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"
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() : basic(TINFO_power)
53 debugmsg("power default ctor",LOGLEVEL_CONSTRUCT);
56 void power::copy(const power & other)
58 inherited::copy(other);
60 exponent = other.exponent;
63 DEFAULT_DESTROY(power)
69 power::power(const ex & lh, const ex & rh) : basic(TINFO_power), basis(lh), exponent(rh)
71 debugmsg("power ctor from ex,ex",LOGLEVEL_CONSTRUCT);
74 /** Ctor from an ex and a bare numeric. This is somewhat more efficient than
75 * the normal ctor from two ex whenever it can be used. */
76 power::power(const ex & lh, const numeric & rh) : basic(TINFO_power), basis(lh), exponent(rh)
78 debugmsg("power ctor from ex,numeric",LOGLEVEL_CONSTRUCT);
85 power::power(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
87 debugmsg("power ctor from archive_node", LOGLEVEL_CONSTRUCT);
88 n.find_ex("basis", basis, sym_lst);
89 n.find_ex("exponent", exponent, sym_lst);
92 void power::archive(archive_node &n) const
94 inherited::archive(n);
95 n.add_ex("basis", basis);
96 n.add_ex("exponent", exponent);
99 DEFAULT_UNARCHIVE(power)
102 // functions overriding virtual functions from bases classes
107 static void print_sym_pow(const print_context & c, const symbol &x, int exp)
109 // Optimal output of integer powers of symbols to aid compiler CSE.
110 // C.f. ISO/IEC 14882:1998, section 1.9 [intro execution], paragraph 15
111 // to learn why such a hack is really necessary.
114 } else if (exp == 2) {
118 } else if (exp & 1) {
121 print_sym_pow(c, x, exp-1);
124 print_sym_pow(c, x, exp >> 1);
126 print_sym_pow(c, x, exp >> 1);
131 void power::print(const print_context & c, unsigned level) const
133 debugmsg("power print", LOGLEVEL_PRINT);
135 if (is_of_type(c, print_tree)) {
137 inherited::print(c, level);
139 } else if (is_of_type(c, print_csrc)) {
141 // Integer powers of symbols are printed in a special, optimized way
142 if (exponent.info(info_flags::integer)
143 && (is_ex_exactly_of_type(basis, symbol) || is_ex_exactly_of_type(basis, constant))) {
144 int exp = ex_to_numeric(exponent).to_int();
149 if (is_of_type(c, print_csrc_cl_N))
154 print_sym_pow(c, ex_to_symbol(basis), exp);
157 // <expr>^-1 is printed as "1.0/<expr>" or with the recip() function of CLN
158 } else if (exponent.compare(_num_1()) == 0) {
159 if (is_of_type(c, print_csrc_cl_N))
166 // Otherwise, use the pow() or expt() (CLN) functions
168 if (is_of_type(c, print_csrc_cl_N))
180 if (exponent.is_equal(_ex1_2())) {
181 if (is_of_type(c, print_latex))
186 if (is_of_type(c, print_latex))
191 if (precedence() <= level) {
192 if (is_of_type(c, print_latex))
197 basis.print(c, precedence());
199 if (is_of_type(c, print_latex))
201 exponent.print(c, precedence());
202 if (is_of_type(c, print_latex))
204 if (precedence() <= level) {
205 if (is_of_type(c, print_latex))
214 bool power::info(unsigned inf) const
217 case info_flags::polynomial:
218 case info_flags::integer_polynomial:
219 case info_flags::cinteger_polynomial:
220 case info_flags::rational_polynomial:
221 case info_flags::crational_polynomial:
222 return exponent.info(info_flags::nonnegint);
223 case info_flags::rational_function:
224 return exponent.info(info_flags::integer);
225 case info_flags::algebraic:
226 return (!exponent.info(info_flags::integer) ||
229 return inherited::info(inf);
232 unsigned power::nops() const
237 ex & power::let_op(int i)
242 return i==0 ? basis : exponent;
245 ex power::map(map_func f) const
247 return (new power(f(basis), f(exponent)))->setflag(status_flags::dynallocated);
250 int power::degree(const ex & s) const
252 if (is_exactly_of_type(*exponent.bp,numeric)) {
253 if (basis.is_equal(s)) {
254 if (ex_to_numeric(exponent).is_integer())
255 return ex_to_numeric(exponent).to_int();
259 return basis.degree(s) * ex_to_numeric(exponent).to_int();
264 int power::ldegree(const ex & s) const
266 if (is_exactly_of_type(*exponent.bp,numeric)) {
267 if (basis.is_equal(s)) {
268 if (ex_to_numeric(exponent).is_integer())
269 return ex_to_numeric(exponent).to_int();
273 return basis.ldegree(s) * ex_to_numeric(exponent).to_int();
278 ex power::coeff(const ex & s, int n) const
280 if (!basis.is_equal(s)) {
281 // basis not equal to s
288 if (is_exactly_of_type(*exponent.bp, 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 ex power::eval(int level) const
307 // simplifications: ^(x,0) -> 1 (0^0 handled here)
309 // ^(0,c1) -> 0 or exception (depending on real value of c1)
311 // ^(c1,c2) -> *(c1^n,c1^(c2-n)) (c1, c2 numeric(), 0<(c2-n)<1 except if c1,c2 are rational, but c1^c2 is not)
312 // ^(^(x,c1),c2) -> ^(x,c1*c2) (c1, c2 numeric(), c2 integer or -1 < c1 <= 1, case c1=1 should not happen, see below!)
