- prepared for 1.0.13 release
[ginac.git] / ginac / power.cpp
index bed6ed2..0730e3c 100644 (file)
@@ -3,7 +3,7 @@
  *  Implementation of GiNaC's symbolic exponentiation (basis^exponent). */
 
 /*
- *  GiNaC Copyright (C) 1999 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 "expairseq.h"
 #include "add.h"
 #include "mul.h"
+#include "ncmul.h"
 #include "numeric.h"
-#include "relational.h"
+#include "constant.h"
+#include "inifcns.h" // for log() in power::derivative()
+#include "matrix.h"
+#include "indexed.h"
 #include "symbol.h"
-#include "debugmsg.h"
+#include "print.h"
+#include "archive.h"
+#include "utils.h"
 
 namespace GiNaC {
 
-typedef vector<int> intvector;
+GINAC_IMPLEMENT_REGISTERED_CLASS(power, basic)
+
+typedef std::vector<int> intvector;
 
 //////////
-// default constructor, destructor, copy constructor assignment operator and helpers
+// default ctor, dtor, copy ctor, assignment operator and helpers
 //////////
 
-// public
+power::power() : inherited(TINFO_power) { }
 
-power::power() : basic(TINFO_power)
+void power::copy(const power & other)
 {
-    debugmsg("power default constructor",LOGLEVEL_CONSTRUCT);
+       inherited::copy(other);
+       basis = other.basis;
+       exponent = other.exponent;
 }
 
-power::~power()
-{
-    debugmsg("power destructor",LOGLEVEL_DESTRUCT);
-    destroy(0);
-}
+DEFAULT_DESTROY(power)
 
-power::power(power const & other)
-{
-    debugmsg("power copy constructor",LOGLEVEL_CONSTRUCT);
-    copy(other);
-}
+//////////
+// other ctors
+//////////
 
-power const & power::operator=(power const & other)
-{
-    debugmsg("power operator=",LOGLEVEL_ASSIGNMENT);
-    if (this != &other) {
-        destroy(1);
-        copy(other);
-    }
-    return *this;
-}
+// all inlined
 
-// protected
+//////////
+// archiving
+//////////
 
-void power::copy(power const & other)
+power::power(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 {
-    basic::copy(other);
-    basis=other.basis;
-    exponent=other.exponent;
+       n.find_ex("basis", basis, sym_lst);
+       n.find_ex("exponent", exponent, sym_lst);
 }
 
-void power::destroy(bool call_parent)
+void power::archive(archive_node &n) const
 {
-    if (call_parent) basic::destroy(call_parent);
+       inherited::archive(n);
+       n.add_ex("basis", basis);
+       n.add_ex("exponent", exponent);
 }
 
+DEFAULT_UNARCHIVE(power)
+
 //////////
-// other constructors
+// functions overriding virtual functions from base classes
 //////////
 
 // public
 
-power::power(ex const & lh, ex const & rh) : basic(TINFO_power), basis(lh), exponent(rh)
+static void print_sym_pow(const print_context & c, const symbol &x, int exp)
 {
-    debugmsg("power constructor from ex,ex",LOGLEVEL_CONSTRUCT);
-    GINAC_ASSERT(basis.return_type()==return_types::commutative);
+       // Optimal output of integer powers of symbols to aid compiler CSE.
+       // C.f. ISO/IEC 14882:1998, section 1.9 [intro execution], paragraph 15
+       // to learn why such a parenthisation is really necessary.
+       if (exp == 1) {
+               x.print(c);
+       } else if (exp == 2) {
+               x.print(c);
+               c.s << "*";
+               x.print(c);
+       } else if (exp & 1) {
+               x.print(c);
+               c.s << "*";
+               print_sym_pow(c, x, exp-1);
+       } else {
+               c.s << "(";
+               print_sym_pow(c, x, exp >> 1);
+               c.s << ")*(";
+               print_sym_pow(c, x, exp >> 1);
+               c.s << ")";
+       }
 }
 
