diff options
Diffstat (limited to 'src/algebra/catdef.spad.pamphlet')
| -rw-r--r-- | src/algebra/catdef.spad.pamphlet | 15 |
1 files changed, 3 insertions, 12 deletions
diff --git a/src/algebra/catdef.spad.pamphlet b/src/algebra/catdef.spad.pamphlet index a7807009..1ea30684 100644 --- a/src/algebra/catdef.spad.pamphlet +++ b/src/algebra/catdef.spad.pamphlet @@ -403,21 +403,12 @@ DifferentialDomain(T: Type): Category == Type with ++ \spad{differentiate(x+y) = differentiate(x)+differentiate(y)} ++ \spad{differentiate(x*y) = x*differentiate(y) + differentiate(x)*y} -DifferentialRing(): Category == 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. +DifferentialRing(): Category == Join(Ring,DifferentialDomain %) with 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 @@ -455,7 +446,7 @@ DifferentialExtension(R:Ring): Category == Ring with 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 DifferentialDomain R then DifferentialRing if R has PartialDifferentialRing(Symbol) then PartialDifferentialRing(Symbol) add @@ -466,7 +457,7 @@ DifferentialExtension(R:Ring): Category == Ring with D(x:%, derivation: R -> R, n:NonNegativeInteger) == differentiate(x, derivation, n) - if R has DifferentialRing then + if R has DifferentialDomain R then differentiate x == differentiate(x, differentiate$R) if R has PartialDifferentialRing Symbol then |