]> www.ginac.de Git - ginac.git/blobdiff - ginac/power.cpp
* Fix a bitch of a bug where 1<I (and all other relationals) returned true.
[ginac.git] / ginac / power.cpp
index eee137bb0cddaebf3c096bc5e03fbdeaa63ba570..47efc2fd3806583b0e61197354111f090b11755e 100644 (file)
 #include "expairseq.h"
 #include "add.h"
 #include "mul.h"
+#include "ncmul.h"
 #include "numeric.h"
-#include "inifcns.h"
-#include "relational.h"
+#include "constant.h"
+#include "inifcns.h" // for log() in power::derivative()
+#include "matrix.h"
 #include "symbol.h"
 #include "print.h"
 #include "archive.h"
@@ -47,7 +49,7 @@ typedef std::vector<int> intvector;
 // default ctor, dtor, copy ctor assignment operator and helpers
 //////////
 
-power::power() : basic(TINFO_power)
+power::power() : inherited(TINFO_power)
 {
        debugmsg("power default ctor",LOGLEVEL_CONSTRUCT);
 }
@@ -65,18 +67,16 @@ DEFAULT_DESTROY(power)
 // other ctors
 //////////
 
-power::power(const ex & lh, const ex & rh) : basic(TINFO_power), basis(lh), exponent(rh)
+power::power(const ex & lh, const ex & rh) : inherited(TINFO_power), basis(lh), exponent(rh)
 {
        debugmsg("power ctor from ex,ex",LOGLEVEL_CONSTRUCT);
-       GINAC_ASSERT(basis.return_type()==return_types::commutative);
 }
 
 /** Ctor from an ex and a bare numeric.  This is somewhat more efficient than
  *  the normal ctor from two ex whenever it can be used. */
-power::power(const ex & lh, const numeric & rh) : basic(TINFO_power), basis(lh), exponent(rh)
+power::power(const ex & lh, const numeric & rh) : inherited(TINFO_power), basis(lh), exponent(rh)
 {
        debugmsg("power ctor from ex,numeric",LOGLEVEL_CONSTRUCT);
-       GINAC_ASSERT(basis.return_type()==return_types::commutative);
 }
 
 //////////
@@ -133,76 +133,80 @@ void power::print(const print_context & c, unsigned level) const
 {
        debugmsg("power print", LOGLEVEL_PRINT);
 
-       if (is_of_type(c, print_tree)) {
+       if (is_a<print_tree>(c)) {
 
                inherited::print(c, level);
 
-       } else if (is_of_type(c, print_csrc)) {
+       } else if (is_a<print_csrc>(c)) {
 
                // Integer powers of symbols are printed in a special, optimized way
                if (exponent.info(info_flags::integer)
-                && (is_ex_exactly_of_type(basis, symbol) || is_ex_exactly_of_type(basis, constant))) {
-                       int exp = ex_to_numeric(exponent).to_int();
+                && (is_exactly_a<symbol>(basis) || is_exactly_a<constant>(basis))) {
+                       int exp = ex_to<numeric>(exponent).to_int();
                        if (exp > 0)
-                               c.s << "(";
+                               c.s << '(';
                        else {
                                exp = -exp;
-                               if (is_of_type(c, print_csrc_cl_N))
+                               if (is_a<print_csrc_cl_N>(c))
                                        c.s << "recip(";
                                else
                                        c.s << "1.0/(";
                        }
-                       print_sym_pow(c, ex_to_symbol(basis), exp);
-                       c.s << ")";
+                       print_sym_pow(c, ex_to<symbol>(basis), exp);
+                       c.s << ')';
 
                // <expr>^-1 is printed as "1.0/<expr>" or with the recip() function of CLN
                } else if (exponent.compare(_num_1()) == 0) {
-                       if (is_of_type(c, print_csrc_cl_N))
+                       if (is_a<print_csrc_cl_N>(c))
                                c.s << "recip(";
                        else
                                c.s << "1.0/(";
                        basis.print(c);
-                       c.s << ")";
+                       c.s << ')';
 
