3 * Implementation of GiNaC's symbolic exponentiation (basis^exponent). */
6 * GiNaC Copyright (C) 1999-2003 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_a<symbol>(basis) || is_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 (is_tex && is_exactly_a<numeric>(exponent) && ex_to<numeric>(exponent).is_negative()) {
177 // Powers with negative numeric exponents are printed as fractions in TeX
179 power(basis, -exponent).eval().print(c);
182 } else if (exponent.is_equal(_ex1_2)) {
184 // Square roots are printed in a special way
185 c.s << (is_tex ? "\\sqrt{" : "sqrt(");
187 c.s << (is_tex ? '}' : ')');
191 // Ordinary output of powers using '^' or '**'
192 if (precedence() <= level)
193 c.s << (is_tex ? "{(" : "(");
194 basis.print(c, precedence());
195 if (is_a<print_python>(c))
201 exponent.print(c, precedence());
204 if (precedence() <= level)
205 c.s << (is_tex ? ")}" : ")");
210 bool power::info(unsigned inf) const
213 case info_flags::polynomial:
214 case info_flags::integer_polynomial:
215 case info_flags::cinteger_polynomial:
216 case info_flags::rational_polynomial:
217 case info_flags::crational_polynomial:
218 return exponent.info(info_flags::nonnegint);
219 case info_flags::rational_function:
220 return exponent.info(info_flags::integer);
221 case info_flags::algebraic:
222 return (!exponent.info(info_flags::integer) ||
225 return inherited::info(inf);
228 unsigned power::nops() const
233 ex & power::let_op(int i)
238 return i==0 ? basis : exponent;
241 ex power::map(map_function & f) const
243 return (new power(f(basis), f(exponent)))->setflag(status_flags::dynallocated);
246 int power::degree(const ex & s) const
248 if (is_equal(ex_to<basic>(s)))
250 else if (is_ex_exactly_of_type(exponent, numeric) && ex_to<numeric>(exponent).is_integer()) {
251 if (basis.is_equal(s))
252 return ex_to<numeric>(exponent).to_int();
254 return basis.degree(s) * ex_to<numeric>(exponent).to_int();
255 } else if (basis.has(s))
256 throw(std::runtime_error("power::degree(): undefined degree because of non-integer exponent"));
261 int power::ldegree(const ex & s) const
263 if (is_equal(ex_to<basic>(s)))
265 else if (is_ex_exactly_of_type(exponent, numeric) && ex_to<numeric>(exponent).is_integer()) {
266 if (basis.is_equal(s))
267 return ex_to<numeric>(exponent).to_int();
269 return basis.ldegree(s) * ex_to<numeric>(exponent).to_int();
270 } else if (basis.has(s))
271 throw(std::runtime_error("power::ldegree(): undefined degree because of non-integer exponent"));
276 ex power::coeff(const ex & s, int n) const
278 if (is_equal(ex_to<basic>(s)))
279 return n==1 ? _ex1 : _ex0;
280 else if (!basis.is_equal(s)) {
281 // basis not equal to s
288 if (is_ex_exactly_of_type(exponent, numeric) && ex_to<numeric>(exponent).is_integer()) {
290 int int_exp = ex_to<numeric>(exponent).to_int();
296 // non-integer exponents are treated as zero
305 /** Perform automatic term rewriting rules in this class. In the following
306 * x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
307 * stand for such expressions that contain a plain number.
308 * - ^(x,0) -> 1 (also handles ^(0,0))
310 * - ^(0,c) -> 0 or exception (depending on the real part of c)
312 * - ^(c1,c2) -> *(c1^n,c1^(c2-n)) (so that 0<(c2-n)<1, try to evaluate roots, possibly in numerator and denominator of c1)
313 * - ^(^(x,c1),c2) -> ^(x,c1*c2) (c2 integer or -1 < c1 <= 1, case c1=1 should not happen, see below!)
