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| author | dos-reis <gdr@axiomatics.org> | 2013-05-20 04:55:09 +0000 |
|---|---|---|
| committer | dos-reis <gdr@axiomatics.org> | 2013-05-20 04:55:09 +0000 |
| commit | 1316b335ecc97eeaaa4c91258b31c789d8f4b0d3 (patch) | |
| tree | ed428505010ccaac4e4d2bfeb4f667b8039c50f1 /src/algebra/derham.spad.pamphlet | |
| parent | 4c3e77d5efc19d097c7995f7d5f64eee0400ff66 (diff) | |
| download | open-axiom-1316b335ecc97eeaaa4c91258b31c789d8f4b0d3.tar.gz | |
Use Functorial more often.
Diffstat (limited to 'src/algebra/derham.spad.pamphlet')
| -rw-r--r-- | src/algebra/derham.spad.pamphlet | 17 |
1 files changed, 6 insertions, 11 deletions
diff --git a/src/algebra/derham.spad.pamphlet b/src/algebra/derham.spad.pamphlet index 1ff71c4c..babf6987 100644 --- a/src/algebra/derham.spad.pamphlet +++ b/src/algebra/derham.spad.pamphlet @@ -112,7 +112,7 @@ ExtAlgBasis(): Export == Implement where )abbrev domain ANTISYM AntiSymm ++ Author: Larry A. Lambe ++ Date : 01/26/91. -++ Revised : 30 Nov 94 +++ Revised : May 19, 2013. ++ ++ based on AntiSymmetric '89 ++ @@ -134,7 +134,7 @@ AntiSymm(R:Ring, lVar:List Symbol): Export == Implement where coef ==> c Term ==> Record(k:EAB,c:R) - Export == Join(LALG(R), RetractableTo(R)) with + Export == Join(LALG(R),RetractableTo(R),Functorial R) with leadingCoefficient : % -> R ++ leadingCoefficient(p) returns the leading ++ coefficient of antisymmetric polynomial p. @@ -164,10 +164,6 @@ AntiSymm(R:Ring, lVar:List Symbol): Export == Implement where ++ i.e., if degree(p) = 0. degree : % -> NNI ++ degree(p) returns the homogeneous degree of p. - map : (R -> R, %) -> % - ++ map(f,p) changes each coefficient of p by the - ++ application of f. - -- 1 corresponds to the empty monomial Nul = [0,...,0] -- from EAB. In terms of the exterior algebra on X, @@ -308,7 +304,7 @@ AntiSymm(R:Ring, lVar:List Symbol): Export == Implement where )abbrev domain DERHAM DeRhamComplex ++ Author: Larry A. Lambe ++ Date : 01/26/91. -++ Revised : 12/01/91. +++ Revised : May 19, 2013. ++ ++ based on code from '89 (AntiSymmetric) ++ @@ -332,7 +328,7 @@ DeRhamComplex(CoefRing,listIndVar:List Symbol): Export == Implement where O ==> OutputForm R ==> Expression(CoefRing) - Export == Join(LALG(R), RetractableTo(R)) with + Export == Join(LALG(R), RetractableTo(R),Functorial R) with leadingCoefficient : % -> R ++ leadingCoefficient(df) returns the leading ++ coefficient of differential form df. @@ -358,9 +354,6 @@ DeRhamComplex(CoefRing,listIndVar:List Symbol): Export == Implement where ++ i.e., if degree(df) = 0. degree : % -> I ++ degree(df) returns the homogeneous degree of differential form df. - map : (R -> R, %) -> % - ++ map(f,df) replaces each coefficient x of differential - ++ form df by \spad{f(x)}. totalDifferential : R -> % ++ totalDifferential(x) returns the total differential ++ (gradient) form for element x. @@ -417,6 +410,8 @@ DeRhamComplex(CoefRing,listIndVar:List Symbol): Export == Implement where <<license>>= --Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd. --All rights reserved. +--Copyright (C) 2007-2013, Gabriel Dos Reis. +--All rights reversed. -- --Redistribution and use in source and binary forms, with or without --modification, are permitted provided that the following conditions are |