-static unsigned exam_series4(void)
-{
- unsigned result = 0;
- ex e, d;
-
- e = 1 + x + pow(x, 2) + pow(x, 3);
- d = Order(1);
- result += check_series(e, 0, d, 0);
- d = 1 + Order(x);
- result += check_series(e, 0, d, 1);
- d = 1 + x + Order(pow(x, 2));
- result += check_series(e, 0, d, 2);
- d = 1 + x + pow(x, 2) + Order(pow(x, 3));
- result += check_series(e, 0, d, 3);
- d = 1 + x + pow(x, 2) + pow(x, 3);
- result += check_series(e, 0, d, 4);
- return result;
-}
-
-// Series of special functions
-static unsigned exam_series5(void)
-{
- unsigned result = 0;
- ex e, d;
-
- // Gamma(-1):
- e = Gamma(2*x);
- d = pow(x+1,-1)*numeric(1,4) +
- pow(x+1,0)*(numeric(3,4) -
- numeric(1,2)*gamma) +
- pow(x+1,1)*(numeric(7,4) -
- numeric(3,2)*gamma +
- numeric(1,2)*pow(gamma,2) +
- numeric(1,12)*pow(Pi,2)) +
- pow(x+1,2)*(numeric(15,4) -
- numeric(7,2)*gamma -
- numeric(1,3)*pow(gamma,3) +
- numeric(1,4)*pow(Pi,2) +
- numeric(3,2)*pow(gamma,2) -
- numeric(1,6)*pow(Pi,2)*gamma -
- numeric(2,3)*zeta(3)) +
- pow(x+1,3)*(numeric(31,4) - pow(gamma,3) -
- numeric(15,2)*gamma +
- numeric(1,6)*pow(gamma,4) +
- numeric(7,2)*pow(gamma,2) +
- numeric(7,12)*pow(Pi,2) -
- numeric(1,2)*pow(Pi,2)*gamma -
- numeric(2)*zeta(3) +
- numeric(1,6)*pow(gamma,2)*pow(Pi,2) +
- numeric(1,40)*pow(Pi,4) +
- numeric(4,3)*zeta(3)*gamma) +
- Order(pow(x+1,4));
- result += check_series(e, -1, d, 4);
-
- // tan(Pi/2)
- e = tan(x*Pi/2);
- d = pow(x-1,-1)/Pi*(-2) +
- pow(x-1,1)*Pi/6 +
- pow(x-1,3)*pow(Pi,3)/360 +
- pow(x-1,5)*pow(Pi,5)/15120 +
- pow(x-1,7)*pow(Pi,7)/604800 +
- Order(pow(x-1,8));
- result += check_series(e,1,d,8);
-
- return result;
-}
-
-unsigned exam_pseries(void)
-{
- unsigned result = 0;
-
- cout << "examining series expansion" << flush;
- clog << "----------series expansion:" << endl;
-
- result += exam_series1(); cout << '.' << flush;
- result += exam_series2(); cout << '.' << flush;
- result += exam_series3(); cout << '.' << flush;
- result += exam_series4(); cout << '.' << flush;
- result += exam_series5(); cout << '.' << flush;
-
- if (!result) {
- cout << " passed " << endl;
- clog << "(no output)" << endl;
- } else {
- cout << " failed " << endl;
- }
- return result;
+static unsigned exam_series5()
+{
+ unsigned result = 0;
+ ex e, d;
+
+ e = 1 + x + pow(x, 2) + pow(x, 3);
+ d = Order(1);
+ result += check_series(e, 0, d, 0);
+ d = 1 + Order(x);
+ result += check_series(e, 0, d, 1);
+ d = 1 + x + Order(pow(x, 2));
+ result += check_series(e, 0, d, 2);
+ d = 1 + x + pow(x, 2) + Order(pow(x, 3));
+ result += check_series(e, 0, d, 3);
+ d = 1 + x + pow(x, 2) + pow(x, 3);
+ result += check_series(e, 0, d, 4);
+ return result;
+}
+
+// Series expansion of tgamma(-1)
+static unsigned exam_series6()
+{
+ using GiNaC::tgamma;
+ ex e = tgamma(2*x);
+ ex d = pow(x+1,-1)*numeric(1,4) +
+ pow(x+1,0)*(numeric(3,4) -
+ numeric(1,2)*Euler) +
+ pow(x+1,1)*(numeric(7,4) -
+ numeric(3,2)*Euler +
+ numeric(1,2)*pow(Euler,2) +
+ numeric(1,12)*pow(Pi,2)) +
+ pow(x+1,2)*(numeric(15,4) -
+ numeric(7,2)*Euler -
+ numeric(1,3)*pow(Euler,3) +
+ numeric(1,4)*pow(Pi,2) +
+ numeric(3,2)*pow(Euler,2) -
