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I want to do certain calculation with posets using GAP. But GAP has no package for posets so I want to use SAGE first to generate all connected posets with a certain number of points and then use the data in GAP. The output of posets in SAGE should have the form ["x1","x2","x3","x4"],[["x1","x2"],["x1","x3"],["x3","x4"],["x2","x4"]] so that I can use them in GAP. Here the poset has 4 elements x1,x2,x3 and x4 and ["x1","x2"] means that x1 is smaller than x2 etc.

So I want the following with SAGE:

Input: A number $n \geq 2$.

Output: The list of all connected posets with $n$ elements displayed in the form (this is an example) ["x1","x2","x3","x4"],[["x1","x2"],["x1","x3"],["x3","x4"],["x2","x4"]].

I want to do certain calculation with posets using GAP. But GAP has no package for posets so I want to use SAGE first to generate all connected posets with a certain number of points and then use the data in GAP. The output of posets in SAGE should have the form ["x1","x2","x3","x4"],[["x1","x2"],["x1","x3"],["x3","x4"],["x2","x4"]] so that I can use them in GAP. Here the poset has 4 elements x1,x2,x3 and x4 and ["x1","x2"] means that x1 is smaller than x2 etc.

So I want the following with SAGE:

Input: A number $n \geq 2$.

Output: The list of all connected posets with $n$ elements displayed in the form (this is an example) ["x1","x2","x3","x4"],[["x1","x2"],["x1","x3"],["x3","x4"],["x2","x4"]].

I want to do certain calculation with posets using GAP. But GAP has no package for posets so I want to use SAGE first to generate all connected posets with a certain number of points and then use the data in GAP. The output of posets in SAGE should have the form ["x1","x2","x3","x4"],[["x1","x2"],["x1","x3"],["x3","x4"],["x2","x4"]] so that I can use them in GAP. Here the poset has 4 elements x1,x2,x3 and x4 and ["x1","x2"] means that x1 is smaller than x2 etc.

So I want the following with SAGE:

Input: A number $n \geq 2$.

Output: The list of all connected posets with $n$ elements displayed in the form (this is an example) ["x1","x2","x3","x4"],[["x1","x2"],["x1","x3"],["x3","x4"],["x2","x4"]].

I want to do certain calculation with posets using GAP. But GAP has no package for posets so I want to use SAGE first to generate all connected posets with a certain number of points and then use the data in GAP. The output of posets in SAGE should have the form ["x1","x2","x3","x4"],[["x1","x2"],["x1","x3"],["x3","x4"],["x2","x4"]] so that I can use them in GAP. Here the poset has 4 elements x1,x2,x3 and x4 and ["x1","x2"] means that x1 is smaller than x2 etc.

So I want the following with SAGE:

Input: A number $n \geq 2$.

Output: The list of all connected posets with $n$ elements displayed in the form (this is an example) ["x1","x2","x3","x4"],[["x1","x2"],["x1","x3"],["x3","x4"],["x2","x4"]].

I want to do certain calculation with posets using GAP. But GAP has no package for posets so I want to use SAGE first to generate all connected posets with a certain number of points and then use the data in GAP. The output of posets in SAGE should have the form ["x1","x2","x3","x4"],[["x1","x2"],["x1","x3"],["x3","x4"],["x2","x4"]] so that I can use them in GAP. Here the poset has 4 elements x1,x2,x3 and x4 and ["x1","x2"] means that x1 is smaller than x2 etc.

So I want the following with SAGE:

Input: A number $n \geq 2$.

Output: The list of all connected posets with $n$ elements displayed in the form (this is an example) ["x1","x2","x3","x4"],[["x1","x2"],["x1","x3"],["x3","x4"],["x2","x4"]].

edit: Here how the output Thank you very much for the two answers. Sadly I cannot comment at the moment directly without approvial of a moderator. Your codes solve my problem in a perfect way expect that the outputs have a ' where there should be for n=3: [ [["x1", a " so that GAP can understand it. (example: instead of ['x1', 'x2', 'x3', 'x4'], [['x1', 'x2'], ['x1', 'x3'], ['x1', 'x4'] the first element should look like ["x1", "x2", "x3"], [["x1", "x2"], ["x1", "x3"]] ], [["x1", "x2", "x3"], [["x1", "x2"], ["x2", "x3"]]], [["x1", "x2", "x3"], [["x1", "x3"], ["x2", "x3"]]]]"x3"]]).