-power::power(ex const & lh, numeric const & rh) : basic(TINFO_power), basis(lh), exponent(rh)
+void power::print(const print_context & c, unsigned level) const
 {
-    debugmsg("power constructor from ex,numeric",LOGLEVEL_CONSTRUCT);
-    GINAC_ASSERT(basis.return_type()==return_types::commutative);
+       if (is_a<print_tree>(c)) {
+
+               inherited::print(c, level);
+
+       } 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_a<symbol>(basis) || is_a<constant>(basis))) {
+                       int exp = ex_to<numeric>(exponent).to_int();
+                       if (exp > 0)
+                               c.s << '(';
+                       else {
+                               exp = -exp;
+                               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 << ')';
+
+               // <expr>^-1 is printed as "1.0/<expr>" or with the recip() function of CLN
+               } else if (exponent.is_equal(_ex_1)) {
+                       if (is_a<print_csrc_cl_N>(c))
+                               c.s << "recip(";
+                       else
+                               c.s << "1.0/(";
+                       basis.print(c);
+                       c.s << ')';
+
+               // Otherwise, use the pow() or expt() (CLN) functions
+               } else {
+                       if (is_a<print_csrc_cl_N>(c))
+                               c.s << "expt(";
+                       else
+                               c.s << "pow(";
+                       basis.print(c);
+                       c.s << ',';
+                       exponent.print(c);
+                       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 {
+
+               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);
+                       c.s << (is_tex ? '}' : ')');
+
+               } else {
+
+                       // Ordinary output of powers using '^' or '**'
+                       if (precedence() <= level)
+                               c.s << (is_tex ? "{(" : "(");
+                       basis.print(c, precedence());
+                       if (is_a<print_python>(c))
+                               c.s << "**";
+                       else
+                               c.s << '^';
+                       if (is_tex)
+                               c.s << '{';
+                       exponent.print(c, precedence());
+                       if (is_tex)
+                               c.s << '}';
+                       if (precedence() <= level)
+                               c.s << (is_tex ? ")}" : ")");
+               }
+       }
 }
 
-//////////
-// functions overriding virtual functions from bases classes
-//////////
-
-// public
-
-basic * power::duplicate() const
+bool power::info(unsigned inf) const
 {
-    debugmsg("power duplicate",LOGLEVEL_DUPLICATE);
-    return new power(*this);
+       switch (inf) {
+               case info_flags::polynomial:
+               case info_flags::integer_polynomial:
+               case info_flags::cinteger_polynomial:
+               case info_flags::rational_polynomial:
+               case info_flags::crational_polynomial:
+                       return exponent.info(info_flags::nonnegint);
+               case info_flags::rational_function:
+                       return exponent.info(info_flags::integer);
+               case info_flags::algebraic:
+                       return (!exponent.info(info_flags::integer) ||
+                                       basis.info(inf));
+       }
+       return inherited::info(inf);
 }
 
-bool power::info(unsigned inf) const
+unsigned power::nops() const
 {
-    if (inf==info_flags::polynomial || inf==info_flags::integer_polynomial || inf==info_flags::rational_polynomial) {
-        return exponent.info(info_flags::nonnegint);
-    } else if (inf==info_flags::rational_function) {
-        return exponent.info(info_flags::integer);
-    } else {
-        return basic::info(inf);
-    }
+       return 2;
 }
 
-int power::nops() const
+ex & power::let_op(int i)
 {
-    return 2;
+       GINAC_ASSERT(i>=0);
+       GINAC_ASSERT(i<2);
+
+       return i==0 ? basis : exponent;
 }
 
-ex & power::let_op(int const i)
+ex power::map(map_function & f) const
 {
-    GINAC_ASSERT(i>=0);
-    GINAC_ASSERT(i<2);
-
-    return i==0 ? basis : exponent;
+       return (new power(f(basis), f(exponent)))->setflag(status_flags::dynallocated);
 }
 
-int power::degree(symbol const & s) const
+int power::degree(const ex & s) const
 {
-    if (is_exactly_of_type(*exponent.bp,numeric)) {
-       if ((*basis.bp).compare(s)==0)
-            return ex_to_numeric(exponent).to_int();
-        else
-            return basis.degree(s) * ex_to_numeric(exponent).to_int();
-    }
-    return 0;
+       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();
+       } else if (basis.has(s))
+               throw(std::runtime_error("power::degree(): undefined degree because of non-integer exponent"));
+       else
+               return 0;
 }
 
-int power::ldegree(symbol const & s) const 
+int power::ldegree(const ex & s) const 
 {
-    if (is_exactly_of_type(*exponent.bp,numeric)) {
-       if ((*basis.bp).compare(s)==0)
-            return ex_to_numeric(exponent).to_int();
-        else
-            return basis.ldegree(s) * ex_to_numeric(exponent).to_int();
-    }
-    return 0;
+       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();
+       } else if (basis.has(s))
+               throw(std::runtime_error("power::ldegree(): undefined degree because of non-integer exponent"));
+       else
+               return 0;
 }
 
