Thanks Nils. You are right. It just takes a bit longer to fail. I guess the
numerical solution is the only way to proceed. just need a way to track the
eigensystem numerically.
On Wednesday, January 21, 2015 at 3:47:12 PM UTC-5, Nils Bruin wrote:
>
> On Wednesday, January 21, 2015 at 10:56:29 AM UTC-8, Jon wrote:
>>
>> Hi all, I used the following code in notebook but it fails to give
>> results. Any suggestions?
>>
>> var('a11,a12,a13,a14,a15,a16,a22,a23,a24,a25,a26,a33,a34,a35,a36,a44,a45,a46,a55,a56,a66,p,q,r',
>>
>> domain='real')
>> g11=a11*p*p+a66*q*q+a55*r*r+2.0*a16*p*q+2.0*a15*p*r+2.0*a56*q*r;
>> g22=a66*p*p+a22*q*q+a44*r*r+2.0*a26*p*q+2.0*a46*p*r+2.0*a24*q*r;
>> g33=a55*p*p+a44*q*q+a33*r*r+2.0*a45*p*q+2.0*a35*p*r+2.0*a34*q*r;
>> g12=a16*p*p+a26*q*q+a45*r*r+(a12+a66)*p*q+(a14+a56)*p*r+(a46+a25)*q*r;
>>
>> g13=a15*p*p+a46*q*q+a35*r*r+(a14+a56)*p*q+(a13+a55)*p*r+(a36+a45)*q*r;
>>
>> g23=a56*p*p+a24*q*q+a34*r*r+(a46+a25)*p*q+(a36+a45)*p*r+(a23+a44)*q*r;
>>
>> g0=matrix(3,3,[g11,g12,g13,g12,g22,g23,g13,g12,g33]).eigenvectors_right()
>>
>> It shows error "TypeError: ECL says: Memory limit reached. Please jump to
>> an outer pointer, quit program and enlarge the memory limits before
>> executing the program again." I have 9GB ram, and it fails before
>> exhausting the ram.
>>
>
> Currently, maxima_calculus (the maxima instance that is used for some
> symbolic calculations, apparently among which is the symbolic computation
> of eigenvectors) has a memory limit of 1GB. You can lift that restriction
> with the following command:
>
> sage: maxima_calculus(1) #trigger the initialization of maxima
> 1
> sage: from sage.libs.ecl import ecl_eval
> sage: ecl_eval("(ext:set-limit 'ext:heap-size 0)")
> <ECL: 0>
>
> That said, I suspect doing so will just postpone failure, since the answer
> you're asking likely doesn't fit in any computer. It tends to be true in
> general that things that maxima is useful for tend to fit in a modest
> amount of memory. So failing be default on a relatively low memory limit
> gives early failure in cases that would likely fail anyway.
>
> To get an idea of how big your answer likely is, you can estimate the
> degree of the coefficients in the characteristic polynomial (3 times the
> degree of the terms in the matrix) and count how many monomials in 24
> variables of that degree exist. That gives you a ballpark number of term
> you're likely asking maxima to work with.
>
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