power::series(): handle someg (trivial) singularities of the exponent...

[ginac.git] / check / exam_pseries.cpp

diff --git a/check/exam_pseries.cpp b/check/exam_pseries.cpp
index a0cea2bc3719e26b52ea9e8487eb9c1b7bab1f07..a0f87eade96c06cadbda75a74ac5045d228c8434 100644 (file)
--- a/check/exam_pseries.cpp
+++ b/check/exam_pseries.cpp
@@ -3,7 +3,7 @@
  *  Series expansion test (Laurent and Taylor series). */
 
 /*
- *  GiNaC Copyright (C) 1999-2004 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2010 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
@@ -17,10 +17,14 @@
  *
  *  You should have received a copy of the GNU General Public License
  *  along with this program; if not, write to the Free Software
- *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+ *  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
  */
 
-#include "exams.h"
+#include "ginac.h"
+using namespace GiNaC;
+
+#include <iostream>
+using namespace std;
 
 static symbol x("x");
 
@@ -28,7 +32,7 @@ static unsigned check_series(const ex &e, const ex &point, const ex &d, int orde
 {
        ex es = e.series(x==point, order);
        ex ep = ex_to<pseries>(es).convert_to_poly();
-       if (!(ep - d).is_zero()) {
+       if (!(ep - d).expand().is_zero()) {
                clog << "series expansion of " << e << " at " << point
                     << " erroneously returned " << ep << " (instead of " << d
                     << ")" << endl;
@@ -43,9 +47,15 @@ static unsigned exam_series1()
 {
        using GiNaC::log;
 
+       symbol a("a");
+       symbol b("b");
        unsigned result = 0;
        ex e, d;
        
+       e = pow(a+b, x);
+       d = 1 + Order(pow(x, 1));
+       result += check_series(e, 0, d, 1);
+
        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);
@@ -71,15 +81,15 @@ static unsigned exam_series1()
        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));
+       d = pow(x, -1) - x + pow(x, 3) - pow(x, 5) + pow(x, 7) + Order(pow(x, 8));
        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));
+       d = pow(x, -2) - 1 + pow(x, 2) - pow(x, 4) + pow(x, 6) + Order(pow(x, 8));
        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));
+       d = pow(x, -2) + numeric(1,3) + pow(x, 2) / 15 + pow(x, 4) * 2/189 + pow(x, 6) / 675  + Order(pow(x, 8));
        result += check_series(e, 0, d);
        
        e = sin(x) / cos(x);
@@ -87,7 +97,7 @@ static unsigned exam_series1()
        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));
+       d = pow(x, -1) - x / 3 - pow(x, 3) / 45 - pow(x, 5) * 2/945 - pow(x, 7) / 4725 + Order(pow(x, 8));
        result += check_series(e, 0, d);
        
        e = pow(numeric(2), x);
@@ -105,6 +115,32 @@ static unsigned exam_series1()
        result += check_series(e, 0, d, 1);
        result += check_series(e, 0, d, 2);
        
+       e = pow(x, 8) * pow(pow(x,3)+ pow(x + pow(x,3), 2), -2);
+       d = pow(x, 4) - 2*pow(x, 5) + Order(pow(x, 6));
+       result += check_series(e, 0, d, 6);
+       
+       e = cos(x) * pow(sin(x)*(pow(x, 5) + 4 * pow(x, 2)), -3);
+       d = pow(x, -9) / 64 - 3 * pow(x, -6) / 256 - pow(x, -5) / 960 + 535 * pow(x, -3) / 96768
+           + pow(x, -2) / 1280 - pow(x, -1) / 14400 - numeric(283, 129024) - 2143 * x / 5322240
+           + Order(pow(x, 2));
+       result += check_series(e, 0, d, 2);
+       
+       e = sqrt(1+x*x) * sqrt(1+2*x*x);
+       d = 1 + Order(pow(x, 2));
+       result += check_series(e, 0, d, 2);
+
+       e = pow(x, 4) * sin(a) + pow(x, 2);
+       d = pow(x, 2) + Order(pow(x, 3));
+       result += check_series(e, 0, d, 3);
+
+       e = log(a*x + b*x*x*log(x));
+       d = log(a*x) + b/a*log(x)*x - pow(b/a, 2)/2*pow(log(x)*x, 2) + Order(pow(x, 3));
+       result += check_series(e, 0, d, 3);
+
+       e = pow((x+a), b);
+       d = pow(a, b) + (pow(a, b)*b/a)*x + (pow(a, b)*b*b/a/a/2 - pow(a, b)*b/a/a/2)*pow(x, 2) + Order(pow(x, 3));
+       result += check_series(e, 0, d, 3);
+
        return result;
 }
 
@@ -115,7 +151,7 @@ static unsigned exam_series2()
        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));
+       d = Order(pow(x, 8));
        result += check_series(e, 0, d);
        
        return result;
@@ -137,6 +173,7 @@ static unsigned exam_series3()
 // Series exponentiation
 static unsigned exam_series4()
 {
+       using GiNaC::tgamma;
        unsigned result = 0;
        ex e, d;
        
@@ -144,8 +181,9 @@ static unsigned exam_series4()
        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);
+       e = pow(tgamma(x), 2).series(x==0, 2);
+       d = pow(x,-2) - 2*Euler/x + (pow(Pi,2)/6+2*pow(Euler,2)) 
+               + x*(-4*pow(Euler, 3)/3 -pow(Pi,2)*Euler/3 - 2*zeta(3)/3) + Order(pow(x, 2));
        result += check_series(e, 0, d);
        
        return result;
@@ -174,6 +212,7 @@ static unsigned exam_series5()
 // 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) -
@@ -209,17 +248,16 @@ 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));
-       return check_series(e,1,d,8);
+             +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
-             +Order(pow(x,8));
-       return check_series(e,0,d,8);
+       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))
@@ -282,8 +320,8 @@ static unsigned exam_series11()
        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);
+       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;
 }
@@ -292,6 +330,7 @@ static unsigned exam_series11()
 static unsigned exam_series12()
 {
        using GiNaC::log;
+       using GiNaC::atanh;
 
        unsigned result = 0;
        ex e, d;
@@ -316,13 +355,42 @@ static unsigned exam_series12()
        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;
-       clog << "----------series expansion:" << endl;
        
        result += exam_series1();  cout << '.' << flush;
        result += exam_series2();  cout << '.' << flush;
@@ -336,12 +404,13 @@ unsigned exam_pseries()
        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;
        
-       if (!result) {
-               cout << " passed " << endl;
-               clog << "(no output)" << endl;
-       } else {
-               cout << " failed " << endl;
-       }
        return result;
 }
+
+int main(int argc, char** argv)
+{
+       return exam_pseries();
+}