                // Otherwise, use the pow() or expt() (CLN) functions
                } else {
-                       if (is_of_type(c, print_csrc_cl_N))
+                       if (is_a<print_csrc_cl_N>(c))
                                c.s << "expt(";
                        else
                                c.s << "pow(";
                        basis.print(c);
-                       c.s << ",";
+                       c.s << ',';
                        exponent.print(c);
-                       c.s << ")";
+                       c.s << ')';
                }
 
        } else {
 
                if (exponent.is_equal(_ex1_2())) {
-                       if (is_of_type(c, print_latex))
+                       if (is_a<print_latex>(c))
                                c.s << "\\sqrt{";
                        else
                                c.s << "sqrt(";
                        basis.print(c);
-                       if (is_of_type(c, print_latex))
-                               c.s << "}";
+                       if (is_a<print_latex>(c))
+                               c.s << '}';
                        else
-                               c.s << ")";
+                               c.s << ')';
                } else {
                        if (precedence() <= level) {
-                               if (is_of_type(c, print_latex))
+                               if (is_a<print_latex>(c))
                                        c.s << "{(";
                                else
                                        c.s << "(";
                        }
                        basis.print(c, precedence());
-                       c.s << "^";
+                       c.s << '^';
+                       if (is_a<print_latex>(c))
+                               c.s << '{';
                        exponent.print(c, precedence());
+                       if (is_a<print_latex>(c))
+                               c.s << '}';
                        if (precedence() <= level) {
-                               if (is_of_type(c, print_latex))
+                               if (is_a<print_latex>(c))
                                        c.s << ")}";
                                else
-                                       c.s << ")";
+                                       c.s << ')';
                        }
                }
        }
@@ -239,16 +243,21 @@ ex & power::let_op(int i)
        return i==0 ? basis : exponent;
 }
 
+ex power::map(map_function & f) const
+{
+       return (new power(f(basis), f(exponent)))->setflag(status_flags::dynallocated);
+}
+
 int power::degree(const ex & s) const
 {
        if (is_exactly_of_type(*exponent.bp,numeric)) {
                if (basis.is_equal(s)) {
-                       if (ex_to_numeric(exponent).is_integer())
-                               return ex_to_numeric(exponent).to_int();
+                       if (ex_to<numeric>(exponent).is_integer())
+                               return ex_to<numeric>(exponent).to_int();
                        else
                                return 0;
                } else
-                       return basis.degree(s) * ex_to_numeric(exponent).to_int();
+                       return basis.degree(s) * ex_to<numeric>(exponent).to_int();
        }
        return 0;
 }
@@ -257,12 +266,12 @@ int power::ldegree(const ex & s) const
 {
        if (is_exactly_of_type(*exponent.bp,numeric)) {
                if (basis.is_equal(s)) {
-                       if (ex_to_numeric(exponent).is_integer())
-                               return ex_to_numeric(exponent).to_int();
+                       if (ex_to<numeric>(exponent).is_integer())
+                               return ex_to<numeric>(exponent).to_int();
                        else
                                return 0;
                } else
-                       return basis.ldegree(s) * ex_to_numeric(exponent).to_int();
+                       return basis.ldegree(s) * ex_to<numeric>(exponent).to_int();
        }
        return 0;
 }
@@ -277,9 +286,9 @@ ex power::coeff(const ex & s, int n) const
                        return _ex0();
        } else {
                // basis equal to s
-               if (is_exactly_of_type(*exponent.bp, numeric) && ex_to_numeric(exponent).is_integer()) {
+               if (is_exactly_of_type(*exponent.bp, numeric) && ex_to<numeric>(exponent).is_integer()) {
                        // integer exponent
-                       int int_exp = ex_to_numeric(exponent).to_int();
+                       int int_exp = ex_to<numeric>(exponent).to_int();
                        if (n == int_exp)
                                return _ex1();
                        else
@@ -316,17 +325,17 @@ ex power::eval(int level) const
        const ex & ebasis    = level==1 ? basis    : basis.eval(level-1);
        const ex & eexponent = level==1 ? exponent : exponent.eval(level-1);
        
