On Fri, Dec 4, 2009 at 9:22 PM, taco <jcho...@gmail.com> wrote:
> I have been using sage to solve for the eigenvectors and eigenvalues
> of a 4x4 symbolic matrix. It takes a few hours, but sage is able to
> return the solutions. My dilemma is that the resulting expressions are
> *HUGE*. If I ask sage to display one of the eigenvalues on screen (not
> using show()) it takes several minutes and then finally displays a
> loooong, truncated string. As a specific example, the full text file
> containing the output of the first eigenvalue.real_part() is 8.6 MB.
>
> Sooo.... I am currently working on trying to simplify the resulting
> expressions in sage to shrink them down to a smaller size. Here is the
> problem: I notice that my expressions contain *a lot* of terms like
> this, arctan2(0, looooooooooooong_expression).  Now I know that
> arctan2(0,x) = 0 for all x and so this should simplify my expressions
> a great deal. However, I cannot get sage to make this simplification
> for me. Simplify() and simplify_full() do not touch these terms. Does
> anyone have an idea about how to address this trigonometric
> simplification?

You might find this example useful:

sage: f = arctan2(0,sin(x)^2)  + cos(x^3) + 1/x
sage: g(x,y) = 0
sage: f.substitute_function(arctan2, g)
1/x + cos(x^3)

William

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