- prepared for 1.0.13 release
[ginac.git] / ginac / power.cpp
index 6618194..0730e3c 100644 (file)
@@ -3,7 +3,7 @@
  *  Implementation of GiNaC's symbolic exponentiation (basis^exponent). */
 
 /*
- *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany
  *
  *  This program is free software; you can redistribute it and/or modify
  *  it under the terms of the GNU General Public License as published by
 #include "constant.h"
 #include "inifcns.h" // for log() in power::derivative()
 #include "matrix.h"
+#include "indexed.h"
 #include "symbol.h"
 #include "print.h"
 #include "archive.h"
-#include "debugmsg.h"
 #include "utils.h"
 
 namespace GiNaC {
@@ -46,13 +46,10 @@ GINAC_IMPLEMENT_REGISTERED_CLASS(power, basic)
 typedef std::vector<int> intvector;
 
 //////////
-// default ctor, dtor, copy ctor assignment operator and helpers
+// default ctor, dtor, copy ctor, assignment operator and helpers
 //////////
 
-power::power() : inherited(TINFO_power)
-{
-       debugmsg("power default ctor",LOGLEVEL_CONSTRUCT);
-}
+power::power() : inherited(TINFO_power) { }
 
 void power::copy(const power & other)
 {
@@ -75,7 +72,6 @@ DEFAULT_DESTROY(power)
 
 power::power(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 {
-       debugmsg("power ctor from archive_node", LOGLEVEL_CONSTRUCT);
        n.find_ex("basis", basis, sym_lst);
        n.find_ex("exponent", exponent, sym_lst);
 }
@@ -121,8 +117,6 @@ static void print_sym_pow(const print_context & c, const symbol &x, int exp)
 
 void power::print(const print_context & c, unsigned level) const
 {
-       debugmsg("power print", LOGLEVEL_PRINT);
-
        if (is_a<print_tree>(c)) {
 
                inherited::print(c, level);
@@ -131,7 +125,7 @@ void power::print(const print_context & c, unsigned level) const
 
                // Integer powers of symbols are printed in a special, optimized way
                if (exponent.info(info_flags::integer)
-                && (is_exactly_a<symbol>(basis) || is_exactly_a<constant>(basis))) {
+                && (is_a<symbol>(basis) || is_a<constant>(basis))) {
                        int exp = ex_to<numeric>(exponent).to_int();
                        if (exp > 0)
                                c.s << '(';
@@ -146,7 +140,7 @@ void power::print(const print_context & c, unsigned level) const
                        c.s << ')';
 
                // <expr>^-1 is printed as "1.0/<expr>" or with the recip() function of CLN
-               } else if (exponent.compare(_num_1()) == 0) {
+               } else if (exponent.is_equal(_ex_1)) {
                        if (is_a<print_csrc_cl_N>(c))
                                c.s << "recip(";
                        else
@@ -166,38 +160,49 @@ void power::print(const print_context & c, unsigned level) const
                        c.s << ')';
                }
 
+       } else if (is_a<print_python_repr>(c)) {
+
+               c.s << class_name() << '(';
+               basis.print(c);
+               c.s << ',';
+               exponent.print(c);
+               c.s << ')';
+
        } else {
 
-               if (exponent.is_equal(_ex1_2())) {
-                       if (is_a<print_latex>(c))
-                               c.s << "\\sqrt{";
-                       else
-                               c.s << "sqrt(";
+               bool is_tex = is_a<print_latex>(c);
+
+               if (is_tex && is_exactly_a<numeric>(exponent) && ex_to<numeric>(exponent).is_negative()) {
+
+                       // Powers with negative numeric exponents are printed as fractions in TeX
+                       c.s << "\\frac{1}{";
+                       power(basis, -exponent).eval().print(c);
+                       c.s << "}";
+
+               } else if (exponent.is_equal(_ex1_2)) {
+
+                       // Square roots are printed in a special way
+                       c.s << (is_tex ? "\\sqrt{" : "sqrt(");
                        basis.print(c);
-                       if (is_a<print_latex>(c))
-                               c.s << '}';
-                       else
-                               c.s << ')';
+                       c.s << (is_tex ? '}' : ')');
+
                } else {
-                       if (precedence() <= level) {
-                               if (is_a<print_latex>(c))
-                                       c.s << "{(";
-                               else
-                                       c.s << "(";
-                       }
+
+                       // Ordinary output of powers using '^' or '**'
+                       if (precedence() <= level)
+                               c.s << (is_tex ? "{(" : "(");
                        basis.print(c, precedence());
-                       c.s << '^';
-                       if (is_a<print_latex>(c))
+                       if (is_a<print_python>(c))
+                               c.s << "**";
+                       else
+                               c.s << '^';
+                       if (is_tex)
                                c.s << '{';
                        exponent.print(c, precedence());
-                       if (is_a<print_latex>(c))
+                       if (is_tex)
                                c.s << '}';
-                       if (precedence() <= level) {
-                               if (is_a<print_latex>(c))
-                                       c.s << ")}";
-                               else
-                                       c.s << ')';
-                       }
+                       if (precedence() <= level)
+                               c.s << (is_tex ? ")}" : ")");
                }
        }
 }
@@ -240,49 +245,59 @@ ex power::map(map_function & f) const
 
