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()
44 GINAC_IMPLEMENT_REGISTERED_CLASS(power, basic)
46 typedef std::vector<int> intvector;
49 // default ctor, dtor, copy ctor, assignment operator and helpers
52 power::power() : inherited(TINFO_power) { }
54 void power::copy(const power & other)
56 inherited::copy(other);
58 exponent = other.exponent;
61 DEFAULT_DESTROY(power)
73 power::power(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
75 n.find_ex("basis", basis, sym_lst);
76 n.find_ex("exponent", exponent, sym_lst);
79 void power::archive(archive_node &n) const
81 inherited::archive(n);
82 n.add_ex("basis", basis);
83 n.add_ex("exponent", exponent);
86 DEFAULT_UNARCHIVE(power)
89 // functions overriding virtual functions from base classes
94 static void print_sym_pow(const print_context & c, const symbol &x, int exp)
96 // Optimal output of integer powers of symbols to aid compiler CSE.
97 // C.f. ISO/IEC 14882:1998, section 1.9 [intro execution], paragraph 15
98 // to learn why such a parenthisation is really necessary.
101 } else if (exp == 2) {
105 } else if (exp & 1) {
108 print_sym_pow(c, x, exp-1);
111 print_sym_pow(c, x, exp >> 1);
113 print_sym_pow(c, x, exp >> 1);
118 void power::print(const print_context & c, unsigned level) const
120 if (is_a<print_tree>(c)) {
122 inherited::print(c, level);
124 } else if (is_a<print_csrc>(c)) {
126 // Integer powers of symbols are printed in a special, optimized way
127 if (exponent.info(info_flags::integer)
128 && (is_exactly_a<symbol>(basis) || is_exactly_a<constant>(basis))) {
129 int exp = ex_to<numeric>(exponent).to_int();
134 if (is_a<print_csrc_cl_N>(c))
139 print_sym_pow(c, ex_to<symbol>(basis), exp);
142 // <expr>^-1 is printed as "1.0/<expr>" or with the recip() function of CLN
143 } else if (exponent.is_equal(_ex_1)) {
144 if (is_a<print_csrc_cl_N>(c))
151 // Otherwise, use the pow() or expt() (CLN) functions
153 if (is_a<print_csrc_cl_N>(c))
163 } else if (is_a<print_python_repr>(c)) {
165 c.s << class_name() << '(';
173 bool is_tex = is_a<print_latex>(c);
175 if (exponent.is_equal(_ex1_2)) {
176 c.s << (is_tex ? "\\sqrt{" : "sqrt(");
178 c.s << (is_tex ? '}' : ')');
180 if (precedence() <= level)
181 c.s << (is_tex ? "{(" : "(");
182 basis.print(c, precedence());
183 if (is_a<print_python>(c))
189 exponent.print(c, precedence());
192 if (precedence() <= level)
193 c.s << (is_tex ? ")}" : ")");
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_equal(ex_to<basic>(s)))
238 else if (is_ex_exactly_of_type(exponent, numeric) && ex_to<numeric>(exponent).is_integer()) {
239 if (basis.is_equal(s))
240 return ex_to<numeric>(exponent).to_int();
242 return basis.degree(s) * ex_to<numeric>(exponent).to_int();
243 } else if (basis.has(s))
244 throw(std::runtime_error("power::degree(): undefined degree because of non-integer exponent"));
249 int power::ldegree(const ex & s) const
251 if (is_equal(ex_to<basic>(s)))
253 else if (is_ex_exactly_of_type(exponent, numeric) && ex_to<numeric>(exponent).is_integer()) {
254 if (basis.is_equal(s))
255 return ex_to<numeric>(exponent).to_int();
257 return basis.ldegree(s) * ex_to<numeric>(exponent).to_int();
258 } else if (basis.has(s))
259 throw(std::runtime_error("power::ldegree(): undefined degree because of non-integer exponent"));
264 ex power::coeff(const ex & s, int n) const
266 if (is_equal(ex_to<basic>(s)))
267 return n==1 ? _ex1 : _ex0;
268 else if (!basis.is_equal(s)) {
269 // basis not equal to s
276 if (is_ex_exactly_of_type(exponent, numeric) && ex_to<numeric>(exponent).is_integer()) {
278 int int_exp = ex_to<numeric>(exponent).to_int();
284 // non-integer exponents are treated as zero
293 /** Perform automatic term rewriting rules in this class. In the following
294 * x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
295 * stand for such expressions that contain a plain number.
