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"Proginoskes" <CCHeckman@xxxxxxxxx> wrote in message
news:1167546864.806173.34110@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
>
> Jon Slaughter wrote:
>> Is there such a thing?
>
> Yes; it's called a potential function.
>
> --- Christopher Heckman
>
Also, not all vector fields are conservative so there is not always a
potential function involved. I suppose here the inverse gradient would be
singular.
What I'm takling about is not what the gradient/inverse gradient do but the
*operators* themselfs.
we have
grad = <partial_x, partial_y, ...>
but what about
invgrad = ?
something like
invgrad = 1/n<int_x, int_y, ...> dot
sorta works but it doesn't.
I also know there is a producedure for finding the potential function from a
conservative vector field and this prodcedure itself is sorta an inverse
grad. What I'm wondering is if there are any other definitions of it.
sorta like how we can define
invcos = sum((-1)^n*z^(2n+1)/(2n+1))
which obviously is the inverse of cosine.
While I'm not saying the inverse gradient has a series expression like this
I'm wondering if there is some expression in terms of other
functions(possibly more elementary).
Obviously what we do know is that the inverse gradient takes a vector field
and returns a scalar field.
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