GradedModule(R, E)ΒΆ

carten.spad line 1

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.
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
latex: % -> String
from SetCategory

BasicType

CoercibleTo OutputForm

SetCategory