genheader.pl: create a header file 'cint_workaround.h' to fix the broken

[ginac.git] / check / series_expansion.cpp

diff --git a/check/series_expansion.cpp b/check/series_expansion.cpp
index 0f8437b247c94da4fdd2e7f205eb18a4677d454b..42170c0b1104323621bb357c0c6deb763d623642 100644 (file)
--- a/check/series_expansion.cpp
+++ b/check/series_expansion.cpp
@@ -1,8 +1,9 @@
 /** @file series_expansion.cpp
  *
 /** @file series_expansion.cpp
  *

- *  Series expansion test (Laurent and Taylor series).
- *
- *  GiNaC Copyright (C) 1999 Johannes Gutenberg University Mainz, Germany
+ *  Series expansion test (Laurent and Taylor series). */
+
+/*
+ *  GiNaC Copyright (C) 1999-2000 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
  *
  *  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


@@ -21,127 +22,201 @@
 
 #include <ginac/ginac.h>
 
 
 #include <ginac/ginac.h>
 

+#ifndef NO_GINAC_NAMESPACE
+using namespace GiNaC;
+#endif // ndef NO_GINAC_NAMESPACE
+

 static symbol x("x");
 
 static symbol x("x");
 

-static unsigned check_series(const ex &e, const ex &point, const ex &d)
+static unsigned check_series(const ex &e, const ex &point, const ex &d, int order = 8)

 {
 {

-       ex es = e.series(x, point, 8);
-       ex ep = static_cast<series *>(es.bp)->convert_to_poly();
-       if ((ep - d).compare(exZERO()) != 0) {
-               clog << "series expansion of " << e << " at " << point
+    ex es = e.series(x, point, order);
+    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;
              << " erroneously returned " << ep << " (instead of " << d
              << ")" << endl;

-               (ep-d).printtree(clog);
-               return 1;
-       }
-       return 0;
+        (ep-d).printtree(clog);
+        return 1;
+    }
+    return 0;

