diff options
Diffstat (limited to 'src/algebra/catdef.spad.pamphlet')
| -rw-r--r-- | src/algebra/catdef.spad.pamphlet | 30 |
1 files changed, 2 insertions, 28 deletions
diff --git a/src/algebra/catdef.spad.pamphlet b/src/algebra/catdef.spad.pamphlet index bad221b9..49ada95e 100644 --- a/src/algebra/catdef.spad.pamphlet +++ b/src/algebra/catdef.spad.pamphlet @@ -516,37 +516,11 @@ DifferentialModule(R: CommutativeRing): Category == ++ Differential extensions of a ring R. ++ Given a differentiation on R, extend it to a differentiation on %. -DifferentialExtension(R:Ring): Category == Ring with - --operations - 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. +DifferentialExtension(R:Ring): Category == + Join(Ring,DifferentialSpaceExtension R) with 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$R) - - if R has PartialDifferentialRing Symbol then - differentiate(x:%, v:Symbol):% == - differentiate(x, differentiate(#1, v)$R) @ |