Algebraic Operads

112 Algebraic Operads: An Algorithmic Companion

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Pick some monomial order, and compute the reduced Gröbner basis for the

defining relations of Tridend for that order.

Exercise 3.11. Consult [2] for the definition of the nonsymmetric operad

of quadri-algebras. Try to guess, based on the example of the dendriform

operad, an optimal monomial order for computing its reduced Gröbner basis.

Check your guess, and compare your results with the investigation for several

different orders undertaken in [182].

Exercise 3.12. Consult [176] for the definition of a certain diagram ...