 int power::degree(const ex & s) const
 {
-       if (is_ex_exactly_of_type(exponent, numeric) && ex_to<numeric>(exponent).is_integer()) {
+       if (is_equal(ex_to<basic>(s)))
+               return 1;
+       else if (is_ex_exactly_of_type(exponent, numeric) && ex_to<numeric>(exponent).is_integer()) {
                if (basis.is_equal(s))
                        return ex_to<numeric>(exponent).to_int();
                else
                        return basis.degree(s) * ex_to<numeric>(exponent).to_int();
-       }
-       return 0;
+       } else if (basis.has(s))
+               throw(std::runtime_error("power::degree(): undefined degree because of non-integer exponent"));
+       else
+               return 0;
 }
 
 int power::ldegree(const ex & s) const 
 {
-       if (is_ex_exactly_of_type(exponent, numeric) && ex_to<numeric>(exponent).is_integer()) {
+       if (is_equal(ex_to<basic>(s)))
+               return 1;
+       else if (is_ex_exactly_of_type(exponent, numeric) && ex_to<numeric>(exponent).is_integer()) {
                if (basis.is_equal(s))
                        return ex_to<numeric>(exponent).to_int();
                else
                        return basis.ldegree(s) * ex_to<numeric>(exponent).to_int();
-       }
-       return 0;
+       } else if (basis.has(s))
+               throw(std::runtime_error("power::ldegree(): undefined degree because of non-integer exponent"));
+       else
+               return 0;
 }
 
 ex power::coeff(const ex & s, int n) const
 {
-       if (!basis.is_equal(s)) {
+       if (is_equal(ex_to<basic>(s)))
+               return n==1 ? _ex1 : _ex0;
+       else if (!basis.is_equal(s)) {
                // basis not equal to s
                if (n == 0)
                        return *this;
                else
-                       return _ex0();
+                       return _ex0;
        } else {
                // basis equal to s
                if (is_ex_exactly_of_type(exponent, numeric) && ex_to<numeric>(exponent).is_integer()) {
                        // integer exponent
                        int int_exp = ex_to<numeric>(exponent).to_int();
                        if (n == int_exp)
-                               return _ex1();
+                               return _ex1;
                        else
-                               return _ex0();
+                               return _ex0;
                } else {
                        // non-integer exponents are treated as zero
                        if (n == 0)
                                return *this;
                        else
-                               return _ex0();
+                               return _ex0;
                }
        }
 }
@@ -303,8 +318,6 @@ ex power::coeff(const ex & s, int n) const
  *  @param level cut-off in recursive evaluation */
 ex power::eval(int level) const
 {
-       debugmsg("power eval",LOGLEVEL_MEMBER_FUNCTION);
-       
        if ((level==1) && (flags & status_flags::evaluated))
                return *this;
        else if (level == -max_recursion_level)
@@ -332,11 +345,11 @@ ex power::eval(int level) const
                if (ebasis.is_zero())
                        throw (std::domain_error("power::eval(): pow(0,0) is undefined"));
                else
-                       return _ex1();
+                       return _ex1;
        }
        
        // ^(x,1) -> x
-       if (eexponent.is_equal(_ex1()))
+       if (eexponent.is_equal(_ex1))
                return ebasis;
 
