X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fpower.cpp;h=a4a33c576ca415e0a3baa7e6b089fd8dae22b81f;hp=5d2ec7046d895bf56ea62fbd64beb7b63ef32f19;hb=4cbc8e8bdf06fd91ec652e9645965a5f1a808d76;hpb=e34ac03e77644ec9f63960f8499c727733ac5abd

diff --git a/ginac/power.cpp b/ginac/power.cpp
index 5d2ec704..a4a33c57 100644
--- a/ginac/power.cpp
+++ b/ginac/power.cpp
@@ -3,7 +3,7 @@
  *  Implementation of GiNaC's symbolic exponentiation (basis^exponent). */
 
 /*
- *  GiNaC Copyright (C) 1999-2006 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2008 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
@@ -41,6 +41,7 @@
 #include "archive.h"
 #include "utils.h"
 #include "relational.h"
+#include "compiler.h"
 
 namespace GiNaC {
 
@@ -49,7 +50,8 @@ GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(power, basic,
   print_func<print_latex>(&power::do_print_latex).
   print_func<print_csrc>(&power::do_print_csrc).
   print_func<print_python>(&power::do_print_python).
-  print_func<print_python_repr>(&power::do_print_python_repr))
+  print_func<print_python_repr>(&power::do_print_python_repr).
+  print_func<print_csrc_cl_N>(&power::do_print_csrc_cl_N))
 
 typedef std::vector<int> intvector;
 
@@ -161,6 +163,21 @@ static void print_sym_pow(const print_context & c, const symbol &x, int exp)
 	}
 }
 
+void power::do_print_csrc_cl_N(const print_csrc_cl_N& c, unsigned level) const
+{
+	if (exponent.is_equal(_ex_1)) {
+		c.s << "recip(";
+		basis.print(c);
+		c.s << ')';
+		return;
+	}
+	c.s << "expt(";
+	basis.print(c);
+	c.s << ", ";
+	exponent.print(c);
+	c.s << ')';
+}
+
 void power::do_print_csrc(const print_csrc & c, unsigned level) const
 {
 	// Integer powers of symbols are printed in a special, optimized way
@@ -171,29 +188,20 @@ void power::do_print_csrc(const print_csrc & c, unsigned level) const
 			c.s << '(';
 		else {
 			exp = -exp;
-			if (is_a<print_csrc_cl_N>(c))
-				c.s << "recip(";
-			else
-				c.s << "1.0/(";
+			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/(";
+		c.s << "1.0/(";
 		basis.print(c);
 		c.s << ')';
 
-	// Otherwise, use the pow() or expt() (CLN) functions
+	// Otherwise, use the pow() function
 	} else {
-		if (is_a<print_csrc_cl_N>(c))
-			c.s << "expt(";
-		else
-			c.s << "pow(";
+		c.s << "pow(";
 		basis.print(c);
 		c.s << ',';
 		exponent.print(c);
@@ -231,6 +239,23 @@ bool power::info(unsigned inf) const
 		case info_flags::algebraic:
 			return !exponent.info(info_flags::integer) ||
 			       basis.info(inf);
+		case info_flags::expanded:
+			return (flags & status_flags::expanded);
+		case info_flags::has_indices: {
+			if (flags & status_flags::has_indices)
+				return true;
+			else if (flags & status_flags::has_no_indices)
+				return false;
+			else if (basis.info(info_flags::has_indices)) {
+				setflag(status_flags::has_indices);
+				clearflag(status_flags::has_no_indices);
+				return true;
+			} else {
+				clearflag(status_flags::has_indices);
+				setflag(status_flags::has_no_indices);
+				return false;
+			}
+		}
 	}
 	return inherited::info(inf);
 }
@@ -467,8 +492,9 @@ ex power::eval(int level) const
 			if (is_exactly_a<numeric>(sub_exponent)) {
 				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_p)).is_negative())
+				if (num_exponent->is_integer() || (abs(num_sub_exponent) - (*_num1_p)).is_negative()) {
 					return power(sub_basis,num_sub_exponent.mul(*num_exponent));
+				}
 			}
 		}
 	
@@ -476,7 +502,35 @@ ex power::eval(int level) const
 		if (num_exponent->is_integer() && is_exactly_a<mul>(ebasis)) {
 			return expand_mul(ex_to<mul>(ebasis), *num_exponent, 0);
 		}
-	
+
+		// (2*x + 6*y)^(-4) -> 1/16*(x + 3*y)^(-4)
+		if (num_exponent->is_integer() && is_exactly_a<add>(ebasis)) {
+			numeric icont = ebasis.integer_content();
+			const numeric lead_coeff = 
+				ex_to<numeric>(ex_to<add>(ebasis).seq.begin()->coeff).div(icont);
+
+			const bool canonicalizable = lead_coeff.is_integer();
+			const bool unit_normal = lead_coeff.is_pos_integer();
+			if (canonicalizable && (! unit_normal))
+				icont = icont.mul(*_num_1_p);
+			
+			if (canonicalizable && (icont != *_num1_p)) {
+				const add& addref = ex_to<add>(ebasis);
+				add* addp = new add(addref);
+				addp->setflag(status_flags::dynallocated);
+				addp->clearflag(status_flags::hash_calculated);
+				addp->overall_coeff = ex_to<numeric>(addp->overall_coeff).div_dyn(icont);
+				for (epvector::iterator i = addp->seq.begin(); i != addp->seq.end(); ++i)
+					i->coeff = ex_to<numeric>(i->coeff).div_dyn(icont);
+
+				const numeric c = icont.power(*num_exponent);
+				if (likely(c != *_num1_p))
+					return (new mul(power(*addp, *num_exponent), c))->setflag(status_flags::dynallocated);
+				else
+					return power(*addp, *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_exactly_a<mul>(ebasis)) {
@@ -581,7 +635,7 @@ bool power::has(const ex & other, unsigned options) const
 }
 