-       bool basis_is_numerical = 0;
-       bool exponent_is_numerical = 0;
+       bool basis_is_numerical = false;
+       bool exponent_is_numerical = false;
        numeric * num_basis;
        numeric * num_exponent;
        
        if (is_exactly_of_type(*ebasis.bp,numeric)) {
-               basis_is_numerical = 1;
+               basis_is_numerical = true;
                num_basis = static_cast<numeric *>(ebasis.bp);
        }
        if (is_exactly_of_type(*eexponent.bp,numeric)) {
-               exponent_is_numerical = 1;
+               exponent_is_numerical = true;
                num_exponent = static_cast<numeric *>(eexponent.bp);
        }
        
@@ -356,89 +365,99 @@ ex power::eval(int level) const
        if (ebasis.is_equal(_ex1()))
                return _ex1();
        
-       if (basis_is_numerical && exponent_is_numerical) {
+       if (exponent_is_numerical) {
+
                // ^(c1,c2) -> c1^c2 (c1, c2 numeric(),
                // except if c1,c2 are rational, but c1^c2 is not)
-               bool basis_is_crational = num_basis->is_crational();
-               bool exponent_is_crational = num_exponent->is_crational();
-               numeric res = num_basis->power(*num_exponent);
+               if (basis_is_numerical) {
+                       bool basis_is_crational = num_basis->is_crational();
+                       bool exponent_is_crational = num_exponent->is_crational();
+                       numeric res = num_basis->power(*num_exponent);
                
-               if ((!basis_is_crational || !exponent_is_crational)
-                       || res.is_crational()) {
-                       return res;
-               }
-               GINAC_ASSERT(!num_exponent->is_integer());  // has been handled by now
-               // ^(c1,n/m) -> *(c1^q,c1^(n/m-q)), 0<(n/m-h)<1, q integer
-               if (basis_is_crational && exponent_is_crational
-                       && num_exponent->is_real()
-                       && !num_exponent->is_integer()) {
-                       numeric n = num_exponent->numer();
-                       numeric m = num_exponent->denom();
-                       numeric r;
-                       numeric q = iquo(n, m, r);
-                       if (r.is_negative()) {
-                               r = r.add(m);
-                               q = q.sub(_num1());
+                       if ((!basis_is_crational || !exponent_is_crational)
+                               || res.is_crational()) {
+                               return res;
                        }
-                       if (q.is_zero())  // the exponent was in the allowed range 0<(n/m)<1
-                               return this->hold();
-                       else {
-                               epvector res;
-                               res.push_back(expair(ebasis,r.div(m)));
-                               return (new mul(res,ex(num_basis->power_dyn(q))))->setflag(status_flags::dynallocated | status_flags::evaluated);
+                       GINAC_ASSERT(!num_exponent->is_integer());  // has been handled by now
+
+                       // ^(c1,n/m) -> *(c1^q,c1^(n/m-q)), 0<(n/m-h)<1, q integer
+                       if (basis_is_crational && exponent_is_crational
+                               && num_exponent->is_real()
+                               && !num_exponent->is_integer()) {
+                               numeric n = num_exponent->numer();
+                               numeric m = num_exponent->denom();
+                               numeric r;
+                               numeric q = iquo(n, m, r);
+                               if (r.is_negative()) {
+                                       r = r.add(m);
+                                       q = q.sub(_num1());
+                               }
+                               if (q.is_zero())  // the exponent was in the allowed range 0<(n/m)<1
+                                       return this->hold();
+                               else {
+                                       epvector res;
+                                       res.push_back(expair(ebasis,r.div(m)));
+                                       return (new mul(res,ex(num_basis->power_dyn(q))))->setflag(status_flags::dynallocated | status_flags::evaluated);
+                               }
                        }
                }
-       }
        
