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2019-08-09 06:22:51 -0600 asked a question Betti numbers of Nakajima Quiver varieties

Is it possible to compute betti numbers of Nakajima Quiver varieties using Sage?

2019-08-01 17:51:53 -0600 received badge  Commentator
2019-08-01 17:51:53 -0600 commented question central idempotent of a finite dimensional algebra

Thanks. I edited . I hope its readable now.

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2019-08-01 07:38:44 -0600 asked a question central idempotent of a finite dimensional algebra

I tried the following

A=Algebras(QQ).FiniteDimensional().WithBasis().Semisimple().Commutative()

B = FiniteDimensionalAlgebra(QQ, [Matrix([[1,0,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0], 
[0,0,0,1,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,1]]), Matrix([[0,1,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0], [1,0,0,0,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0]]), Matrix([[0,0,1,0,0,0,0,0,0], [1,0,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0]]), Matrix([[0,0,0,1,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,1,0,0,0,0,1,0,0], [0,0,1,0,0,0,0,1,0], [1,0,0,0,0,0,0,0,1], [2,0,0,0,2,0,0,0,0], [0,2,0,0,0,2,0,0,0], [0,0,2,2,0,0,0,0,0]]), Matrix([[0,0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,1,0,0,0,0,1,0], [1,0,0,0,0,0,0,0,1], [0,1,0,0,0,0,1,0,0], [0,2,0,0,0,2,0,1,0], [0,0,2,2,0,0,0,1,0], [2,0,0,0,2,0,0,0,0]]), Matrix([[0,0,0,0,0,1,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [1,0,0,0,0,0,0,0,1], [0,1,0,0,0,0,1,0,0], [0,0,1,0,0,0,0,1,0], [0,0,2,2,0,0,0,0,0], [2,0,0,0,2,0,0,0,0], [0,2,0,0,0,2,0,0,0]]), Matrix([[0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,1], [2,0,0,0,2,0,0,0,0], [0,2,0,0,0,2,0,0,0], [0,0,2,2,0,0,0,0,0], [0,0,2,2,0,0,0,1,0], [2,0,0,0,2,0,0,0,1], [0,2,0,0,0,2,1,0,0]]), Matrix([[0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,1,0,0], [0,2,0,0,0,2,0,0,0], [0,0,2,2,0,0,0,0,0], [2,0,0,0,2,0,0,0,0], [2,0,0,0,2,0,0,0,1], [0,2,0,0,0,2,1,0,0], [0,0,2,2,0,0,0,1,0]]), Matrix([[0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [0,0,2,2,0,0,0,0,0], [2,0,0,0,2,0,0,0,0], [0,2,0,0,0,2,0,0,0], [0,2,0,0,0,2,1,0,0], [0,0,2,2,0,0,0,1,0], [2,0,0,0,2,0,0,0,1]])], category=A)

B.central_orthogonal_idempotents()

The above code gives me error. Could anyone tell me how to fix the code?enter code here

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2014-02-02 17:43:47 -0600 commented answer converting a set into a list?

@ndomes But it keeps only one 1 in the list.But i want to write set([1,1,2,2,2,3,4,5]) in partition form.That means i want output to be the list [5,4,3,2,2,2,1,1].Could you please tell me how to do it?

2014-02-02 07:29:49 -0600 asked a question converting a set into a list?

how to convert a set into a list in sage?

2013-06-26 08:30:52 -0600 asked a question writting a code for finding the kostant partition function

How to write a code for finding the kostant partition function for the elements of root lattice of rank 1 affine lie algebra $A_{1}^{(1)}$ which is defined as follows: $K(\beta)$ = the co-efficient of $e^{\beta}$ in $\prod _{\alpha \in \bigtriangleup}(1-e^{\alpha})$ where $\bigtriangleup$ is the set of positive roots of $A_{1}^{(1)}$ and $\beta$ is an element of the root lattice ?

2013-05-04 00:17:57 -0600 commented answer solving a set of equations involving both inequalities and equalities

sorry for the inconvenience.Actually i want to find all the lattice points of the polytope given by 20 equations.since i can not write all those 20 equations,hence i wanted to know if there is any code with which i can write equations in stead of tuples.

2013-05-03 22:28:41 -0600 commented answer solving a set of equations involving both inequalities and equalities

I want solutions in terms of tuples of integers not in terms of same equations in different form.

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2013-05-03 21:34:54 -0600 commented answer solving a set of equations involving both inequalities and equalities

Is there any way to define polyhedron in terms of equations rather than points since the number of equations and number of variables might be too large in which case it would not be possible to write all equations in terms of tuples.?

2013-05-02 22:00:22 -0600 received badge  Editor (source)
2013-05-02 21:59:25 -0600 asked a question solving a set of equations involving both inequalities and equalities

How to write a code in sage to find solutions of a set of equalities and inequalities in more than one variables.for example i want to find solutions for the equations $\sum_{1 \leq i \leq 3}x_i =10$ , x_1 < x_2 < x_3 .

2013-05-01 04:54:34 -0600 commented answer multiplicity of elements in a list

i want the keys in the dictionary of the output to be in matrix form but in your code keys are not in matrix form instead it puts all the entries of matrix in one row.

2013-05-01 01:08:57 -0600 asked a question multiplicity of elements in a list

if one has a list of matrices how do we build a dictionary whose keys are the distinct matrices in the list and values are the number of times that matrix appears in the list (or the multiplicity of that matrix in the list).

2013-04-22 02:33:13 -0600 commented answer code for tail and head of an edge in a bipartite graph

i looked to that but could not find proper code which i wanted..

2013-04-22 01:05:23 -0600 asked a question code for tail and head of an edge in a bipartite graph

how to write a code for finding tail and head of an edge in a bipartite graph?

2013-04-22 01:03:47 -0600 asked a question code for finding tail and head of an edge in a bipartite graph

How to write code to find the tail and head of an edge in a bipartite graph?

2013-03-28 20:09:38 -0600 commented question code which counts the number of edges

yeah,you are right.

2013-03-28 08:27:52 -0600 commented answer code for bipartite graphs

yeah because it is difficult to read the labels from the edges.so is there any code so that labels will be clear?

2013-03-28 08:20:38 -0600 asked a question code which counts the number of edges

How to write a code which counts the number of edges from a one vertex to another vertex in a directed bipartite graph?

2013-03-28 08:06:31 -0600 received badge  Supporter (source)
2013-03-28 08:03:38 -0600 commented answer code for bipartite graphs

but in your code the labels are merged on the edges.can i do so that labels will show above the edges without merging on them?

2013-03-28 07:32:13 -0600 asked a question code for bipartite graphs

How to write a code for obtaining a bipartite graph where the edges are indexed by some numbers?e.g if i write the code as D = DiGraph({ 0: [1,2,3], 1: [0,2], 2: [3], 3: [4], 4: [0,5], 5: [1] }) then only graph is coming but the edges are not indexed here.How should i modify this so that edges of the graph will be indexed?