296 * - ^(x,0) -> 1 (also handles ^(0,0))
298 * - ^(0,c) -> 0 or exception (depending on the real part of c)
300 * - ^(c1,c2) -> *(c1^n,c1^(c2-n)) (so that 0<(c2-n)<1, try to evaluate roots, possibly in numerator and denominator of c1)
301 * - ^(^(x,c1),c2) -> ^(x,c1*c2) (c2 integer or -1 < c1 <= 1, case c1=1 should not happen, see below!)
302 * - ^(*(x,y,z),c) -> *(x^c,y^c,z^c) (if c integer)
303 * - ^(*(x,c1),c2) -> ^(x,c2)*c1^c2 (c1>0)
304 * - ^(*(x,c1),c2) -> ^(-x,c2)*c1^c2 (c1<0)
306 * @param level cut-off in recursive evaluation */
307 ex power::eval(int level) const
309 if ((level==1) && (flags & status_flags::evaluated))
311 else if (level == -max_recursion_level)
312 throw(std::runtime_error("max recursion level reached"));
314 const ex & ebasis = level==1 ? basis : basis.eval(level-1);
315 const ex & eexponent = level==1 ? exponent : exponent.eval(level-1);
317 bool basis_is_numerical = false;
318 bool exponent_is_numerical = false;
319 const numeric *num_basis;
320 const numeric *num_exponent;
322 if (is_ex_exactly_of_type(ebasis, numeric)) {
323 basis_is_numerical = true;
324 num_basis = &ex_to<numeric>(ebasis);
326 if (is_ex_exactly_of_type(eexponent, numeric)) {
327 exponent_is_numerical = true;
328 num_exponent = &ex_to<numeric>(eexponent);
331 // ^(x,0) -> 1 (0^0 also handled here)
332 if (eexponent.is_zero()) {
333 if (ebasis.is_zero())
334 throw (std::domain_error("power::eval(): pow(0,0) is undefined"));
340 if (eexponent.is_equal(_ex1))
343 // ^(0,c1) -> 0 or exception (depending on real value of c1)
344 if (ebasis.is_zero() && exponent_is_numerical) {
345 if ((num_exponent->real()).is_zero())
346 throw (std::domain_error("power::eval(): pow(0,I) is undefined"));
347 else if ((num_exponent->real()).is_negative())
348 throw (pole_error("power::eval(): division by zero",1));
354 if (ebasis.is_equal(_ex1))
357 if (exponent_is_numerical) {
359 // ^(c1,c2) -> c1^c2 (c1, c2 numeric(),
360 // except if c1,c2 are rational, but c1^c2 is not)
361 if (basis_is_numerical) {
362 const bool basis_is_crational = num_basis->is_crational();
363 const bool exponent_is_crational = num_exponent->is_crational();
364 if (!basis_is_crational || !exponent_is_crational) {
365 // return a plain float
366 return (new numeric(num_basis->power(*num_exponent)))->setflag(status_flags::dynallocated |
367 status_flags::evaluated |
368 status_flags::expanded);
371 const numeric res = num_basis->power(*num_exponent);
372 if (res.is_crational()) {
375 GINAC_ASSERT(!num_exponent->is_integer()); // has been handled by now
377 // ^(c1,n/m) -> *(c1^q,c1^(n/m-q)), 0<(n/m-q)<1, q integer
378 if (basis_is_crational && exponent_is_crational
379 && num_exponent->is_real()
380 && !num_exponent->is_integer()) {
381 const numeric n = num_exponent->numer();
382 const numeric m = num_exponent->denom();
384 numeric q = iquo(n, m, r);
385 if (r.is_negative()) {
389 if (q.is_zero()) { // the exponent was in the allowed range 0<(n/m)<1
390 if (num_basis->is_rational() && !num_basis->is_integer()) {
391 // try it for numerator and denominator separately, in order to
392 // partially simplify things like (5/8)^(1/3) -> 1/2*5^(1/3)
393 const numeric bnum = num_basis->numer();
394 const numeric bden = num_basis->denom();
395 const numeric res_bnum = bnum.power(*num_exponent);
396 const numeric res_bden = bden.power(*num_exponent);
397 if (res_bnum.is_integer())
398 return (new mul(power(bden,-*num_exponent),res_bnum))->setflag(status_flags::dynallocated | status_flags::evaluated);
399 if (res_bden.is_integer())
400 return (new mul(power(bnum,*num_exponent),res_bden.inverse()))->setflag(status_flags::dynallocated | status_flags::evaluated);
404 // assemble resulting product, but allowing for a re-evaluation,
405 // because otherwise we'll end up with something like
406 // (7/8)^(4/3) -> 7/8*(1/2*7^(1/3))
407 // instead of 7/16*7^(1/3).