314 * - ^(*(x,y,z),c) -> *(x^c,y^c,z^c) (if c integer)
315 * - ^(*(x,c1),c2) -> ^(x,c2)*c1^c2 (c1>0)
316 * - ^(*(x,c1),c2) -> ^(-x,c2)*c1^c2 (c1<0)
318 * @param level cut-off in recursive evaluation */
319 ex power::eval(int level) const
321 if ((level==1) && (flags & status_flags::evaluated))
323 else if (level == -max_recursion_level)
324 throw(std::runtime_error("max recursion level reached"));
326 const ex & ebasis = level==1 ? basis : basis.eval(level-1);
327 const ex & eexponent = level==1 ? exponent : exponent.eval(level-1);
329 bool basis_is_numerical = false;
330 bool exponent_is_numerical = false;
331 const numeric *num_basis;
332 const numeric *num_exponent;
334 if (is_ex_exactly_of_type(ebasis, numeric)) {
335 basis_is_numerical = true;
336 num_basis = &ex_to<numeric>(ebasis);
338 if (is_ex_exactly_of_type(eexponent, numeric)) {
339 exponent_is_numerical = true;
340 num_exponent = &ex_to<numeric>(eexponent);
343 // ^(x,0) -> 1 (0^0 also handled here)
344 if (eexponent.is_zero()) {
345 if (ebasis.is_zero())
346 throw (std::domain_error("power::eval(): pow(0,0) is undefined"));
352 if (eexponent.is_equal(_ex1))
355 // ^(0,c1) -> 0 or exception (depending on real value of c1)
356 if (ebasis.is_zero() && exponent_is_numerical) {
357 if ((num_exponent->real()).is_zero())
358 throw (std::domain_error("power::eval(): pow(0,I) is undefined"));
359 else if ((num_exponent->real()).is_negative())
360 throw (pole_error("power::eval(): division by zero",1));
366 if (ebasis.is_equal(_ex1))
369 if (exponent_is_numerical) {
371 // ^(c1,c2) -> c1^c2 (c1, c2 numeric(),
372 // except if c1,c2 are rational, but c1^c2 is not)
373 if (basis_is_numerical) {
374 const bool basis_is_crational = num_basis->is_crational();
375 const bool exponent_is_crational = num_exponent->is_crational();
376 if (!basis_is_crational || !exponent_is_crational) {
377 // return a plain float
378 return (new numeric(num_basis->power(*num_exponent)))->setflag(status_flags::dynallocated |
379 status_flags::evaluated |
380 status_flags::expanded);
383 const numeric res = num_basis->power(*num_exponent);
384 if (res.is_crational()) {
387 GINAC_ASSERT(!num_exponent->is_integer()); // has been handled by now
389 // ^(c1,n/m) -> *(c1^q,c1^(n/m-q)), 0<(n/m-q)<1, q integer
390 if (basis_is_crational && exponent_is_crational
391 && num_exponent->is_real()
392 && !num_exponent->is_integer()) {
393 const numeric n = num_exponent->numer();
394 const numeric m = num_exponent->denom();
396 numeric q = iquo(n, m, r);
397 if (r.is_negative()) {
401 if (q.is_zero()) { // the exponent was in the allowed range 0<(n/m)<1
402 if (num_basis->is_rational() && !num_basis->is_integer()) {
403 // try it for numerator and denominator separately, in order to
404 // partially simplify things like (5/8)^(1/3) -> 1/2*5^(1/3)
405 const numeric bnum = num_basis->numer();
406 const numeric bden = num_basis->denom();
407 const numeric res_bnum = bnum.power(*num_exponent);
408 const numeric res_bden = bden.power(*num_exponent);
409 if (res_bnum.is_integer())
410 return (new mul(power(bden,-*num_exponent),res_bnum))->setflag(status_flags::dynallocated | status_flags::evaluated);
411 if (res_bden.is_integer())
412 return (new mul(power(bnum,*num_exponent),res_bden.inverse()))->setflag(status_flags::dynallocated | status_flags::evaluated);
416 // assemble resulting product, but allowing for a re-evaluation,
417 // because otherwise we'll end up with something like
418 // (7/8)^(4/3) -> 7/8*(1/2*7^(1/3))
419 // instead of 7/16*7^(1/3).
