* Series expansion test (Laurent and Taylor series). */
/*
- * GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2002 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
static unsigned check_series(const ex &e, const ex &point, const ex &d, int order = 8)
{
ex es = e.series(x==point, order);
- ex ep = ex_to_pseries(es).convert_to_poly();
+ ex ep = ex_to<pseries>(es).convert_to_poly();
if (!(ep - d).is_zero()) {
clog << "series expansion of " << e << " at " << point
<< " erroneously returned " << ep << " (instead of " << d
d = 1 + t + pow(t, 2) / 2 + pow(t, 3) / 6 + pow(t, 4) / 24 + pow(t, 5) / 120 + pow(t, 6) / 720 + pow(t, 7) / 5040 + Order(pow(x, 8));
result += check_series(e, 0, d.expand());
+ e = log(x);
+ d = e;
+ result += check_series(e, 0, d, 1);
+ result += check_series(e, 0, d, 2);
+
return result;
}
return result;
}
-// Order term handling
+// Series exponentiation
static unsigned exam_series4(void)
+{
+ unsigned result = 0;
+ ex e, d;
+
+ e = pow((2*cos(x)).series(x==0, 5), 2).series(x==0, 5);
+ d = 4 - 4*pow(x, 2) + 4*pow(x, 4)/3 + Order(pow(x, 5));
+ result += check_series(e, 0, d);
+
+ e = pow(tgamma(x), 2).series(x==0, 3);
+ d = pow(x,-2) - 2*Euler/x + (pow(Pi,2)/6+2*pow(Euler,2)) + Order(x);
+ result += check_series(e, 0, d);
+
+ return result;
+}
+
+// Order term handling
+static unsigned exam_series5(void)
{
unsigned result = 0;
ex e, d;
}
// Series expansion of tgamma(-1)
-static unsigned exam_series5(void)
+static unsigned exam_series6(void)
{
ex e = tgamma(2*x);
ex d = pow(x+1,-1)*numeric(1,4) +
}
// Series expansion of tan(x==Pi/2)
-static unsigned exam_series6(void)
+static unsigned exam_series7(void)
{
ex e = tan(x*Pi/2);
ex d = pow(x-1,-1)/Pi*(-2) + pow(x-1,1)*Pi/6 + pow(x-1,3)*pow(Pi,3)/360
}
// Series expansion of log(sin(x==0))
-static unsigned exam_series7(void)
+static unsigned exam_series8(void)
{
ex e = log(sin(x));
ex d = log(x) - pow(x,2)/6 - pow(x,4)/180 - pow(x,6)/2835
}
// Series expansion of Li2(sin(x==0))
-static unsigned exam_series8(void)
+static unsigned exam_series9(void)
{
ex e = Li2(sin(x));
ex d = x + pow(x,2)/4 - pow(x,3)/18 - pow(x,4)/48
}
// Series expansion of Li2((x==2)^2), caring about branch-cut
-static unsigned exam_series9(void)
+static unsigned exam_series10(void)
{
ex e = Li2(pow(x,2));
ex d = Li2(4) + (-log(3) + I*Pi*csgn(I-I*pow(x,2))) * (x-2)
}
// Series expansion of logarithms around branch points
-static unsigned exam_series10(void)
+static unsigned exam_series11(void)
{
unsigned result = 0;
ex e, d;
}
// Series expansion of other functions around branch points
-static unsigned exam_series11(void)
+static unsigned exam_series12(void)
{
unsigned result = 0;
ex e, d;
result += exam_series9(); cout << '.' << flush;
result += exam_series10(); cout << '.' << flush;
result += exam_series11(); cout << '.' << flush;
+ result += exam_series12(); cout << '.' << flush;
if (!result) {
cout << " passed " << endl;