        // ^(0,c1) -> 0 or exception  (depending on real value of c1)
@@ -346,12 +359,12 @@ ex power::eval(int level) const
                else if ((num_exponent->real()).is_negative())
                        throw (pole_error("power::eval(): division by zero",1));
                else
-                       return _ex0();
+                       return _ex0;
        }
 
        // ^(1,x) -> 1
-       if (ebasis.is_equal(_ex1()))
-               return _ex1();
+       if (ebasis.is_equal(_ex1))
+               return _ex1;
 
        if (exponent_is_numerical) {
 
@@ -420,7 +433,7 @@ ex power::eval(int level) const
                        if (is_ex_exactly_of_type(sub_exponent,numeric)) {
                                const numeric & num_sub_exponent = ex_to<numeric>(sub_exponent);
                                GINAC_ASSERT(num_sub_exponent!=numeric(1));
-                               if (num_exponent->is_integer() || (abs(num_sub_exponent) - _num1()).is_negative())
+                               if (num_exponent->is_integer() || (abs(num_sub_exponent) - _num1).is_negative())
                                        return power(sub_basis,num_sub_exponent.mul(*num_exponent));
                        }
                }
@@ -435,21 +448,21 @@ ex power::eval(int level) const
                if (is_ex_exactly_of_type(ebasis,mul)) {
                        GINAC_ASSERT(!num_exponent->is_integer()); // should have been handled above
                        const mul & mulref = ex_to<mul>(ebasis);
-                       if (!mulref.overall_coeff.is_equal(_ex1())) {
+                       if (!mulref.overall_coeff.is_equal(_ex1)) {
                                const numeric & num_coeff = ex_to<numeric>(mulref.overall_coeff);
                                if (num_coeff.is_real()) {
                                        if (num_coeff.is_positive()) {
                                                mul *mulp = new mul(mulref);
-                                               mulp->overall_coeff = _ex1();
+                                               mulp->overall_coeff = _ex1;
                                                mulp->clearflag(status_flags::evaluated);
                                                mulp->clearflag(status_flags::hash_calculated);
                                                return (new mul(power(*mulp,exponent),
                                                                power(num_coeff,*num_exponent)))->setflag(status_flags::dynallocated);
                                        } else {
-                                               GINAC_ASSERT(num_coeff.compare(_num0())<0);
-                                               if (num_coeff.compare(_num_1())!=0) {
+                                               GINAC_ASSERT(num_coeff.compare(_num0)<0);
+                                               if (!num_coeff.is_equal(_num_1)) {
                                                        mul *mulp = new mul(mulref);
-                                                       mulp->overall_coeff = _ex_1();
+                                                       mulp->overall_coeff = _ex_1;
                                                        mulp->clearflag(status_flags::evaluated);
                                                        mulp->clearflag(status_flags::hash_calculated);
                                                        return (new mul(power(*mulp,exponent),
@@ -478,8 +491,6 @@ ex power::eval(int level) const
 
 ex power::evalf(int level) const
 {
-       debugmsg("power evalf",LOGLEVEL_MEMBER_FUNCTION);
-       
        ex ebasis;
        ex eexponent;
        
@@ -490,7 +501,7 @@ ex power::evalf(int level) const
                throw(std::runtime_error("max recursion level reached"));
        } else {
                ebasis = basis.evalf(level-1);
-               if (!is_ex_exactly_of_type(exponent,numeric))
+               if (!is_exactly_a<numeric>(exponent))
                        eexponent = exponent.evalf(level-1);
                else
                        eexponent = exponent;
@@ -538,20 +549,20 @@ ex power::derivative(const symbol & s) const
                // D(b^r) = r * b^(r-1) * D(b) (faster than the formula below)
                epvector newseq;
                newseq.reserve(2);
-               newseq.push_back(expair(basis, exponent - _ex1()));
-               newseq.push_back(expair(basis.diff(s), _ex1()));
+               newseq.push_back(expair(basis, exponent - _ex1));
+               newseq.push_back(expair(basis.diff(s), _ex1));
                return mul(newseq, exponent);
        } else {
                // D(b^e) = b^e * (D(e)*ln(b) + e*D(b)/b)
                return mul(*this,
                           add(mul(exponent.diff(s), log(basis)),
-                          mul(mul(exponent, basis.diff(s)), power(basis, _ex_1()))));
+                          mul(mul(exponent, basis.diff(s)), power(basis, _ex_1))));
        }
 }
 
 int power::compare_same_type(const basic & other) const
 {
-       GINAC_ASSERT(is_exactly_of_type(other, power));
+       GINAC_ASSERT(is_exactly_a<power>(other));
        const power &o = static_cast<const power &>(other);
 
        int cmpval = basis.compare(o.basis);
@@ -645,89 +656,90 @@ ex power::expand(unsigned options) const
 // non-virtual functions in this class
 //////////
 
