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### Obtaining all simply laced graphs with SAGE for GAP

Hi, I work with GAP and have not much experience with SAGE. I wonder whether there is an easy way to obtain a program with SAGE that gives as output a list of all directed simply laced acyclic connected graphs on n points up to equivalence that is readable for GAP (via the GAP-package QPA).

Here a more detailed description of what the program should do:

Input: A natural number n >=2. Output: The list of directed simply laced acyclic connected graphs on n points up to equivalence. Here we call two such graphs equivalent in case they have the same underlying undirected graph (in case it is a problem to do it up to equivalence, we can first look at the problem without up to equivalence).

Here how to output should look in the first 3 cases for n<=4 so that it is readable for GAP: Note that graphs are also often called quivers. GAP reads those graphs as Quiver(n,[[p1,p2,"a1"],...[pnminusone,pn,"ar"]]) where we name the points pi and the arrows between them as ar for some index sets i and r. (I hope it will be clear with the following examples).

n=2: [Quiver(2,[[1,2,"a1"]])];

n=3: [Quiver(3,[[1,2,"a1"],[2,3,"a2"]])]; (note here that the quiver Quiver(3,[[1,2,"a1"],[2,3,"a2"]]) is equivalent to the quiver Quiver(3,[[1,2,"a1"],[3,2,"a2"]]) since they are equal when looking at their undirected graphs)

n=4: [Quiver(4,[[1,2,"a1"],[2,3,"a2"],[3,4,"a4"]]),Quiver(4,[[1,2,"a1"],[2,3,"a2"],[4,2,"a3"]]); (here we have two non-equivalent quivers).

Thanks you very much for any help.

n=3

### Obtaining all simply laced graphs with SAGE for GAP

Hi, I work with GAP and have not much experience with SAGE. I wonder whether there is an easy way to obtain a program with SAGE that gives as output a list of all directed simply laced acyclic connected graphs on n points up to equivalence that is readable for GAP (via the GAP-package QPA).

Here a more detailed description of what the program should do:

Input: A natural number n >=2. Output: The list of directed simply laced acyclic connected graphs on n points up to equivalence. Here we call two such graphs equivalent in case they have the same underlying undirected graph (in case it is a problem to do it up to equivalence, we can first look at the problem without up to equivalence).

Here how to output should look in the first 3 cases for n<=4 so that it is readable for GAP: Note that graphs are also often called quivers. GAP reads those graphs as Quiver(n,[[p1,p2,"a1"],...[pnminusone,pn,"ar"]]) where we name the points pi and the arrows between them as ar for some index sets i and r. (I hope it will be clear with the following examples).

n=2: [Quiver(2,[[1,2,"a1"]])];

n=3: [Quiver(3,[[1,2,"a1"],[2,3,"a2"]])]; (note here that the quiver Quiver(3,[[1,2,"a1"],[2,3,"a2"]]) is equivalent to the quiver Quiver(3,[[1,2,"a1"],[3,2,"a2"]]) since they are equal when looking at their undirected graphs)

n=4: [Quiver(4,[[1,2,"a1"],[2,3,"a2"],[3,4,"a4"]]),Quiver(4,[[1,2,"a1"],[2,3,"a2"],[4,2,"a3"]]); (here we have two non-equivalent quivers).

Thanks you very much for any help.

n=3

### Obtaining all simply laced graphs with SAGE for GAP

Hi, I work with GAP and have not much experience with SAGE. I wonder whether there is an easy way to obtain a program with SAGE that gives as output a list of all directed simply laced acyclic connected graphs on n points up to equivalence that is readable for GAP (via the GAP-package QPA).QPA). I know that SAGE can generate the list of such combinatorial collections in an easy way but I do not know how to present it in the needed output and how to obtain all restrictions on the graphs.

