_integer() ||
667 !is_exactly_a<add>(ex_to<power>(b).basis) ||
668 !is_exactly_a<mul>(ex_to<power>(b).basis) ||
669 !is_exactly_a<power>(ex_to<power>(b).basis));
670 if (is_ex_exactly_of_type(b,mul))
671 term.push_back(expand_mul(ex_to<mul>(b),numeric(k[l])));
673 term.push_back(power(b,k[l]));
676 const ex & b = a.op(l);
677 GINAC_ASSERT(!is_exactly_a<add>(b));
678 GINAC_ASSERT(!is_exactly_a<power>(b) ||
679 !is_exactly_a<numeric>(ex_to<power>(b).exponent) ||
680 !ex_to<numeric>(ex_to<power>(b).exponent).is_pos_integer() ||
681 !is_exactly_a<add>(ex_to<power>(b).basis) ||
682 !is_exactly_a<mul>(ex_to<power>(b).basis) ||
683 !is_exactly_a<power>(ex_to<power>(b).basis));
684 if (is_ex_exactly_of_type(b,mul))
685 term.push_back(expand_mul(ex_to<mul>(b),numeric(n-k_cum[m-2])));
687 term.push_back(power(b,n-k_cum[m-2]));
689 numeric f = binomial(numeric(n),numeric(k[0]));
690 for (l=1; l<m-1; l++)
691 f *= binomial(numeric(n-k_cum[l-1]),numeric(k[l]));
695 // TODO: Can we optimize this? Alex seemed to think so...
696 sum.push_back((new mul(term))->setflag(status_flags::dynallocated));
700 while ((l>=0) && ((++k[l])>upper_limit[l])) {
706 // recalc k_cum[] and upper_limit[]
710 k_cum[l] = k_cum[l-1]+k[l];
712 for (int i=l+1; i<m-1; i++)
713 k_cum[i] = k_cum[i-1]+k[i];
715 for (int i=l+1; i<m-1; i++)
716 upper_limit[i] = n-k_cum[i-1];
718 return (new add(sum))->setflag(status_flags::dynallocated |
719 status_flags::expanded );
723 /** Special case of power::expand_add. Expands a^2 where a is an add.
724 * @see power::expand_add */
725 ex power::expand_add_2(const add & a) const
728 unsigned a_nops = a.nops();
729 sum.reserve((a_nops*(a_nops+1))/2);
730 epvector::const_iterator last = a.seq.end();
732 // power(+(x,...,z;c),2)=power(+(x,...,z;0),2)+2*c*+(x,...,z;0)+c*c
733 // first part: ignore overall_coeff and expand other terms
734 for (epvector::const_iterator cit0=a.seq.begin(); cit0!=last; ++cit0) {
735 const ex & r = cit0->rest;
736 const ex & c = cit0->coeff;
738 GINAC_ASSERT(!is_exactly_a<add>(r));
739 GINAC_ASSERT(!is_exactly_a<power>(r) ||
740 !is_exactly_a<numeric>(ex_to<power>(r).exponent) ||
741 !ex_to<numeric>(ex_to<power>(r).exponent).is_pos_integer() ||
742 !is_exactly_a<add>(ex_to<power>(r).basis) ||
743 !is_exactly_a<mul>(ex_to<power>(r).basis) ||
744 !is_exactly_a<power>(ex_to<power>(r).basis));
746 if (are_ex_trivially_equal(c,_ex1)) {
747 if (is_ex_exactly_of_type(r,mul)) {
748 sum.push_back(expair(expand_mul(ex_to<mul>(r),_num2),
751 sum.push_back(expair((new power(r,_ex2))->setflag(status_flags::dynallocated),
755 if (is_ex_exactly_of_type(r,mul)) {
756 sum.push_back(expair(expand_mul(ex_to<mul>(r),_num2),
757 ex_to<numeric>(c).power_dyn(_num2)));
759 sum.push_back(expair((new power(r,_ex2))->setflag(status_flags::dynallocated),
760 ex_to<numeric>(c).power_dyn(_num2)));
764 for (epvector::const_iterator cit1=cit0+1; cit1!=last; ++cit1) {
765 const ex & r1 = cit1->rest;
766 const ex & c1 = cit1->coeff;
767 sum.push_back(a.combine_ex_with_coeff_to_pair((new mul(r,r1))->setflag(status_flags::dynallocated),
768 _num2.mul(ex_to<numeric>(c)).mul_dyn(ex_to<numeric>(c1))));
772 GINAC_ASSERT(sum.size()==(a.seq.size()*(a.seq.size()+1))/2);
774 // second part: add terms coming from overall_factor (if != 0)
775 if (!a.overall_coeff.is_zero()) {
776 epvector::const_iterator i = a.seq.begin(), end = a.seq.end();
778 sum.push_back(a.combine_pair_with_coeff_to_pair(*i, ex_to<numeric>(a.overall_coeff).mul_dyn(_num2)));
781 sum.push_back(expair(ex_to<numeric>(a.overall_coeff).power_dyn(_num2),_ex1));
784 GINAC_ASSERT(sum.size()==(a_nops*(a_nops+1))/2);
786 return (new add(sum))->setflag(status_flags::dynallocated | status_flags::expanded);
789 /** Expand factors of m in m^n where m is a mul and n is and integer
790 * @see power::expand */
791 ex power::expand_mul(const mul & m, const numeric & n) const
797 distrseq.reserve(m.seq.size());
798 epvector::const_iterator last = m.seq.end();
799 epvector::const_iterator cit = m.seq.begin();
801 if (is_ex_exactly_of_type((*cit).rest,numeric)) {
802 distrseq.push_back(m.combine_pair_with_coeff_to_pair(*cit,n));
804 // it is safe not to call mul::combine_pair_with_coeff_to_pair()
805 // since n is an integer
806 distrseq.push_back(expair((*cit).rest, ex_to<numeric>((*cit).coeff).mul(n)));
810 return (new mul(distrseq,ex_to<numeric>(m.overall_coeff).power_dyn(n)))->setflag(status_flags::dynallocated);