ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Thu, 09 Nov 2017 21:42:47 +0100Visualizing Toric fans in Sagehttps://ask.sagemath.org/question/39468/visualizing-toric-fans-in-sage/I am learning basics of toric geometry as applied to physics. I would like to know if there's a way to visualize toric fans using Sagemath, and also draw dual toric diagrams.
For example, if I give explicit coordinates of vectors defining a fan, can I visualize the fan and also its dual toric fan using Sage?
I have found resources on the net about using Sage for toric varieties, but I am currently looking for answers to much simpler questions.toricwebThu, 09 Nov 2017 21:42:47 +0100https://ask.sagemath.org/question/39468/Is there a way to compute the secondary (GKZ) fan with sage?https://ask.sagemath.org/question/37758/is-there-a-way-to-compute-the-secondary-gkz-fan-with-sage/I am doing research in Toric varieties and I am hoping for a quick way to look at examples.
Looking through "Rational Polyhedral Fans" and "Toric Varieties" pages there is a lot of information that can be calculated about fans/toric varieties but I have not found code to calculate the secondary fan.
I am looking for a simple way to do this either given a Toric variety (or its fan), or from starting from the set of $\beta$'s, as described in Chapter 14 of "Toric Varieties" by Cox, Little, Schenck.
Does anyone know if Sage has anyway to do this?CEHThu, 01 Jun 2017 17:52:35 +0200https://ask.sagemath.org/question/37758/Can the star of a ray of a fan be computed in sage?https://ask.sagemath.org/question/36303/can-the-star-of-a-ray-of-a-fan-be-computed-in-sage/Let `p` be a ray of a fan `F` in a lattice `N`. Let `Np` be the quotient lattice `N / N.span(p)`. The *star* of `p` is the fan in `Np` defined by
Star(p) = {bar(sigma) | p <= sigma}
(This definition is taken from Definition 4.4 on page 55 of [this paper](http://algant.eu/documents/theses/gualdi.pdf). Is there an algorithm to compute `Star(p)` in `sage`? If so, what about the embedding morphism `Star(p) --> F`?done_with_fishSun, 15 Jan 2017 22:55:25 +0100https://ask.sagemath.org/question/36303/Can the fan of a decomposable toric vector bundle be computed in sage?https://ask.sagemath.org/question/34572/can-the-fan-of-a-decomposable-toric-vector-bundle-be-computed-in-sage/Given r Cartier divisors D1,...,Dr on a toric variety X we have a locally free sheaf
OO_X(D1)+...+OO_X(Dr)
of rank r. Cox, Little, and Schenck outline an algorithm for constructing the fan of the corresponding vector bundle on page 337 of their book Toric Varieties. Is this algorithm a feature of sage? If not, has anyone written it down in sage?done_with_fishWed, 24 Aug 2016 18:11:27 +0200https://ask.sagemath.org/question/34572/Problems with heft vectors in M2https://ask.sagemath.org/question/24038/problems-with-heft-vectors-in-m2/I hope this question is on-topic on this forum.
I am working with the "NormalToricVarieties" package in M2.
Part of my research involves determining when the higher cohomology groups of certain twists of the structure sheaf of a toric variety vanish. I have a specific example where in computing HH^1(X,OO_X(1,1)) I am confronted with the following error:
stdio:8:3:(3): error: heft vector required that is positive on the degrees of the variables {0, 1, 2, 3, 4, 5, 6}
I know that this group should be trivial but somehow the absence of a heft vector is bothering the compiler. I'm not sure whether or not there is a way to get M2 to compute this group.
Does anyone happen to know of any workarounds in this situation?
The example I am using is as follows:
loadPackage "NormalToricVarieties";
Rho = {
{ 0 , 0 , 0 , 0 , 1 }
, { 1 , 0 , 0 , 0 , 1 }
, { 0 , 1 , 0 , 0 , 1 }
, { 0 , 0 , 1 , 0 , 1 }
, { 0 , 0 , 0 , 1 , 1 }
, { -1 , -2 , -1 , -1 , 1 }
, { -2 , -1 , -1 , -1 , 1 }
};
Sigma = {
{ 2 , 3 , 4 , 5 , 6 }
, { 0 , 1 , 2 , 3 , 4 }
, { 0 , 1 , 2 , 3 , 5 }
, { 0 , 1 , 2 , 4 , 5 }
, { 0 , 1 , 3 , 4 , 5 }
, { 0 , 2 , 3 , 4 , 5 }
};
X = normalToricVariety(Rho,Sigma);
HH^2(X,OO_X(1,1)) -- HH^n for n=2 works fine
HH^1(X,OO_X(1,1)) -- HH^n for n=1 gives an errorbfitzpatFri, 05 Sep 2014 22:49:05 +0200https://ask.sagemath.org/question/24038/