Multivariable Series Expansion #25483
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The example is not great because it is already basically in a series format: A more interesting example could be (if it worked): |
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Correct me if I'm wrong but simply chaining the series command does not generally result in the correct Taylor approximation. x0,y0 = 0,-2
AP = {x:x0,y:y0}
dx = z.diff(x)
dy = z.diff(y)
Z_tan = z.subs(AP) + dx.subs(AP)*(x-x0) + dy.subs(AP)*(y-y0)
Z_tanFor now I'll have to do with my own unoptimized functions, but this would be some very handy functionality of the series method. |
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That is correct. I was just saying that a function like the one that you showed is not that interesting as an example because it does not get any
Yes, but it is not a simple thing to do. For starters the whole approach of representing series as just a sum with a |
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Ah I get what you're saying now. That would explain why it hasn't been implemented yet. What about a completely seperate function that computes only finite series, so you can scrap the residual term. Something like |
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See #26941 (comment) |
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Native support for multivariable series
As Taylor approximations are a very common problem in engineering I would love to see the
expr.seriesmethod expanded to natively support more than one variable. This would work intuitively with already existing syntax.I'd imagine something like this:
which would result in the equation for the tangential plane at$P(0;2)$ .
I'd love to hear you guys opinion though, maybe there's already a perfect function for this.
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