-ex power::coeff(symbol const & s, int const n) const
+ex power::coeff(const ex & s, int n) const
 {
-    if ((*basis.bp).compare(s)!=0) {
-        // basis not equal to s
-        if (n==0) {
-            return *this;
-        } else {
-            return exZERO();
-        }
-    } else if (is_exactly_of_type(*exponent.bp,numeric)&&
-               (static_cast<numeric const &>(*exponent.bp).compare(numeric(n))==0)) {
-        return exONE();
-    }
-
-    return exZERO();
+       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;
+       } 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;
+                       else
+                               return _ex0;
+               } else {
+                       // non-integer exponents are treated as zero
+                       if (n == 0)
+                               return *this;
+                       else
+                               return _ex0;
+               }
+       }
 }
 
+/** Perform automatic term rewriting rules in this class.  In the following
+ *  x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
+ *  stand for such expressions that contain a plain number.
+ *  - ^(x,0) -> 1  (also handles ^(0,0))
+ *  - ^(x,1) -> x
+ *  - ^(0,c) -> 0 or exception  (depending on the real part of c)
+ *  - ^(1,x) -> 1
+ *  - ^(c1,c2) -> *(c1^n,c1^(c2-n))  (so that 0<(c2-n)<1, try to evaluate roots, possibly in numerator and denominator of c1)
+ *  - ^(^(x,c1),c2) -> ^(x,c1*c2)  (c2 integer or -1 < c1 <= 1, case c1=1 should not happen, see below!)
+ *  - ^(*(x,y,z),c) -> *(x^c,y^c,z^c)  (if c integer)
+ *  - ^(*(x,c1),c2) -> ^(x,c2)*c1^c2  (c1>0)
+ *  - ^(*(x,c1),c2) -> ^(-x,c2)*c1^c2  (c1<0)
+ *
+ *  @param level cut-off in recursive evaluation */
 ex power::eval(int level) const
 {
-    // simplifications: ^(x,0) -> 1 (0^0 handled here)
-    //                  ^(x,1) -> x
-    //                  ^(0,x) -> 0 (except if x is real and negative, in which case an exception is thrown)
-    //                  ^(1,x) -> 1
-    //                  ^(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)
-    //                  ^(^(x,c1),c2) -> ^(x,c1*c2) (c1, c2 numeric(), c2 integer or -1 < c1 <= 1, case c1=1 should not happen, see below!)
-    //                  ^(*(x,y,z),c1) -> *(x^c1,y^c1,z^c1) (c1 integer)
-    //                  ^(*(x,c1),c2) -> ^(x,c2)*c1^c2 (c1, c2 numeric(), c1>0)
-    //                  ^(*(x,c1),c2) -> ^(-x,c2)*c1^c2 (c1, c2 numeric(), c1<0)
-    
-    debugmsg("power eval",LOGLEVEL_MEMBER_FUNCTION);
-
-    if ((level==1)&&(flags & status_flags::evaluated)) {
-        return *this;
-    } else if (level == -max_recursion_level) {
-        throw(std::runtime_error("max recursion level reached"));
-    }
-    
-    ex const & ebasis    = level==1 ? basis    : basis.eval(level-1);
-    ex const & eexponent = level==1 ? exponent : exponent.eval(level-1);
-
-    bool basis_is_numerical=0;
-    bool exponent_is_numerical=0;
-    numeric * num_basis;
-    numeric * num_exponent;
-
-    if (is_exactly_of_type(*ebasis.bp,numeric)) {
-        basis_is_numerical=1;
-        num_basis=static_cast<numeric *>(ebasis.bp);
-    }
-    if (is_exactly_of_type(*eexponent.bp,numeric)) {
-        exponent_is_numerical=1;
-        num_exponent=static_cast<numeric *>(eexponent.bp);
-    }
-
-    // ^(x,0) -> 1 (0^0 also handled here)
-    if (eexponent.is_zero())
-        return exONE();
-
-    // ^(x,1) -> x
-    if (eexponent.is_equal(exONE()))
-        return ebasis;
-
-    // ^(0,x) -> 0 (except if x is real and negative)
-    if (ebasis.is_zero()) {
-        if (exponent_is_numerical && num_exponent->is_negative()) {
-            throw(std::overflow_error("power::eval(): division by zero"));
-        } else
-            return exZERO();
-    }
-
-    // ^(1,x) -> 1
-    if (ebasis.is_equal(exONE()))
-        return exONE();
-
-    if (basis_is_numerical && exponent_is_numerical) {
-        // ^(c1,c2) -> c1^c2 (c1, c2 numeric(),
-        // except if c1,c2 are rational, but c1^c2 is not)
-        bool basis_is_rational = num_basis->is_rational();
-        bool exponent_is_rational = num_exponent->is_rational();
-        numeric res = (*num_basis).power(*num_exponent);
-        
-        if ((!basis_is_rational || !exponent_is_rational)
-            || res.is_rational()) {
-            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_rational && exponent_is_rational
-            && num_exponent->is_real()
-            && !num_exponent->is_integer()) {
-            numeric r, q, n, m;
-            n = num_exponent->numer();
-            m = num_exponent->denom();
-            q = iquo(n, m, r);
-            if (r.is_negative()) {
-                r = r.add(m);
-                q = q.sub(numONE());
-            }
-            if (q.is_zero())  // the exponent was in the allowed range 0<(n/m)<1
-                return this->hold();
-            else {
-                epvector res(2);
-                res.push_back(expair(ebasis,r.div(m)));
-                res.push_back(expair(ex(num_basis->power(q)),exONE()));
-                return (new mul(res))->setflag(status_flags::dynallocated | status_flags::evaluated);
-                /*return mul(num_basis->power(q),
-                           power(ex(*num_basis),ex(r.div(m)))).hold();
-                */
-                /* return (new mul(num_basis->power(q),
-                   power(*num_basis,r.div(m)).hold()))->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)) {
-        power const & sub_power=ex_to_power(ebasis);
-        ex const & sub_basis=sub_power.basis;
-        ex const & sub_exponent=sub_power.exponent;
-        if (is_ex_exactly_of_type(sub_exponent,numeric)) {
-            numeric const & 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,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;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
-        mul const & mulref=ex_to_mul(ebasis);
-        if (!mulref.overall_coeff.is_equal(exONE())) {
-            numeric const & num_coeff=ex_to_numeric(mulref.overall_coeff);
-            if (num_coeff.is_real()) {
-                if (num_coeff.is_positive()>0) {
-                    mul * mulp=new mul(mulref);
-                    mulp->overall_coeff=exONE();
-                    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(numZERO())<0);
-                    if (num_coeff.compare(numMINUSONE())!=0) {
-                        mul * mulp=new mul(mulref);
-                        mulp->overall_coeff=exMINUSONE();
-                        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);