408 ex prod = power(*num_basis,r.div(m));
409 return prod*power(*num_basis,q);
414 // ^(^(x,c1),c2) -> ^(x,c1*c2)
415 // (c1, c2 numeric(), c2 integer or -1 < c1 <= 1,
416 // case c1==1 should not happen, see below!)
417 if (is_ex_exactly_of_type(ebasis,power)) {
418 const power & sub_power = ex_to<power>(ebasis);
419 const ex & sub_basis = sub_power.basis;
420 const ex & sub_exponent = sub_power.exponent;
421 if (is_ex_exactly_of_type(sub_exponent,numeric)) {
422 const numeric & num_sub_exponent = ex_to<numeric>(sub_exponent);
423 GINAC_ASSERT(num_sub_exponent!=numeric(1));
424 if (num_exponent->is_integer() || (abs(num_sub_exponent) - _num1).is_negative())
425 return power(sub_basis,num_sub_exponent.mul(*num_exponent));
429 // ^(*(x,y,z),c1) -> *(x^c1,y^c1,z^c1) (c1 integer)
430 if (num_exponent->is_integer() && is_ex_exactly_of_type(ebasis,mul)) {
431 return expand_mul(ex_to<mul>(ebasis), *num_exponent);
434 // ^(*(...,x;c1),c2) -> *(^(*(...,x;1),c2),c1^c2) (c1, c2 numeric(), c1>0)
435 // ^(*(...,x;c1),c2) -> *(^(*(...,x;-1),c2),(-c1)^c2) (c1, c2 numeric(), c1<0)
436 if (is_ex_exactly_of_type(ebasis,mul)) {
437 GINAC_ASSERT(!num_exponent->is_integer()); // should have been handled above
438 const mul & mulref = ex_to<mul>(ebasis);
439 if (!mulref.overall_coeff.is_equal(_ex1)) {
440 const numeric & num_coeff = ex_to<numeric>(mulref.overall_coeff);
441 if (num_coeff.is_real()) {
442 if (num_coeff.is_positive()) {
443 mul *mulp = new mul(mulref);
444 mulp->overall_coeff = _ex1;
445 mulp->clearflag(status_flags::evaluated);
446 mulp->clearflag(status_flags::hash_calculated);
447 return (new mul(power(*mulp,exponent),
448 power(num_coeff,*num_exponent)))->setflag(status_flags::dynallocated);
450 GINAC_ASSERT(num_coeff.compare(_num0)<0);
451 if (!num_coeff.is_equal(_num_1)) {
452 mul *mulp = new mul(mulref);
453 mulp->overall_coeff = _ex_1;
454 mulp->clearflag(status_flags::evaluated);
455 mulp->clearflag(status_flags::hash_calculated);
456 return (new mul(power(*mulp,exponent),
457 power(abs(num_coeff),*num_exponent)))->setflag(status_flags::dynallocated);
464 // ^(nc,c1) -> ncmul(nc,nc,...) (c1 positive integer, unless nc is a matrix)
465 if (num_exponent->is_pos_integer() &&
466 ebasis.return_type() != return_types::commutative &&
467 !is_ex_of_type(ebasis,matrix)) {
468 return ncmul(exvector(num_exponent->to_int(), ebasis), true);
472 if (are_ex_trivially_equal(ebasis,basis) &&
473 are_ex_trivially_equal(eexponent,exponent)) {
476 return (new power(ebasis, eexponent))->setflag(status_flags::dynallocated |
477 status_flags::evaluated);
480 ex power::evalf(int level) const
487 eexponent = exponent;
488 } else if (level == -max_recursion_level) {
489 throw(std::runtime_error("max recursion level reached"));
491 ebasis = basis.evalf(level-1);
492 if (!is_exactly_a<numeric>(exponent))
493 eexponent = exponent.evalf(level-1);
495 eexponent = exponent;
498 return power(ebasis,eexponent);
501 ex power::evalm(void) const
503 const ex ebasis = basis.evalm();
