+// Series expansion of logarithms around branch points
+static unsigned exam_series11()
+{
+ using GiNaC::log;
+
+ 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_series12()
+{
+ using GiNaC::log;
+
+ 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()