Bug in NullSpace?
- To: mathgroup at yoda.ncsa.uiuc.edu
- Subject: Bug in NullSpace?
- From: uunet!mathnx.byu.edu!smithw (William V. Smith)
- Date: Tue, 19 Jun 90 09:37:05 MDT
I turned mathematica loose on finding the null space of this matrix:
{{(p1^2*(p1^2 + p2^2 + p3^2 - s*z - z^2))/(p1^2 + p3^2), 0,
(p1*p3*(p1^2 + p2^2 + p3^2 - s*z - z^2))/(p1^2 + p3^2),
-((p1^2*p2*(s + z))/(p1^2 + p3^2)), p1*(s + z),
-((p1*p2*p3*(s + z))/(p1^2 + p3^2)),
-((p1*p3*(p1^2 + p2^2 + p3^2))/(p1^2 + p3^2)), 0,
(p1^2*(p1^2 + p2^2 + p3^2))/(p1^2 + p3^2)}, {0, 0, 0, 0, 0, 0, 0, 0, 0},
{(p1*p3*(p1^2 + p2^2 + p3^2 - s*z - z^2))/(p1^2 + p3^2), 0,
(p3^2*(p1^2 + p2^2 + p3^2 - s*z - z^2))/(p1^2 + p3^2),
-((p1*p2*p3*(s + z))/(p1^2 + p3^2)), p3*(s + z),
-((p2*p3^2*(s + z))/(p1^2 + p3^2)),
-((p3^2*(p1^2 + p2^2 + p3^2))/(p1^2 + p3^2)), 0,
(p1*p3*(p1^2 + p2^2 + p3^2))/(p1^2 + p3^2)},
{-((p1^2*p2*(s + z))/(p1^2 + p3^2)), 0,
-((p1*p2*p3*(s + z))/(p1^2 + p3^2)),
-((p1^2*p2^2*(s + 2*z))/((p1^2 + p3^2)*z)), (p1*p2*(s + 2*z))/z,
-((p1*p2^2*p3*(s + 2*z))/((p1^2 + p3^2)*z)),
-((p1*p2*p3*z)/(p1^2 + p3^2)), 0, (p1^2*p2*z)/(p1^2 + p3^2)},
{p1*(s + z), 0, p3*(s + z), (p1*p2*(s + 2*z))/z,
-(((p1^2 + p3^2)*(s + 2*z))/z), (p2*p3*(s + 2*z))/z, p3*z, 0, -(p1*z)},
{-((p1*p2*p3*(s + z))/(p1^2 + p3^2)), 0,
-((p2*p3^2*(s + z))/(p1^2 + p3^2)),
-((p1*p2^2*p3*(s + 2*z))/((p1^2 + p3^2)*z)), (p2*p3*(s + 2*z))/z,
-((p2^2*p3^2*(s + 2*z))/((p1^2 + p3^2)*z)), -((p2*p3^2*z)/(p1^2 + p3^2)),
0, (p1*p2*p3*z)/(p1^2 + p3^2)},
{-((p1*p3*(p1^2 + p2^2 + p3^2))/(p1^2 + p3^2)), 0,
-((p3^2*(p1^2 + p2^2 + p3^2))/(p1^2 + p3^2)),
-((p1*p2*p3*z)/(p1^2 + p3^2)), p3*z, -((p2*p3^2*z)/(p1^2 + p3^2)),
-((p3^2*(p1^2 + p2^2 + p3^2)*z)/((p1^2 + p3^2)*(s + z))), 0,
(p1*p3*(p1^2 + p2^2 + p3^2)*z)/((p1^2 + p3^2)*(s + z))},
{0, 0, 0, 0, 0, 0, 0, 0, 0}, {(p1^2*(p1^2 + p2^2 + p3^2))/(p1^2 + p3^2), 0,
(p1*p3*(p1^2 + p2^2 + p3^2))/(p1^2 + p3^2), (p1^2*p2*z)/(p1^2 + p3^2),
-(p1*z), (p1*p2*p3*z)/(p1^2 + p3^2),
(p1*p3*(p1^2 + p2^2 + p3^2)*z)/((p1^2 + p3^2)*(s + z)), 0,
-((p1^2*(p1^2 + p2^2 + p3^2)*z)/((p1^2 + p3^2)*(s + z)))}}
and it ground on for a day until I finally put it out of its misery.
I let Maple have a crack at it and the following (correct!) answer came
back in about, oh, 4.5 seconds: p1
{array(1 .. 9,[0,1,0,0,0,0,0,0,0]), array(1 .. 9,[1,0,- ----,0,0,0,0,0,0]),
p3
p1
array(1 .. 9,[0,0,0,1,0,- ----,0,0,0]),
p3
2 2
p1 + p3
array(1 .. 9,[0,0,0,0,1,---------,0,0,0]),
p3 p2
p1
array(1 .. 9,[0,0,0,0,0,0,0,1,0]), array(1 .. 9,[0,0,0,0,0,0,----,0,1])}
p3
So is this the result of a known bug or something? Linear algebra
functions seem rather weak in Mathematica in my experience.
These computations were done on a NeXT, 16 MB ram (660 meg disk with
about 300 meg available for swap [I don't think it needed it!]). Some body
else want to try this. Maybe its just my system. Hold it! Just
tried same problem on a MIPS. Same results, seems to just grind on it.
This can't be that tough can it??