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2015-12-29 09:30:07 +0100 asked a question How to plot lattice paths ?

I have seen that the command

for D in DyckWords(n):
    D.pretty_print(type="NE-SE")

gives a nice plot of all Dyck paths.

Is there an analogous command for the set of all 2^n lattice paths of length n with up- and downsteps of height 1? Please give details, I am a newcomer to Sage.

Edit: Sorry if my question is not properly formulated. Perhaps I should modify my question somewhat: The command

D = DyckWords(6)[3]
D.pretty_print(type="NE-SE")

gives a nice picture (which I unfortunately cannot copy) of the Dyckpath corresponding to [1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0] by interpreting 0 with a down-step and 1 with an up-step.

How can I print a corresponding picture for a word which corresponds to a path with negative values?

2015-12-23 09:39:11 +0100 commented answer How to compute the set of Dyck paths ?

Thank you very much. I wanted to do the same as in the second answer: def prim(w):

for i in range(1,len(w)): w[i] = w[i-1] + 2*w[i]-1

[prim(w) for w in DyckWords(4)]

but got TypeError: 'CompleteDyckWords_size_with_category.element_class' object does not support item assignment. How can this be corrected?

2015-12-23 09:32:53 +0100 commented answer How to compute the set of Dyck paths ?

Thank you very much. I would also like to know where I can find more about lattice paths in SAGE, e.g. how to compute number of peaks or valleys, Motzkin paths, etc.

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2015-12-22 17:40:03 +0100 asked a question How to compute the set of Dyck paths ?

I am new to SAGE and try to experiment with it. So I apologize if my question is too trivial. I am interested to do Dyck paths with SAGE. I understand that

D=DyckWords(n)

D.list()

gives Dyck words as 2n-tuples of n numbers 0,1. But I want to get the corresponding Dyck paths by replacing 1 with an up-step (1,1) and 0 with a down-step (1,-1) represented by the (2n+1)-tuple of the heights of the path.

Thus instead of w=[1,1,1,0,0,1,0,0] I want d=[0,1,2,3,2,1,2,1,0] with height h(d)=3.

How do I get this? And how to compute the height of the path? More precisely how to compute the set of all (d,h(d))for d in D?