[PATCH] Improve normalisation of negative exponents.

[ginac.git] / check / exam_normalization.cpp

diff --git a/check/exam_normalization.cpp b/check/exam_normalization.cpp
index d98dec681a79d9071d03ccc3cfd300f36545cdcc..17cf83db1ea1e83cc37c3db5424ee75edc4a1175 100644 (file)
--- a/check/exam_normalization.cpp
+++ b/check/exam_normalization.cpp
@@ -3,7 +3,7 @@
  *  Rational function normalization test suite. */
 
 /*
- *  GiNaC Copyright (C) 1999-2015 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2021 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
@@ -223,6 +223,113 @@ static unsigned exam_content()
        return result;
 }
 
+static unsigned exam_exponent_law()
+{
+       unsigned result = 0;
+       ex e, d;
+
+       // simple case
+       e = exp(2*x)-1;
+       e /= exp(x)-1;
+       d = exp(x)+1;
+       result += check_normal(e, d);
+
+       // More involved with powers of two exponents
+       e = exp(15*x)+exp(12*x)+2*exp(10*x)+2*exp(7*x);
+       e /= exp(5*x)+exp(2*x);
+       d = pow(exp(5*x), 2) +2*exp(5*x);
+       result += check_normal(e, d);
+
+       lst bases = {
+                5*exp(3*x)+7, // Powers of a single exponent
+                5*exp(3*x)+7*exp(2*x), // Two different factors of a single variable
+                5*exp(3*x)+7*exp(2*y) // Exponent with different variable
+       };
+
+       for (auto den : bases) {
+               e = pow(den, 3).expand();
+               e /= pow(den, 2).expand();
+               result += check_normal(e, den);
+       }
+
+       // Negative exponents
+       e = (exp(2*x)-exp(-2*x))/(exp(x)-exp(-x));
+       ex en = e.normal();
+       // Either exp(x) or exp(-x) can be viewed as a "symbol" during run-time
+       // thus two different forms of the result are possible
+       ex r1 = (exp(2*x)+1)/exp(x) ;
+       ex r2 = (exp(-2*x)+1)/exp(-x);
+
+       if (!en.is_equal(r1) && !en.is_equal(r2)) {
+               clog << "normal form of " << e << " erroneously returned "
+                    << en << " (should be " << r1 << " or " << r2 << ")" << endl;
+               result += 1;
+       }
+
+       return result;
+}
+
+static unsigned exam_power_law()
+{
+       unsigned result = 0;
+       ex e, d;
+
+       lst bases = {x, pow(x, numeric(1,3)), exp(x), sin(x)}; // We run all check for power base of different kinds
+
+       for ( auto b : bases ) {
+
+               // simple case
+               e = 4*b-9;
+               e /= 2*sqrt(b)-3;
+               d = 2*sqrt(b)+3;
+               result += check_normal(e, d);
+
+               // Fractional powers
+               e = 4*pow(b, numeric(2,3))-9;
+               e /= 2*pow(b, numeric(1,3))-3;
+               d = 2*pow(b, numeric(1,3))+3;
+               result += check_normal(e, d);
+
+               // Different powers with the same base
+               e = 4*b-9*sqrt(b);
+               e /= 2*sqrt(b)-3*pow(b, numeric(1,4));
+               d = 2*sqrt(b)+3*pow(b, numeric(1,4));
+               result += check_normal(e, d);
+
+               // Non-numeric powers
+               e = 4*pow(b, 2*y)-9;
+               e /= 2*pow(b, y)-3;
+               d = 2*pow(b, y)+3;
+               result += check_normal(e, d);
+
+               // Non-numeric fractional powers
+               e = 4*pow(b, y)-9;
+               e /= 2*pow(b, y/2)-3;
+               d = 2*pow(b, y/2)+3;
+               result += check_normal(e, d);
+
+               // Different non-numeric powers
+               e = 4*pow(b, 2*y)-9*pow(b, 2*z);
+               e /= 2*pow(b, y)-3*pow(b, z);
+               d = 2*pow(b, y)+3*pow(b, z);
+               result += check_normal(e, d);
+
+               // Different non-numeric fractional powers
+               e = 4*pow(b, y)-9*pow(b, z);
+               e /= 2*pow(b, y/2)-3*pow(b, z/2);
+               d = 2*pow(b, y/2)+3*pow(b, z/2);
+               result += check_normal(e, d);
+
+               // Negative powers
+               e = (b -pow(b,-1));
+               e /= (pow(b, numeric(1,2)) - pow(b, numeric(-1,2)));
+               d = (b+1)*pow(b, numeric(-1,2));
+               result += check_normal(e, d);
+       }
+
+       return result;
+}
+
 unsigned exam_normalization()
 {
        unsigned result = 0;
@@ -234,6 +341,8 @@ unsigned exam_normalization()
        result += exam_normal3(); cout << '.' << flush;
        result += exam_normal4(); cout << '.' << flush;
        result += exam_content(); cout << '.' << flush;
+       result += exam_exponent_law(); cout << '.' << flush;
+       result += exam_power_law(); cout << '.' << flush;
        
        return result;
 }