Here a more detailed description of what the program should do:

Input: A natural number n >=2. Output: The list of directed simply laced acyclic connected graphs on n points up to equivalence. Here we call two such graphs equivalent in case they have the same underlying undirected graph (in case it is a problem to do it up to equivalence, we can first look at the problem without up to equivalence).

Here how to output should look in the first 3 cases for n<=4 so that it is readable for GAP: Note that graphs are also often called quivers. GAP reads those graphs as Quiver(n,[[p1,p2,"a1"],...[pnminusone,pn,"ar"]]) where we name the points pi and the arrows between them as ar for some index sets i and r. (I hope it will be clear with the following examples).

n=2: [Quiver(2,[[1,2,"a1"]])];

n=3: [Quiver(3,[[1,2,"a1"],[2,3,"a2"]])]; (note here that the quiver Quiver(3,[[1,2,"a1"],[2,3,"a2"]]) is equivalent to the quiver Quiver(3,[[1,2,"a1"],[3,2,"a2"]]) since they are equal when looking at their undirected graphs)

n=4: [Quiver(4,[[1,2,"a1"],[2,3,"a2"],[3,4,"a4"]]),Quiver(4,[[1,2,"a1"],[2,3,"a2"],[4,2,"a3"]]); (here we have two non-equivalent quivers).

Thanks you very much for any help.

### Obtaining all simply laced graphs with SAGE for GAP

Hi, I work with GAP and have not much experience with SAGE. I wonder whether there is an easy way to obtain a program with SAGE that gives as output a list of all directed simply laced acyclic connected graphs on n points up to equivalence that is readable for GAP (via the GAP-package QPA). I know that SAGE can generate the list of such combinatorial collections in an easy way but I do not know how to present it in the needed output and how to obtain all restrictions on the graphs.

Here a more detailed description of what the program should do:

Input: A natural number n >=2. Output: The list of directed simply laced acyclic connected graphs on n points up to equivalence. Here we call two such graphs equivalent in case they have the same underlying undirected graph (in case it is a problem to do it up to equivalence, we can first look at the problem without up to equivalence).

Here how to output should look in the first 3 cases for n<=4 so that it is readable for GAP: Note that graphs are also often called quivers. GAP reads those graphs as Quiver(n,[[p1,p2,"a1"],...[pnminusone,pn,"ar"]]) where we name the points pi and the arrows between them as ar for some index sets i and r. (I hope it will be clear with the following examples).

n=2: [Quiver(2,[[1,2,"a1"]])];

n=3: [Quiver(3,[[1,2,"a1"],[2,3,"a2"]])]; (note here that the quiver Quiver(3,[[1,2,"a1"],[2,3,"a2"]]) is equivalent to the quiver Quiver(3,[[1,2,"a1"],[3,2,"a2"]]) since they are equal when looking at their undirected graphs)

n=4: [Quiver(4,[[1,2,"a1"],[2,3,"a2"],[3,4,"a4"]]),Quiver(4,[[1,2,"a1"],[2,3,"a2"],[4,2,"a3"]]); (here we have two non-equivalent quivers).

Thanks you very much for any help.

### Obtaining all simply laced graphs with SAGE for GAP

Hi, I work with GAP and have not much experience with SAGE. I wonder whether there is an easy way to obtain a program with SAGE that gives as output a list of all directed simply laced acyclic connected graphs on n points up to equivalence that is readable for GAP (via the GAP-package QPA). I know that SAGE can generate the list of such combinatorial collections in an easy way but I do not know how to present it in the needed output and how to obtain all restrictions on the graphs.

Here a more detailed description of what the program should do:

Input: A natural number n >=2. Output: The list of directed simply laced acyclic connected graphs on n points up to equivalence. Here we call two such graphs equivalent in case they have the same underlying undirected graph (in case it is a problem to do it up to equivalence, we can first look at the problem without up to equivalence).

Here how to output should look in the first 3 cases for n<=4 so that it is readable for GAP: equivalence). It is not important what the concrete orientation of the arrows of a representative in an equivalence class is.