-                    }
-                }
-            }
-        }
-    }
-        
-    if (are_ex_trivially_equal(ebasis,basis) &&
-        are_ex_trivially_equal(eexponent,exponent)) {
-        return this->hold();
-    }
-    return (new power(ebasis, eexponent))->setflag(status_flags::dynallocated |
-                                                   status_flags::evaluated);
+       if ((level==1) && (flags & status_flags::evaluated))
+               return *this;
+       else if (level == -max_recursion_level)
+               throw(std::runtime_error("max recursion level reached"));
+       
+       const ex & ebasis    = level==1 ? basis    : basis.eval(level-1);
+       const ex & eexponent = level==1 ? exponent : exponent.eval(level-1);
+       
+       bool basis_is_numerical = false;
+       bool exponent_is_numerical = false;
+       const numeric *num_basis;
+       const numeric *num_exponent;
+       
+       if (is_ex_exactly_of_type(ebasis, numeric)) {
+               basis_is_numerical = true;
+               num_basis = &ex_to<numeric>(ebasis);
+       }
+       if (is_ex_exactly_of_type(eexponent, numeric)) {
+               exponent_is_numerical = true;
+               num_exponent = &ex_to<numeric>(eexponent);
+       }
+       
+       // ^(x,0) -> 1  (0^0 also handled here)
+       if (eexponent.is_zero()) {
+               if (ebasis.is_zero())
+                       throw (std::domain_error("power::eval(): pow(0,0) is undefined"));
+               else
+                       return _ex1;
+       }
+       
+       // ^(x,1) -> x
+       if (eexponent.is_equal(_ex1))
+               return ebasis;
+
+       // ^(0,c1) -> 0 or exception  (depending on real value of c1)
+       if (ebasis.is_zero() && exponent_is_numerical) {
+               if ((num_exponent->real()).is_zero())
+                       throw (std::domain_error("power::eval(): pow(0,I) is undefined"));
+               else if ((num_exponent->real()).is_negative())
+                       throw (pole_error("power::eval(): division by zero",1));
+               else
+                       return _ex0;
+       }
+
+       // ^(1,x) -> 1
+       if (ebasis.is_equal(_ex1))
+               return _ex1;
+
+       if (exponent_is_numerical) {
+
+               // ^(c1,c2) -> c1^c2  (c1, c2 numeric(),
+               // except if c1,c2 are rational, but c1^c2 is not)
+               if (basis_is_numerical) {
+                       const bool basis_is_crational = num_basis->is_crational();
+                       const bool exponent_is_crational = num_exponent->is_crational();
+                       if (!basis_is_crational || !exponent_is_crational) {
+                               // return a plain float
+                               return (new numeric(num_basis->power(*num_exponent)))->setflag(status_flags::dynallocated |
+                                                                                              status_flags::evaluated |
+                                                                                              status_flags::expanded);
+                       }
+
+                       const numeric res = num_basis->power(*num_exponent);
+                       if (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-q)<1, q integer
+                       if (basis_is_crational && exponent_is_crational
+                           && num_exponent->is_real()
+                           && !num_exponent->is_integer()) {
+                               const numeric n = num_exponent->numer();
+                               const numeric m = num_exponent->denom();
+                               numeric r;
+                               numeric q = iquo(n, m, r);
+                               if (r.is_negative()) {
+                                       r += m;
+                                       --q;
+                               }
+                               if (q.is_zero()) {  // the exponent was in the allowed range 0<(n/m)<1
+                                       if (num_basis->is_rational() && !num_basis->is_integer()) {
+                                               // try it for numerator and denominator separately, in order to
+                                               // partially simplify things like (5/8)^(1/3) -> 1/2*5^(1/3)
+                                               const numeric bnum = num_basis->numer();
+                                               const numeric bden = num_basis->denom();
+                                               const numeric res_bnum = bnum.power(*num_exponent);
+                                               const numeric res_bden = bden.power(*num_exponent);
+                                               if (res_bnum.is_integer())
+                                                       return (new mul(power(bden,-*num_exponent),res_bnum))->setflag(status_flags::dynallocated | status_flags::evaluated);
+                                               if (res_bden.is_integer())
+                                                       return (new mul(power(bnum,*num_exponent),res_bden.inverse()))->setflag(status_flags::dynallocated | status_flags::evaluated);
+                                       }
+                                       return this->hold();
+                               } else {
+                                       // assemble resulting product, but allowing for a re-evaluation,
+                                       // because otherwise we'll end up with something like
+                                       //    (7/8)^(4/3)  ->  7/8*(1/2*7^(1/3))
+                                       // instead of 7/16*7^(1/3).
+                                       ex prod = power(*num_basis,r.div(m));
+                                       return prod*power(*num_basis,q);
+                               }
+                       }
+               }
+       
+               // ^(^(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 (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 (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.is_equal(_num_1)) {
+                                                       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) &&
+           are_ex_trivially_equal(eexponent,exponent)) {
+               return this->hold();
+       }
+       return (new power(ebasis, eexponent))->setflag(status_flags::dynallocated |
+                                                      status_flags::evaluated);
 }
 
