synced to 1.1
[ginac.git] / check / exam_pseries.cpp
index 133f01b0ba728f9ac2efa245fb267406d673ade3..8bd785a623ace37925cee58d1e8cda521d7ce9ae 100644 (file)
@@ -3,7 +3,7 @@
  *  Series expansion test (Laurent and Taylor series). */
 
 /*
- *  GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2003 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
@@ -27,20 +27,22 @@ static symbol x("x");
 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
-                        << ")" << endl;
-               (ep-d).printtree(clog);
+                    << " erroneously returned " << ep << " (instead of " << d
+                    << ")" << endl;
+               clog << tree << (ep-d) << dflt;
                return 1;
        }
        return 0;
 }
 
 // Series expansion
-static unsigned exam_series1(void)
+static unsigned exam_series1()
 {
+       using GiNaC::log;
+
        unsigned result = 0;
        ex e, d;
        
@@ -98,11 +100,16 @@ static unsigned exam_series1(void)
        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;
 }
 
 // Series addition
-static unsigned exam_series2(void)
+static unsigned exam_series2()
 {
        unsigned result = 0;
        ex e, d;
@@ -115,7 +122,7 @@ static unsigned exam_series2(void)
 }
 
 // Series multiplication
-static unsigned exam_series3(void)
+static unsigned exam_series3()
 {
        unsigned result = 0;
        ex e, d;
@@ -127,8 +134,25 @@ static unsigned exam_series3(void)
        return result;
 }
 
+// Series exponentiation
+static unsigned exam_series4()
+{
+       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_series4(void)
+static unsigned exam_series5()
 {
        unsigned result = 0;
        ex e, d;
@@ -148,79 +172,152 @@ static unsigned exam_series4(void)
 }
 
 // Series expansion of tgamma(-1)
-static unsigned exam_series5(void)
+static unsigned exam_series6()
 {
        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));
+              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_series6(void)
+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-1,8));
+             +pow(x-1,5)*pow(Pi,5)/15120 + pow(x-1,7)*pow(Pi,7)/604800
+             +Order(pow(x-1,8));
        return check_series(e,1,d,8);
 }
 
 // Series expansion of log(sin(x==0))
-static unsigned exam_series7(void)
+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
-                 +Order(pow(x,8));
+             +Order(pow(x,8));
        return check_series(e,0,d,8);
 }
 
 // Series expansion of Li2(sin(x==0))
-static unsigned exam_series8(void)
+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));
+              - 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_series9(void)
+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));
+              + (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);
 }
 
-unsigned exam_pseries(void)
+// 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()
 {
        unsigned result = 0;
        
@@ -236,6 +333,9 @@ unsigned exam_pseries(void)
        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;
        
        if (!result) {
                cout << " passed " << endl;