-       // ^(^(x,c1),c2) -> ^(x,c1*c2)
-       // (c1, c2 numeric(), c2 integer or -1 < c1 <= 1,
-       // case c1==1 should not happen, see below!)
-       if (exponent_is_numerical && is_ex_exactly_of_type(ebasis,power)) {
-               const power & sub_power = ex_to_power(ebasis);
-               const ex & sub_basis = sub_power.basis;
-               const ex & sub_exponent = sub_power.exponent;
-               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)<1)
-                               return power(sub_basis,num_sub_exponent.mul(*num_exponent));
+               // ^(^(x,c1),c2) -> ^(x,c1*c2)
+               // (c1, c2 numeric(), c2 integer or -1 < c1 <= 1,
+               // case c1==1 should not happen, see below!)
+               if (is_ex_exactly_of_type(ebasis,power)) {
+                       const power & sub_power = ex_to<power>(ebasis);
+                       const ex & sub_basis = sub_power.basis;
+                       const ex & sub_exponent = sub_power.exponent;
+                       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())
+                                       return power(sub_basis,num_sub_exponent.mul(*num_exponent));
+                       }
                }
-       }
        
-       // ^(*(x,y,z),c1) -> *(x^c1,y^c1,z^c1) (c1 integer)
-       if (exponent_is_numerical && num_exponent->is_integer() &&
-               is_ex_exactly_of_type(ebasis,mul)) {
-               return expand_mul(ex_to_mul(ebasis), *num_exponent);
-       }
+               // ^(*(x,y,z),c1) -> *(x^c1,y^c1,z^c1) (c1 integer)
+               if (num_exponent->is_integer() && is_ex_exactly_of_type(ebasis,mul)) {
+                       return expand_mul(ex_to<mul>(ebasis), *num_exponent);
+               }
        
-       // ^(*(...,x;c1),c2) -> ^(*(...,x;1),c2)*c1^c2 (c1, c2 numeric(), c1>0)
-       // ^(*(...,x,c1),c2) -> ^(*(...,x;-1),c2)*(-c1)^c2 (c1, c2 numeric(), c1<0)
-       if (exponent_is_numerical && 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())) {
-                       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->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) {
+               // ^(*(...,x;c1),c2) -> ^(*(...,x;1),c2)*c1^c2 (c1, c2 numeric(), c1>0)
+               // ^(*(...,x,c1),c2) -> ^(*(...,x;-1),c2)*(-c1)^c2 (c1, c2 numeric(), c1<0)
+               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())) {
+                               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 = _ex_1();
+                                               mulp->overall_coeff = _ex1();
                                                mulp->clearflag(status_flags::evaluated);
                                                mulp->clearflag(status_flags::hash_calculated);
                                                return (new mul(power(*mulp,exponent),
-                                                               power(abs(num_coeff),*num_exponent)))->setflag(status_flags::dynallocated);
+                                                               power(num_coeff,*num_exponent)))->setflag(status_flags::dynallocated);
+                                       } else {
+                                               GINAC_ASSERT(num_coeff.compare(_num0())<0);
+                                               if (num_coeff.compare(_num_1())!=0) {
+                                                       mul * mulp = new mul(mulref);
+                                                       mulp->overall_coeff = _ex_1();
+                                                       mulp->clearflag(status_flags::evaluated);
+                                                       mulp->clearflag(status_flags::hash_calculated);
+                                                       return (new mul(power(*mulp,exponent),
+                                                                       power(abs(num_coeff),*num_exponent)))->setflag(status_flags::dynallocated);
+                                               }
                                        }
                                }
                        }
                }
+
+               // ^(nc,c1) -> ncmul(nc,nc,...) (c1 positive integer, unless nc is a matrix)
+               if (num_exponent->is_pos_integer() &&
+                   ebasis.return_type() != return_types::commutative &&
+                   !is_ex_of_type(ebasis,matrix)) {
+                       return ncmul(exvector(num_exponent->to_int(), ebasis), true);
+               }
        }
        
        if (are_ex_trivially_equal(ebasis,basis) &&
@@ -472,17 +491,28 @@ ex power::evalf(int level) const
        return power(ebasis,eexponent);
 }
 