313 // ^(*(x,y,z),c1) -> *(x^c1,y^c1,z^c1) (c1 integer)
314 // ^(*(x,c1),c2) -> ^(x,c2)*c1^c2 (c1, c2 numeric(), c1>0)
315 // ^(*(x,c1),c2) -> ^(-x,c2)*c1^c2 (c1, c2 numeric(), c1<0)
317 debugmsg("power eval",LOGLEVEL_MEMBER_FUNCTION);
319 if ((level==1) && (flags & status_flags::evaluated))
321 else if (level == -max_recursion_level)
322 throw(std::runtime_error("max recursion level reached"));
324 const ex & ebasis = level==1 ? basis : basis.eval(level-1);
325 const ex & eexponent = level==1 ? exponent : exponent.eval(level-1);
327 bool basis_is_numerical = false;
328 bool exponent_is_numerical = false;
330 numeric * num_exponent;
332 if (is_exactly_of_type(*ebasis.bp,numeric)) {
333 basis_is_numerical = true;
334 num_basis = static_cast<numeric *>(ebasis.bp);
336 if (is_exactly_of_type(*eexponent.bp,numeric)) {
337 exponent_is_numerical = true;
338 num_exponent = static_cast<numeric *>(eexponent.bp);
341 // ^(x,0) -> 1 (0^0 also handled here)
342 if (eexponent.is_zero()) {
343 if (ebasis.is_zero())
344 throw (std::domain_error("power::eval(): pow(0,0) is undefined"));
350 if (eexponent.is_equal(_ex1()))
353 // ^(0,c1) -> 0 or exception (depending on real value of c1)
354 if (ebasis.is_zero() && exponent_is_numerical) {
355 if ((num_exponent->real()).is_zero())
356 throw (std::domain_error("power::eval(): pow(0,I) is undefined"));
357 else if ((num_exponent->real()).is_negative())
358 throw (pole_error("power::eval(): division by zero",1));
364 if (ebasis.is_equal(_ex1()))
367 if (exponent_is_numerical) {
369 // ^(c1,c2) -> c1^c2 (c1, c2 numeric(),
370 // except if c1,c2 are rational, but c1^c2 is not)
371 if (basis_is_numerical) {
372 bool basis_is_crational = num_basis->is_crational();
373 bool exponent_is_crational = num_exponent->is_crational();
374 numeric res = num_basis->power(*num_exponent);
376 if ((!basis_is_crational || !exponent_is_crational)
377 || res.is_crational()) {
380 GINAC_ASSERT(!num_exponent->is_integer()); // has been handled by now
382 // ^(c1,n/m) -> *(c1^q,c1^(n/m-q)), 0<(n/m-h)<1, q integer
383 if (basis_is_crational && exponent_is_crational
384 && num_exponent->is_real()
385 && !num_exponent->is_integer()) {
386 numeric n = num_exponent->numer();
387 numeric m = num_exponent->denom();
389 numeric q = iquo(n, m, r);
390 if (r.is_negative()) {
394 if (q.is_zero()) // the exponent was in the allowed range 0<(n/m)<1
398 res.push_back(expair(ebasis,r.div(m)));
399 return (new mul(res,ex(num_basis->power_dyn(q))))->setflag(status_flags::dynallocated | status_flags::evaluated);
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.compare(_num_1())!=0) {
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
472 debugmsg("power evalf",LOGLEVEL_MEMBER_FUNCTION);
479 eexponent = exponent;
480 } else if (level == -max_recursion_level) {
481 throw(std::runtime_error("max recursion level reached"));
483 ebasis = basis.evalf(level-1);
484 if (!is_ex_exactly_of_type(eexponent,numeric))
485 eexponent = exponent.evalf(level-1);
487 eexponent = exponent;
490 return power(ebasis,eexponent);
493 ex power::evalm(void) const
495 ex ebasis = basis.evalm();
496 ex eexponent = exponent.evalm();
497 if (is_ex_of_type(ebasis,matrix)) {
498 if (is_ex_of_type(eexponent,numeric)) {
499 return (new matrix(ex_to_matrix(ebasis).pow(eexponent)))->setflag(status_flags::dynallocated);
502 return (new power(ebasis, eexponent))->setflag(status_flags::dynallocated);
505 ex power::subs(const lst & ls, const lst & lr, bool no_pattern) const
507 const ex &subsed_basis = basis.subs(ls, lr, no_pattern);
508 const ex &subsed_exponent = exponent.subs(ls, lr, no_pattern);