420 ex prod = power(*num_basis,r.div(m));
421 return prod*power(*num_basis,q);
426 // ^(^(x,c1),c2) -> ^(x,c1*c2)
427 // (c1, c2 numeric(), c2 integer or -1 < c1 <= 1,
428 // case c1==1 should not happen, see below!)
429 if (is_ex_exactly_of_type(ebasis,power)) {
430 const power & sub_power = ex_to<power>(ebasis);
431 const ex & sub_basis = sub_power.basis;
432 const ex & sub_exponent = sub_power.exponent;
433 if (is_ex_exactly_of_type(sub_exponent,numeric)) {
434 const numeric & num_sub_exponent = ex_to<numeric>(sub_exponent);
435 GINAC_ASSERT(num_sub_exponent!=numeric(1));
436 if (num_exponent->is_integer() || (abs(num_sub_exponent) - _num1).is_negative())
437 return power(sub_basis,num_sub_exponent.mul(*num_exponent));
441 // ^(*(x,y,z),c1) -> *(x^c1,y^c1,z^c1) (c1 integer)
442 if (num_exponent->is_integer() && is_ex_exactly_of_type(ebasis,mul)) {
443 return expand_mul(ex_to<mul>(ebasis), *num_exponent);
446 // ^(*(...,x;c1),c2) -> *(^(*(...,x;1),c2),c1^c2) (c1, c2 numeric(), c1>0)
447 // ^(*(...,x;c1),c2) -> *(^(*(...,x;-1),c2),(-c1)^c2) (c1, c2 numeric(), c1<0)
448 if (is_ex_exactly_of_type(ebasis,mul)) {
449 GINAC_ASSERT(!num_exponent->is_integer()); // should have been handled above
450 const mul & mulref = ex_to<mul>(ebasis);
451 if (!mulref.overall_coeff.is_equal(_ex1)) {
452 const numeric & num_coeff = ex_to<numeric>(mulref.overall_coeff);
453 if (num_coeff.is_real()) {
454 if (num_coeff.is_positive()) {
455 mul *mulp = new mul(mulref);
456 mulp->overall_coeff = _ex1;
457 mulp->clearflag(status_flags::evaluated);
458 mulp->clearflag(status_flags::hash_calculated);
459 return (new mul(power(*mulp,exponent),
460 power(num_coeff,*num_exponent)))->setflag(status_flags::dynallocated);
462 GINAC_ASSERT(num_coeff.compare(_num0)<0);
463 if (!num_coeff.is_equal(_num_1)) {
464 mul *mulp = new mul(mulref);
465 mulp->overall_coeff = _ex_1;
466 mulp->clearflag(status_flags::evaluated);
467 mulp->clearflag(status_flags::hash_calculated);
468 return (new mul(power(*mulp,exponent),
469 power(abs(num_coeff),*num_exponent)))->setflag(status_flags::dynallocated);
476 // ^(nc,c1) -> ncmul(nc,nc,...) (c1 positive integer, unless nc is a matrix)
477 if (num_exponent->is_pos_integer() &&
478 ebasis.return_type() != return_types::commutative &&
479 !is_ex_of_type(ebasis,matrix)) {
480 return ncmul(exvector(num_exponent->to_int(), ebasis), true);
484 if (are_ex_trivially_equal(ebasis,basis) &&
485 are_ex_trivially_equal(eexponent,exponent)) {
488 return (new power(ebasis, eexponent))->setflag(status_flags::dynallocated |
489 status_flags::evaluated);
492 ex power::evalf(int level) const
499 eexponent = exponent;
500 } else if (level == -max_recursion_level) {
501 throw(std::runtime_error("max recursion level reached"));
503 ebasis = basis.evalf(level-1);
504 if (!is_exactly_a<numeric>(exponent))
505 eexponent = exponent.evalf(level-1);
507 eexponent = exponent;
510 return power(ebasis,eexponent);
513 ex power::evalm(void) const
515 const ex ebasis = basis.evalm();
516 const ex eexponent = exponent.evalm();
517 if (is_ex_of_type(ebasis,matrix)) {
518 if (is_ex_of_type(eexponent,numeric)) {
519 return (new matrix(ex_to<matrix>(ebasis).pow(eexponent)))->setflag(status_flags::dynallocated);
522 return (new power(ebasis, eexponent))->setflag(status_flags::dynallocated);
525 ex power::subs(const lst & ls, const lst & lr, bool no_pattern) const
527 const ex &subsed_basis = basis.subs(ls, lr, no_pattern);
528 const ex &subsed_exponent = exponent.subs(ls, lr, no_pattern);
530 if (are_ex_trivially_equal(basis, subsed_basis)
531 && are_ex_trivially_equal(exponent, subsed_exponent))
532 return basic::subs(ls, lr, no_pattern);
534 return power(subsed_basis, subsed_exponent).basic::subs(ls, lr, no_pattern);
537 ex power::simplify_ncmul(const exvector & v) const
539 return inherited::simplify_ncmul(v);
544 /** Implementation of ex::diff() for a power.
