Ask Your Question

klaaa's profile - activity

2024-02-09 13:53:17 +0100 commented answer Obtaining mutation class of a quiver in Sage with Sage

Thank you very much again! I noted that there is an error for E7: Q = ClusterQuiver(['E',7]) Ts = Q.mutation_class() g

2024-02-09 13:51:58 +0100 commented answer Obtaining mutation class of a quiver in Sage with Sage

Thank you very much again! A last small question: Is there an easy command to filter out those quivers, which are not ac

2024-02-09 09:24:32 +0100 commented answer Obtaining mutation class of a quiver in Sage with Sage

Thank you very much. The first way works in the sage online cell, while the second outputs nothing (I dont know why). Bu

2024-02-09 07:31:19 +0100 asked a question Obtaining mutation class of a quiver in Sage with Sage

Obtaining mutation class of a quiver in Sage with Sage Given a quiver $Q$ of finite mutation class (such as a Dynkin qui

2023-10-14 11:44:34 +0100 marked best answer Generating a certain list of non-commuting polynomials with Sage

I have a set of variables $x_1,...,x_n$ and $y_1,...,y_m$ for $n,m >=1$.

Now I can build all quadratic monomials of the form $x_i y_j$ and $y_j x_i$ (but we do not have $x_i y_j= y_j x_i$ as we calcualte in the non-commutative polynomial ring). But something like $x_i x_j$ is not allowed as after an $x_i$ there must come an $y_j$ and after an $y_i$ there must come an $x_i$.

Now I want with Sage the list of all possible relations of the form $w_1 \pm w_2 \pm w_3 \cdots$ such that all $w_i$ are different quadratic relations that all start either with a $x_i$ or a $y_j$.

For example for $n=2$ and $m=1$, possible relations are (I hope I did not forget any relation) : $x_1 y_1, x_1 y_1-x_2 y_2, x_1 y_2 + x_2 y_2 , x_2 y_1,y_1 x_1, y_1 x_2, y_1 x_1 - y_1 x_2 , y_1x_1+y_1 x_2$.

I am not sure how to do this in an easy way with Sage, but maybe someone knows a simple trick.

Thanks for any help.

2023-10-13 06:56:59 +0100 commented question Generating a certain list of non-commuting polynomials with Sage

For this purpose one could also define $xi$ and $yj$ just as strings probably or formal non-commutative variables in sag

2023-10-13 06:56:48 +0100 commented question Generating a certain list of non-commuting polynomials with Sage

For this purpose one could also define $xi$ and $yj$ just as string probably or formal non-commutative variables in sage

2023-10-13 06:55:59 +0100 commented question Generating a certain list of non-commuting polynomials with Sage

For this purpose one could also define $xi$ and $yj$ just as string probably to get the needed output.

2023-10-13 06:45:43 +0100 commented question Generating a certain list of non-commuting polynomials with Sage

I omitted a formal definition because it is a bit complicated. A formal definition would be to take the connected quiver

2023-10-13 06:43:24 +0100 commented question Generating a certain list of non-commuting polynomials with Sage

I omitted a formal definition because it is a bit complicated. A formal definition would be to take the connected quiver

2023-10-13 00:15:02 +0100 edited question Generating a certain list of non-commuting polynomials with Sage

Generating a certain list of non-commuting polynomials with Sage I have a set of variables $x_1,...,x_n$ and $y_1,...,y_

2023-10-13 00:14:43 +0100 edited question Generating a certain list of non-commuting polynomials with Sage

Generating a certain list of non-commuting polynomials with Sage I have a set of variables $x_1,...,x_n$ and $y_1,...,y_

2023-10-13 00:14:20 +0100 asked a question Generating a certain list of non-commuting polynomials with Sage

Generating a certain list of non-commuting polynomials with Sage I have a set of variables $x_1,...,x_n$ and $y_1,...,y_

2023-10-12 09:51:17 +0100 marked best answer Fundamental polynomials with Sage

Let $N>0$ be a positive natural number and let $k \geq 0$ be natural number with $N \geq k$.Let $S$ be a subset of the set {1,2,...,k-1}. Define the fundamental polynomial in $N$ variables as $F_{k,S}(x_1,x_2,...,x_N):= \sum\limits_{1 \leq i_1 \leq i_2 \leq \cdots \leq i_k \leq N \ ; \ j \in S \implies i_j < i_{j+1}}^{}{x_{i_1} x_{i_2} \cdots x_{i_k}}$.

For example we have $F_{k,\emptyset}=h_k$, the complete symmetric function and $F_{k,S}=e_k$ for S={1,...,k-1}, the elementary symmetric function.

Question: Is there an existing command or another easy way to obtain those polynomials for a given triple $(N,k,S)$ via Sage?

I found a section about quasi-symmetric functions in Sage but it uses the language of Hopf algebras and I am not sure whether this contains the fundamental polynomials already in this form.