+ numeric(1,6)*pow(Pi,2)*Euler -
+ numeric(2,3)*zeta(3)) +
+ pow(x+1,3)*(numeric(31,4) - pow(Euler,3) -
+ numeric(15,2)*Euler +
+ numeric(1,6)*pow(Euler,4) +
+ numeric(7,2)*pow(Euler,2) +
+ numeric(7,12)*pow(Pi,2) -
+ numeric(1,2)*pow(Pi,2)*Euler -
+ numeric(2)*zeta(3) +
+ numeric(1,6)*pow(Euler,2)*pow(Pi,2) +
+ numeric(1,40)*pow(Pi,4) +
+ numeric(4,3)*zeta(3)*Euler) +
+ Order(pow(x+1,4));
+ return check_series(e, -1, d, 4);
+}
+
+// Series expansion of tan(x==Pi/2)
+static unsigned exam_series7()
+{
+ 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
+ +pow(x-1,5)*pow(Pi,5)/15120 + pow(x-1,7)*pow(Pi,7)/604800
+ +Order(pow(x-1,9));
+ return check_series(e,1,d,9);
+}
+
+// Series expansion of log(sin(x==0))
+static unsigned exam_series8()
+{
+ ex e = log(sin(x));
+ ex d = log(x) - pow(x,2)/6 - pow(x,4)/180 - pow(x,6)/2835 - pow(x,8)/37800 + Order(pow(x,9));
+ return check_series(e,0,d,9);
+}
+
+// Series expansion of Li2(sin(x==0))
+static unsigned exam_series9()
+{
+ ex e = Li2(sin(x));
+ ex d = x + pow(x,2)/4 - pow(x,3)/18 - pow(x,4)/48
+ - 13*pow(x,5)/1800 - pow(x,6)/360 - 23*pow(x,7)/21168
+ + Order(pow(x,8));
+ return check_series(e,0,d,8);
+}
+
+// Series expansion of Li2((x==2)^2), caring about branch-cut
+static unsigned exam_series10()
+{
+ using GiNaC::log;
+
+ ex e = Li2(pow(x,2));
+ ex d = Li2(4) + (-log(3) + I*Pi*csgn(I-I*pow(x,2))) * (x-2)
+ + (numeric(-2,3) + log(3)/4 - I*Pi/4*csgn(I-I*pow(x,2))) * pow(x-2,2)
+ + (numeric(11,27) - log(3)/12 + I*Pi/12*csgn(I-I*pow(x,2))) * pow(x-2,3)
+ + (numeric(-155,648) + log(3)/32 - I*Pi/32*csgn(I-I*pow(x,2))) * pow(x-2,4)
+ + Order(pow(x-2,5));
+ return check_series(e,2,d,5);
+}
+
+// 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 + pow(x-1,4)/4 + Order(pow(x-1,5));
+ result += check_series(e,1,d,5);
+
+ return result;
+}
+
+// Series expansion of other functions around branch points
+static unsigned exam_series12()
+{
+ using GiNaC::log;
+ using GiNaC::atanh;
+
+ 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;
+}
+
+// Test of the patch of Stefan Weinzierl that prevents an infinite loop if
+// a factor in a product is a complicated way of writing zero.
+static unsigned exam_series13()
+{
+ unsigned result = 0;
+
+ ex e = (new mul(pow(2,x), (1/x*(-(1+x)/(1-x)) + (1+x)/x/(1-x)))
+ )->setflag(status_flags::evaluated);
+ ex d = Order(x);
+ result += check_series(e,0,d,1);
+
+ 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;
+
+ cout << "examining series expansion" << flush;
+
+ result += exam_series1(); cout << '.' << flush;
+ result += exam_series2(); cout << '.' << flush;
+ result += exam_series3(); cout << '.' << flush;
+ result += exam_series4(); cout << '.' << flush;
+ result += exam_series5(); cout << '.' << flush;
+ result += exam_series6(); cout << '.' << flush;
+ 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;
+ result += exam_series12(); cout << '.' << flush;
+ result += exam_series13(); cout << '.' << flush;
+ result += exam_series14(); cout << '.' << flush;
+
+ return result;
+}
+
+int main(int argc, char** argv)
+{
+ return exam_pseries();