CombinatorialOpsCategoryΒΆ

combfunc.spad line 1

CombinatorialOpsCategory is the category obtaining by adjoining summations and products to the usual combinatorial operations.

binomial: (%, %) -> %
from CombinatorialFunctionCategory
factorial: % -> %
from CombinatorialFunctionCategory
factorials: % -> %
factorials(f) rewrites the permutations and binomials in f in terms of factorials.
factorials: (%, Symbol) -> %
factorials(f, x) rewrites the permutations and binomials in f involving x in terms of factorials.
permutation: (%, %) -> %
from CombinatorialFunctionCategory
product: (%, SegmentBinding %) -> %
product(f(n), n = a..b) returns f(a) * ... * f(b) as a formal product.
product: (%, Symbol) -> %
product(f(n), n) returns the formal product P(n) which verifies P(n+1)/P(n) = f(n).
summation: (%, SegmentBinding %) -> %
summation(f(n), n = a..b) returns f(a) + ... + f(b) as a formal sum.
summation: (%, Symbol) -> %
summation(f(n), n) returns the formal sum S(n) which verifies S(n+1) - S(n) = f(n).

CombinatorialFunctionCategory