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| author | dos-reis <gdr@axiomatics.org> | 2010-06-19 02:29:06 +0000 |
|---|---|---|
| committer | dos-reis <gdr@axiomatics.org> | 2010-06-19 02:29:06 +0000 |
| commit | e61f5a0fa4656dd256ad664528e9a6355638bd41 (patch) | |
| tree | d7241a1c01fda05575d09af5a845340fa8084a74 /src/algebra | |
| parent | dd685997f154b236057a386a046f3202efaaac91 (diff) | |
| download | open-axiom-e61f5a0fa4656dd256ad664528e9a6355638bd41.tar.gz | |
* algebra/catdef.spad.pamphlet (LinearlyExplicitRingOver)
[reducedSystem]: Add overload.
* algebra/si.spad.pamphlet (SingleInteger)[reducedSystem]: Tidy.
Diffstat (limited to 'src/algebra')
| -rw-r--r-- | src/algebra/catdef.spad.pamphlet | 8 | ||||
| -rw-r--r-- | src/algebra/si.spad.pamphlet | 2 |
2 files changed, 8 insertions, 2 deletions
diff --git a/src/algebra/catdef.spad.pamphlet b/src/algebra/catdef.spad.pamphlet index 4e077bec..3cf7aab9 100644 --- a/src/algebra/catdef.spad.pamphlet +++ b/src/algebra/catdef.spad.pamphlet @@ -1086,7 +1086,7 @@ LeftModule(R:Rng):Category == Join(AbelianGroup, LeftLinearSet R) )abbrev category LINEXP LinearlyExplicitRingOver ++ Author: ++ Date Created: -++ Date Last Updated: June 14, 2010 +++ Date Last Updated: June 18, 2010 ++ Basic Functions: ++ Related Constructors: ++ Also See: @@ -1101,6 +1101,12 @@ LinearlyExplicitRingOver(R:Ring): Category == LeftModule R with ++ with coefficients in \spad{R} such that the system of equations ++ \spad{c1*v1 + ... + cn*vn = 0$%} has the same solution as ++ \spad{c * M = 0} where \spad{c} is the row vector \spad{[c1,...cn]}. + reducedSystem: (Vector %,%) -> Record(mat: Matrix R,vec: Vector R) + ++ \spad{reducedSystem([v1,...,vn],u)} returns a matrix \spad{M} + ++ with coefficients in \spad{R} and a vector \spad{w} such + ++ that the system of equations \spad{c1*v1 + ... + cn*vn = u} + ++ has the same solution as \spad{c * M = w} where \spad{c} + ++ is the row vector \spad{[c1,...cn]}. reducedSystem: Matrix % -> Matrix R ++ reducedSystem(A) returns a matrix B such that \spad{A x = 0} and \spad{B x = 0} ++ have the same solutions in R. diff --git a/src/algebra/si.spad.pamphlet b/src/algebra/si.spad.pamphlet index e9e5637c..b62da15a 100644 --- a/src/algebra/si.spad.pamphlet +++ b/src/algebra/si.spad.pamphlet @@ -317,7 +317,7 @@ SingleInteger(): Join(IntegerNumberSystem,OrderedFinite,BooleanLogic,Logic,OpenM (x -$Lisp MININT +$Lisp 1$Lisp) pretend PositiveInteger - reducedSystem(m, v) == + reducedSystem(m: Matrix %, v: Vector %) == [m pretend Matrix(Integer), v pretend Vector(Integer)] positiveRemainder(x,n) == |