A = freeAlgebra(R,xs)
This function creates a free algebra over $R$ with variables from the BasicList xs. Options are also passed as part of the BasicList. The variables are not in scope after a call to this function by default. If you wish to have them in scope, one may use the return value, or pass the option true to UseVariables.
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Other options are Degrees, DegreeRank, Weights, and Heft which use the same syntax and play the same role as in the case of a commutative polynomial ring.
In particular, to create noncommutative elimination orders, one must use Weights that are chosen accordingly. The following example is the graph ideal of the ring homomorphism from $\mathbb{Q}\langle a,b,c\rangle$ to $\mathbb{Q}\langle x,y\rangle$ satisfying $a \mapsto xyx$, $b \mapsto yxy$ and $c \mapsto xy$.
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This general construction is automated in ncGraphIdeal and ncKernel.
The object freeAlgebra is a method function.