oldani's profile - activity

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

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

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

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

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

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.

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

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

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

Thanks Sebastien good to know anyway

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

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())

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?

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

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.

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

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 $A^{-1} = 1 - k \cdot B \ mod(N)$

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

Thanks for your help

Hi,

Real beginner in Sage I want to ask you this question:

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?

Any advise or web pointer would be appreciated

Thanks for yor help