546 ex power::derivative(const symbol & s) const
548 if (exponent.info(info_flags::real)) {
549 // D(b^r) = r * b^(r-1) * D(b) (faster than the formula below)
552 newseq.push_back(expair(basis, exponent - _ex1));
553 newseq.push_back(expair(basis.diff(s), _ex1));
554 return mul(newseq, exponent);
556 // D(b^e) = b^e * (D(e)*ln(b) + e*D(b)/b)
558 add(mul(exponent.diff(s), log(basis)),
559 mul(mul(exponent, basis.diff(s)), power(basis, _ex_1))));
563 int power::compare_same_type(const basic & other) const
565 GINAC_ASSERT(is_exactly_a<power>(other));
566 const power &o = static_cast<const power &>(other);
568 int cmpval = basis.compare(o.basis);
572 return exponent.compare(o.exponent);
575 unsigned power::return_type(void) const
577 return basis.return_type();
580 unsigned power::return_type_tinfo(void) const
582 return basis.return_type_tinfo();
585 ex power::expand(unsigned options) const
587 if (options == 0 && (flags & status_flags::expanded))
590 const ex expanded_basis = basis.expand(options);
591 const ex expanded_exponent = exponent.expand(options);
593 // x^(a+b) -> x^a * x^b
594 if (is_ex_exactly_of_type(expanded_exponent, add)) {
595 const add &a = ex_to<add>(expanded_exponent);
597 distrseq.reserve(a.seq.size() + 1);
598 epvector::const_iterator last = a.seq.end();
599 epvector::const_iterator cit = a.seq.begin();
601 distrseq.push_back(power(expanded_basis, a.recombine_pair_to_ex(*cit)));
605 // Make sure that e.g. (x+y)^(2+a) expands the (x+y)^2 factor
606 if (ex_to<numeric>(a.overall_coeff).is_integer()) {
607 const numeric &num_exponent = ex_to<numeric>(a.overall_coeff);
608 int int_exponent = num_exponent.to_int();
609 if (int_exponent > 0 && is_ex_exactly_of_type(expanded_basis, add))
610 distrseq.push_back(expand_add(ex_to<add>(expanded_basis), int_exponent));
612 distrseq.push_back(power(expanded_basis, a.overall_coeff));
614 distrseq.push_back(power(expanded_basis, a.overall_coeff));
616 // Make sure that e.g. (x+y)^(1+a) -> x*(x+y)^a + y*(x+y)^a
617 ex r = (new mul(distrseq))->setflag(status_flags::dynallocated);
621 if (!is_ex_exactly_of_type(expanded_exponent, numeric) ||
622 !ex_to<numeric>(expanded_exponent).is_integer()) {
623 if (are_ex_trivially_equal(basis,expanded_basis) && are_ex_trivially_equal(exponent,expanded_exponent)) {
626 return (new power(expanded_basis,expanded_exponent))->setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
630 // integer numeric exponent
631 const numeric & num_exponent = ex_to<numeric>(expanded_exponent);
632 int int_exponent = num_exponent.to_int();
635 if (int_exponent > 0 && is_ex_exactly_of_type(expanded_basis,add))
636 return expand_add(ex_to<add>(expanded_basis), int_exponent);
638 // (x*y)^n -> x^n * y^n
639 if (is_ex_exactly_of_type(expanded_basis,mul))
640 return expand_mul(ex_to<mul>(expanded_basis), num_exponent);
642 // cannot expand further
643 if (are_ex_trivially_equal(basis,expanded_basis) && are_ex_trivially_equal(exponent,expanded_exponent))
646 return (new power(expanded_basis,expanded_exponent))->setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
650 // new virtual functions which can be overridden by derived classes
656 // non-virtual functions in this class
659 /** expand a^n where a is an add and n is a positive integer.