510 if (are_ex_trivially_equal(basis, subsed_basis)
511 && are_ex_trivially_equal(exponent, subsed_exponent))
512 return basic::subs(ls, lr, no_pattern);
514 return ex(power(subsed_basis, subsed_exponent)).bp->basic::subs(ls, lr, no_pattern);
517 ex power::simplify_ncmul(const exvector & v) const
519 return inherited::simplify_ncmul(v);
524 /** Implementation of ex::diff() for a power.
526 ex power::derivative(const symbol & s) const
528 if (exponent.info(info_flags::real)) {
529 // D(b^r) = r * b^(r-1) * D(b) (faster than the formula below)
532 newseq.push_back(expair(basis, exponent - _ex1()));
533 newseq.push_back(expair(basis.diff(s), _ex1()));
534 return mul(newseq, exponent);
536 // D(b^e) = b^e * (D(e)*ln(b) + e*D(b)/b)
538 add(mul(exponent.diff(s), log(basis)),
539 mul(mul(exponent, basis.diff(s)), power(basis, _ex_1()))));
543 int power::compare_same_type(const basic & other) const
545 GINAC_ASSERT(is_exactly_of_type(other, power));
546 const power & o=static_cast<const power &>(const_cast<basic &>(other));
549 cmpval=basis.compare(o.basis);
551 return exponent.compare(o.exponent);
556 unsigned power::return_type(void) const
558 return basis.return_type();
561 unsigned power::return_type_tinfo(void) const
563 return basis.return_type_tinfo();
566 ex power::expand(unsigned options) const
568 if (flags & status_flags::expanded)
571 ex expanded_basis = basis.expand(options);
572 ex expanded_exponent = exponent.expand(options);
574 // x^(a+b) -> x^a * x^b
575 if (is_ex_exactly_of_type(expanded_exponent, add)) {
576 const add &a = ex_to_add(expanded_exponent);
578 distrseq.reserve(a.seq.size() + 1);
579 epvector::const_iterator last = a.seq.end();
580 epvector::const_iterator cit = a.seq.begin();
582 distrseq.push_back(power(expanded_basis, a.recombine_pair_to_ex(*cit)));
586 // Make sure that e.g. (x+y)^(2+a) expands the (x+y)^2 factor
587 if (ex_to_numeric(a.overall_coeff).is_integer()) {
588 const numeric &num_exponent = ex_to_numeric(a.overall_coeff);
589 int int_exponent = num_exponent.to_int();
590 if (int_exponent > 0 && is_ex_exactly_of_type(expanded_basis, add))
591 distrseq.push_back(expand_add(ex_to_add(expanded_basis), int_exponent));
593 distrseq.push_back(power(expanded_basis, a.overall_coeff));
595 distrseq.push_back(power(expanded_basis, a.overall_coeff));
597 // Make sure that e.g. (x+y)^(1+a) -> x*(x+y)^a + y*(x+y)^a
598 ex r = (new mul(distrseq))->setflag(status_flags::dynallocated);
602 if (!is_ex_exactly_of_type(expanded_exponent, numeric) ||
603 !ex_to_numeric(expanded_exponent).is_integer()) {
604 if (are_ex_trivially_equal(basis,expanded_basis) && are_ex_trivially_equal(exponent,expanded_exponent)) {
607 return (new power(expanded_basis,expanded_exponent))->setflag(status_flags::dynallocated | status_flags::expanded);
611 // integer numeric exponent
612 const numeric & num_exponent = ex_to_numeric(expanded_exponent);
613 int int_exponent = num_exponent.to_int();
616 if (int_exponent > 0 && is_ex_exactly_of_type(expanded_basis,add))
617 return expand_add(ex_to_add(expanded_basis), int_exponent);
619 // (x*y)^n -> x^n * y^n
620 if (is_ex_exactly_of_type(expanded_basis,mul))
621 return expand_mul(ex_to_mul(expanded_basis), num_exponent);
623 // cannot expand further
624 if (are_ex_trivially_equal(basis,expanded_basis) && are_ex_trivially_equal(exponent,expanded_exponent))
627 return (new power(expanded_basis,expanded_exponent))->setflag(status_flags::dynallocated | status_flags::expanded);
631 // new virtual functions which can be overridden by derived classes
637 // non-virtual functions in this class
640 /** expand a^n where a is an add and n is an integer.
