GradedModule(R, E)

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.

* : (%, 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.

0 : () -> %

0 denotes the zero of degree 0.

= : (%, %) -> 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
~= : (%, %) -> Boolean
from BasicType

CoercibleTo(OutputForm)

SetCategory

BasicType