ASKSAGE: Sage Q&A Forum - Individual question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sun, 15 Feb 2015 13:35:34 -0600Detecting extrema and asymptotes of (nasty) functions of two variableshttps://ask.sagemath.org/question/25829/detecting-extrema-and-asymptotes-of-nasty-functions-of-two-variables/ I have a rational function of two variables* whose extrema and limiting behavior I am intersted in. Basically I want to know what values it *cannot* contain, so, I want to know limits and asymptotics. I could do this more or less manually by plotting at zooming in, zooming out until I come up with a thesis, and then taking limits to verify, but I want to do a large number of examples at once, and I'd like to write a function that just spits out the relevant values without having me look at the plot. Any ideas? A quick search turned up no useful information on taking 2D limits.
*For those interested, the function is the j-invariant of an elliptic curve, and I'm interested in a family of such curves. It's a function of two variables as the curve is found as a particular hyperplane section of a surface, and I have a two parameter family. Sat, 14 Feb 2015 13:33:18 -0600https://ask.sagemath.org/question/25829/detecting-extrema-and-asymptotes-of-nasty-functions-of-two-variables/Comment by vdelecroix for <p>I have a rational function of two variables* whose extrema and limiting behavior I am intersted in. Basically I want to know what values it <em>cannot</em> contain, so, I want to know limits and asymptotics. I could do this more or less manually by plotting at zooming in, zooming out until I come up with a thesis, and then taking limits to verify, but I want to do a large number of examples at once, and I'd like to write a function that just spits out the relevant values without having me look at the plot. Any ideas? A quick search turned up no useful information on taking 2D limits. </p>
<p>*For those interested, the function is the j-invariant of an elliptic curve, and I'm interested in a family of such curves. It's a function of two variables as the curve is found as a particular hyperplane section of a surface, and I have a two parameter family. </p>
https://ask.sagemath.org/question/25829/detecting-extrema-and-asymptotes-of-nasty-functions-of-two-variables/?comment=25830#post-id-25830Could you be more precise in what you mean? There are many ways to go to infinity in R^2 or C^2Sun, 15 Feb 2015 05:23:53 -0600https://ask.sagemath.org/question/25829/detecting-extrema-and-asymptotes-of-nasty-functions-of-two-variables/?comment=25830#post-id-25830Comment by unit 3000-21 for <p>I have a rational function of two variables* whose extrema and limiting behavior I am intersted in. Basically I want to know what values it <em>cannot</em> contain, so, I want to know limits and asymptotics. I could do this more or less manually by plotting at zooming in, zooming out until I come up with a thesis, and then taking limits to verify, but I want to do a large number of examples at once, and I'd like to write a function that just spits out the relevant values without having me look at the plot. Any ideas? A quick search turned up no useful information on taking 2D limits. </p>
<p>*For those interested, the function is the j-invariant of an elliptic curve, and I'm interested in a family of such curves. It's a function of two variables as the curve is found as a particular hyperplane section of a surface, and I have a two parameter family. </p>
https://ask.sagemath.org/question/25829/detecting-extrema-and-asymptotes-of-nasty-functions-of-two-variables/?comment=25834#post-id-25834@vdelecroix P.S. That limiting value can either be a relative extreme or an asymptote. I don't care which.Sun, 15 Feb 2015 13:35:34 -0600https://ask.sagemath.org/question/25829/detecting-extrema-and-asymptotes-of-nasty-functions-of-two-variables/?comment=25834#post-id-25834Comment by unit 3000-21 for <p>I have a rational function of two variables* whose extrema and limiting behavior I am intersted in. Basically I want to know what values it <em>cannot</em> contain, so, I want to know limits and asymptotics. I could do this more or less manually by plotting at zooming in, zooming out until I come up with a thesis, and then taking limits to verify, but I want to do a large number of examples at once, and I'd like to write a function that just spits out the relevant values without having me look at the plot. Any ideas? A quick search turned up no useful information on taking 2D limits. </p>
<p>*For those interested, the function is the j-invariant of an elliptic curve, and I'm interested in a family of such curves. It's a function of two variables as the curve is found as a particular hyperplane section of a surface, and I have a two parameter family. </p>
https://ask.sagemath.org/question/25829/detecting-extrema-and-asymptotes-of-nasty-functions-of-two-variables/?comment=25833#post-id-25833@vdelecroix Sure: what I want is either a limiting value or to know that every value is attainable. I don't care where in the domain I have to go to get there. I want to know if Sage has an algorithmic way to do this. You're right about the ambiguity though, but in practice, I look at single examples at a time and am able to quickly determine limiting behavior. I'd like to do a few hundred (or more) at once though. Does this answer your question?Sun, 15 Feb 2015 13:00:22 -0600https://ask.sagemath.org/question/25829/detecting-extrema-and-asymptotes-of-nasty-functions-of-two-variables/?comment=25833#post-id-25833