Note that graphs are also often called quivers. GAP reads those graphs as Quiver(n,[[p1,p2,"a1"],...[pnminusone,pn,"ar"]]) where we name the points pi and the arrows between them as ar for some index sets i and r. (I hope it will be clear with the following examples). Here how to output should look in the first 3 cases for n<=4 so that it is readable for GAP:

n=2: [Quiver(2,[[1,2,"a1"]])];

n=3: [Quiver(3,[[1,2,"a1"],[2,3,"a2"]])]; (note here that the quiver Quiver(3,[[1,2,"a1"],[2,3,"a2"]]) is equivalent to the quiver Quiver(3,[[1,2,"a1"],[3,2,"a2"]]) since they are equal when looking at their undirected graphs)

n=4: [Quiver(4,[[1,2,"a1"],[2,3,"a2"],[3,4,"a4"]]),Quiver(4,[[1,2,"a1"],[2,3,"a2"],[4,2,"a3"]]); (here we have two non-equivalent quivers).

Thanks you very much for any help.

### Obtaining all simply laced graphs with SAGE for GAP

Hi, I work with GAP and have not much experience with SAGE. I wonder whether there is an easy way to obtain a program with SAGE that gives as output a list of all directed simply laced acyclic connected graphs on n points up to equivalence that is readable for GAP (via the GAP-package QPA). I know that SAGE can generate the list of such combinatorial collections in an easy way but I do not know how to present it in the needed output and how to obtain all restrictions on the graphs.

Here a more detailed description of what the program should do:

Input: A natural number n >=2. Output: The list of directed simply laced acyclic connected graphs on n points up to equivalence. Here we call two such graphs equivalent in case they have the same underlying undirected graph (in case it is a problem to do it up to equivalence, we can first look at the problem without up to equivalence). It is not important what the concrete orientation of the arrows of a representative in an equivalence class is.

Note that graphs are also often called quivers. GAP reads those graphs as Quiver(n,[[p1,p2,"a1"],...[pnminusone,pn,"ar"]]) where we name the points pi and the arrows between them as ar for some index sets i and r. (I hope it will be clear with the following examples). Here how to output should look in the first 3 cases for n<=4 so that it is readable for GAP:

n=2: [Quiver(2,[[1,2,"a1"]])];

n=3: [Quiver(3,[[1,2,"a1"],[2,3,"a2"]])]; (note here that the quiver Quiver(3,[[1,2,"a1"],[2,3,"a2"]]) is equivalent to the quiver Quiver(3,[[1,2,"a1"],[3,2,"a2"]]) since they are equal when looking at their undirected graphs)

n=4: [Quiver(4,[[1,2,"a1"],[2,3,"a2"],[3,4,"a4"]]),Quiver(4,[[1,2,"a1"],[2,3,"a2"],[4,2,"a3"]]); (here we have two non-equivalent quivers).

Thanks you very much for any help.

### Obtaining all connected simply laced graphs with SAGE for GAP

Hi, I work with GAP and have not much experience with SAGE. I wonder whether there is an easy way to obtain a program with SAGE that gives as output a list of all directed simply laced acyclic connected graphs on n points up to equivalence that is readable for GAP (via the GAP-package QPA). I know that SAGE can generate the list of such combinatorial collections in an easy way but I do not know how to present it in the needed output and how to obtain all restrictions on the graphs.graphs. With acyclic I mean acyclic as an directed graph (but in case this makes problems, you can also assume acyclic as undirected graphs).

Here a more detailed description of what the program should do:

Input: A natural number n >=2. Output: The list of directed simply laced acyclic connected graphs on n points up to equivalence. Here we call two such graphs equivalent in case they have the same underlying undirected graph (in case it is a problem to do it up to equivalence, we can first look at the problem without up to equivalence). It is not important what the concrete orientation of the arrows of a representative in an equivalence class is.