 }
 
 // Series expansion
 static unsigned series1(void)
 {
 }
 
 // Series expansion
 static unsigned series1(void)
 {

-       unsigned result = 0;
-       ex e, d;
-
-       e = sin(x);
-       d = x - pow(x, 3) / 6 + pow(x, 5) / 120 - pow(x, 7) / 5040 + Order(pow(x, 8));
-       result += check_series(e, exZERO(), d);
-
-       e = cos(x);
-       d = 1 - pow(x, 2) / 2 + pow(x, 4) / 24 - pow(x, 6) / 720 + Order(pow(x, 8));
-       result += check_series(e, exZERO(), d);
-
-       e = exp(x);
-       d = 1 + x + pow(x, 2) / 2 + pow(x, 3) / 6 + pow(x, 4) / 24 + pow(x, 5) / 120 + pow(x, 6) / 720 + pow(x, 7) / 5040 + Order(pow(x, 8));
-       result += check_series(e, exZERO(), d);
-
-       e = pow(1 - x, -1);
-       d = 1 + x + pow(x, 2) + pow(x, 3) + pow(x, 4) + pow(x, 5) + pow(x, 6) + pow(x, 7) + Order(pow(x, 8));
-       result += check_series(e, exZERO(), d);
-
-       e = x + pow(x, -1);
-       d = x + pow(x, -1);
-       result += check_series(e, exZERO(), d);
-
-       e = x + pow(x, -1);
-       d = 2 + pow(x-1, 2) - pow(x-1, 3) + pow(x-1, 4) - pow(x-1, 5) + pow(x-1, 6) - pow(x-1, 7) + Order(pow(x-1, 8));
-       result += check_series(e, exONE(), d);
-
-       e = pow(x + pow(x, 3), -1);
-       d = pow(x, -1) - x + pow(x, 3) - pow(x, 5) + Order(pow(x, 7));
-       result += check_series(e, exZERO(), d);
-
-       e = pow(pow(x, 2) + pow(x, 4), -1);
-       d = pow(x, -2) - 1 + pow(x, 2) - pow(x, 4) + Order(pow(x, 6));
-       result += check_series(e, exZERO(), d);
-
-       e = pow(sin(x), -2);
-       d = pow(x, -2) + numeric(1,3) + pow(x, 2) / 15 + pow(x, 4) * 2/189 + Order(pow(x, 5));
-       result += check_series(e, exZERO(), d);
-
-       e = sin(x) / cos(x);
-       d = x + pow(x, 3) / 3 + pow(x, 5) * 2/15 + pow(x, 7) * 17/315 + Order(pow(x, 8));
-       result += check_series(e, exZERO(), d);
-
-       e = cos(x) / sin(x);
-       d = pow(x, -1) - x / 3 - pow(x, 3) / 45 - pow(x, 5) * 2/945 + Order(pow(x, 6));
-       result += check_series(e, exZERO(), d);
-
-       e = pow(numeric(2), x);
-       ex t = log(ex(2)) * x;
-       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, exZERO(), d.expand());
-
-       e = pow(Pi, x);
-       t = log(Pi) * x;
-       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, exZERO(), d.expand());
-
-       return result;
+    unsigned result = 0;
+    ex e, d;
+    
+    e = sin(x);
+    d = x - pow(x, 3) / 6 + pow(x, 5) / 120 - pow(x, 7) / 5040 + Order(pow(x, 8));
+    result += check_series(e, 0, d);
+    
+    e = cos(x);
+    d = 1 - pow(x, 2) / 2 + pow(x, 4) / 24 - pow(x, 6) / 720 + Order(pow(x, 8));
+    result += check_series(e, 0, d);
+    
+    e = exp(x);
+    d = 1 + x + pow(x, 2) / 2 + pow(x, 3) / 6 + pow(x, 4) / 24 + pow(x, 5) / 120 + pow(x, 6) / 720 + pow(x, 7) / 5040 + Order(pow(x, 8));
+    result += check_series(e, 0, d);
+    
+    e = pow(1 - x, -1);
+    d = 1 + x + pow(x, 2) + pow(x, 3) + pow(x, 4) + pow(x, 5) + pow(x, 6) + pow(x, 7) + Order(pow(x, 8));
+    result += check_series(e, 0, d);
+    
+    e = x + pow(x, -1);
+    d = x + pow(x, -1);
+    result += check_series(e, 0, d);
+    
+    e = x + pow(x, -1);
+    d = 2 + pow(x-1, 2) - pow(x-1, 3) + pow(x-1, 4) - pow(x-1, 5) + pow(x-1, 6) - pow(x-1, 7) + Order(pow(x-1, 8));
+    result += check_series(e, 1, d);
+    
+    e = pow(x + pow(x, 3), -1);
+    d = pow(x, -1) - x + pow(x, 3) - pow(x, 5) + Order(pow(x, 7));
+    result += check_series(e, 0, d);
+    
+    e = pow(pow(x, 2) + pow(x, 4), -1);
+    d = pow(x, -2) - 1 + pow(x, 2) - pow(x, 4) + Order(pow(x, 6));
+    result += check_series(e, 0, d);
+    
+    e = pow(sin(x), -2);
+    d = pow(x, -2) + numeric(1,3) + pow(x, 2) / 15 + pow(x, 4) * 2/189 + Order(pow(x, 5));
+    result += check_series(e, 0, d);
+    
+    e = sin(x) / cos(x);
+    d = x + pow(x, 3) / 3 + pow(x, 5) * 2/15 + pow(x, 7) * 17/315 + Order(pow(x, 8));
+    result += check_series(e, 0, d);
+    
+    e = cos(x) / sin(x);
+    d = pow(x, -1) - x / 3 - pow(x, 3) / 45 - pow(x, 5) * 2/945 + Order(pow(x, 6));
+    result += check_series(e, 0, d);
+    
+    e = pow(numeric(2), x);
+    ex t = log(ex(2)) * x;
+    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 = pow(Pi, x);
+    t = log(Pi) * x;
+    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());
+    
+    return result;

