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Diffstat (limited to 'src/algebra/catdef.spad.pamphlet')
| -rw-r--r-- | src/algebra/catdef.spad.pamphlet | 8 |
1 files changed, 7 insertions, 1 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. |