/usr/share/axiom-20170501/src/algebra/DIFEXT.spad is in axiom-source 20170501-3.
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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 39 40 41 42 43 44 45 46 47 48 49 50 | )abbrev category DIFEXT DifferentialExtension
++ Description:
++ Differential extensions of a ring R.
++ Given a differentiation on R, extend it to a differentiation on %.
DifferentialExtension(R) : Category == SIG where
R : Ring
SIG ==> Ring with
differentiate : (%, R -> R) -> %
++ differentiate(x, deriv) differentiates x extending
++ the derivation deriv on R.
differentiate : (%, R -> R, NonNegativeInteger) -> %
++ differentiate(x, deriv, n) differentiate x n times
++ using a derivation which extends deriv on R.
D : (%, R -> R) -> %
++ D(x, deriv) differentiates x extending
++ the derivation deriv on R.
D : (%, R -> R, NonNegativeInteger) -> %
++ D(x, deriv, n) differentiate x n times
++ using a derivation which extends deriv on R.
if R has DifferentialRing then DifferentialRing
if R has PartialDifferentialRing(Symbol) then
PartialDifferentialRing(Symbol)
add
differentiate(x:%, derivation: R -> R, n:NonNegativeInteger):% ==
for i in 1..n repeat x := differentiate(x, derivation)
x
D(x:%, derivation: R -> R) == differentiate(x, derivation)
D(x:%, derivation: R -> R, n:NonNegativeInteger) ==
differentiate(x, derivation, n)
if R has DifferentialRing then
differentiate x == differentiate(x, differentiate$R)
if R has PartialDifferentialRing Symbol then
differentiate(x:%, v:Symbol):% ==
differentiate(x, s +-> differentiate(s, v)$R)
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