504 const ex eexponent = exponent.evalm();
505 if (is_ex_of_type(ebasis,matrix)) {
506 if (is_ex_of_type(eexponent,numeric)) {
507 return (new matrix(ex_to<matrix>(ebasis).pow(eexponent)))->setflag(status_flags::dynallocated);
510 return (new power(ebasis, eexponent))->setflag(status_flags::dynallocated);
513 ex power::subs(const lst & ls, const lst & lr, bool no_pattern) const
515 const ex &subsed_basis = basis.subs(ls, lr, no_pattern);
516 const ex &subsed_exponent = exponent.subs(ls, lr, no_pattern);
518 if (are_ex_trivially_equal(basis, subsed_basis)
519 && are_ex_trivially_equal(exponent, subsed_exponent))
520 return basic::subs(ls, lr, no_pattern);
522 return power(subsed_basis, subsed_exponent).basic::subs(ls, lr, no_pattern);
525 ex power::simplify_ncmul(const exvector & v) const
527 return inherited::simplify_ncmul(v);
532 /** Implementation of ex::diff() for a power.
534 ex power::derivative(const symbol & s) const
536 if (exponent.info(info_flags::real)) {
537 // D(b^r) = r * b^(r-1) * D(b) (faster than the formula below)
540 newseq.push_back(expair(basis, exponent - _ex1));
541 newseq.push_back(expair(basis.diff(s), _ex1));
542 return mul(newseq, exponent);
544 // D(b^e) = b^e * (D(e)*ln(b) + e*D(b)/b)
546 add(mul(exponent.diff(s), log(basis)),
547 mul(mul(exponent, basis.diff(s)), power(basis, _ex_1))));
551 int power::compare_same_type(const basic & other) const
553 GINAC_ASSERT(is_exactly_a<power>(other));
554 const power &o = static_cast<const power &>(other);
556 int cmpval = basis.compare(o.basis);
560 return exponent.compare(o.exponent);
563 unsigned power::return_type(void) const
565 return basis.return_type();
568 unsigned power::return_type_tinfo(void) const
570 return basis.return_type_tinfo();
573 ex power::expand(unsigned options) const
575 if (options == 0 && (flags & status_flags::expanded))
578 const ex expanded_basis = basis.expand(options);
579 const ex expanded_exponent = exponent.expand(options);
581 // x^(a+b) -> x^a * x^b
582 if (is_ex_exactly_of_type(expanded_exponent, add)) {
583 const add &a = ex_to<add>(expanded_exponent);
585 distrseq.reserve(a.seq.size() + 1);
586 epvector::const_iterator last = a.seq.end();
587 epvector::const_iterator cit = a.seq.begin();
589 distrseq.push_back(power(expanded_basis, a.recombine_pair_to_ex(*cit)));
593 // Make sure that e.g. (x+y)^(2+a) expands the (x+y)^2 factor
594 if (ex_to<numeric>(a.overall_coeff).is_integer()) {
595 const numeric &num_exponent = ex_to<numeric>(a.overall_coeff);
596 int int_exponent = num_exponent.to_int();
597 if (int_exponent > 0 && is_ex_exactly_of_type(expanded_basis, add))
598 distrseq.push_back(expand_add(ex_to<add>(expanded_basis), int_exponent));
600 distrseq.push_back(power(expanded_basis, a.overall_coeff));
602 distrseq.push_back(power(expanded_basis, a.overall_coeff));
604 // Make sure that e.g. (x+y)^(1+a) -> x*(x+y)^a + y*(x+y)^a
605 ex r = (new mul(distrseq))->setflag(status_flags::dynallocated);
609 if (!is_ex_exactly_of_type(expanded_exponent, numeric) ||
