indexed by lambda.Cat::GradedModuleWithBasis – the category of graded modules with a distinguished basis
Cat::GradedModuleWithBasis represents the category of graded modules with a distinguished basis.
Creating the Category
Cat::GradedModuleWithBasis(coeffRing)
Parameters:
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coeffRing: |
A domain which must be from the category Cat::Ring. |
Categories
Cat::ModuleWithBasis(coeffRing)
Details:
A Cat::GradedModuleWithBasis is a graded module with a distinguished basis whose elements are homogeneous.
Entries
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"typeDegree" |
The type of the degrees.The default value Type::AnyType should cause no problem; however, domains in this category should preferably set this to a more specific value, like Type::NonNegInt. |
degree – degree of an element
Cat::GradedModuleWithBasis::degree(dom x)
Returns the degree of the element x.
degreeBasis – degree of a basis element
Cat::GradedModuleWithBasis::degreeBasis(baseClass lambda)
Returns the degree of the basis element indexed by lambda.
isHomogeneous – homogeneity test
Cat::GradedModuleWithBasis::isHomogeneous(dom x)
Returns whether the element x is homogeneous, that is whether if x is a linear combination of basis elements of same degree.
homogeneousComponents – homogeneous components
Cat::GradedModuleWithBasis::homogeneousComponents(dom x)
Returns a table of the form table(
, ...), where x1 is the homogeneous component of x of degree d1, and so on. Only non-zero homogeneous components are listed; in particular, the empty table is returned for dom::zero.
homogeneousComponent – homogeneous component of given degree
Cat::GradedModuleWithBasis::homogeneousComponent(dom x, degree d)
Returns the homogeneous component of x of degree d.
truncate – truncate
Cat::GradedModuleWithBasis::truncate(dom x, degree order)
Returns a copy of x with all homogeneous components of degree order or more killed.
Changes in MuPAD 3.1
New Function.