Note that graphs are also often called quivers. GAP reads those graphs as Quiver(n,[[p1,p2,"a1"],...[pnminusone,pn,"ar"]]) where we name the points pi and the arrows between them as ar for some index sets i and r. (I hope it will be clear with the following examples). Here how to output should look in the first 3 cases for n<=4 so that it is readable for GAP:

n=2: [Quiver(2,[[1,2,"a1"]])];

n=3: [Quiver(3,[[1,2,"a1"],[2,3,"a2"]])]; (note here that the quiver Quiver(3,[[1,2,"a1"],[2,3,"a2"]]) is equivalent to the quiver Quiver(3,[[1,2,"a1"],[3,2,"a2"]]) since they are equal when looking at their undirected graphs)

n=4: [Quiver(4,[[1,2,"a1"],[2,3,"a2"],[3,4,"a4"]]),Quiver(4,[[1,2,"a1"],[2,3,"a2"],[4,2,"a3"]]); (here we have two non-equivalent quivers).

Thanks you very much for any help.

### Obtaining all connected simply laced graphs with SAGE for GAP

Hi, I work with GAP and have not much experience with SAGE. I wonder whether there is an easy way to obtain a program with SAGE that gives as output a list of all directed simply laced acyclic connected graphs on n points up to equivalence that is readable for GAP (via the GAP-package QPA). I know that SAGE can generate the list of such combinatorial collections in an easy way but I do not know how to present it in the needed output and how to obtain all restrictions on the graphs. With acyclic I mean acyclic as an directed graph (but in case this makes problems, you can also assume acyclic as undirected graphs).

Here a more detailed description of what the program should do:

Input: A natural number n >=2. Output: The list of directed simply laced acyclic connected graphs on n points up to equivalence. Here we call two such graphs equivalent in case they have the same underlying undirected graph (in case it is a problem to do it up to equivalence, we can first look at the problem without up to equivalence). It is not important what the concrete orientation of the arrows of a representative in an equivalence class is.

Note that graphs are also often called quivers. GAP reads those graphs as Quiver(n,[[p1,p2,"a1"],...[pnminusone,pn,"ar"]]) where we name the points pi and the arrows between them as ar for some index sets i and r. (I hope it will be clear with the following examples). Here how to output should look in the first 3 2 cases for n<=4 n<=3 so that it is readable for GAP:

n=2: [Quiver(2,[[1,2,"a1"]])];

n=3: [Quiver(3,[[1,2,"a1"],[2,3,"a2"]])]; [Quiver(3,[[1,2,"a1"],[2,3,"a2"]]),Quiver(3,[[1,2,"a1"],[2,3,"a2"],[1,3,"a3"]])]; (note for example here here that the quiver Quiver(3,[[1,2,"a1"],[2,3,"a2"]]) is equivalent to the quiver Quiver(3,[[1,2,"a1"],[3,2,"a2"]]) since they are equal when looking at their undirected graphs)

n=4: [Quiver(4,[[1,2,"a1"],[2,3,"a2"],[3,4,"a4"]]),Quiver(4,[[1,2,"a1"],[2,3,"a2"],[4,2,"a3"]]); (here we have two non-equivalent quivers).

Thanks you very much for any help.

### Obtaining all connected simply laced graphs with SAGE for GAP

Hi, I work with GAP and have not much experience with SAGE. I wonder whether there is an easy way to obtain a program with SAGE that gives as output a list of all directed simply laced acyclic connected graphs on n points up to equivalence that is readable for GAP (via the GAP-package QPA). I know that SAGE can generate the list of such combinatorial collections in an easy way but I do not know how to present it in the needed output and how to obtain all restrictions on the graphs. With acyclic I mean acyclic as an directed graph (but in case this makes problems, you can also assume acyclic as undirected graphs).

