/usr/share/axiom-20170501/src/algebra/COMBOPC.spad is in axiom-source 20170501-3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 | )abbrev category COMBOPC CombinatorialOpsCategory
++ Author: Manuel Bronstein
++ Date Last Updated: 22 February 1993 (JHD/BMT)
++ Description:
++ CombinatorialOpsCategory is the category obtaining by adjoining
++ summations and products to the usual combinatorial operations;
CombinatorialOpsCategory() : Category == SIG where
SIG ==> CombinatorialFunctionCategory with
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;
summation : ($, Symbol) -> $
++ summation(f(n), n) returns the formal sum S(n) which verifies
++ S(n+1) - S(n) = f(n);
summation : ($, SegmentBinding $) -> $
++ summation(f(n), n = a..b) returns f(a) + ... + f(b) as a
++ formal sum;
product : ($, Symbol) -> $
++ product(f(n), n) returns the formal product P(n) which verifies
++ P(n+1)/P(n) = f(n);
product : ($, SegmentBinding $) -> $
++ product(f(n), n = a..b) returns f(a) * ... * f(b) as a
++ formal product;
|