* Series expansion test (Laurent and Taylor series). */
/*
- * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ * 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
return check_series(e,2,d,5);
}
+// Series expansion of logarithms around branch points
+static unsigned exam_series10(void)
+{
+ unsigned result = 0;
+ ex e, d;
+ symbol a("a");
+
+ e = log(x);
+ d = log(x);
+ result += check_series(e,0,d,5);
+
+ e = log(3/x);
+ d = log(3)-log(x);
+ result += check_series(e,0,d,5);
+
+ e = log(3*pow(x,2));
+ d = log(3)+2*log(x);
+ result += check_series(e,0,d,5);
+
+ // These ones must not be expanded because it would result in a branch cut
+ // running in the wrong direction. (Other systems tend to get this wrong.)
+ e = log(-x);
+ d = e;
+ result += check_series(e,0,d,5);
+
+ e = log(I*(x-123));
+ d = e;
+ result += check_series(e,123,d,5);
+
+ e = log(a*x);
+ d = e; // we don't know anything about a!
+ result += check_series(e,0,d,5);
+
+ e = log((1-x)/x);
+ d = log(1-x) - (x-1) + pow(x-1,2)/2 - pow(x-1,3)/3 + Order(pow(x-1,4));
+ result += check_series(e,1,d,4);
+
+ return result;
+}
+
+// Series expansion of other functions around branch points
+static unsigned exam_series11(void)
+{
+ unsigned result = 0;
+ ex e, d;
+
+ // NB: Mma and Maple give different results, but they agree if one
+ // takes into account that by assumption |x|<1.
+ e = atan(x);
+ d = (I*log(2)/2-I*log(1+I*x)/2) + (x-I)/4 + I*pow(x-I,2)/16 + Order(pow(x-I,3));
+ result += check_series(e,I,d,3);
+
+ // NB: here, at -I, Mathematica disagrees, but it is wrong -- they
+ // pick up a complex phase by incorrectly expanding logarithms.
+ e = atan(x);
+ d = (-I*log(2)/2+I*log(1-I*x)/2) + (x+I)/4 - I*pow(x+I,2)/16 + Order(pow(x+I,3));
+ result += check_series(e,-I,d,3);
+
+ // This is basically the same as above, the branch point is at +/-1:
+ e = atanh(x);
+ d = (-log(2)/2+log(x+1)/2) + (x+1)/4 + pow(x+1,2)/16 + Order(pow(x+1,3));
+ result += check_series(e,-1,d,3);
+
+ return result;
+}
+
+
unsigned exam_pseries(void)
{
unsigned result = 0;
result += exam_series7(); cout << '.' << flush;
result += exam_series8(); cout << '.' << flush;
result += exam_series9(); cout << '.' << flush;
+ result += exam_series10(); cout << '.' << flush;
+ result += exam_series11(); cout << '.' << flush;
if (!result) {
cout << " passed " << endl;