Here a more detailed description of what the program should do:

Input: A natural number n >=2. Output: The list of directed simply laced acyclic connected graphs on n points up to equivalence. Here we call two such graphs equivalent in case they have the same underlying undirected graph (in case it is a problem to do it up to equivalence, we can first look at the problem without up to equivalence). It is not important what the concrete orientation of the arrows of a representative in an equivalence class is.

Note that graphs are also often called quivers. GAP reads those graphs as Quiver(n,[[p1,p2,"a1"],...[pnminusone,pn,"ar"]]) where we name the points pi and the arrows between them as ar for some index sets i and r. (I hope it will be clear with the following examples). Here how to output should look in the first 2 cases for n<=3 so that it is readable for GAP:

n=2: [Quiver(2,[[1,2,"a1"]])];

n=3: [Quiver(3,[[1,2,"a1"],[2,3,"a2"]]),Quiver(3,[[1,2,"a1"],[2,3,"a2"],[1,3,"a3"]])]; (note for example here here that the quiver Quiver(3,[[1,2,"a1"],[2,3,"a2"]]) is equivalent to the quiver Quiver(3,[[1,2,"a1"],[3,2,"a2"]]) since they are equal when looking at their undirected graphs)

So for n=2 there is one equivalence class, while for n=3 there are two (so that for n=3 the output is a list of two elements readable by GAP).

Thanks you very much for any help.

 10 None slelievre 10233 ●9 ●107 ●206 http://carva.org/samue...

### Obtaining all connected simply laced graphs with SAGE for GAP

Hi, I work with GAP and have not much experience with SAGE. I wonder whether there is an easy way to obtain a program with SAGE that gives as output a list of all directed simply laced acyclic connected graphs on n points up to equivalence that is readable for GAP (via the GAP-package QPA). I know that SAGE can generate the list of such combinatorial collections in an easy way but I do not know how to present it in the needed output and how to obtain all restrictions on the graphs. With acyclic I mean acyclic as an directed graph (but in case this makes problems, you can also assume acyclic as undirected graphs).

Here a more detailed description of what the program should do:

Input: A natural number n >=2. Output: The list of directed simply laced acyclic connected graphs on n points up to equivalence. Here we call two such graphs equivalent in case they have the same underlying undirected graph (in case it is a problem to do it up to equivalence, we can first look at the problem without up to equivalence). It is not important what the concrete orientation of the arrows of a representative in an equivalence class is.

Note that graphs are also often called quivers. GAP reads those graphs as Quiver(n,[[p1,p2,"a1"],...[pnminusone,pn,"ar"]]) where we name the points pi and the arrows between them as ar for some index sets i and r. (I hope it will be clear with the following examples). Here how to output should look in the first 2 cases for n<=3 so that it is readable for GAP:

n=2: [Quiver(2,[[1,2,"a1"]])];

n=3: [Quiver(3,[[1,2,"a1"],[2,3,"a2"]]),Quiver(3,[[1,2,"a1"],[2,3,"a2"],[1,3,"a3"]])]; (note for example here here that the quiver Quiver(3,[[1,2,"a1"],[2,3,"a2"]]) is equivalent to the quiver Quiver(3,[[1,2,"a1"],[3,2,"a2"]]) since they are equal when looking at their undirected graphs)

So for n=2 there is one equivalence class, while for n=3 there are two (so that for n=3 the output is a list of two elements readable by GAP).

Thanks you very much for any help.

 11 None slelievre 10233 ●9 ●107 ●206 http://carva.org/samue...

### Obtaining all connected simply laced graphs with SAGE Sage for GAP

Hi, I work with GAP and have not much experience with SAGE. Sage. I wonder whether there is an easy way to obtain a program with SAGE Sage that gives as output a list of all directed simply laced acyclic connected graphs on n points up to equivalence that is readable for GAP (via the GAP-package QPA). I know that SAGE Sage can generate the list of such combinatorial collections in an easy way but I do not know how to present it in the needed output and how to obtain all restrictions on the graphs. With acyclic I mean acyclic as an directed graph (but in case this makes problems, you can also assume acyclic as undirected graphs).