 ex power::evalf(int level) const
 {
-    debugmsg("power evalf",LOGLEVEL_MEMBER_FUNCTION);
-
-    ex ebasis;
-    ex eexponent;
-    
-    if (level==1) {
-        ebasis=basis;
-        eexponent=exponent;
-    } else if (level == -max_recursion_level) {
-        throw(std::runtime_error("max recursion level reached"));
-    } else {
-        ebasis=basis.evalf(level-1);
-        eexponent=exponent.evalf(level-1);
-    }
-
-    return power(ebasis,eexponent);
+       ex ebasis;
+       ex eexponent;
+       
+       if (level==1) {
+               ebasis = basis;
+               eexponent = exponent;
+       } else if (level == -max_recursion_level) {
+               throw(std::runtime_error("max recursion level reached"));
+       } else {
+               ebasis = basis.evalf(level-1);
+               if (!is_exactly_a<numeric>(exponent))
+                       eexponent = exponent.evalf(level-1);
+               else
+                       eexponent = exponent;
+       }
+
+       return power(ebasis,eexponent);
+}
+
+ex power::evalm(void) const
+{
+       const ex ebasis = basis.evalm();
+       const 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 (new power(ebasis, eexponent))->setflag(status_flags::dynallocated);
 }
 
-ex power::subs(lst const & ls, lst const & lr) const
+ex power::subs(const lst & ls, const lst & lr, bool no_pattern) const
 {
-    ex const & subsed_basis=basis.subs(ls,lr);
-    ex const & subsed_exponent=exponent.subs(ls,lr);
-
-    if (are_ex_trivially_equal(basis,subsed_basis)&&
-        are_ex_trivially_equal(exponent,subsed_exponent)) {
-        return *this;
-    }
-    
-    return power(subsed_basis, subsed_exponent);
+       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 power(subsed_basis, subsed_exponent).basic::subs(ls, lr, no_pattern);
 }
 
