# oldani's profile - activity

2021-09-14 11:50:29 +0200 asked a question Working with unlabelled graphs

Working with unlabelled graphs I'm studying certain properties of graphs but I want to work with unlabelled ones i.e. I

2021-09-03 13:06:23 +0200 asked a question Permutations and transpositions

Permutations and transpositions Is it possible in Sage to get the decomposition in transpositions of a permutation?

2021-08-23 11:56:20 +0200 asked a question Symbolic expression of the quotient of a continued fraction

Symbolic expression of the quotient of a continued fraction Hi, Is it possible to get the symbolic expression of the nu

2021-01-07 18:21:18 +0200 asked a question Counting lattice path with Sage

Quite newbie with Sage but I try to count very standard lattice path with steps (1,0) and (0,1) on a grin (0,0) to (m,n) for positive integers n and m. I want also put constraints like for example "not touching the main. diagonal".

I can program it but maybe there are Sage libraries that can help me?

Thanks for any suggestions Gianfranco

2020-05-03 18:52:09 +0200 asked a question Working with rationals without simplification

Hi, Is there a way to force Sage to not simplify rational fraction, I mean to not convert for example $\frac{5}{10}$ into $\frac{1}{2}$, just leave it as $\frac{5}{10}$. I could work with paires of integers instead of rational fractions but it would be a lot more convenient to use the standard operations on $\mathbb Q$

Thanks

2020-04-16 23:54:13 +0200 commented question Changing display labels of nodes on a graph

Mmmh sorry for my bad english. I found finally another way to solve my problem, I think there was no solution to what I wanted to do. Thanks a lot for your time.

2020-04-16 15:24:20 +0200 commented question Changing display labels of nodes on a graph

The idea is the following. Let's imagine I have defined the graph : G2 = Graph([('a', 'b', 'edge label')]). Like that it is displayed with node labels 'a' et 'b'.

But I want to display G2 (as it is defined) but as G3 = Graph([('Good', 'Morning')]) will be displayed

2020-04-16 15:10:43 +0200 commented answer Changing display labels of nodes on a graph

Oh! yes good idea, if I remove the node labels and keep only edge labels can be a way to go. Thanks

2020-04-15 09:33:36 +0200 asked a question Changing display labels of nodes on a graph

Hi, I have created a graph which is in fact a tree. Each node has a label that I gave at creation time. Now, when I plot the graph for each node this "internal" label is displayed. Is it possible to have different display labels than this "internal" label?

Thanks

2020-04-14 20:44:04 +0200 commented question Continued fractions with various algorithms

Thanks Sebastien good to know anyway

2020-04-14 11:05:37 +0200 asked a question Continued fractions with various algorithms

Hi, Can I find a package allowing to compute continued fractions and convergents with an algorithm different than the euclidian division ? nearest integer for example or others...

Thanks

2020-04-06 17:06:06 +0200 commented answer Group given by congruence relation

Got it. Jesus here is how it works for me...don't ask me why...

def my_congruence_group(B, N): M = MatrixSpace(Zmod(N), 2) print(M)

assert (B**2).is_zero()

B = M(B)
G = SL(2, Zmod(N))
H = G.subgroup([1 + k*B for k in range(N)])
C = libgap.RightCosets(G, H)

M1 = M([[1,1],[0,1]])
M2 = M([[1,0],[1,1]])
M3 = M([[0,-1],[1,0]])
M4 = M([[0,1],[-1,1]])

l = libgap.Permutation( M1, C, libgap.OnRight)
r = libgap.Permutation( M2, C, libgap.OnRight)
s2 = libgap.Permutation( M3, C, libgap.OnRight)
s3 = libgap.Permutation( M4, C, libgap.OnRight)

return ArithmeticSubgroup_Permutation(L=l.sage(), R=r.sage(), S2=s2.sage(), S3=s3.sage())

2020-04-06 16:44:31 +0200 commented answer Group given by congruence relation

Thanks. I have the 8.9 version which is recent. I have tried here: https://sagecell.sagemath.org/ and I got the same error....strange. Don't worries I don't want to waste your time I will do my investigatio and tell you if I find something...Maybe a Python 3 compatibility issue?

2020-04-06 14:13:04 +0200 commented answer Group given by congruence relation

Hi, Sorry to disturb you again but I have tried various ways and I get always the same error when I run the above code:

Here is an extract of the fullstack just in case :

## Starts with:

GAPError Traceback (most recent call last) .........continue..... ---> 23 G = my_congruence_group(B, N) 24 G.gens() # some generators for the group 25 .........continue..... ends with

GAPError: Syntax error: ] expected in stream:1 [1 1] ^

Thanks for any clue

2020-04-05 21:44:28 +0200 commented answer Group given by congruence relation

Wonderful, thank you so much for your time and your great answer. You taught me a lot in this last two hours. I will study that with great pleasure.

2020-04-05 20:12:27 +0200 commented question Group given by congruence relation

Yes sorry for that, you are right, fixed. Great thanks for this point of view, gives me a step further.
Yes , in fact $G \cap \Gamma_0 = \Gamma(N)$

2020-04-05 19:17:01 +0200 commented question Group given by congruence relation

Hi,

Thanks for your interest in my question . Here is the argument

Essentially because $B^2 = 0$.

Just to be clear, saying that $A=B \ mod(N)$ means that $A - B = N \cdot X$ where $X$ is an integral matrix

1) $I \in G$, take k=0

2) Take $A = I + mB + N\cdot X, B = I + nB + N\cdot Y\in G$ , $X,Y$ being any integer coefficients matrices. Write the product and you will see that (because $B^2=0$) we have $A \cdot B = I + (m+n)\cdot B \ mod(N)$

3) For the inverse, you see easily that if $A = 1 + k \cdot B \mod(N)$ then $A^{-1} = 1 - k \cdot B \ mod(N)$

2020-04-05 14:07:20 +0200 asked a question Group given by congruence relation

Hi,

Beginner in Sage (I love it!) , I want to ask you this maybe naive question:

I have a group $G$ defined by $\lbrace M \in SL_2(Z) \ | \ M = I + kB \ mod(N) \rbrace$, where $I$ is the identity, $N$ a given positive integer, $B$ is a given fixed matrix verifying $B^2 = 0$ and $k$ (not fixed) any integer in { 0,1,2,....,N-1 }. I want to explore conjugacy classes/subgroups of this group $G$ for some specific $B$ and $N$. Is this subgroup finitely generated for some $N$? subgroups of finite index? etc... Do I have a way to do that with SageMath?

Remark that

It is subgroup of a finitely generated group butv that do not imply that it is finitely generated

$B^2 = 0$ gives that $I + kB = \Lambda^k \ with \ \Lambda = I + B$.

An obvious subgroup is $H = \lbrace \Lambda^k, \ k \in \mathbb Z \rbrace$

Any advise or web pointer would be appreciated

I have a subgroup $G = \lbrace M \in SL_2(Z) | \ M = I + kB \ mod(N) \rbrace$, where $I$ is the identity, $B$ is a given fixed matrix verifying $B^2 = 0$ and $k \in \mathbb Z /N\mathbb Z$. I want to explore subgroups of this group $G$. Do I have a way to do that with SageMath?