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2020-02-20 02:06:06 +0200 marked best answer Partially commutative monoid of a graph

I am interested in the free partially commutative monoid associated to a graph whose definition can be seen here www.sciencedirect.com/science/article... and here https://en.m.wikipedia.org/wiki/Trace....

Basically I need a free monoid in which some variables commutes.

My questions are

  1. whether this notion is already implemented in Sage?

  2. If not how to implement this in Sage?

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2019-09-10 11:41:54 +0200 asked a question $p$-adic extension of $n$th root of unity.

I have used the following command to define the 5-adic Unramified extension ring in c defined by the polynomial $x^3 + 3x + 3$:

Sage: R.<c> = zq(125, prec=20)

Now, I want to find all the $n$th root of unity in this ring for $n$ dividing $124$. I dont know, how the $n$-th roots are implemented. Kindly help me with this.

Thank you.

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2019-08-19 12:05:49 +0200 asked a question Automorphism group of Coxeter groups

Coxeter groups can be invoked using the comment

W = CoxeterGroup(['A',3],implementation='reflection')

Now, W has three simple reflections S_1, S_2 and S_3. and I am interested in studying the automorphism S_1 -----> S_3, S_2 -----> S_2 and S_3 -----> S_1. Can any one please tell me, how to implement this automorphism of W in sage?

Thank you.

2019-08-08 08:13:05 +0200 commented question tree ordering in sage

Sorry, I shall paste it like this in future. Thanks for your comment.

2019-08-08 08:11:29 +0200 commented answer removing the repeated rows of a matrix

This is a great answer and it works perfectly. Thanks for your valuable time.

2019-08-07 13:54:59 +0200 asked a question removing the repeated rows of a matrix

My sage program outputs a matrix with integer entries in which some rows are repeated. But I want to remove the multiple entries of rows in the output. Kindly somebody explains to me how to do this.

Thank you.

2019-08-07 06:18:41 +0200 asked a question tree ordering in sage

I am using the following code to generate the isomorphism class of trees of order $n$.

sage: from sage.graphs.trees import TreeIterator
sage: def check_trees(n):
....:     trees = []
....:     for t in TreeIterator(n):    
....:         if not t.is_tree():  
....:             return False 
....:         if t.num_verts() != n: 
....:             return False   
....:         if t.num_edges() != n - 1:
....:             return False
....:         for tree in trees:
....:             if tree.is_isomorphic(t):
....:                 return False
....:         trees.append(t)
....:     return True

Then when I print the trees in TreeIterator using loops it is giving the trees in a particular order.

Can anyone explain to me what is this predefined order on trees of order $n$ on sage?

For n = 6, we have the following order.

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2019-08-05 10:43:37 +0200 commented answer caterpillar graphs in sage

Can you please explain to me what is the number of vertices and vertices of degree on in $G$? It keeps changing when I run. Thank you.

2019-08-05 08:57:15 +0200 asked a question caterpillar graphs in sage

A caterpillar or caterpillar tree is a tree in which all the vertices are within distance 1 of a central path.

How to define caterpillar graphs in sage? is it already implemented?

Kindly help me with this.

Thank you.

2019-08-04 08:32:11 +0200 commented answer graphs of order n

Thank you. one doubt. graphs(5) gives the list of graphs up to isomorphism?

2019-08-03 15:13:02 +0200 asked a question graphs of order n

How to generate all the graphs of particular order $n$ in sage?

is it possible to do the same up to isomorphism at least for small $n$?

Thank you.

2019-08-03 13:34:18 +0200 asked a question plot comment not working

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Why the image of the graph is not displayed here? Kindly help me with resolving this.

I am using Mac.

Thank you.

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2019-01-19 16:39:09 +0200 asked a question periodicity of a word

I have the following code to create words.

sage: M.<x,y,z> = FreeMonoid(3)
sage: Word(x^3*y*x*z^2*x)
word: xxxyxzzx

I want find the periodicity of a given word.

For example ababab has periodicity 3 and abcdabcde has periodicity 1.

Kindly help me with this.

Thank you.

2018-10-10 09:04:43 +0200 asked a question Graph with partial edge labelling

Hello all,

I need to draw a graph in which some edges are labelled and some edges are not. I know how to make all the edges labelled. But I need mixed edges (some are labelled and some are not).

Kindly help me with this.

Thank you

2018-10-10 08:17:11 +0200 commented answer creating graph with dotted edges

Also in the output graph with dotted edges and ordinary edges, I am getting axes also part of the output. But I need only the graph in order to add it in my paper. Kindly tell me how to get rid of this measurement axes. Thank yu.

2018-10-10 08:03:52 +0200 commented answer creating graph with dotted edges

Thanks. It works nicely. Can you please tell me how to add labels only on certain edges? thank you.

2018-10-10 08:02:49 +0200 marked best answer creating graph with dotted edges

Hello all, I need to draw a graph in which some edges are usual and some edges are dotted. I know how to make all the edges dotted (using the option "dotted" for the parameter edge_style of plot). But I need mixed edges (some are dotted and some are usual). Kindly help me with this. Thank you.