2023-10-12 01:47:27 +0100 edited question Fundamental polynomials with Sage

Fundamental polynomials with Sage Let $N>0$ be a positive natural number and let $k \geq 0$ be natural number with $N

2023-10-12 01:46:34 +0100 edited question Fundamental polynomials with Sage

Fundamental polynomials with Sage Let $N>0$ be a positive natural number and let $k \geq 0$ be natural number with $N

2023-10-12 01:46:04 +0100 edited question Fundamental polynomials with Sage

Fundamental polynomials with Sage Let $N>0$ be a positive natural number and let $k \geq 0$ be natural number with $N

2023-10-12 01:45:47 +0100 edited question Fundamental polynomials with Sage

Fundamental polynomials with Sage Let $N>0$ be a positive natural number and let $k \geq 0$ be natural number with $N

2023-10-12 01:44:51 +0100 edited question Fundamental polynomials with Sage

Fundamental polynomials with Sage Let $N>0$ be a positive natural number and let $k \geq 0$ be natural number with $N

2023-10-12 01:40:04 +0100 asked a question Fundamental polynomials with Sage

Fundamental polynomials with Sage Let $N>0$ be a positive natural number and let $k \geq 0$ be natural number with $N

2023-10-06 05:27:28 +0100 received badge  Popular Question (source)
2023-09-26 08:27:21 +0100 received badge  Popular Question (source)
2023-09-24 22:09:26 +0100 received badge  Popular Question (source)
2023-09-24 03:24:41 +0100 received badge  Popular Question (source)
2023-09-16 14:52:49 +0100 answered a question Digraphs with Sage

I think I found another solution using Posets: n=4 P=Posets(n) U=[p for p in P if p.is_connected() and ((p.hasse_diagra

2023-09-16 14:40:47 +0100 commented answer Digraphs with Sage

Thank you very much! Is the an easy way to impose the additional restriction that all indegrees and outdegrees of a vert

2023-09-16 09:52:15 +0100 edited question Digraphs with Sage

Digraphs with Sage Is there an easy way to obtain with Sage the following for a given n: All connected Digraphs (up to

2023-09-15 20:49:14 +0100 asked a question Digraphs with Sage

Digraphs with Sage Is there an easy way to obtain with Sage the following for a given n: All connected Digraphs (up to

2023-09-06 09:45:03 +0100 received badge  Popular Question (source)
2023-08-15 13:00:09 +0100 edited question Obtaining the reduced incidence algebra as a matrix algebra

Obtaining the reduced incidence algebra as a matrix algebra I want to use Sage to give me the reduced incidence algebra

2023-08-15 12:59:06 +0100 asked a question Obtaining the reduced incidence algebra as a matrix algebra

Obtaining the reduced incidence algebra as a matrix algebra I want to use Sage to give me the reduced incidence algebra

2023-08-09 19:45:36 +0100 commented question Finding all atomic lattices with Sage

Thanks. I added some more explanation for what an atomic lattice is.

2023-08-09 19:44:23 +0100 edited question Finding all atomic lattices with Sage

Finding all atomic lattices with Sage Question: Is there a quick way to obtain all atomic lattices with $n$ elements

2023-08-07 22:15:02 +0100 asked a question Finding all atomic lattices with Sage

Finding all atomic lattices with Sage Question: Is there a quick way to obtain all atomic lattices with $n$ elements

2023-07-31 16:58:05 +0100 received badge  Notable Question (source)
2023-07-31 16:47:42 +0100 received badge  Notable Question (source)
2023-07-17 21:36:40 +0100 commented question Intersection posets via Sage

Thank you for the comment. I think if you take A={1,2,3,4,5,6} and A_1={1,2,3,4}, A_2={3,4,5,6} , A_3={3} then you get t

2023-07-17 17:07:43 +0100 edited question Intersection posets via Sage

Intersection posets via Sage Let A={1,...,m} be a set with $m$ elements and let $A_1,A_2,...,A_n$ be $n$ subsets of $A$.

2023-07-17 16:04:57 +0100 edited question Intersection posets via Sage

Intersection posets via Sage Let A={1,...,m} be a set with $m$ elements and let $A_1,A_2,...,A_n$ be $n$ subsets of $A$.

2023-07-17 16:04:18 +0100 edited question Intersection posets via Sage

Intersection posets via Sage Let A={1,...,m} be a set with $m$ elements and let $A_1,A_2,...,A_n$ be $n$ subsets of $A$.

2023-07-17 16:04:09 +0100 edited question Intersection posets via Sage

Intersection posets via Sage Let A={1,...,m} be a set with $m$ elements and let $A_1,A_2,...,A_n$ be $n$ subsets of $A$.

2023-07-17 16:03:24 +0100 asked a question Intersection posets via Sage

Intersection posets via Sage Let A={1,...,m} be a set with $m$ elements and let $A_1,A_2,...,A_n$ be $n$ subsets of $A$.

2023-07-16 19:08:18 +0100 asked a question Obtaining the posets of ideals of a given finite poset

Obtaining the posets of ideals of a given finite poset Let $P$ be a finite connected poset. Following https://www.jstor.

2023-07-16 19:03:25 +0100 received badge  Notable Question (source)
2023-07-13 04:01:59 +0100 received badge  Famous Question (source)
2023-05-26 06:31:46 +0100 received badge  Notable Question (source)
2023-05-23 15:00:02 +0100 received badge  Popular Question (source)
2023-05-21 22:41:49 +0100 edited question Action of a cyclic group on the interval poset of a Boolean lattice

Action of a cyclic group on the interval poset of a Boolean lattice Let $G$ be a cyclic group of order $n$ and $B=B_n$ t

2023-05-21 22:39:23 +0100 asked a question Action of a cyclic group on the interval poset of a Boolean lattice

Action of a cyclic group on the interval poset of a Boolean lattice Let $G$ be a cyclic group of order $n$ and $B=B_n$ t