641 * @see power::expand */
642 ex power::expand_add(const add & a, int n) const
645 return expand_add_2(a);
649 sum.reserve((n+1)*(m-1));
651 intvector k_cum(m-1); // k_cum[l]:=sum(i=0,l,k[l]);
652 intvector upper_limit(m-1);
655 for (int l=0; l<m-1; l++) {
664 for (l=0; l<m-1; l++) {
665 const ex & b = a.op(l);
666 GINAC_ASSERT(!is_ex_exactly_of_type(b,add));
667 GINAC_ASSERT(!is_ex_exactly_of_type(b,power) ||
668 !is_ex_exactly_of_type(ex_to_power(b).exponent,numeric) ||
669 !ex_to_numeric(ex_to_power(b).exponent).is_pos_integer() ||
670 !is_ex_exactly_of_type(ex_to_power(b).basis,add) ||
671 !is_ex_exactly_of_type(ex_to_power(b).basis,mul) ||
672 !is_ex_exactly_of_type(ex_to_power(b).basis,power));
673 if (is_ex_exactly_of_type(b,mul))
674 term.push_back(expand_mul(ex_to_mul(b),numeric(k[l])));
676 term.push_back(power(b,k[l]));
679 const ex & b = a.op(l);
680 GINAC_ASSERT(!is_ex_exactly_of_type(b,add));
681 GINAC_ASSERT(!is_ex_exactly_of_type(b,power) ||
682 !is_ex_exactly_of_type(ex_to_power(b).exponent,numeric) ||
683 !ex_to_numeric(ex_to_power(b).exponent).is_pos_integer() ||
684 !is_ex_exactly_of_type(ex_to_power(b).basis,add) ||
685 !is_ex_exactly_of_type(ex_to_power(b).basis,mul) ||
686 !is_ex_exactly_of_type(ex_to_power(b).basis,power));
687 if (is_ex_exactly_of_type(b,mul))
688 term.push_back(expand_mul(ex_to_mul(b),numeric(n-k_cum[m-2])));
690 term.push_back(power(b,n-k_cum[m-2]));
692 numeric f = binomial(numeric(n),numeric(k[0]));
693 for (l=1; l<m-1; l++)
694 f *= binomial(numeric(n-k_cum[l-1]),numeric(k[l]));
699 cout << "begin term" << endl;
700 for (int i=0; i<m-1; i++) {
701 cout << "k[" << i << "]=" << k[i] << endl;
702 cout << "k_cum[" << i << "]=" << k_cum[i] << endl;
703 cout << "upper_limit[" << i << "]=" << upper_limit[i] << endl;
705 for_each(term.begin(), term.end(), ostream_iterator<ex>(cout, "\n"));
706 cout << "end term" << endl;
709 // TODO: optimize this
710 sum.push_back((new mul(term))->setflag(status_flags::dynallocated));
714 while ((l>=0)&&((++k[l])>upper_limit[l])) {
720 // recalc k_cum[] and upper_limit[]
724 k_cum[l] = k_cum[l-1]+k[l];
726 for (int i=l+1; i<m-1; i++)
727 k_cum[i] = k_cum[i-1]+k[i];
729 for (int i=l+1; i<m-1; i++)
730 upper_limit[i] = n-k_cum[i-1];
732 return (new add(sum))->setflag(status_flags::dynallocated |
733 status_flags::expanded );
737 /** Special case of power::expand_add. Expands a^2 where a is an add.