-ex power::simplify_ncmul(exvector const & v) const
+ex power::simplify_ncmul(const exvector & v) const
 {
-    return basic::simplify_ncmul(v);
+       return inherited::simplify_ncmul(v);
 }
 
 // protected
 
-int power::compare_same_type(basic const & other) const
+/** Implementation of ex::diff() for a power.
+ *  @see ex::diff */
+ex power::derivative(const symbol & s) const
+{
+       if (exponent.info(info_flags::real)) {
+               // 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));
+               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))));
+       }
+}
+
+int power::compare_same_type(const basic & other) const
 {
-    GINAC_ASSERT(is_exactly_of_type(other, power));
-    power const & o=static_cast<power const &>(const_cast<basic &>(other));
-
-    int cmpval;
-    cmpval=basis.compare(o.basis);
-    if (cmpval==0) {
-        return exponent.compare(o.exponent);
-    }
-    return cmpval;
+       GINAC_ASSERT(is_exactly_a<power>(other));
+       const power &o = static_cast<const power &>(other);
+
+       int cmpval = basis.compare(o.basis);
+       if (cmpval)
+               return cmpval;
+       else
+               return exponent.compare(o.exponent);
 }
 
 unsigned power::return_type(void) const
 {
-    return basis.return_type();
+       return basis.return_type();
 }
    
 unsigned power::return_type_tinfo(void) const
 {
-    return basis.return_type_tinfo();
+       return basis.return_type_tinfo();
 }
 
 ex power::expand(unsigned options) const
 {
-    ex expanded_basis=basis.expand(options);
-
-    if (!is_ex_exactly_of_type(exponent,numeric)||
-        !ex_to_numeric(exponent).is_integer()) {
-        if (are_ex_trivially_equal(basis,expanded_basis)) {
-            return this->hold();
-        } else {
-            return (new power(expanded_basis,exponent))->
-                    setflag(status_flags::dynallocated);
-        }
-    }
-
-    // integer numeric exponent
-    numeric const & num_exponent=ex_to_numeric(exponent);
-    int int_exponent = num_exponent.to_int();
-
-    if (int_exponent > 0 && is_ex_exactly_of_type(expanded_basis,add)) {
-        return expand_add(ex_to_add(expanded_basis), int_exponent);
-    }
-
-    if (is_ex_exactly_of_type(expanded_basis,mul)) {
-        return expand_mul(ex_to_mul(expanded_basis), num_exponent);
-    }
-
-    // cannot expand further
-    if (are_ex_trivially_equal(basis,expanded_basis)) {
-        return this->hold();
-    } else {
-        return (new power(expanded_basis,exponent))->
-               setflag(status_flags::dynallocated);
-    }
+       if (options == 0 && (flags & status_flags::expanded))
+               return *this;
+       
+       const ex expanded_basis = basis.expand(options);
+       const ex expanded_exponent = exponent.expand(options);
+       
+       // x^(a+b) -> x^a * x^b
+       if (is_ex_exactly_of_type(expanded_exponent, add)) {
+               const add &a = ex_to<add>(expanded_exponent);
+               exvector distrseq;
+               distrseq.reserve(a.seq.size() + 1);
+               epvector::const_iterator last = a.seq.end();
+               epvector::const_iterator cit = a.seq.begin();
+               while (cit!=last) {
+                       distrseq.push_back(power(expanded_basis, a.recombine_pair_to_ex(*cit)));
+                       ++cit;
+               }
+               
+               // 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);
+                       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));
+                       else
+                               distrseq.push_back(power(expanded_basis, a.overall_coeff));
+               } else
+                       distrseq.push_back(power(expanded_basis, a.overall_coeff));
+               
+               // Make sure that e.g. (x+y)^(1+a) -> x*(x+y)^a + y*(x+y)^a
+               ex r = (new mul(distrseq))->setflag(status_flags::dynallocated);
+               return r.expand();
+       }
+       
+       if (!is_ex_exactly_of_type(expanded_exponent, numeric) ||
+               !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 {
+                       return (new power(expanded_basis,expanded_exponent))->setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
+               }
+       }
+       
+       // integer numeric 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);
+       
+       // (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);
+       
+       // cannot expand further
+       if (are_ex_trivially_equal(basis,expanded_basis) && are_ex_trivially_equal(exponent,expanded_exponent))
+               return this->hold();
+       else
+               return (new power(expanded_basis,expanded_exponent))->setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 }
 