 }
 
 // Series addition
 static unsigned series2(void)
 {
 }
 
 // Series addition
 static unsigned series2(void)
 {

-       unsigned result = 0;
-       ex e, d;
-
-       e = pow(sin(x), -1).series(x, exZERO(), 8) + pow(sin(-x), -1).series(x, exZERO(), 12);
-       d = Order(pow(x, 6));
-       result += check_series(e, exZERO(), d);
-
-       return result;
+    unsigned result = 0;
+    ex e, d;
+    
+    e = pow(sin(x), -1).series(x, 0, 8) + pow(sin(-x), -1).series(x, 0, 12);
+    d = Order(pow(x, 6));
+    result += check_series(e, 0, d);
+    
+    return result;

 }
 
 // Series multiplication
 static unsigned series3(void)
 {
 }
 
 // Series multiplication
 static unsigned series3(void)
 {

-       unsigned result = 0;
-       ex e, d;
+    unsigned result = 0;
+    ex e, d;
+    
+    e = sin(x).series(x, 0, 8) * pow(sin(x), -1).series(x, 0, 12);
+    d = 1 + Order(pow(x, 7));
+    result += check_series(e, 0, d);
+    
+    return result;
+}

 
 

-       e = sin(x).series(x, exZERO(), 8) * pow(sin(x), -1).series(x, exZERO(), 12);
-       d = 1 + Order(pow(x, 7));
-       result += check_series(e, exZERO(), d);
+// Order term handling
+static unsigned 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;
+}

 
 

-       return result;
+// Series of special functions
+static unsigned 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)*EulerGamma) +
+        pow(x+1,1)*(numeric(7,4) -
+                    numeric(3,2)*EulerGamma +
+                    numeric(1,2)*pow(EulerGamma,2) +
+                    numeric(1,12)*pow(Pi,2)) +
+        pow(x+1,2)*(numeric(15,4) -
+                    numeric(7,2)*EulerGamma -
+                    numeric(1,3)*pow(EulerGamma,3) +
+                    numeric(1,4)*pow(Pi,2) +
+                    numeric(3,2)*pow(EulerGamma,2) -
+                    numeric(1,6)*pow(Pi,2)*EulerGamma -
+                    numeric(2,3)*zeta(3)) +
+        pow(x+1,3)*(numeric(31,4) - pow(EulerGamma,3) -
+                    numeric(15,2)*EulerGamma +
+                    numeric(1,6)*pow(EulerGamma,4) +
+                    numeric(7,2)*pow(EulerGamma,2) +
+                    numeric(7,12)*pow(Pi,2) -
+                    numeric(1,2)*pow(Pi,2)*EulerGamma -
+                    numeric(2)*zeta(3) +
+                    numeric(1,6)*pow(EulerGamma,2)*pow(Pi,2) +
+                    numeric(1,40)*pow(Pi,4) +
+                    numeric(4,3)*zeta(3)*EulerGamma) +
+        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 series_expansion(void)
 {
 }
 
 unsigned series_expansion(void)
 {

-       unsigned result = 0;
-
-       cout << "checking series expansion..." << flush;
-       clog << "---------series expansion:" << endl;
-
-       result += series1();
-       result += series2();
-       result += series3();
-
-       if (!result) {
-               cout << " passed ";
-               clog << "(no output)" << endl;
-       } else {
-               cout << " failed ";
-       }
-       return result;
+    unsigned result = 0;
+    
+    cout << "checking series expansion..." << flush;
+    clog << "---------series expansion:" << endl;
+    
+    result += series1();
+    result += series2();
+    result += series3();
+    result += series4();
+    result += series5();
+    
+    if (!result) {
+        cout << " passed ";
+        clog << "(no output)" << endl;
+    } else {
+        cout << " failed ";
+    }
+    return result;

 }
 }