Sorry for taking so long to answer this. In short, yes, it is. The group 
version is implemented in Sage under the name right-angled Artin group (see 
groups/raag.py). That code trivially lifts up to the monoid case. Although 
a list of the letters (rather than syllables) might be better data 
structure for the elements as there are no inverses to worry about.

Best,
Travis


On Sunday, March 25, 2018 at 11:23:35 AM UTC-5, Samuel Lelievre wrote:
>
> Dear sage-combinat-devel,
>
> Someone just asked on Ask Sage whether the
> free partially commutative monoid (or trace monoid)
> associated to a graph is implemented in Sage,
> and if not, how to do it.
>
>     
> https://ask.sagemath.org/question/41756/partially-commutative-monoid-of-a-graph/
>
> Maybe someone on this list has an answer?
>
> Searching the source seems to reveal there currently
> is no implementation in Sage, as both these commands
>
>     sage: search_src("trace_monoid")
>     sage: search_src("partially_commutative")
>
> return nothing.
>
> But maybe it is implemented under another name?
> Or an implementation exists in a ticket somewhere?
> Or someone here can suggest how to implement it?
>
> Thanks in advance,
> Samuel
>
>
>

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