Here a more detailed description of what the program should do:

Input: A natural number n >=2. >= 2.

Output: The list of directed simply laced acyclic connected graphs on n points up to equivalence. Here we call two such graphs equivalent in case they have the same underlying undirected graph (in case it is a problem to do it up to equivalence, we can first look at the problem without up to equivalence). It is not important what the concrete orientation of the arrows of a representative in an equivalence class is.

Note that graphs are also often called quivers. GAP reads those graphs as Quiver(n,[[p1,p2,"a1"],...[pnminusone,pn,"ar"]]) Quiver(n, [[p1, p2, "a1"], ...,[pm, pn, "ar"]]) where we name the points pi pi and the arrows between them as ar aj for some index sets i i and r. j. (I hope it will be clear with the following examples). Here how to output should look in the first 2 cases for n<=3 n <= 3 so that it is readable for GAP:

n=2: [Quiver(2,[[1,2,"a1"]])];

n=3: [Quiver(3,[[1,2,"a1"],[2,3,"a2"]]),Quiver(3,[[1,2,"a1"],[2,3,"a2"],[1,3,"a3"]])]; [Quiver(3,[[1,2,"a1"],[2,3,"a2"]]),Quiver(3,[[1,2,"a1"],[2,3,"a2"],[1,3,"a3"]])]; (note for example here here that the quiver Quiver(3,[[1,2,"a1"],[2,3,"a2"]]) Quiver(3,[[1,2,"a1"],[2,3,"a2"]]) is equivalent to the quiver Quiver(3,[[1,2,"a1"],[3,2,"a2"]]) Quiver(3,[[1,2,"a1"],[3,2,"a2"]]) since they are equal when looking at their undirected graphs)

So for n=2 there is one equivalence class, while for n=3 there are two (so that for n=3 the output is a list of two elements readable by GAP).

Thanks you very much for any help.

 12 retagged slelievre 10233 ●9 ●107 ●206 http://carva.org/samue...

### Obtaining all connected simply laced graphs with Sage for GAP

I work with GAP and have not much experience with Sage. I wonder whether there is an easy way to obtain a program with Sage that gives as output a list of all directed simply laced acyclic connected graphs on n points up to equivalence that is readable for GAP (via the GAP-package QPA). I know that Sage can generate the list of such combinatorial collections in an easy way but I do not know how to present it in the needed output and how to obtain all restrictions on the graphs. With acyclic I mean acyclic as an directed graph (but in case this makes problems, you can also assume acyclic as undirected graphs).

Here a more detailed description of what the program should do:

Input: A natural number n >= 2.

Output: The list of directed simply laced acyclic connected graphs on n points up to equivalence. Here we call two such graphs equivalent in case they have the same underlying undirected graph (in case it is a problem to do it up to equivalence, we can first look at the problem without up to equivalence). It is not important what the concrete orientation of the arrows of a representative in an equivalence class is.

Note that graphs are also often called quivers. GAP reads those graphs as Quiver(n, [[p1, p2, "a1"], ...,[pm, pn, "ar"]]) where we name the points pi and the arrows between them as aj for some index sets i and j. (I hope it will be clear with the following examples). Here how to output should look in the first 2 cases for n <= 3 so that it is readable for GAP:

n=2: [Quiver(2,[[1,2,"a1"]])];

n=3: [Quiver(3,[[1,2,"a1"],[2,3,"a2"]]),Quiver(3,[[1,2,"a1"],[2,3,"a2"],[1,3,"a3"]])]; (note for example here here that the quiver Quiver(3,[[1,2,"a1"],[2,3,"a2"]]) is equivalent to the quiver Quiver(3,[[1,2,"a1"],[3,2,"a2"]]) since they are equal when looking at their undirected graphs)

So for n=2 there is one equivalence class, while for n=3 there are two (so that for n=3 the output is a list of two elements readable by GAP).