-/** expand a^n where a is an add and n is an integer.
+/** expand a^n where a is an add and n is a positive integer.
  *  @see power::expand */
 ex power::expand_add(const add & a, int n) const
 {
        if (n==2)
                return expand_add_2(a);
-       
-       int m = a.nops();
-       exvector sum;
-       sum.reserve((n+1)*(m-1));
+
+       const int m = a.nops();
+       exvector result;
+       // The number of terms will be the number of combinatorial compositions,
+       // i.e. the number of unordered arrangement of m nonnegative integers
+       // which sum up to n.  It is frequently written as C_n(m) and directly
+       // related with binomial coefficients:
+       result.reserve(binomial(numeric(n+m-1), numeric(m-1)).to_int());
        intvector k(m-1);
        intvector k_cum(m-1); // k_cum[l]:=sum(i=0,l,k[l]);
        intvector upper_limit(m-1);
        int l;
-       
-       for (int l=0; l<m-1; l++) {
+
+       for (int l=0; l<m-1; ++l) {
                k[l] = 0;
                k_cum[l] = 0;
                upper_limit[l] = n;
        }
-       
+
        while (true) {
                exvector term;
                term.reserve(m+1);
-               for (l=0; l<m-1; l++) {
+               for (l=0; l<m-1; ++l) {
                        const ex & b = a.op(l);
-                       GINAC_ASSERT(!is_ex_exactly_of_type(b,add));
-                       GINAC_ASSERT(!is_ex_exactly_of_type(b,power) ||
-                                    !is_ex_exactly_of_type(ex_to<power>(b).exponent,numeric) ||
+                       GINAC_ASSERT(!is_exactly_a<add>(b));
+                       GINAC_ASSERT(!is_exactly_a<power>(b) ||
+                                    !is_exactly_a<numeric>(ex_to<power>(b).exponent) ||
                                     !ex_to<numeric>(ex_to<power>(b).exponent).is_pos_integer() ||
-                                    !is_ex_exactly_of_type(ex_to<power>(b).basis,add) ||
-                                    !is_ex_exactly_of_type(ex_to<power>(b).basis,mul) ||
-                                    !is_ex_exactly_of_type(ex_to<power>(b).basis,power));
+                                    !is_exactly_a<add>(ex_to<power>(b).basis) ||
+                                    !is_exactly_a<mul>(ex_to<power>(b).basis) ||
+                                    !is_exactly_a<power>(ex_to<power>(b).basis));
                        if (is_ex_exactly_of_type(b,mul))
                                term.push_back(expand_mul(ex_to<mul>(b),numeric(k[l])));
                        else
                                term.push_back(power(b,k[l]));
                }
-               
+
                const ex & b = a.op(l);
-               GINAC_ASSERT(!is_ex_exactly_of_type(b,add));
-               GINAC_ASSERT(!is_ex_exactly_of_type(b,power) ||
-                            !is_ex_exactly_of_type(ex_to<power>(b).exponent,numeric) ||
+               GINAC_ASSERT(!is_exactly_a<add>(b));
+               GINAC_ASSERT(!is_exactly_a<power>(b) ||
+                            !is_exactly_a<numeric>(ex_to<power>(b).exponent) ||
                             !ex_to<numeric>(ex_to<power>(b).exponent).is_pos_integer() ||
-                            !is_ex_exactly_of_type(ex_to<power>(b).basis,add) ||
-                            !is_ex_exactly_of_type(ex_to<power>(b).basis,mul) ||
-                            !is_ex_exactly_of_type(ex_to<power>(b).basis,power));
+                            !is_exactly_a<add>(ex_to<power>(b).basis) ||
+                            !is_exactly_a<mul>(ex_to<power>(b).basis) ||
+                            !is_exactly_a<power>(ex_to<power>(b).basis));
                if (is_ex_exactly_of_type(b,mul))
                        term.push_back(expand_mul(ex_to<mul>(b),numeric(n-k_cum[m-2])));
                else
                        term.push_back(power(b,n-k_cum[m-2]));
-               
+
                numeric f = binomial(numeric(n),numeric(k[0]));
-               for (l=1; l<m-1; l++)
+               for (l=1; l<m-1; ++l)
                        f *= binomial(numeric(n-k_cum[l-1]),numeric(k[l]));
-               
+
                term.push_back(f);
-               
-               // TODO: Can we optimize this?  Alex seemed to think so...
-               sum.push_back((new mul(term))->setflag(status_flags::dynallocated));
-               
+
+               result.push_back((new mul(term))->setflag(status_flags::dynallocated));
+
                // increment k[]
                l = m-2;
                while ((l>=0) && ((++k[l])>upper_limit[l])) {
-                       k[l] = 0;    
+                       k[l] = 0;
                        --l;
                }
                if (l<0) break;
-               
+
                // recalc k_cum[] and upper_limit[]
-               if (l==0)
-                       k_cum[0] = k[0];
-               else
-                       k_cum[l] = k_cum[l-1]+k[l];
-               
-               for (int i=l+1; i<m-1; i++)
+               k_cum[l] = (l==0 ? k[0] : k_cum[l-1]+k[l]);
+
+               for (int i=l+1; i<m-1; ++i)
                        k_cum[i] = k_cum[i-1]+k[i];
-               
-               for (int i=l+1; i<m-1; i++)
+
+               for (int i=l+1; i<m-1; ++i)
                        upper_limit[i] = n-k_cum[i-1];
        }
-       return (new add(sum))->setflag(status_flags::dynallocated |
-                                      status_flags::expanded );
+
+       return (new add(result))->setflag(status_flags::dynallocated |
+                                         status_flags::expanded);
 }
 
