Following up with another data point:
Sage 4.3.4 under some version of Redhat Linux on an intel computer
with 64GB RAM.
The case that failed on the 4GB macbookpro succeeds here: minimize()
returns a value.
A larger case fails in the same manner, minimize() returning without
a value:
S is a polynomial over Q in 48 variables
S is a quartic polynomial
S contains 71138 terms.
Daniel Friedan
On Jul 13, 1:07 pm, 8fjm39j <[email protected]> wrote:
> I am trying to minimize numerically (over the reals) a polynomial S
> with rational coefficients.
>
> The function sage.numerical.optimize.minimize() returns without
> returning a value.
>
> Here's the relevant fragment of Sage code (executed using the menu
> item 'evaluate all')
>
> ===== BEGIN CODE FRAGMENT =====================================
>
> N
> 44
>
> # RQ = PolynomialRing(QQ, N, 'x', sparse=True); # this was executed
> earlier
>
> S in RQ
> True
>
> print 'S is a polynomial over Q in', len(S.variables()), 'variables';
> print 'S is a quartic polynomial';
> print 'S contains', len(S.coefficients()), 'terms';
> S is a polynomial over Q in 44 variables
> S is a quartic polynomial
> S contains 55188 terms
>
> S_exp =SR(S);
> init_values = [0] * len(S_exp.variables());
> soln=sage.numerical.optimize.minimize(S_exp,init_values);
> soln
> Traceback (click to the left of this block for traceback)
> ...
> NameError: name 'soln' is not defined
>
> ===== END OF CODE FRAGMENT =====================================
>
> This does not happen for a smaller problem:
> S is a polynomial over Q in 40 variables
> S is a quartic polynomial
> S contains 34766 terms
> i.e., minimize() does successfully return a value.
>
> I'm running Sage Version 4.4.4 under OS X 10.6.4 on a macbookpro with
> 4GB RAM, acquired in the form
> sage-4.4.4-OSX-64bit-10.6-i386-Darwin.dmg
>
> I would attach the worksheet itself to this posting, if I saw a way to
> do so.
>
> Any help would be much appreciated. Also any pointers towards a more
> efficient method to minimize such polynomials. I'm just starting to
> learn Sage and Python. At the moment, the bottlenecks appear to be
> the conversion to a symbolic expression, 'S_exp =SR(S); ' and the
> execution of minimize(). The polynomial algebra used to construct S
> executes relatively quickly. The number of variables is of the form
> N=4mn where m and n are positive integers. I'd like to take N slightly
> larger, though I don't expect that my computing resources will allow
> taking N much larger, even if I use a more efficient method to
> minimize S.
>
> thanks,
> Daniel Friedan
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