GradedAlgebra(R, E)

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.

* : (%, R) -> %
from GradedModule(R, E)
* : (R, %) -> %
from GradedModule(R, E)
+ : (%, %) -> %
from GradedModule(R, E)
- : % -> %
from GradedModule(R, E)
- : (%, %) -> %
from GradedModule(R, E)
0 : () -> %
from GradedModule(R, E)
1 : () -> %

1 is the identity for product.

= : (%, %) -> Boolean
from BasicType
coerce : R -> %
from CoercibleFrom(R)
coerce : % -> OutputForm
from CoercibleTo(OutputForm)
degree : % -> E
from GradedModule(R, E)
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)
~= : (%, %) -> Boolean
from BasicType

CoercibleTo(OutputForm)

CoercibleFrom(R)

SetCategory

GradedModule(R, E)

BasicType

RetractableTo(R)