GradedAlgebra(R, E)ΒΆ

carten.spad line 48

GradedAlgebra(R, E) denotes E-graded \ ``R-algebra''. A graded algebra is a graded module together with a degree preserving R-linear map, called the product. The name product\ ``'' is written out in full so inner and outer products with the same mapping type can be distinguished by name.

0: %
from GradedModule(R, E)
1: %
1 is the identity for product.
*: (%, R) -> %
from GradedModule(R, E)
*: (R, %) -> %
from GradedModule(R, E)
+: (%, %) -> %
from GradedModule(R, E)
-: % -> %
from GradedModule(R, E)
-: (%, %) -> %
from GradedModule(R, E)
=: (%, %) -> Boolean
from BasicType
~=: (%, %) -> Boolean
from BasicType
coerce: % -> OutputForm
from CoercibleTo OutputForm
coerce: R -> %
from RetractableTo R
degree: % -> E
from GradedModule(R, E)
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
latex: % -> String
from SetCategory
product: (%, %) -> %
product(a, b) is the degree-preserving R-linear product: degree product(a, b) = degree a + degree b product(a1+a2, b) = product(a1, b) + product(a2, b) product(a, b1+b2) = product(a, b1) + product(a, b2) product(r*a, b) = product(a, r*b) = r*product(a, b) product(a, product(b, c)) = product(product(a, b), c)
retract: % -> R
from RetractableTo R
retractIfCan: % -> Union(R, failed)
from RetractableTo R

BasicType

CoercibleTo OutputForm

GradedModule(R, E)

RetractableTo R

SetCategory