 //////////
@@ -445,280 +656,183 @@ ex power::expand(unsigned options) const
 // non-virtual functions in this class
 //////////
 
-ex power::expand_add(add const & a, int const n) const
+/** 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
 {
-    // expand a^n where a is an add and n is an integer
-
-    if (n==2) {
-        return expand_add_2(a);
-    }
-    
-    int m=a.nops();
-    exvector sum;
-    sum.reserve((n+1)*(m-1));
-    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++) {
-        k[l]=0;
-        k_cum[l]=0;
-        upper_limit[l]=n;
-    }
-
-    while (1) {
-        exvector term;
-        term.reserve(m+1);
-        for (l=0; l<m-1; l++) {
-            ex const & 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());
-            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]));
-            }
-        }
-
-        ex const & 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());
-        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++) {
-            f=f*binomial(numeric(n-k_cum[l-1]),numeric(k[l]));
-        }
-        term.push_back(f);
-
-        /*
-        cout << "begin term" << endl;
-        for (int i=0; i<m-1; i++) {
-            cout << "k[" << i << "]=" << k[i] << endl;
-            cout << "k_cum[" << i << "]=" << k_cum[i] << endl;
-            cout << "upper_limit[" << i << "]=" << upper_limit[i] << endl;
-        }
-        for (exvector::const_iterator cit=term.begin(); cit!=term.end(); ++cit) {
-            cout << *cit << endl;
-        }
-        cout << "end term" << endl;
-        */
-
-        // TODO: optimize this
-        sum.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;    
-            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[i]=k_cum[i-1]+k[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);
+       if (n==2)
+               return expand_add_2(a);
+
+       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) {
+               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) {
+                       const ex & b = a.op(l);
+                       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_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_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_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)
+                       f *= binomial(numeric(n-k_cum[l-1]),numeric(k[l]));
+
+               term.push_back(f);
+
+               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;
+                       --l;
+               }
+               if (l<0) break;
+
+               // recalc k_cum[] and upper_limit[]
+               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)
+                       upper_limit[i] = n-k_cum[i-1];
+       }
+
+       return (new add(result))->setflag(status_flags::dynallocated |
+                                         status_flags::expanded);
 }
 
-/*
-ex power::expand_add_2(add const & a) const
-{
-    // special case: expand a^2 where a is an add
-
-    epvector sum;
-    sum.reserve((a.seq.size()*(a.seq.size()+1))/2);
-    epvector::const_iterator last=a.seq.end();
-
-    for (epvector::const_iterator cit0=a.seq.begin(); cit0!=last; ++cit0) {
-        ex const & b=a.recombine_pair_to_ex(*cit0);
-        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());
-        if (is_ex_exactly_of_type(b,mul)) {
-            sum.push_back(a.split_ex_to_pair(expand_mul(ex_to_mul(b),numTWO())));
-        } else {
-            sum.push_back(a.split_ex_to_pair((new power(b,exTWO()))->
-                                              setflag(status_flags::dynallocated)));
-        }
-        for (epvector::const_iterator cit1=cit0+1; cit1!=last; ++cit1) {
-            sum.push_back(a.split_ex_to_pair((new mul(a.recombine_pair_to_ex(*cit0),
-                                                      a.recombine_pair_to_ex(*cit1)))->
-                                              setflag(status_flags::dynallocated),
-                                             exTWO()));
-        }
-    }
-
-    GINAC_ASSERT(sum.size()==(a.seq.size()*(a.seq.size()+1))/2);
-
-    return (new add(sum))->setflag(status_flags::dynallocated);
-}
-*/
-
-ex power::expand_add_2(add const & a) const
-{
-    // special case: expand a^2 where a is an add
-
-    epvector sum;
-    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) {
-        ex const & r=(*cit0).rest;
-        ex const & 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)||
-               !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,exONE())) {
-            if (is_ex_exactly_of_type(r,mul)) {
-                sum.push_back(expair(expand_mul(ex_to_mul(r),numTWO()),exONE()));
-            } else {
-                sum.push_back(expair((new power(r,exTWO()))->setflag(status_flags::dynallocated),
-                                     exONE()));
-            }
-        } else {
-            if (is_ex_exactly_of_type(r,mul)) {
-                sum.push_back(expair(expand_mul(ex_to_mul(r),numTWO()),
-                                     ex_to_numeric(c).power_dyn(numTWO())));
-            } else {
-                sum.push_back(expair((new power(r,exTWO()))->setflag(status_flags::dynallocated),
-                                     ex_to_numeric(c).power_dyn(numTWO())));
-            }
-        }
-            
-        for (epvector::const_iterator cit1=cit0+1; cit1!=last; ++cit1) {
-            ex const & r1=(*cit1).rest;
-            ex const & c1=(*cit1).coeff;
-            sum.push_back(a.combine_ex_with_coeff_to_pair((new mul(r,r1))->setflag(status_flags::dynallocated),
-                                                          numTWO().mul(ex_to_numeric(c)).mul_dyn(ex_to_numeric(c1))));
-        }
-    }
-
-    GINAC_ASSERT(sum.size()==(a.seq.size()*(a.seq.size()+1))/2);
-
-    // second part: add terms coming from overall_factor (if != 0)
-    if (!a.overall_coeff.is_equal(exZERO())) {
-        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(numTWO())));
-        }
-        sum.push_back(expair(ex_to_numeric(a.overall_coeff).power_dyn(numTWO()),exONE()));
-    }
-        
-    GINAC_ASSERT(sum.size()==(a_nops*(a_nops+1))/2);
-    
-    return (new add(sum))->setflag(status_flags::dynallocated);
-}
-
-ex power::expand_mul(mul const & m, numeric const & n) const
-{
-    // expand m^n where m is a mul and n is and integer
-
-    if (n.is_equal(numZERO())) {
-        return exONE();
-    }
-    
-    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));
-        } 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)));
-        }
-        ++cit;
-    }
-    return (new mul(distrseq,ex_to_numeric(m.overall_coeff).power_dyn(n)))
-                 ->setflag(status_flags::dynallocated);
-}
 