738 * @see power::expand_add */
739 ex power::expand_add_2(const add & a) const
742 unsigned a_nops = a.nops();
743 sum.reserve((a_nops*(a_nops+1))/2);
744 epvector::const_iterator last = a.seq.end();
746 // power(+(x,...,z;c),2)=power(+(x,...,z;0),2)+2*c*+(x,...,z;0)+c*c
747 // first part: ignore overall_coeff and expand other terms
748 for (epvector::const_iterator cit0=a.seq.begin(); cit0!=last; ++cit0) {
749 const ex & r = (*cit0).rest;
750 const ex & c = (*cit0).coeff;
752 GINAC_ASSERT(!is_ex_exactly_of_type(r,add));
753 GINAC_ASSERT(!is_ex_exactly_of_type(r,power) ||
754 !is_ex_exactly_of_type(ex_to_power(r).exponent,numeric) ||
755 !ex_to_numeric(ex_to_power(r).exponent).is_pos_integer() ||
756 !is_ex_exactly_of_type(ex_to_power(r).basis,add) ||
757 !is_ex_exactly_of_type(ex_to_power(r).basis,mul) ||
758 !is_ex_exactly_of_type(ex_to_power(r).basis,power));
760 if (are_ex_trivially_equal(c,_ex1())) {
761 if (is_ex_exactly_of_type(r,mul)) {
762 sum.push_back(expair(expand_mul(ex_to_mul(r),_num2()),
765 sum.push_back(expair((new power(r,_ex2()))->setflag(status_flags::dynallocated),
769 if (is_ex_exactly_of_type(r,mul)) {
770 sum.push_back(expair(expand_mul(ex_to_mul(r),_num2()),
771 ex_to_numeric(c).power_dyn(_num2())));
773 sum.push_back(expair((new power(r,_ex2()))->setflag(status_flags::dynallocated),
774 ex_to_numeric(c).power_dyn(_num2())));
778 for (epvector::const_iterator cit1=cit0+1; cit1!=last; ++cit1) {
779 const ex & r1 = (*cit1).rest;
780 const ex & c1 = (*cit1).coeff;
781 sum.push_back(a.combine_ex_with_coeff_to_pair((new mul(r,r1))->setflag(status_flags::dynallocated),
782 _num2().mul(ex_to_numeric(c)).mul_dyn(ex_to_numeric(c1))));
786 GINAC_ASSERT(sum.size()==(a.seq.size()*(a.seq.size()+1))/2);
788 // second part: add terms coming from overall_factor (if != 0)
789 if (!a.overall_coeff.is_zero()) {
790 for (epvector::const_iterator cit=a.seq.begin(); cit!=a.seq.end(); ++cit) {
791 sum.push_back(a.combine_pair_with_coeff_to_pair(*cit,ex_to_numeric(a.overall_coeff).mul_dyn(_num2())));
793 sum.push_back(expair(ex_to_numeric(a.overall_coeff).power_dyn(_num2()),_ex1()));
796 GINAC_ASSERT(sum.size()==(a_nops*(a_nops+1))/2);
798 return (new add(sum))->setflag(status_flags::dynallocated | status_flags::expanded);
801 /** Expand factors of m in m^n where m is a mul and n is and integer
802 * @see power::expand */
803 ex power::expand_mul(const mul & m, const numeric & n) const
809 distrseq.reserve(m.seq.size());
810 epvector::const_iterator last = m.seq.end();
811 epvector::const_iterator cit = m.seq.begin();
813 if (is_ex_exactly_of_type((*cit).rest,numeric)) {
814 distrseq.push_back(m.combine_pair_with_coeff_to_pair(*cit,n));
816 // it is safe not to call mul::combine_pair_with_coeff_to_pair()
817 // since n is an integer
818 distrseq.push_back(expair((*cit).rest, ex_to_numeric((*cit).coeff).mul(n)));
822 return (new mul(distrseq,ex_to_numeric(m.overall_coeff).power_dyn(n)))->setflag(status_flags::dynallocated);
826 ex power::expand_noncommutative(const ex & basis, const numeric & exponent,
827 unsigned options) const
829 ex rest_power = ex(power(basis,exponent.add(_num_1()))).
830 expand(options | expand_options::internal_do_not_expand_power_operands);
832 return ex(mul(rest_power,basis),0).
833 expand(options | expand_options::internal_do_not_expand_mul_operands);
839 ex sqrt(const ex & a)
841 return power(a,_ex1_2());