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
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"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.