660 * @see power::expand */
661 ex power::expand_add(const add & a, int n) const
664 return expand_add_2(a);
666 const int m = a.nops();
668 // The number of terms will be the number of combinatorial compositions,
669 // i.e. the number of unordered arrangement of m nonnegative integers
670 // which sum up to n. It is frequently written as C_n(m) and directly
671 // related with binomial coefficients:
672 result.reserve(binomial(numeric(n+m-1), numeric(m-1)).to_int());
674 intvector k_cum(m-1); // k_cum[l]:=sum(i=0,l,k[l]);
675 intvector upper_limit(m-1);
678 for (int l=0; l<m-1; ++l) {
687 for (l=0; l<m-1; ++l) {
688 const ex & b = a.op(l);
689 GINAC_ASSERT(!is_exactly_a<add>(b));
690 GINAC_ASSERT(!is_exactly_a<power>(b) ||
691 !is_exactly_a<numeric>(ex_to<power>(b).exponent) ||
692 !ex_to<numeric>(ex_to<power>(b).exponent).is_pos_integer() ||
693 !is_exactly_a<add>(ex_to<power>(b).basis) ||
694 !is_exactly_a<mul>(ex_to<power>(b).basis) ||
695 !is_exactly_a<power>(ex_to<power>(b).basis));
696 if (is_ex_exactly_of_type(b,mul))
697 term.push_back(expand_mul(ex_to<mul>(b),numeric(k[l])));
699 term.push_back(power(b,k[l]));
702 const ex & b = a.op(l);
703 GINAC_ASSERT(!is_exactly_a<add>(b));
704 GINAC_ASSERT(!is_exactly_a<power>(b) ||
705 !is_exactly_a<numeric>(ex_to<power>(b).exponent) ||
706 !ex_to<numeric>(ex_to<power>(b).exponent).is_pos_integer() ||
707 !is_exactly_a<add>(ex_to<power>(b).basis) ||
708 !is_exactly_a<mul>(ex_to<power>(b).basis) ||
709 !is_exactly_a<power>(ex_to<power>(b).basis));
710 if (is_ex_exactly_of_type(b,mul))
711 term.push_back(expand_mul(ex_to<mul>(b),numeric(n-k_cum[m-2])));
713 term.push_back(power(b,n-k_cum[m-2]));
715 numeric f = binomial(numeric(n),numeric(k[0]));
716 for (l=1; l<m-1; ++l)
717 f *= binomial(numeric(n-k_cum[l-1]),numeric(k[l]));
721 result.push_back((new mul(term))->setflag(status_flags::dynallocated));
725 while ((l>=0) && ((++k[l])>upper_limit[l])) {
731 // recalc k_cum[] and upper_limit[]
732 k_cum[l] = (l==0 ? k[0] : k_cum[l-1]+k[l]);
734 for (int i=l+1; i<m-1; ++i)
735 k_cum[i] = k_cum[i-1]+k[i];
737 for (int i=l+1; i<m-1; ++i)
738 upper_limit[i] = n-k_cum[i-1];
741 return (new add(result))->setflag(status_flags::dynallocated |
742 status_flags::expanded);
746 /** Special case of power::expand_add. Expands a^2 where a is an add.
