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??

```

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