# [Maxima] Testsuite failures in rtesthyp.mac

Dieter Kaiser drdieterkaiser at web.de
Thu Dec 18 17:06:41 CST 2008

```I am preparing a commit to correct the wrong result in the function
facsum-expand.

But at first I have run the testsuite. I have got the following failures in
hyp.lisp for GCL 2.6.8 on Windows XP. I do not get these failures with CLISP
2.44 on Windows XP.

I never observed these failures.

********************** Problem 85 ***************
Input:
hgfred([-a,a],[3/2],zn)-(1-zn)^(3/2)/2/(1/2-a)
*diff((1-zn)^((-1)/2)*hgfred([-a,a],[1/2],zn),zn,1)
/(a+1/2)

Result:
(1-zn)^(5/2)*zn^(a-1/2)
*((3/2-a)*((2*a*(%i/(2*sqrt(zn))-1/(2*sqrt(1-zn)))
*(%i*sqrt(zn)+sqrt(1-zn))^(2*a-1)
+2*a*(-%i/(2*sqrt(zn))-1/(2*sqrt(1-zn)))
*(sqrt(1-zn)-%i*sqrt(zn))^(2*a-1))
/(2*sqrt(1-zn))
+((%i*sqrt(zn)+sqrt(1-zn))^(2*a)
+(sqrt(1-zn)-%i*sqrt(zn))^(2*a))
/(4*(1-zn)^(3/2)))
/zn^((2*a-1)/2)
+((2*a*(-%i/(4*zn^(3/2))-1/(4*(1-zn)^(3/2)))
*(%i*sqrt(zn)+sqrt(1-zn))^(2*a-1)
+2*a*(2*a-1)*(%i/(2*sqrt(zn))-1/(2*sqrt(1-zn)))^2
*(%i*sqrt(zn)+sqrt(1-zn))^(2*a-2)
+2*a*(%i/(4*zn^(3/2))-1/(4*(1-zn)^(3/2)))
*(sqrt(1-zn)-%i*sqrt(zn))^(2*a-1)
+2*a*(2*a-1)*(-%i/(2*sqrt(zn))-1/(2*sqrt(1-zn)))^2
*(sqrt(1-zn)-%i*sqrt(zn))^(2*a-2))
/(2*sqrt(1-zn))
+(2*a*(%i/(2*sqrt(zn))-1/(2*sqrt(1-zn)))
*(%i*sqrt(zn)+sqrt(1-zn))^(2*a-1)
+2*a*(-%i/(2*sqrt(zn))-1/(2*sqrt(1-zn)))
*(sqrt(1-zn)-%i*sqrt(zn))^(2*a-1))
/(2*(1-zn)^(3/2))
+3*((%i*sqrt(zn)+sqrt(1-zn))^(2*a)
+(sqrt(1-zn)-%i*sqrt(zn))^(2*a))
/(8*(1-zn)^(5/2)))
*zn^(3/2-a))
/(2*(1/2-a)*(3/2-a)*(a+1/2))
-((2*a*(%i/(2*sqrt(zn))-1/(2*sqrt(1-zn)))*(%i*sqrt(zn)+sqrt(1-zn))^(2*a-1)
+2*a*(-%i/(2*sqrt(zn))-1/(2*sqrt(1-zn)))*(sqrt(1-zn)-%i*sqrt(zn))^(2*a-1))
/(2*sqrt(1-zn))
+((%i*sqrt(zn)+sqrt(1-zn))^(2*a)+(sqrt(1-zn)-%i*sqrt(zn))^(2*a))
/(4*(1-zn)^(3/2)))
*(1-zn)^(3/2)
/(2*(1/2-a)*(a+1/2))

This differed from the expected result:
0

********************** Problem 86 ***************
Input:
hgfred([2+a,-a],[1/2],zn)-zn^(1-a)*diff(zn^(1+a)*hgfred([a,-a],[1/2],zn),zn,2)
/(a*(1+a))

Result:
(1-zn)^(3/2)*zn^(a+1/2)
*((1/2-a)*((%i*sqrt(zn)+sqrt(1-zn))^(2*a)
+(sqrt(1-zn)-%i*sqrt(zn))^(2*a))
