Make polynomial .diff() accept optional argument times for repeated differentiation.

[ncalexan]

Make polynomial .diff() accept optional argument times for repeated differentiation.

Makes diff do its thing multiple time if requested.

-    def diff(self, MPolynomial_libsingular variable, have_ring=True):
+    def diff(self, MPolynomial_libsingular variable, times=1, have_ring=True):

Component: commutative algebra

Keywords: polynomial diff times repeat

Issue created by migration from https://trac.sagemath.org/ticket/1578

[ncalexan]

comment:1

Hmm, bundle and patch might need to be rebased. Sorry.

[mwhansen]

comment:3

The failures are okay, since they just have redundant information. I tested things out and all tests passed.

[ncalexan]

Attachment: ncalexan-mpoly-diff-times-updated.patch.gz

This should be the final version; use this over the two earlier bundles and one earlier patch.

[sagetrac-mabshoff]

comment:6

I deleted the older patches and bundles.

Cheers,

Michael

[robertwb]

comment:7

'times' seems like an odd name for the argument--it returns the "times-th derivative"?

[malb]

comment:8

How about accepting monomials instead of variables only. Then x² would encode 2-times x, and x²y³ would mean 3-times y and 2-times x.

[robertwb]

comment:9

I don't know if we implement any, but there are functions such that d^2f/dxdy != d^2 f/dydx.

However, I think the ability to pass in a monomial is an excellent idea. Perhaps beyond the scope of this patch though.

[jasongrout]

comment:11

In mathematica, you can pass a list to the differentiate command and the function will be differentiated with respect to successive elements of the list. So maybe something like:

f.diff([x,y,y,x])

could specify differentiating first wrt x, then y, then y, and then x again.

The command in the patch could be invoked as:

f.diff([x]*3)

I agree that f.diff(x,3) looks better, though.

[jasongrout]

comment:12

We should probably note that this is supported by symbolic polynomials already.

sage: x,y=var('x y')
sage: f=exp(2*x*y)
sage: f.diff(x)
2*y*e^(2*x*y)
sage: f.diff(x,x)
4*y^2*e^(2*x*y)
sage: f.diff(x,2)
4*y^2*e^(2*x*y)
sage: f.diff(x,2,y)
8*x*y^2*e^(2*x*y) + 8*y*e^(2*x*y)
sage: f.diff(x,2,y,y)
16*x^2*y^2*e^(2*x*y) + 32*x*y*e^(2*x*y) + 8*e^(2*x*y)
sage: f.diff(x,2,y,2)
16*x^2*y^2*e^(2*x*y) + 32*x*y*e^(2*x*y) + 8*e^(2*x*y)

[JohnCremona]

comment:13

The patch looks ok to me, looking at the diffs (I have not tried applying it).

[sagetrac-dmharvey]

comment:14

there is action on this at #753

[sagetrac-dmharvey]

comment:15

I am closing this since it has been superseded by #753.

[sagetrac-mabshoff]

comment:17

This isn't really a duplicate and I consider this fixed. It looks like a borderline case, so I tend to call those tickets fixed.

Cheers,

Michael