610 !ex_to<numeric>(expanded_exponent).is_integer()) {
611 if (are_ex_trivially_equal(basis,expanded_basis) && are_ex_trivially_equal(exponent,expanded_exponent)) {
614 return (new power(expanded_basis,expanded_exponent))->setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
618 // integer numeric exponent
619 const numeric & num_exponent = ex_to<numeric>(expanded_exponent);
620 int int_exponent = num_exponent.to_int();
623 if (int_exponent > 0 && is_ex_exactly_of_type(expanded_basis,add))
624 return expand_add(ex_to<add>(expanded_basis), int_exponent);
626 // (x*y)^n -> x^n * y^n
627 if (is_ex_exactly_of_type(expanded_basis,mul))
628 return expand_mul(ex_to<mul>(expanded_basis), num_exponent);
630 // cannot expand further
631 if (are_ex_trivially_equal(basis,expanded_basis) && are_ex_trivially_equal(exponent,expanded_exponent))
634 return (new power(expanded_basis,expanded_exponent))->setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
638 // new virtual functions which can be overridden by derived classes
644 // non-virtual functions in this class
647 /** expand a^n where a is an add and n is a positive integer.
648 * @see power::expand */
649 ex power::expand_add(const add & a, int n) const
652 return expand_add_2(a);
654 const int m = a.nops();
656 // The number of terms will be the number of combinatorial compositions,
657 // i.e. the number of unordered arrangement of m nonnegative integers
658 // which sum up to n. It is frequently written as C_n(m) and directly
659 // related with binomial coefficients:
660 result.reserve(binomial(numeric(n+m-1), numeric(m-1)).to_int());
662 intvector k_cum(m-1); // k_cum[l]:=sum(i=0,l,k[l]);
663 intvector upper_limit(m-1);
666 for (int l=0; l<m-1; ++l) {
675 for (l=0; l<m-1; ++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(k[l])));
687 term.push_back(power(b,k[l]));
690 const ex & b = a.op(l);
691 GINAC_ASSERT(!is_exactly_a<add>(b));
692 GINAC_ASSERT(!is_exactly_a<power>(b) ||
693 !is_exactly_a<numeric>(ex_to<power>(b).exponent) ||
694 !ex_to<numeric>(ex_to<power>(b).exponent).is_pos_integer() ||
695 !is_exactly_a<add>(ex_to<power>(b).basis) ||
696 !is_exactly_a<mul>(ex_to<power>(b).basis) ||
697 !is_exactly_a<power>(ex_to<power>(b).basis));
698 if (is_ex_exactly_of_type(b,mul))
699 term.push_back(expand_mul(ex_to<mul>(b),numeric(n-k_cum[m-2])));
701 term.push_back(power(b,n-k_cum[m-2]));
703 numeric f = binomial(numeric(n),numeric(k[0]));
704 for (l=1; l<m-1; ++l)
705 f *= binomial(numeric(n-k_cum[l-1]),numeric(k[l]));
709 result.push_back((new mul(term))->setflag(status_flags::dynallocated));
713 while ((l>=0) && ((++k[l])>upper_limit[l])) {
719 // recalc k_cum[] and upper_limit[]
720 k_cum[l] = (l==0 ? k[0] : k_cum[l-1]+k[l]);
722 for (int i=l+1; i<m-1; ++i)
723 k_cum[i] = k_cum[i-1]+k[i];
725 for (int i=l+1; i<m-1; ++i)
726 upper_limit[i] = n-k_cum[i-1];
729 return (new add(result))->setflag(status_flags::dynallocated |
730 status_flags::expanded);
734 /** Special case of power::expand_add. Expands a^2 where a is an add.
