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Calculus with formal functions: substitution?

asked 2014-01-16 01:18:05 -0500

Alasdair gravatar image

If I enter

var('f,x,y')
y = function('y',x)
f = function('f',x,y)

then

f.diff(x)

returns

D[1](f)(x, y(x))*D[0](y)(x) + D[0](f)(x, y(x))

In order to perform more computations later on, I want to rewrite this, using substitutions, so it looks something like

Fy*yx + Fx

But I've got no idea how to do this. In Maxima I'd just use 'diff(f,x) as the expression to substitute for, but even trying to use dummy_diff doesn't seem to work:

from sage.calculus.calculus import dummy_diff
dummy_diff(f,x)

produces the same result as f.diff(x) above.

Does anybody know how I can use substitutions to express the results of a formal differentiation with other symbols?

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answered 2014-01-16 07:36:00 -0500

ndomes gravatar image

A suggestion: convert to a string, use string method replace and reconvert to a sage expression.

F = function('F',x)
print diff(F(2*x))
f = function('f',x)
f(x) = sage_eval(str(diff(F(2*x))).replace('D[0](F)','f'),locals={'x':x,'f':f})
f(x)
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Asked: 2014-01-16 01:18:05 -0500

Seen: 132 times

Last updated: Jan 16 '14