GradedAlgebra(R, E)ΒΆ

carten.spad line 48 [edit on github]

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 CoercibleFrom 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

CoercibleFrom R

CoercibleTo OutputForm

GradedModule(R, E)

RetractableTo R

SetCategory