Cat::OperadWithBasis – the category of operads over a distinguished basis

Cat::OperadWithBasis represents the category of operads with a distinguished basis.

Creating the Category

Cat::OperadWithBasis(coeffRing)

Parameters:

coeffRing

A domain which must be from the category Cat::Ring.

Categories

Cat::GradedModuleWithBasis(coeffRing), Cat::Operad(coeffRing)

Details:

A Cat::OperadWithBasis is an operad (Cat::Operad) with a distinguished basis. The composition is typically implemented by extending by linearity its definition on the basis elements.

Entries

"oneBasis"

If the unit of the operad is a basis element, the index of this basis element can be provided here, instead of defining "one".

compositionBasis – composition of basis elements (optional)

Cat::OperadWithBasis::compositionBasis(dom::basisIndices x, dom::basisIndices y, positive integer i)

Returns the composition of the basis elements indexed by x and y at position i.

This method is used to provide a definition of the composition by extending by linearity.

ground – ground coefficient

Cat::OperadWithBasis::ground(dom x)

Returns the ground coefficient of x, that is the coefficient of x on the unit of the algebra.

This only makes sense if the unit of the operad is a basis element, so this method is optional. A default implementation is provided when "oneBasis" is defined.

Changes in MuPAD 3.1

New Function.