REKHA BISWAL's profile - activity

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

Thanks. I edited . I hope its readable now.

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

@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?

how to convert a set into a list in sage?

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 ?

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.

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

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.?

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 .

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.

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).

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

how to write a 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?

yeah,you are right.

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

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

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?

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?