/(2*sqrt(1-zn)*zn^((2*a+1)/2))
+(2*a*(%i/(2*sqrt(zn))-1/(2*sqrt(1-zn)))
*(%i*sqrt(zn)+sqrt(1-zn))^(2*a-1)
+2*a*(-%i/(2*sqrt(zn))-1/(2*sqrt(1-zn)))
*(sqrt(1-zn)-%i*sqrt(zn))^(2*a-1))
*zn^(1/2-a)
/(2*sqrt(1-zn))
+((%i*sqrt(zn)+sqrt(1-zn))^(2*a)+(sqrt(1-zn)-%i*sqrt(zn))^(2*a))
*zn^(1/2-a)
/(4*(1-zn)^(3/2)))
/(1/2-a)
-zn^(1-a)*((2*a*(-%i/(4*zn^(3/2))-1/(4*(1-zn)^(3/2)))
*(%i*sqrt(zn)+sqrt(1-zn))^(2*a-1)
+2*a*(2*a-1)*(%i/(2*sqrt(zn))-1/(2*sqrt(1-zn)))^2
*(%i*sqrt(zn)+sqrt(1-zn))^(2*a-2)
+2*a*(%i/(4*zn^(3/2))-1/(4*(1-zn)^(3/2)))
*(sqrt(1-zn)-%i*sqrt(zn))^(2*a-1)
+2*a*(2*a-1)*(-%i/(2*sqrt(zn))-1/(2*sqrt(1-zn)))^2
*(sqrt(1-zn)-%i*sqrt(zn))^(2*a-2))
*zn^(a+1)
/2
+(a+1)*(2*a*(%i/(2*sqrt(zn))-1/(2*sqrt(1-zn)))
*(%i*sqrt(zn)+sqrt(1-zn))^(2*a-1)
+2*a*(-%i/(2*sqrt(zn))-1/(2*sqrt(1-zn)))
*(sqrt(1-zn)-%i*sqrt(zn))^(2*a-1))*zn^a
+a*(a+1)
*((%i*sqrt(zn)+sqrt(1-zn))^(2*a)+(sqrt(1-zn)-%i*sqrt(zn))^(2*a))
*zn^(a-1)
/2)
/(a*(a+1))

This differed from the expected result:
0

********************** Problem 88 ***************
Input:
ratsimp(hgfred([a,-a],[(-1)/2],zn)-zn^(3/2)
*diff(zn^((-1)/2)*hgfred([a,-a],[1/2],zn),
zn,1)
/((-1)/2))

Result:
-((%i*a*(sqrt(1-zn)-%i*sqrt(zn))^(2*a)-%i*a*(%i*sqrt(zn)+sqrt(1-zn))^(2*a))
*zn^2
+(a*(%i*sqrt(zn)+sqrt(1-zn))^(2*a)+a*(sqrt(1-zn)-%i*sqrt(zn))^(2*a))
*sqrt(1-zn)*zn^(3/2))
/(sqrt(1-zn)*sqrt(zn))

This differed from the expected result:
0

********************** Problem 90 ***************
Input:
ratsimp(hgfred([a-2,-a],[(-1)/2],zn)-zn^(3/2)*(1-zn)^(1/2+a)
*diff(
zn^a*(1-zn)^(2-a)
*diff(
zn^(1/2-a)*(1-zn)^((-1)/2)
*hgfred([a,-a],[1/2],zn),
zn,1),zn,1)
/((-1)/2*(1/2-a)))

Result:
-(sqrt(zn)*((2*%i*a*(sqrt(1-zn)-%i*sqrt(zn))^(2*a)
-2*%i*a*(%i*sqrt(zn)+sqrt(1-zn))^(2*a))
*zn^2
+(2*%i*a*(%i*sqrt(zn)+sqrt(1-zn))^(2*a)
-2*%i*a*(sqrt(1-zn)-%i*sqrt(zn))^(2*a))
*zn)
+sqrt(1-zn)*((2*a*(%i*sqrt(zn)+sqrt(1-zn))^(2*a)
+2*a*(sqrt(1-zn)-%i*sqrt(zn))^(2*a))
*zn^2
+(-a*(%i*sqrt(zn)+sqrt(1-zn))^(2*a)
-a*(sqrt(1-zn)-%i*sqrt(zn))^(2*a))
*zn))
/sqrt(1-zn)

This differed from the expected result:
0

254/258 tests passed.

The following 4 problems failed: (85 86 88 90)

Dieter Kaiser

```