747 * @see power::expand_add */
748 ex power::expand_add_2(const add & a) const
751 unsigned a_nops = a.nops();
752 sum.reserve((a_nops*(a_nops+1))/2);
753 epvector::const_iterator last = a.seq.end();
755 // power(+(x,...,z;c),2)=power(+(x,...,z;0),2)+2*c*+(x,...,z;0)+c*c
756 // first part: ignore overall_coeff and expand other terms
757 for (epvector::const_iterator cit0=a.seq.begin(); cit0!=last; ++cit0) {
758 const ex & r = cit0->rest;
759 const ex & c = cit0->coeff;
761 GINAC_ASSERT(!is_exactly_a<add>(r));
762 GINAC_ASSERT(!is_exactly_a<power>(r) ||
763 !is_exactly_a<numeric>(ex_to<power>(r).exponent) ||
764 !ex_to<numeric>(ex_to<power>(r).exponent).is_pos_integer() ||
765 !is_exactly_a<add>(ex_to<power>(r).basis) ||
766 !is_exactly_a<mul>(ex_to<power>(r).basis) ||
767 !is_exactly_a<power>(ex_to<power>(r).basis));
769 if (are_ex_trivially_equal(c,_ex1)) {
770 if (is_ex_exactly_of_type(r,mul)) {
771 sum.push_back(expair(expand_mul(ex_to<mul>(r),_num2),
774 sum.push_back(expair((new power(r,_ex2))->setflag(status_flags::dynallocated),
778 if (is_ex_exactly_of_type(r,mul)) {
779 sum.push_back(a.combine_ex_with_coeff_to_pair(expand_mul(ex_to<mul>(r),_num2),
780 ex_to<numeric>(c).power_dyn(_num2)));
782 sum.push_back(a.combine_ex_with_coeff_to_pair((new power(r,_ex2))->setflag(status_flags::dynallocated),
783 ex_to<numeric>(c).power_dyn(_num2)));
787 for (epvector::const_iterator cit1=cit0+1; cit1!=last; ++cit1) {
788 const ex & r1 = cit1->rest;
789 const ex & c1 = cit1->coeff;
790 sum.push_back(a.combine_ex_with_coeff_to_pair((new mul(r,r1))->setflag(status_flags::dynallocated),
791 _num2.mul(ex_to<numeric>(c)).mul_dyn(ex_to<numeric>(c1))));
795 GINAC_ASSERT(sum.size()==(a.seq.size()*(a.seq.size()+1))/2);
797 // second part: add terms coming from overall_factor (if != 0)
798 if (!a.overall_coeff.is_zero()) {
799 epvector::const_iterator i = a.seq.begin(), end = a.seq.end();
801 sum.push_back(a.combine_pair_with_coeff_to_pair(*i, ex_to<numeric>(a.overall_coeff).mul_dyn(_num2)));
804 sum.push_back(expair(ex_to<numeric>(a.overall_coeff).power_dyn(_num2),_ex1));
807 GINAC_ASSERT(sum.size()==(a_nops*(a_nops+1))/2);
809 return (new add(sum))->setflag(status_flags::dynallocated | status_flags::expanded);
812 /** Expand factors of m in m^n where m is a mul and n is and integer.
813 * @see power::expand */
814 ex power::expand_mul(const mul & m, const numeric & n) const
816 GINAC_ASSERT(n.is_integer());
822 distrseq.reserve(m.seq.size());
823 epvector::const_iterator last = m.seq.end();
824 epvector::const_iterator cit = m.seq.begin();
826 if (is_ex_exactly_of_type(cit->rest,numeric)) {
827 distrseq.push_back(m.combine_pair_with_coeff_to_pair(*cit, n));
829 // it is safe not to call mul::combine_pair_with_coeff_to_pair()
830 // since n is an integer
831 distrseq.push_back(expair(cit->rest, ex_to<numeric>(cit->coeff).mul(n)));
835 return (new mul(distrseq, ex_to<numeric>(m.overall_coeff).power_dyn(n)))->setflag(status_flags::dynallocated);