-ex power::subs(const lst & ls, const lst & lr) const
+ex power::evalm(void) const
 {
-       const ex & subsed_basis=basis.subs(ls,lr);
-       const ex & subsed_exponent=exponent.subs(ls,lr);
-
-       if (are_ex_trivially_equal(basis,subsed_basis)&&
-               are_ex_trivially_equal(exponent,subsed_exponent)) {
-               return inherited::subs(ls, lr);
+       ex ebasis = basis.evalm();
+       ex eexponent = exponent.evalm();
+       if (is_ex_of_type(ebasis,matrix)) {
+               if (is_ex_of_type(eexponent,numeric)) {
+                       return (new matrix(ex_to<matrix>(ebasis).pow(eexponent)))->setflag(status_flags::dynallocated);
+               }
        }
-       
-       return power(subsed_basis, subsed_exponent);
+       return (new power(ebasis, eexponent))->setflag(status_flags::dynallocated);
+}
+
+ex power::subs(const lst & ls, const lst & lr, bool no_pattern) const
+{
+       const ex &subsed_basis = basis.subs(ls, lr, no_pattern);
+       const ex &subsed_exponent = exponent.subs(ls, lr, no_pattern);
+
+       if (are_ex_trivially_equal(basis, subsed_basis)
+        && are_ex_trivially_equal(exponent, subsed_exponent))
+               return basic::subs(ls, lr, no_pattern);
+       else
+               return ex(power(subsed_basis, subsed_exponent)).bp->basic::subs(ls, lr, no_pattern);
 }
 
 ex power::simplify_ncmul(const exvector & v) const
@@ -544,7 +574,7 @@ ex power::expand(unsigned options) const
        
        // x^(a+b) -> x^a * x^b
        if (is_ex_exactly_of_type(expanded_exponent, add)) {
-               const add &a = ex_to_add(expanded_exponent);
+               const add &a = ex_to<add>(expanded_exponent);
                exvector distrseq;
                distrseq.reserve(a.seq.size() + 1);
                epvector::const_iterator last = a.seq.end();
@@ -555,11 +585,11 @@ ex power::expand(unsigned options) const
                }
                
                // Make sure that e.g. (x+y)^(2+a) expands the (x+y)^2 factor
-               if (ex_to_numeric(a.overall_coeff).is_integer()) {
-                       const numeric &num_exponent = ex_to_numeric(a.overall_coeff);
+               if (ex_to<numeric>(a.overall_coeff).is_integer()) {
+                       const numeric &num_exponent = ex_to<numeric>(a.overall_coeff);
                        int int_exponent = num_exponent.to_int();
                        if (int_exponent > 0 && is_ex_exactly_of_type(expanded_basis, add))
-                               distrseq.push_back(expand_add(ex_to_add(expanded_basis), int_exponent));
+                               distrseq.push_back(expand_add(ex_to<add>(expanded_basis), int_exponent));
                        else
                                distrseq.push_back(power(expanded_basis, a.overall_coeff));
                } else
@@ -571,7 +601,7 @@ ex power::expand(unsigned options) const
        }
        
        if (!is_ex_exactly_of_type(expanded_exponent, numeric) ||
-               !ex_to_numeric(expanded_exponent).is_integer()) {
+               !ex_to<numeric>(expanded_exponent).is_integer()) {
                if (are_ex_trivially_equal(basis,expanded_basis) && are_ex_trivially_equal(exponent,expanded_exponent)) {
                        return this->hold();
                } else {
@@ -580,16 +610,16 @@ ex power::expand(unsigned options) const
        }
        
        // integer numeric exponent
-       const numeric & num_exponent = ex_to_numeric(expanded_exponent);
+       const numeric & num_exponent = ex_to<numeric>(expanded_exponent);
        int int_exponent = num_exponent.to_int();
        