-/*
-ex power::expand_commutative_3(ex const & basis, numeric const & exponent,
-                             unsigned options) const
+/** Special case of power::expand_add. Expands a^2 where a is an add.
+ *  @see power::expand_add */
+ex power::expand_add_2(const add & a) const
 {
-    // obsolete
-
-    exvector distrseq;
-    epvector splitseq;
-
-    add const & addref=static_cast<add const &>(*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::sub_expanded |
-                                           status_flags::expanded |
-                                           status_flags::dynallocated  )).
-           expand(options);
+       epvector sum;
+       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_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_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 (is_ex_exactly_of_type(r,mul)) {
+                               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));
+                       }
+               } else {
+                       if (is_ex_exactly_of_type(r,mul)) {
+                               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(a.combine_ex_with_coeff_to_pair((new power(r,_ex2))->setflag(status_flags::dynallocated),
+                                                    ex_to<numeric>(c).power_dyn(_num2)));
+                       }
+               }
+                       
+               for (epvector::const_iterator cit1=cit0+1; cit1!=last; ++cit1) {
+                       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))));
+               }
+       }
+       
+       GINAC_ASSERT(sum.size()==(a.seq.size()*(a.seq.size()+1))/2);
+       
+       // second part: add terms coming from overall_factor (if != 0)
+       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)));
+                       ++i;
+               }
+               sum.push_back(expair(ex_to<numeric>(a.overall_coeff).power_dyn(_num2),_ex1));
+       }
+       
+       GINAC_ASSERT(sum.size()==(a_nops*(a_nops+1))/2);
+       
+       return (new add(sum))->setflag(status_flags::dynallocated | status_flags::expanded);
 }
-*/
 
-/*
-ex power::expand_noncommutative(ex const & basis, numeric const & exponent,
-                                unsigned options) const
+/** 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
 {
-    ex rest_power=ex(power(basis,exponent.add(numMINUSONE()))).
-                  expand(options | expand_options::internal_do_not_expand_power_operands);
-
-    return ex(mul(rest_power,basis),0).
-           expand(options | expand_options::internal_do_not_expand_mul_operands);
+       GINAC_ASSERT(n.is_integer());
+
+       if (n.is_zero())
+               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));
+               } 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)));
+               }
+               ++cit;
+       }
+       return (new mul(distrseq, ex_to<numeric>(m.overall_coeff).power_dyn(n)))->setflag(status_flags::dynallocated);
 }
-*/
-
-//////////
-// static member variables
-//////////
-
-// protected
-
-unsigned power::precedence=60;
-
-//////////
-// global constants
-//////////
-
-const power some_power;
-type_info const & typeid_power=typeid(some_power);
 
 } // namespace GiNaC