diff options
Diffstat (limited to 'src/algebra/catdef.spad.pamphlet')
| -rw-r--r-- | src/algebra/catdef.spad.pamphlet | 44 |
1 files changed, 38 insertions, 6 deletions
diff --git a/src/algebra/catdef.spad.pamphlet b/src/algebra/catdef.spad.pamphlet index 49ada95e..f5ecae65 100644 --- a/src/algebra/catdef.spad.pamphlet +++ b/src/algebra/catdef.spad.pamphlet @@ -495,8 +495,9 @@ DifferentialRing(): Category == Join(Ring,DifferentialSpace) ++ \spad{differentiate(x + y) = differentiate(x) + differentiate(x)} ++ \spad{differentiate(r*y) = r*differentiate(y) + differentiate(r)*y} -DifferentialModule(R: CommutativeRing): Category == - Join(Module R, DifferentialSpace) +DifferentialModule(R: Ring): Category == + Join(BiModule(R,R), DifferentialSpace) with + if R has CommutativeRing then Module R @ @@ -537,8 +538,11 @@ DifferentialExtension(R:Ring): Category == ++ Description: ++ Category of modules that extend differential rings. ++ -DifferentialModuleExtension(R: CommutativeRing): Category == - Join(Module(R),DifferentialSpaceExtension R) +DifferentialModuleExtension(R: Ring): Category == + Join(BiModule(R,R),DifferentialSpaceExtension R) with + if R has DifferentialSpace then DifferentialModule R + if R has PartialDifferentialSpace Symbol then + PartialDifferentialModule(R,Symbol) @ @@ -1544,8 +1548,6 @@ PartialDifferentialSpace(S: SetCategory): Category == @ - - \section{category PDRING PartialDifferentialRing} <<category PDRING PartialDifferentialRing>>= )abbrev category PDRING PartialDifferentialRing @@ -1569,6 +1571,35 @@ PartialDifferentialRing(S:SetCategory): Category == Join(Ring,PartialDifferentialSpace S) @ + +\section{Partial Differential Module} + +<<category PDMOD PartialDifferentialModule>>= +)abbrev category PDMOD PartialDifferentialModule +++ Author: Gabriel Dos Reis +++ Date Created: June 16, 2010 +++ Date Last Updated: June 18, 2010 +++ Related Constructors: +++ Also See: +++ AMS Classifications: +++ Keywords: +++ References: +++ Description: +++ A partial differential R-module with differentiations +++ indexed by a parameter type S. +++ +++ Axioms: +++ \spad{differentiate(x+y,e) = differentiate(x,e)+differentiate(y,e)} +++ \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 == + Join(BiModule(R,R),PartialDifferentialSpace S) with + if R has CommutativeRing then Module R + +@ + + \section{category PFECAT PolynomialFactorizationExplicit} <<category PFECAT PolynomialFactorizationExplicit>>= )abbrev category PFECAT PolynomialFactorizationExplicit @@ -2031,6 +2062,7 @@ VectorSpace(S:Field): Category == Module(S) with <<category PDDOM PartialDifferentialDomain>> <<category PDSPC PartialDifferentialSpace>> <<category PDRING PartialDifferentialRing>> +<<category PDMOD PartialDifferentialModule>> <<category DIFEXT DifferentialExtension>> <<category DSEXT DifferentialSpaceExtension>> @ |