 
@@ -739,36 +751,36 @@ ex power::expand_add_2(const add & a) const
        unsigned a_nops = a.nops();
        sum.reserve((a_nops*(a_nops+1))/2);
        epvector::const_iterator last = a.seq.end();
-       
+
        // power(+(x,...,z;c),2)=power(+(x,...,z;0),2)+2*c*+(x,...,z;0)+c*c
        // first part: ignore overall_coeff and expand other terms
        for (epvector::const_iterator cit0=a.seq.begin(); cit0!=last; ++cit0) {
                const ex & r = cit0->rest;
                const ex & c = cit0->coeff;
                
-               GINAC_ASSERT(!is_ex_exactly_of_type(r,add));
-               GINAC_ASSERT(!is_ex_exactly_of_type(r,power) ||
-                            !is_ex_exactly_of_type(ex_to<power>(r).exponent,numeric) ||
+               GINAC_ASSERT(!is_exactly_a<add>(r));
+               GINAC_ASSERT(!is_exactly_a<power>(r) ||
+                            !is_exactly_a<numeric>(ex_to<power>(r).exponent) ||
                             !ex_to<numeric>(ex_to<power>(r).exponent).is_pos_integer() ||
-                            !is_ex_exactly_of_type(ex_to<power>(r).basis,add) ||
-                            !is_ex_exactly_of_type(ex_to<power>(r).basis,mul) ||
-                            !is_ex_exactly_of_type(ex_to<power>(r).basis,power));
+                            !is_exactly_a<add>(ex_to<power>(r).basis) ||
+                            !is_exactly_a<mul>(ex_to<power>(r).basis) ||
+                            !is_exactly_a<power>(ex_to<power>(r).basis));
                