        // (x+y)^n, n>0
        if (int_exponent > 0 && is_ex_exactly_of_type(expanded_basis,add))
-               return expand_add(ex_to_add(expanded_basis), int_exponent);
+               return expand_add(ex_to<add>(expanded_basis), int_exponent);
        
        // (x*y)^n -> x^n * y^n
        if (is_ex_exactly_of_type(expanded_basis,mul))
-               return expand_mul(ex_to_mul(expanded_basis), num_exponent);
+               return expand_mul(ex_to<mul>(expanded_basis), num_exponent);
        
        // cannot expand further
        if (are_ex_trivially_equal(basis,expanded_basis) && are_ex_trivially_equal(exponent,expanded_exponent))
@@ -636,13 +666,13 @@ ex power::expand_add(const add & a, int n) const
                        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) ||
-                                    !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_ex_exactly_of_type(ex_to<power>(b).exponent,numeric) ||
+                                    !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));
                        if (is_ex_exactly_of_type(b,mul))
-                               term.push_back(expand_mul(ex_to_mul(b),numeric(k[l])));
+                               term.push_back(expand_mul(ex_to<mul>(b),numeric(k[l])));
                        else
                                term.push_back(power(b,k[l]));
                }
@@ -650,13 +680,13 @@ ex power::expand_add(const add & a, int n) const
                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) ||
-                            !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_ex_exactly_of_type(ex_to<power>(b).exponent,numeric) ||
+                            !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));
                if (is_ex_exactly_of_type(b,mul))
-                       term.push_back(expand_mul(ex_to_mul(b),numeric(n-k_cum[m-2])));
+                       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]));
                
@@ -722,15 +752,15 @@ ex power::expand_add_2(const add & a) const
                
                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) ||
-                            !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_ex_exactly_of_type(ex_to<power>(r).exponent,numeric) ||
+                            !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));
                
                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()),
+                               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),
@@ -738,11 +768,11 @@ ex power::expand_add_2(const add & a) const
                        }
                } 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(expair(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())));
+                                                    ex_to<numeric>(c).power_dyn(_num2())));
                        }
                }
                        
@@ -750,7 +780,7 @@ 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))));
                }
        }
        
@@ -759,9 +789,9 @@ ex power::expand_add_2(const add & a) const
        // second part: add terms coming from overall_factor (if != 0)
        if (!a.overall_coeff.is_zero()) {
                for (epvector::const_iterator cit=a.seq.begin(); cit!=a.seq.end(); ++cit) {
-                       sum.push_back(a.combine_pair_with_coeff_to_pair(*cit,ex_to_numeric(a.overall_coeff).mul_dyn(_num2())));
+                       sum.push_back(a.combine_pair_with_coeff_to_pair(*cit,ex_to<numeric>(a.overall_coeff).mul_dyn(_num2())));
                }
-               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);
@@ -786,37 +816,12 @@ ex power::expand_mul(const mul & m, const numeric & n) const
                } 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);
-}
-
-/*
-ex power::expand_commutative_3(const ex & basis, const numeric & exponent,
-                               unsigned options) const
-{
-       // obsolete
-
-       exvector distrseq;
-       epvector splitseq;
-
-       const add & addref=static_cast<const add &>(*basis.bp);
-
-       splitseq=addref.seq;
-       splitseq.pop_back();
-       ex first_operands=add(splitseq);
-       ex last_operand=addref.recombine_pair_to_ex(*(addref.seq.end()-1));
-       
-       int n=exponent.to_int();
-       for (int k=0; k<=n; k++) {
-               distrseq.push_back(binomial(n,k) * power(first_operands,numeric(k))
-                                                * power(last_operand,numeric(n-k)));
-       }
-       return ex((new add(distrseq))->setflag(status_flags::expanded | status_flags::dynallocated)).expand(options);
+       return (new mul(distrseq,ex_to<numeric>(m.overall_coeff).power_dyn(n)))->setflag(status_flags::dynallocated);
 }
-*/
 
 /*
 ex power::expand_noncommutative(const ex & basis, const numeric & exponent,