Coefficient of an AsymptoticExpansion

[cheuberg]

The following would be convenient:

sage: R.<m, n> = AsymptoticRing("m^QQ*n^QQ", ZZ)
sage: ae = 1 + 42/n + 2/n/m + O(n^-2)
sage: ae.monomial_coefficient(1/n)
42

The choice of the method name monomial_coefficient is motivated by the homonymous method of multivariate polynomial rings.

CC: @dkrenn @behackl

Component: asymptotic expansions

Author: Clemens Heuberger

Branch/Commit: f04154b

Reviewer: Daniel Krenn

Issue created by migration from https://trac.sagemath.org/ticket/22340

[cheuberg]

Branch: u/cheuberg/coefficient-asymptotic-expansion

[cheuberg]

Author: Clemens Heuberger

[cheuberg]

New commits:

6242878

Trac #22340: Coefficient of an AsymptoticExpansion

[cheuberg]

Commit: 6242878

[dkrenn]

comment:3

Looks good; I only have very small things to discuss:

+        - ``monomial`` -- a monomial element which can be converted
+          into the parent of this element.

What about rephrasing this to the following, so that the technical term "parent" is avoided

a monomial element which can be converted into the asymptotic ring of this element

2. Remove period after "element." above (convention in SageMath; not used in the asymptotic_ring file much...).

+            raise ValueError("non-exact monomial")
+            raise ValueError("not a monomial")

Within the asymptotic ring module usually error messages include the element (in the above, the monimial), i.e.

raise ValueError('non-exact monimal {}'.format(monomial))
raise ValueError('{} not a monomial'.format(monomial))

(Maybe inserting "is" in the latter, but not sure.)

[dkrenn]

Reviewer: Daniel Krenn

[dkrenn]

comment:4

4. The method in the multivariate polynomial ring returns 0 if the monomial is not in the polynomial. Here a KeyError will be raised. If there is no reason against 0, I think the behavior should coincide.

[dkrenn]

comment:5

5. FYI, the following (undocumented) feature of a polynomial is present:

sage: P.<x,y> = ZZ[]
sage: a=(1+2*x*y+3*x^2)
sage: a[x*y]
2
sage: a[x^2]
3

So maybe __getitem__ should have this behavior as well...

[sagetrac-git]

Changed commit from 6242878 to f04154b

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

b6f670b	Trac #22340.1+2 rephrase input documentation
621a006	Trac #22340.3: Mention monomial in error message
f04154b	Trac #22340.4: return 0 when appropriate

[cheuberg]

comment:7

1.-4. done
5. I am not convinced: If this is not a documented and tested behaviour of polynomial rings, I am slightly hesitant to introduce this here. I am not against the concept, but IMHO it should be done in the polynomial ring first (and not on this ticket).

[dkrenn]

comment:8

Replying to @cheuberg:

1.-4. done

Thank you.

5. I am not convinced: If this is not a documented and tested behaviour of polynomial rings, I am slightly hesitant to introduce this here. I am not against the concept, but IMHO it should be done in the polynomial ring first (and not on this ticket).

Fine for me not to do this now.

Patch LGTM; positive_review modulo non-finished patchbot

[dkrenn]

comment:9

Two patchbot tested this ticket now; each timed out on a single, but different doctest, and these tests are not related to this ticket. Thus I set it to positive review

[vbraun]

Changed branch from u/cheuberg/coefficient-asymptotic-expansion to f04154b