From: Alexei Sheplyakov <alexei.sheplyakov@gmail.com>
Date: Tue, 9 Nov 2010 07:27:47 +0000 (+0100)
Subject: power::series(): handle someg (trivial) singularities of the exponent...
X-Git-Tag: release_1-6-0~18^2~1^2~4
X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=commitdiff_plain;h=1d73fed17debbc88819dc7f84a4a2e608d8eb978

power::series(): handle someg (trivial) singularities of the exponent...

... so GiNaC can expand expressions like

cos(x)^(sin(x)/x) // (x -> 0)
(1 + x)^(1/x) // x -> 0

and so on.

[Reported by Camille Gillot.]
(cherry picked from commit 079c558d4f9758cd2777a2808a02d64cb1f70c8e)
---

diff --git a/check/exam_pseries.cpp b/check/exam_pseries.cpp
index 42650cc0..a0f87ead 100644
--- a/check/exam_pseries.cpp
+++ b/check/exam_pseries.cpp
@@ -369,6 +369,23 @@ static unsigned exam_series13()
 	return result;
 }
 
+// Test if (1+x)^(1/x) can be expanded.
+static unsigned exam_series14()
+{
+	unsigned result = 0;
+
+	ex e = pow(1+x, sin(x)/x);
+	ex d = 1 + x - pow(x,3)/6 + Order(pow(x,4));
+	try {
+		result += check_series(e,0,d,4);
+	} catch (const pole_error& err) {
+		clog << "series expansion of " << e << " at 0 raised an exception." << endl;
+		++result;
+	}
+
+	return result;
+}
+
 unsigned exam_pseries()
 {
 	unsigned result = 0;
@@ -388,6 +405,7 @@ unsigned exam_pseries()
 	result += exam_series11();  cout << '.' << flush;
 	result += exam_series12();  cout << '.' << flush;
 	result += exam_series13();  cout << '.' << flush;
+	result += exam_series14();  cout << '.' << flush;
 	
 	return result;
 }
diff --git a/ginac/pseries.cpp b/ginac/pseries.cpp
index 4a8d7d6a..c290fe0a 100644
--- a/ginac/pseries.cpp
+++ b/ginac/pseries.cpp
@@ -1116,6 +1116,29 @@ ex power::series(const relational & r, int order, unsigned options) const
 		must_expand_basis = true;
 	}
 
+	bool exponent_is_regular = true;
+	try {
+		exponent.subs(r, subs_options::no_pattern);
+	} catch (pole_error) {
+		exponent_is_regular = false;
+	}
+
+	if (!exponent_is_regular) {
+		ex l = exponent*log(basis);
+		// this == exp(l);
+		ex le = l.series(r, order, options);
+		// Note: expanding exp(l) won't help, since that will attempt
+		// Taylor expansion, and fail (because exponent is "singular")
+		// Still l itself might be expanded in Taylor series.
+		// Examples:
+		// sin(x)/x*log(cos(x))
+		// 1/x*log(1 + x)
+		return exp(le).series(r, order, options);
+		// Note: if l happens to have a Laurent expansion (with
+		// negative powers of (var - point)), expanding exp(le)
+		// will barf (which is The Right Thing).
+	}
+
 	// Is the expression of type something^(-int)?
 	if (!must_expand_basis && !exponent.info(info_flags::negint)
 	 && (!is_a<add>(basis) || !is_a<numeric>(exponent)))