diff options
| author | dos-reis <gdr@axiomatics.org> | 2013-06-17 07:20:46 +0000 |
|---|---|---|
| committer | dos-reis <gdr@axiomatics.org> | 2013-06-17 07:20:46 +0000 |
| commit | d69a5741c16f450e981b7d8f4b28c217f388890d (patch) | |
| tree | 67bf6dccc4bdc6221e9160749232402b91d29d96 /src/algebra/catdef.spad.pamphlet | |
| parent | eff8995031482604470f31c7cc24e525c5edadb2 (diff) | |
| download | open-axiom-d69a5741c16f450e981b7d8f4b28c217f388890d.tar.gz | |
Weaken conditions on parameter of partial differential domains.
Diffstat (limited to 'src/algebra/catdef.spad.pamphlet')
| -rw-r--r-- | src/algebra/catdef.spad.pamphlet | 6 |
1 files changed, 3 insertions, 3 deletions
diff --git a/src/algebra/catdef.spad.pamphlet b/src/algebra/catdef.spad.pamphlet index 2711ff4e..b2daad4e 100644 --- a/src/algebra/catdef.spad.pamphlet +++ b/src/algebra/catdef.spad.pamphlet @@ -1694,7 +1694,7 @@ PartialDifferentialDomain(T: Type, S: Type): Category == Type with ++ differentiation with respect to variables from some domain. ++ See Also: ++ PartialDifferentialDomain -PartialDifferentialSpace(S: SetCategory): Category == +PartialDifferentialSpace(S: BasicType): Category == PartialDifferentialDomain(%,S) with differentiate: (%,List S) -> % ++ \spad{differentiate(x,[s1,...sn])} computes successive @@ -1759,7 +1759,7 @@ PartialDifferentialSpace(S: SetCategory): Category == ++ \spad{differentiate(x+y,e) = differentiate(x,e)+differentiate(y,e)} ++ \spad{differentiate(x*y,e) = x*differentiate(y,e) + differentiate(x,e)*y} -PartialDifferentialRing(S:SetCategory): Category == +PartialDifferentialRing(S: BasicType): Category == Join(Ring,PartialDifferentialSpace S) @ @@ -1785,7 +1785,7 @@ PartialDifferentialRing(S:SetCategory): Category == ++ \spad{differentiate(r*x,e) = r*differentiate(x,e) + differentiate(r,e)*x} ++ \spad{differentiate(x*r,e) = x*differentiate(r,e) + differentiate(x,e)*r} -PartialDifferentialModule(R: Ring,S: SetCategory): Category == +PartialDifferentialModule(R: Ring,S: BasicType): Category == Join(BiModule(R,R),PartialDifferentialSpace S) with if R has CommutativeRing then Module R |