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Sep 18, 2010, 6:20:29 AM9/18/10

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x = var("x")

d = function("d",x)

diff(x, d)

d = function("d",x)

diff(x, d)

output:

Traceback (click to the left of this block for traceback)

...

TypeError: argument symb must be a symbol

Sep 18, 2010, 9:42:17 PM9/18/10

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On Sep 18, 6:20 am, alien308 <alien3...@gmail.com> wrote:

> x = var("x")

> d = function("d",x)

> diff(x, d)

>

message is totally unhelpful, though presumably this derivative

doesn't make sense 'as is'.

If you instead do

sage: diff(d,x)

D[0](d)(x)

Which is probably what you want, though the representation leaves

something to be desired (which is a long-standing debate on several

Trac tickets).

But there are other issues here, at least to me - maybe someone can

explain this:

If you don't do let d = function("d", x), but just do function("d",x),

you get a different error. The error comes from trying to make d an

element of the symbolic ring, which perhaps isn't a bug per se, though

at the very least the error message for such a case could be more

helpful.

Moreover,

sage: diff(d,x)

gives an error

TypeError:

Not even an error message! Although

sage: function?

doesn't say you can do this (not assign function("d",x) to a Python

variable), it also doesn't say you can't.

- kcrisman

Sep 18, 2010, 9:43:57 PM9/18/10

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Actually, the subject of your email now makes a little more sense.

But I don't think that one can define an inverse function quite this

easily! That would indeed be *very* obscure notation! I don't know

if we can define a symbolic inverse of this kind yet, or whether that

would even be easy - much less to differentiate it. Anyone?

- kcrisman

But I don't think that one can define an inverse function quite this

easily! That would indeed be *very* obscure notation! I don't know

if we can define a symbolic inverse of this kind yet, or whether that

would even be easy - much less to differentiate it. Anyone?

- kcrisman

Sep 19, 2010, 12:50:51 AM9/19/10

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Thanks.

Sep 19, 2010, 12:44:59 PM9/19/10

to sage-support

On Sep 18, 6:43 pm, kcrisman <kcris...@gmail.com> wrote:

> Actually, the subject of your email now makes a little more sense.

> But I don't think that one can define an inverse function quite this

> easily! That would indeed be *very* obscure notation! I don't know

> if we can define a symbolic inverse of this kind yet, or whether that

> would even be easy - much less to differentiate it. Anyone?

Finding an expression for the derivative of an inverse is part of most
> Actually, the subject of your email now makes a little more sense.

> But I don't think that one can define an inverse function quite this

> easily! That would indeed be *very* obscure notation! I don't know

> if we can define a symbolic inverse of this kind yet, or whether that

> would even be easy - much less to differentiate it. Anyone?

first calculus courses:

Suppose that f : R -> R is a differentiable function and that y=f(x).

Suppose that g : R -> R is an inverse to f, i.e., x=g(y).

Find an expression for g'(y) in terms of f'(x). [HINT: use the chain

rule on f(g(y) or g(f(x))]

One usually continues with stating the inverse function theorem to

conclude that if this computation doesn't rule out the existence of a

differentiable inverse, then the inverse exists locally, an expression

for which you can now find by integration [so, probably rather hard to

do in general on a symbolic level]

Sep 19, 2010, 3:03:22 PM9/19/10

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looking for a generic way to express the inverse of a symbolic

function, perhaps similarly to the way Mathematica's "InverseFunction"

works:

http://reference.wolfram.com/mathematica/ref/InverseFunction.html

I don't know what sort of features are available in Sage or any of its

standard packages that could provide this sort of functionality.

Then again, I might have gotten this all wrong.

-- Tianwei

Sep 19, 2010, 9:39:57 PM9/19/10

to sage-support

sure whether I understood the point of the thread :) But hopefully I

did. It seemed that this is what the poster wanted.

- kcrisman

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