From c814fb2991fc9d44c7466da5bbf20e58c0f4238f Mon Sep 17 00:00:00 2001
From: Vladimir Kisil <kisilv@maths.leeds.ac.uk>
Date: Tue, 14 Apr 2015 23:14:09 +0200
Subject: [PATCH] Make power::expand() (x*p)^c -> x^c * p^c, if p>0.

This expansion seems to be helpful in many cases.
---
 check/exam_powerlaws.cpp | 32 ++++++++++++++++++++++++++++
 ginac/power.cpp          | 45 ++++++++++++++++++++++++++++++++++++++++
 2 files changed, 77 insertions(+)

diff --git a/check/exam_powerlaws.cpp b/check/exam_powerlaws.cpp
index 0903c4e1..b8176035 100644
--- a/check/exam_powerlaws.cpp
+++ b/check/exam_powerlaws.cpp
@@ -288,6 +288,37 @@ static unsigned exam_powerlaws5()
 	return 0;
 }
 
+static unsigned exam_powerlaws6()
+{
+	// check expansion rules for positive symbols
+
+	symbol a("a");
+	symbol b("b");
+	symbol c("c");
+	realsymbol x("x");
+	realsymbol y("y");
+	possymbol p("p");
+	possymbol q("q");
+	numeric half=numeric(1,2);
+
+	ex e1 = pow(5*pow(3*a*b*x*y*p*q,2),7*half*c).expand();
+	ex e2 = pow(p,7*c)*pow(q,7*c)*pow(pow(a*b*x*y,2),numeric(7,2)*c)*pow(45,numeric(7,2)*c);
+	if (!e1.is_equal(e2)) {
+		clog << "Could not expand exponents with positive bases in " << e1 << endl;
+		return 1;
+	}
+
+	ex e3 = pow(-pow(-a*x*p,3)*pow(b*y*p,3),half*c).expand().normal();
+	ex e4 = pow(p,3*c)*pow(pow(a*b*x*y,3),half*c);
+
+	if (!e3.is_equal(e4)) {
+		clog << "Could not expand exponents with positive bases in " << e3 << endl;
+		return 1;
+	}
+
+	return 0;
+}
+
 unsigned exam_powerlaws()
 {
 	unsigned result = 0;
@@ -299,6 +330,7 @@ unsigned exam_powerlaws()
 	result += exam_powerlaws3();  cout << '.' << flush;
 	result += exam_powerlaws4();  cout << '.' << flush;
 	result += exam_powerlaws5();  cout << '.' << flush;
+	result += exam_powerlaws6();  cout << '.' << flush;
 	
 	return result;
 }
diff --git a/ginac/power.cpp b/ginac/power.cpp
index 6d6f81da..82200d7a 100644
--- a/ginac/power.cpp
+++ b/ginac/power.cpp
@@ -799,6 +799,51 @@ ex power::expand(unsigned options) const
 		return *this;
 	}
 
+	// (x*p)^c -> x^c * p^c, if p>0
+	// makes sense before expanding the basis
+	if (is_exactly_a<mul>(basis) && !basis.info(info_flags::indefinite)) {
+		const mul &m = ex_to<mul>(basis);
+		exvector prodseq;
+		epvector powseq;
+		prodseq.reserve(m.seq.size() + 1);
+		powseq.reserve(m.seq.size() + 1);
+		epvector::const_iterator last = m.seq.end();
+		epvector::const_iterator cit = m.seq.begin();
+		bool possign = true;
+
+		// search for positive/negative factors
+		while (cit!=last) {
+			ex e=m.recombine_pair_to_ex(*cit);
+			if (e.info(info_flags::positive))
+				prodseq.push_back(pow(e, exponent).expand(options));
+			else if (e.info(info_flags::negative)) {
+				prodseq.push_back(pow(-e, exponent).expand(options));
+				possign = !possign;
+			} else
+				powseq.push_back(*cit);
+			++cit;
+		}
+
+		// take care on the numeric coefficient
+		ex coeff=(possign? _ex1 : _ex_1);
+		if (m.overall_coeff.info(info_flags::positive) && m.overall_coeff != _ex1)
+			prodseq.push_back(power(m.overall_coeff, exponent));
+		else if (m.overall_coeff.info(info_flags::negative) && m.overall_coeff != _ex_1)
+			prodseq.push_back(power(-m.overall_coeff, exponent));
+		else
+			coeff *= m.overall_coeff;
+
+		// If positive/negative factors are found, then extract them.
+		// In either case we set a flag to avoid the second run on a part
+		// which does not have positive/negative terms.
+		if (prodseq.size() > 0) {
+			ex newbasis = coeff*mul(powseq);
+			ex_to<basic>(newbasis).setflag(status_flags::purely_indefinite);
+			return ((new mul(prodseq))->setflag(status_flags::dynallocated)*(new power(newbasis, exponent))->setflag(status_flags::dynallocated).expand(options)).expand(options);
+		} else
+			ex_to<basic>(basis).setflag(status_flags::purely_indefinite);
+	}
+
 	const ex expanded_basis = basis.expand(options);
 	const ex expanded_exponent = exponent.expand(options);
 	
-- 
2.44.0