/** @file power.cpp
 *
 *  Implementation of GiNaC's symbolic exponentiation (basis^exponent). */

/*
 *  GiNaC Copyright (C) 1999-2001 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
 *  the Free Software Foundation; either version 2 of the License, or
 *  (at your option) any later version.
 *
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 *
 *  You should have received a copy of the GNU General Public License
 *  along with this program; if not, write to the Free Software
 *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 */

#include <vector>
#include <iostream>
#include <stdexcept>

#include "power.h"
#include "expairseq.h"
#include "add.h"
#include "mul.h"
#include "numeric.h"
#include "inifcns.h"
#include "relational.h"
#include "symbol.h"
#include "print.h"
#include "archive.h"
#include "debugmsg.h"
#include "utils.h"

namespace GiNaC {

GINAC_IMPLEMENT_REGISTERED_CLASS(power, basic)

typedef std::vector<int> intvector;

//////////
// default ctor, dtor, copy ctor assignment operator and helpers
//////////

power::power() : basic(TINFO_power)
{
	debugmsg("power default ctor",LOGLEVEL_CONSTRUCT);
}

void power::copy(const power & other)
{
	inherited::copy(other);
	basis = other.basis;
	exponent = other.exponent;
}

DEFAULT_DESTROY(power)

//////////
// other ctors
//////////

power::power(const ex & lh, const ex & rh) : basic(TINFO_power), basis(lh), exponent(rh)
{
	debugmsg("power ctor from ex,ex",LOGLEVEL_CONSTRUCT);
	GINAC_ASSERT(basis.return_type()==return_types::commutative);
}

power::power(const ex & lh, const numeric & rh) : basic(TINFO_power), basis(lh), exponent(rh)
{
	debugmsg("power ctor from ex,numeric",LOGLEVEL_CONSTRUCT);
	GINAC_ASSERT(basis.return_type()==return_types::commutative);
}

//////////
// archiving
//////////

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);
}

void power::archive(archive_node &n) const
{
	inherited::archive(n);
	n.add_ex("basis", basis);
	n.add_ex("exponent", exponent);
}

DEFAULT_UNARCHIVE(power)

//////////
// functions overriding virtual functions from bases classes
//////////

// public

static void print_sym_pow(const print_context & c, const symbol &x, int exp)
{
	// 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 hack 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 << ")";
	}
}

void power::print(const print_context & c, unsigned level) const
{
	debugmsg("power print", LOGLEVEL_PRINT);

	if (is_of_type(c, print_tree)) {

		inherited::print(c, level);

	} else if (is_of_type(c, print_csrc)) {

		// 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();
			if (exp > 0)
				c.s << "(";
			else {
				exp = -exp;
				if (is_of_type(c, print_csrc_cl_N))
					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.compare(_num_1()) == 0) {
			if (is_of_type(c, print_csrc_cl_N))
				c.s << "recip(";
			else
				c.s << "1.0/(";
			basis.print(c);
			c.s << ")";

		// Otherwise, use the pow() or expt() (CLN) functions
		} else {
			if (is_of_type(c, print_csrc_cl_N))
				c.s << "expt(";
			else
				c.s << "pow(";
			basis.print(c);
			c.s << ",";
			exponent.print(c);
			c.s << ")";
		}

	} else {

		if (exponent.is_equal(_ex1_2())) {
			c.s << "sqrt(";
			basis.print(c);
			c.s << ")";
		} else {
			if (precedence <= level)
				c.s << "(";
			basis.print(c, precedence);
			c.s << "^";
			exponent.print(c, precedence);
			if (precedence <= level)
				c.s << ")";
		}
	}
}

bool power::info(unsigned inf) const
{
	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);
}

unsigned power::nops() const
{
	return 2;
}

ex & power::let_op(int i)
{
	GINAC_ASSERT(i>=0);
	GINAC_ASSERT(i<2);

	return i==0 ? basis : exponent;
}

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();
			else
				return 0;
		} else
			return basis.degree(s) * ex_to_numeric(exponent).to_int();
	}
	return 0;
}

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();
			else
				return 0;
		} else
			return basis.ldegree(s) * ex_to_numeric(exponent).to_int();
	}
	return 0;
}

ex power::coeff(const ex & s, int n) const
{
	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_exactly_of_type(*exponent.bp, 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();
		}
	}
}

ex power::eval(int level) const
{
	// simplifications: ^(x,0) -> 1 (0^0 handled here)
	//                  ^(x,1) -> x
	//                  ^(0,c1) -> 0 or exception (depending on real value of c1)
	//                  ^(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"));
	
	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;
	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()) {
		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 (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_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 (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,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
		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) {
						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);
					}
				}
			}
		}
	}
	
	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);
		if (!is_ex_exactly_of_type(eexponent,numeric))
			eexponent = exponent.evalf(level-1);
		else
			eexponent = exponent;
	}

	return power(ebasis,eexponent);
}

ex power::subs(const lst & ls, const lst & lr) 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);
	}
	
	return power(subsed_basis, subsed_exponent);
}

ex power::simplify_ncmul(const exvector & v) const
{
	return inherited::simplify_ncmul(v);
}

// protected

/** 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));
	const power & o=static_cast<const power &>(const_cast<basic &>(other));

	int cmpval;
	cmpval=basis.compare(o.basis);
	if (cmpval==0) {
		return exponent.compare(o.exponent);
	}
	return cmpval;
}

unsigned power::return_type(void) const
{
	return basis.return_type();
}
   
unsigned power::return_type_tinfo(void) const
{
	return basis.return_type_tinfo();
}

ex power::expand(unsigned options) const
{
	if (flags & status_flags::expanded)
		return *this;
	
	ex expanded_basis = basis.expand(options);
	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 | status_flags::expanded);
		}
	}
	
	// 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 | status_flags::expanded);
}

//////////
// new virtual functions which can be overridden by derived classes
//////////

// none

//////////
// non-virtual functions in this class
//////////

/** expand a^n where a is an add and n is an 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));
	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++) {
			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));
			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) ||
		             !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])));
		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);
		
		/*
		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 |
								   status_flags::expanded );
}


/** 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
{
	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_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,_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(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())));
			}
		}
			
		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()) {
		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(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);
}

/** 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
{
	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);
}

/*
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);
}
*/

/*
ex power::expand_noncommutative(const ex & basis, const numeric & exponent,
								unsigned options) const
{
	ex rest_power = ex(power(basis,exponent.add(_num_1()))).
	                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);
}
*/

//////////
// static member variables
//////////

// protected

unsigned power::precedence = 60;

// helper function

ex sqrt(const ex & a)
{
	return power(a,_ex1_2());
}

} // namespace GiNaC