GradedModule(R, E)ΒΆ

carten.spad line 1 [edit on github]

GradedModule(R, E) denotes E-graded \ ``R-module'', i.e. collection of R-modules indexed by an abelian monoid E. An element g of G[s] for some specific s in E is said to be an element of G with degree s. Sums are defined in each module G[s] so two elements of G have a sum if they have the same degree. Morphisms can be defined and composed by degree to give the mathematical category of graded modules.

0: %

0 denotes the zero of degree 0.

*: (%, R) -> %

g*r is right module multiplication.

*: (R, %) -> %

r*g is left module multiplication.

+: (%, %) -> %

g+h is the sum of g and h in the module of elements of the same degree as g and h. Error: if g and h have different degrees.

-: % -> %

-g is the additive inverse of g in the module of elements of the same grade as g.

-: (%, %) -> %

g-h is the difference of g and h in the module of elements of the same degree as g and h. Error: if g and h have different degrees.

=: (%, %) -> Boolean

from BasicType

~=: (%, %) -> Boolean

from BasicType

coerce: % -> OutputForm

from CoercibleTo OutputForm

degree: % -> E

degree(g) names the degree of g. The set of all elements of a given degree form an R-module.

latex: % -> String

from SetCategory

BasicType

CoercibleTo OutputForm

SetCategory