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Spec and patches for singular affine toric varieties / algebraic schemes #10540
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comment:2
My first version was a bit naive with the toric ideals. The updated patch implements the Hosten&Sturmfels algorithm to find a finite generating set of toric ideals. |
comment:3
One more bug fixed. Also, the syntax is now much more sensible, in particular |
comment:4
Given the issue #10708 where the ideal dimension is completely off for some term orders, I find it prudent to convert the ideal to the standard reverse-degree lex order. The updated patch does precisely this. |
Reviewer: Andrey Novoseltsev |
comment:5
From PEP8: "Method definitions inside a class are separated by a single blank line." While this ticket inserts a bunch of second blank lines ;-) |
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comment:6
From PEP8: "A Foolish Consistency is the Hobgoblin of Little Minds" :-) I changed to single blank lines in |
comment:7
Comments/questions on the first patch (toric ideals):
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comment:8
I've added a possibility to specify the polynomial ring directly and documentation. As for the base ring, really you only have to work over |
comment:9
Looks good! For the second patch:
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comment:10
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Updated patch |
comment:11
Attachment: trac_10540_Spec_of_affine_toric_variety.patch.gz I am getting the following:
Also, it seems that with |
Work Issues: doctest failures |
Attachment: trac_10540_toric_ideals.patch.gz Updated patch |
comment:12
Andrey reported a performance regression in Sage-4.7.1.alpha2 for the long doctests. The reason is that the syntax for computing the LLL-reduced kernel changed from The updated patch switches to the new syntax and works as fast as before. |
Changed keywords from none to sd31 |
Changed work issues from doctest failures to none |
comment:13
One of the doctests crashes with Sage-4.7.alpha2 because of #11481. |
comment:14
The doctests pass with the patch from #11481. |
comment:17
Hi Jeroen, if there is any chance to include this ticket into 4.7.1, it would be greatly appreciated! (I am participating in a toric summer school in a month and it would be great if this functionality was available in a stable release by then.) |
Merged: sage-4.7.1.alpha4 |
This patch implements
In particular, Sage can now compute the dimension and smoothness for algebraic subschemes of singular toric varieties as well.
This uses both the Hilbert basis for cones and the algebraic schemes, and, therefore, depends on
Apply
Depends on #9918
Depends on #10525
Depends on #10023
Depends on #10529
Depends on #11481
CC: @novoselt @jdemeyer
Component: algebraic geometry
Keywords: sd31
Author: Volker Braun
Reviewer: Andrey Novoseltsev
Merged: sage-4.7.1.alpha4
Issue created by migration from https://trac.sagemath.org/ticket/10540
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