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| author | dos-reis <gdr@axiomatics.org> | 2010-06-18 11:28:03 +0000 |
|---|---|---|
| committer | dos-reis <gdr@axiomatics.org> | 2010-06-18 11:28:03 +0000 |
| commit | bd813c8607938e8ff0d8f112987300e22e3dc712 (patch) | |
| tree | cfaf242955f84d1810219e7143188c2170b2b566 /src/algebra/catdef.spad.pamphlet | |
| parent | f515cb4cfd86ecb9933897178a6618fdc1f4cbfb (diff) | |
| download | open-axiom-bd813c8607938e8ff0d8f112987300e22e3dc712.tar.gz | |
* algebra/catdef.spad.pamphlet (DifferentialExtension): Now
extends DifferentialSpaceExtension.
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) @ |