ToricVarieties_project 2.0 #74
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I started a jupyter notebook at https://github.com/lkastner/polymakejl4tv . Optionally we could also go via |
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I have already tried the standard procedure for installing the packages
on Julia Version 1.5.2 (2020-09-23), Ubuntu 18.04 and both succeeded. We can meet this week to figure out what is happening, if it is a serious issue, then an issue in With regard to offering Polymake as an alternative to
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@lkastner @fingolfin @kamalsaleh @mohamed-barakat: I have just added the first version of the new (gap4) package Convex, which mediates between
To circumvent this, I have made a few minor modifications to Long story short, here is what you currently want to do to use the ToricVarieties_project in Julia:
The test suite of |
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👋 First steps & summary of discussion on Monday, February 22 (2021):
First of all, here are the first minimal steps, that we agreed to perform:
ToricVarieties
should become accessible from Oscar/Julia. The dependencies include NConvex (>= 2017.01.01), which in turn depends on CddInterface (https://github.com/homalg-project/CddInterface). I briefly discussed this with @kamalsaleh , but could not (yet) get CddInterface to work in Julia. @fingolfin: Suggestions/ideas/help on this is very much appreciated.Beyond that, we of course have various applications in mind. Inspired by my interest, the current form of the ToricVarieties_project focuses on coherent sheaves and their cohomologies. Computations of the latter rely among others on
NormalizInterface
. @fingolfin: I have not tried if this is available in Julia. Maybe you could briefly report the status? Thank you!Similarly, it can be checked if an f.p. graded S-module (S the Cox/coordinate ring) sheafifies to zero. For the latter, I provide an alternative to https://github.com/homalg-project/CAP_project/tree/master/ToricSheaves, which I believe is at least better documented: https://github.com/homalg-project/ToricVarieties_project/tree/master/CoherentSheavesOnToricVarieties.
@mohamed-barakat , here is an example of how this test works:
Based on our discussion, other future extension include (but are not limited to):
@ Anne Frühbis-Krüger (sorry - I could not find your github account): Here is an example of the current down-to-earth blow-up resolution routine. It computes the blow-up of C^3 at the origin. This is facilitated by a star subdivision of the fan of C^3. This star subdivision is implemented in NConvex. A more extensive example is outlined in section 3.1.5 of the manual of the ToricVarieties package:
Please feel free to elaborate on what functionality for ToricVarieties you would like to see realized in the future. A minimal pseudo-code is very much appreciated. For example:
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