735 * @see power::expand_add */
736 ex power::expand_add_2(const add & a) const
739 unsigned a_nops = a.nops();
740 sum.reserve((a_nops*(a_nops+1))/2);
741 epvector::const_iterator last = a.seq.end();
743 // power(+(x,...,z;c),2)=power(+(x,...,z;0),2)+2*c*+(x,...,z;0)+c*c
744 // first part: ignore overall_coeff and expand other terms
745 for (epvector::const_iterator cit0=a.seq.begin(); cit0!=last; ++cit0) {
746 const ex & r = cit0->rest;
747 const ex & c = cit0->coeff;
749 GINAC_ASSERT(!is_exactly_a<add>(r));
750 GINAC_ASSERT(!is_exactly_a<power>(r) ||
751 !is_exactly_a<numeric>(ex_to<power>(r).exponent) ||
752 !ex_to<numeric>(ex_to<power>(r).exponent).is_pos_integer() ||
753 !is_exactly_a<add>(ex_to<power>(r).basis) ||
754 !is_exactly_a<mul>(ex_to<power>(r).basis) ||
755 !is_exactly_a<power>(ex_to<power>(r).basis));
757 if (are_ex_trivially_equal(c,_ex1)) {
758 if (is_ex_exactly_of_type(r,mul)) {
759 sum.push_back(expair(expand_mul(ex_to<mul>(r),_num2),
762 sum.push_back(expair((new power(r,_ex2))->setflag(status_flags::dynallocated),
766 if (is_ex_exactly_of_type(r,mul)) {
767 sum.push_back(expair(expand_mul(ex_to<mul>(r),_num2),
768 ex_to<numeric>(c).power_dyn(_num2)));
770 sum.push_back(expair((new power(r,_ex2))->setflag(status_flags::dynallocated),
771 ex_to<numeric>(c).power_dyn(_num2)));
775 for (epvector::const_iterator cit1=cit0+1; cit1!=last; ++cit1) {
776 const ex & r1 = cit1->rest;
777 const ex & c1 = cit1->coeff;
778 sum.push_back(a.combine_ex_with_coeff_to_pair((new mul(r,r1))->setflag(status_flags::dynallocated),
779 _num2.mul(ex_to<numeric>(c)).mul_dyn(ex_to<numeric>(c1))));
783 GINAC_ASSERT(sum.size()==(a.seq.size()*(a.seq.size()+1))/2);
785 // second part: add terms coming from overall_factor (if != 0)
786 if (!a.overall_coeff.is_zero()) {
787 epvector::const_iterator i = a.seq.begin(), end = a.seq.end();
789 sum.push_back(a.combine_pair_with_coeff_to_pair(*i, ex_to<numeric>(a.overall_coeff).mul_dyn(_num2)));
792 sum.push_back(expair(ex_to<numeric>(a.overall_coeff).power_dyn(_num2),_ex1));
795 GINAC_ASSERT(sum.size()==(a_nops*(a_nops+1))/2);
797 return (new add(sum))->setflag(status_flags::dynallocated | status_flags::expanded);
800 /** Expand factors of m in m^n where m is a mul and n is and integer.
801 * @see power::expand */
802 ex power::expand_mul(const mul & m, const numeric & n) const
804 GINAC_ASSERT(n.is_integer());
810 distrseq.reserve(m.seq.size());
811 epvector::const_iterator last = m.seq.end();
812 epvector::const_iterator cit = m.seq.begin();
814 if (is_ex_exactly_of_type((*cit).rest,numeric)) {
815 distrseq.push_back(m.combine_pair_with_coeff_to_pair(*cit,n));
817 // it is safe not to call mul::combine_pair_with_coeff_to_pair()
818 // since n is an integer
819 distrseq.push_back(expair((*cit).rest, ex_to<numeric>((*cit).coeff).mul(n)));
823 return (new mul(distrseq,ex_to<numeric>(m.overall_coeff).power_dyn(n)))->setflag(status_flags::dynallocated);