 // from mul.cpp
-extern bool tryfactsubs(const ex &, const ex &, int &, lst &);
+extern bool tryfactsubs(const ex &, const ex &, int &, exmap&);
 
 ex power::subs(const exmap & m, unsigned options) const
 {	
@@ -597,9 +651,13 @@ ex power::subs(const exmap & m, unsigned options) const
 
 	for (exmap::const_iterator it = m.begin(); it != m.end(); ++it) {
 		int nummatches = std::numeric_limits<int>::max();
-		lst repls;
-		if (tryfactsubs(*this, it->first, nummatches, repls))
-			return (ex_to<basic>((*this) * power(it->second.subs(ex(repls), subs_options::no_pattern) / it->first.subs(ex(repls), subs_options::no_pattern), nummatches))).subs_one_level(m, options);
+		exmap repls;
+		if (tryfactsubs(*this, it->first, nummatches, repls)) {
+			ex anum = it->second.subs(repls, subs_options::no_pattern);
+			ex aden = it->first.subs(repls, subs_options::no_pattern);
+			ex result = (*this)*power(anum/aden, nummatches);
+			return (ex_to<basic>(result)).subs_one_level(m, options);
+		}
 	}
 
 	return subs_one_level(m, options);
@@ -718,9 +776,12 @@ tinfo_t power::return_type_tinfo() const
 
 ex power::expand(unsigned options) const
 {
-	if (options == 0 && (flags & status_flags::expanded))
+	if (is_a<symbol>(basis) && exponent.info(info_flags::integer)) {
+		// A special case worth optimizing.
+		setflag(status_flags::expanded);
 		return *this;
-	
+	}
+
 	const ex expanded_basis = basis.expand(options);
 	const ex expanded_exponent = exponent.expand(options);
 	
@@ -807,7 +868,6 @@ ex power::expand_add(const add & a, int n, unsigned options) const
 	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 (size_t l=0; l<m-1; ++l) {
 		k[l] = 0;
@@ -818,7 +878,7 @@ ex power::expand_add(const add & a, int n, unsigned options) const
 	while (true) {
 		exvector term;
 		term.reserve(m+1);
-		for (l=0; l<m-1; ++l) {
+		for (std::size_t 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) ||
@@ -833,7 +893,7 @@ ex power::expand_add(const add & a, int n, unsigned options) const
 				term.push_back(power(b,k[l]));
 		}
 
-		const ex & b = a.op(l);
+		const ex & b = a.op(m - 1);
 		GINAC_ASSERT(!is_exactly_a<add>(b));
 		GINAC_ASSERT(!is_exactly_a<power>(b) ||
 		             !is_exactly_a<numeric>(ex_to<power>(b).exponent) ||
@@ -847,7 +907,7 @@ ex power::expand_add(const add & a, int n, unsigned options) const
 			term.push_back(power(b,n-k_cum[m-2]));
 
 		numeric f = binomial(numeric(n),numeric(k[0]));
-		for (l=1; l<m-1; ++l)
+		for (std::size_t l = 1; l < m - 1; ++l)
 			f *= binomial(numeric(n-k_cum[l-1]),numeric(k[l]));
 
 		term.push_back(f);
@@ -855,12 +915,19 @@ ex power::expand_add(const add & a, int n, unsigned options) const
 		result.push_back(ex((new mul(term))->setflag(status_flags::dynallocated)).expand(options));
 
 		// increment k[]
-		l = m-2;
-		while ((l>=0) && ((++k[l])>upper_limit[l])) {
+		bool done = false;
+		std::size_t l = m - 2;
+		while ((++k[l]) > upper_limit[l]) {
 			k[l] = 0;
-			--l;
+			if (l != 0)
+				--l;
+			else {
+				done = true;
+				break;
+			}
 		}
-		if (l<0) break;
+		if (done)
+			break;
 
 		// recalc k_cum[] and upper_limit[]
 		k_cum[l] = (l==0 ? k[0] : k_cum[l-1]+k[l]);
@@ -943,7 +1010,7 @@ ex power::expand_add_2(const add & a, unsigned options) const
 	return (new add(sum))->setflag(status_flags::dynallocated | status_flags::expanded);
 }
 
-/** Expand factors of m in m^n where m is a mul and n is and integer.
+/** Expand factors of m in m^n where m is a mul and n is an integer.
  *  @see power::expand */
 ex power::expand_mul(const mul & m, const numeric & n, unsigned options, bool from_expand) const
 {
@@ -953,8 +1020,13 @@ ex power::expand_mul(const mul & m, const numeric & n, unsigned options, bool fr
 		return _ex1;
 	}
 
+	// do not bother to rename indices if there are no any.
+	if ((!(options & expand_options::expand_rename_idx)) 
+			&& m.info(info_flags::has_indices))
+		options |= expand_options::expand_rename_idx;
 	// Leave it to multiplication since dummy indices have to be renamed
-	if (get_all_dummy_indices(m).size() > 0 && n.is_positive()) {
+	if ((options & expand_options::expand_rename_idx) &&
+		(get_all_dummy_indices(m).size() > 0) && n.is_positive()) {
 		ex result = m;
 		exvector va = get_all_dummy_indices(m);
 		sort(va.begin(), va.end(), ex_is_less());