[Maxima-commits] CVS: maxima/tests rtestint.mac,1.10,1.11

[Raymond T. <rt...@us...>]

Update of /cvsroot/maxima/maxima/tests
In directory sc8-pr-cvs1.sourceforge.net:/tmp/cvs-serv21111/tests

Modified Files:
	rtestint.mac 
Log Message:
o Change the test integrate(log(x)^k1,x,0,1) to
  integrate((-log(x))^k1,x,0,1) because the former integrand is
  complex for 0 <= x <= 1.
o The integral integrate(x^(1/3)/sqrt(-log(x)),x,0,1) had the wrong
  sign for the result because radexpand is true.  Correct the sign,
  and set radexpand:false for this test.
o Add comments about these to the tests.


Index: rtestint.mac
===================================================================
RCS file: /cvsroot/maxima/maxima/tests/rtestint.mac,v
retrieving revision 1.10
retrieving revision 1.11
diff -u -d -r1.10 -r1.11
--- rtestint.mac	15 Mar 2006 18:14:12 -0000	1.10
+++ rtestint.mac	16 Mar 2006 17:36:35 -0000	1.11
@@ -606,19 +606,49 @@
 /*
  * Maxima asks if k is an integer, but it doesn't matter,
  * and I don't know how to tell maxima that k isn't an integer.
+ *
  */
-(assume(k1>0),declare(k1,integer),0);
+(assume(k1>0),declare(k1,noninteger),0);
 0;
+/*
+ * This is not such a good integral to use.  log(x) is negative over the integration
+ * limits, so integrand is complex.  Let's change the integrand to be
+ * (-log(x))^k1 instead, which is real-valued.
+ *
+ * In this case, it's easy to see that the substitution y=-log(x)
+ * gives as a gamma function.
+ */
+/*
 integrate(log(x)^k1,x,0,1);
 (-1)^k1*gamma(k1+1);
+*/
+integrate((-log(x))^k1,x,0,1);
+gamma(k1+1);
+
 
 /* p. 120 */
 integrate(sqrt(log(x))/x^2,x,1,inf);
 sqrt(%pi)/2;
 
 /* p. 120 */
+/*
+ * Wang says -sqrt(%pi)/sqrt(4/3) = -sqrt(3)*sqrt(%pi)/2.
+ *
+ * This is wrong.  Clearly, the integrand is positive, so the integral
+ * must be positive.
+ *
+ * The issue is that radexpand is true so the Risch integrator is
+ * doing something not quite right and getting the sign wrong.  If we
+ * set radexpand to false, we get the correct answer.
+ */
+radexpand:false;
+false;
+
 integrate(x^(1/3)/sqrt(-log(x)),x,0,1);
--sqrt(3)*sqrt(%pi)/2;
+sqrt(3)*sqrt(%pi)/2;
+
+radexpand:true;
+true;
 
 /* p. 121 */
 /*