-               if (are_ex_trivially_equal(c,_ex1())) {
+               if (are_ex_trivially_equal(c,_ex1)) {
                        if (is_ex_exactly_of_type(r,mul)) {
-                               sum.push_back(expair(expand_mul(ex_to<mul>(r),_num2()),
-                                                    _ex1()));
+                               sum.push_back(expair(expand_mul(ex_to<mul>(r),_num2),
+                                                    _ex1));
                        } else {
-                               sum.push_back(expair((new power(r,_ex2()))->setflag(status_flags::dynallocated),
-                                                    _ex1()));
+                               sum.push_back(expair((new power(r,_ex2))->setflag(status_flags::dynallocated),
+                                                    _ex1));
                        }
                } else {
                        if (is_ex_exactly_of_type(r,mul)) {
-                               sum.push_back(expair(expand_mul(ex_to<mul>(r),_num2()),
-                                                    ex_to<numeric>(c).power_dyn(_num2())));
+                               sum.push_back(a.combine_ex_with_coeff_to_pair(expand_mul(ex_to<mul>(r),_num2),
+                                                    ex_to<numeric>(c).power_dyn(_num2)));
                        } else {
-                               sum.push_back(expair((new power(r,_ex2()))->setflag(status_flags::dynallocated),
-                                                    ex_to<numeric>(c).power_dyn(_num2())));
+                               sum.push_back(a.combine_ex_with_coeff_to_pair((new power(r,_ex2))->setflag(status_flags::dynallocated),
+                                                    ex_to<numeric>(c).power_dyn(_num2)));
                        }
                }
                        
@@ -776,7 +788,7 @@ ex power::expand_add_2(const add & a) const
                        const ex & r1 = cit1->rest;
                        const ex & c1 = cit1->coeff;
                        sum.push_back(a.combine_ex_with_coeff_to_pair((new mul(r,r1))->setflag(status_flags::dynallocated),
-                                                                     _num2().mul(ex_to<numeric>(c)).mul_dyn(ex_to<numeric>(c1))));
+                                                                     _num2.mul(ex_to<numeric>(c)).mul_dyn(ex_to<numeric>(c1))));
                }
        }
        
@@ -786,10 +798,10 @@ ex power::expand_add_2(const add & a) const
        if (!a.overall_coeff.is_zero()) {
                epvector::const_iterator i = a.seq.begin(), end = a.seq.end();
                while (i != end) {
-                       sum.push_back(a.combine_pair_with_coeff_to_pair(*i, ex_to<numeric>(a.overall_coeff).mul_dyn(_num2())));
+                       sum.push_back(a.combine_pair_with_coeff_to_pair(*i, ex_to<numeric>(a.overall_coeff).mul_dyn(_num2)));
                        ++i;
                }
-               sum.push_back(expair(ex_to<numeric>(a.overall_coeff).power_dyn(_num2()),_ex1()));
+               sum.push_back(expair(ex_to<numeric>(a.overall_coeff).power_dyn(_num2),_ex1));
        }
        
        GINAC_ASSERT(sum.size()==(a_nops*(a_nops+1))/2);
@@ -797,35 +809,30 @@ ex power::expand_add_2(const add & a) const
        return (new add(sum))->setflag(status_flags::dynallocated | status_flags::expanded);
 }
 
-/** Expand factors of m in m^n where m is a mul and n is and integer
+/** Expand factors of m in m^n where m is a mul and n is and integer.
  *  @see power::expand */
 ex power::expand_mul(const mul & m, const numeric & n) const
 {
+       GINAC_ASSERT(n.is_integer());
+
        if (n.is_zero())
-               return _ex1();
-       
+               return _ex1;
+
        epvector distrseq;
        distrseq.reserve(m.seq.size());
        epvector::const_iterator last = m.seq.end();
        epvector::const_iterator cit = m.seq.begin();
        while (cit!=last) {
-               if (is_ex_exactly_of_type((*cit).rest,numeric)) {
-                       distrseq.push_back(m.combine_pair_with_coeff_to_pair(*cit,n));
+               if (is_ex_exactly_of_type(cit->rest,numeric)) {
+                       distrseq.push_back(m.combine_pair_with_coeff_to_pair(*cit, n));
                } else {
                        // it is safe not to call mul::combine_pair_with_coeff_to_pair()
                        // since n is an integer
-                       distrseq.push_back(expair((*cit).rest, ex_to<numeric>((*cit).coeff).mul(n)));
+                       distrseq.push_back(expair(cit->rest, ex_to<numeric>(cit->coeff).mul(n)));
                }
                ++cit;
        }
-       return (new mul(distrseq,ex_to<numeric>(m.overall_coeff).power_dyn(n)))->setflag(status_flags::dynallocated);
-}
-
-// helper function
-
-ex sqrt(const ex & a)
-{
-       return power(a,_ex1_2());
+       return (new mul(distrseq, ex_to<numeric>(m.overall_coeff).power_dyn(n)))->setflag(status_flags::dynallocated);
 }
 
 } // namespace GiNaC