Timeline for How to only evaluate this function in the new variables after the derivative has been taken?
Current License: CC BY-SA 4.0
19 events
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| Oct 25 at 22:01 | answer | added | lericr | timeline score: 0 | |
| Oct 25 at 20:02 | comment | added | user1620696 |
@lericr I think that it is probably better to work all the time with Function, I'll try to recast the code using that, because I feel it might be a better solution in the end.
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| Oct 25 at 20:02 | comment | added | user1620696 |
@TedErsek: I will write in plain math then. Imagine that you have some collection of functions $F_{AB}(x,y)$ that takes values in $\mathbb{R}^2$. I want to construct the matrix of derivatives $\partial_i [F_{AB}]_j$. I coded the functions $F_{AB}(x,y)$ as linear combinations of symbols e[i] that play the role of the basis vectors. So I wanted to extract the coefficient and differentiate. But I want the final result to be again a function, so that I can use whatever argument I want. The problem is that to take the derivatives I'm using that coords list...
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| Oct 25 at 19:31 | comment | added | Ted Ersek | If you would explain what result you expect to get, people will provide far smarter solutions. | |
| Oct 25 at 17:50 | answer | added | lericr | timeline score: 1 | |
| Oct 25 at 17:26 | comment | added | lericr |
So, you either need to do everything with x and y and the do a replacement {x->t, y->s} or you could just do all the work with pure Functions and just use Derivative on the resulting pure function. You might even want to skip taking the coefficient and just do Derivative[1,0] or Derivative[0,1] depending on what i was passed in. Not sure if that's exactly the semantic you want, but that feels like what you're trying to do to me.
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| Oct 25 at 17:23 | comment | added | lericr |
Basically, in this expression D[coeff[i][a, b][x, y], coords[[j]]], when you pass in t and s to derF[a, b][t, s] you're going to end up taking the derivative with respect to a variable that doesn't exist in the expression your taking the derivate of.
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| Oct 25 at 17:20 | comment | added | lericr |
Okay, sorry for not having an actual answer to post yet, but I think we need to first decide whether you want to operate with polynomial expressions or with functions (functions in the sense of Function[...]. You keep referring to x and y in your code, which implies you like using those as indeterminates (formal variables), but then at the end you want to get expressions using other variables, e.g. t and s. If your end goal is to be able to use any arbitrary symbols/inputs, then probably we should lean toward using just pure Functions.
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| Oct 25 at 17:09 | comment | added | lericr |
My first thought is to use Derivative instead of D
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| Oct 25 at 17:09 | comment | added | user1620696 |
Yes, exactly! Everything works with x and y but when I change the argument it doesn't. I understood why (I hard-coded x and y in the coords list), but don't know the best work-around
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| Oct 25 at 17:07 | comment | added | lericr |
Yeah, you're sort of hard-coding everything to x and y. Don't do that. :)
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| Oct 25 at 17:07 | comment | added | lericr |
Oh, so everything works okay when you pass in x and y, just not other arguments like t and s, is that it?
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| Oct 25 at 16:49 | comment | added | user1620696 |
Hi @lericr, sorry, I should have used e[i] instead. It is always just either e[1] or e[2]. Now, I don't have a general formula for F[a,b] as a function of a and b. I have manually defined F[a, b] for a = 1,2,3 and b=1,2,3, but here I just put one of them as an example. The point is that I have a $3\times 3$ matrix of functions of {x,y} which are linear combinations of the symbols e[1] and e[2]
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| Oct 25 at 15:11 | answer | added | Ted Ersek | timeline score: 1 | |
| Oct 25 at 15:01 | comment | added | lericr |
Also, just a nit, but E is a pre-defined symbol, so you may want to avoid it.
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| Oct 25 at 15:00 | comment | added | lericr |
I'm sorry, I'm having trouble understanding what you're saying. It seems to me that you either want f1 = Function[{x, y}, x^2 e[1] + y^2 e[2]] or f2[a_, b_] := Function[{x, y}, x^2 e[a] + y^2 e[b]]. Maybe you can give a concrete example of what you expect for f[a,b] for some specific a and b. And then what you expect for coeff[i][a,b][x,y] for some specific i, a, and b.
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| Oct 25 at 14:51 | comment | added | lericr |
You have an expression like this F[a, b][x, y], but you've only defined F with F[1,2]. Does that mean a and b will always be 1 or 2? Or is that your actual question--how to define F for any a and b?
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| Oct 25 at 14:46 | comment | added | lericr |
So, the E[i] are always either E[1] or E[2]?
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| Oct 25 at 14:12 | history | asked | user1620696 | CC BY-SA 4.0 |