/usr/share/axiom-20170501/src/algebra/DIFRING.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 35 36 37 38 | )abbrev category DIFRING DifferentialRing
++ Description:
++ An ordinary differential ring, that is, a ring with an operation
++ \spadfun{differentiate}.
++
++ Axioms\br
++ \tab{5}\spad{differentiate(x+y) = differentiate(x)+differentiate(y)}\br
++ \tab{5}\spad{differentiate(x*y) = x*differentiate(y) + differentiate(x)*y}
DifferentialRing() : Category == SIG where
SIG ==> Ring with
differentiate : % -> %
++ differentiate(x) returns the derivative of x.
++ This function is a simple differential operator
++ where no variable needs to be specified.
D : % -> %
++ D(x) returns the derivative of x.
++ This function is a simple differential operator
++ where no variable needs to be specified.
differentiate : (%, NonNegativeInteger) -> %
++ differentiate(x, n) returns the n-th derivative of x.
D : (%, NonNegativeInteger) -> %
++ D(x, n) returns the n-th derivative of x.
add
D r == differentiate r
differentiate(r, n) ==
for i in 1..n repeat r := differentiate r
r
D(r,n) == differentiate(r,n)
|