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| author | dos-reis <gdr@axiomatics.org> | 2010-06-14 15:46:03 +0000 |
|---|---|---|
| committer | dos-reis <gdr@axiomatics.org> | 2010-06-14 15:46:03 +0000 |
| commit | 82929c32be58e92dccd449f8a874dc1419980f50 (patch) | |
| tree | 727f016cd1ff5a76b30a0e4c2830fabf8224a541 /src/algebra | |
| parent | 5f7a5c1a81c50807bf1315260f94108dd9a5ac2e (diff) | |
| download | open-axiom-82929c32be58e92dccd449f8a874dc1419980f50.tar.gz | |
* algebra/catdef.spad.pamphlet (LinearlyExplicitRingOver): Now
extends LeftModule R.
[reducedSystem: Vector % -> Matrix R]: New overload.
* algebra/lindep.spad.pamphlet (LinearDependence): Additionally
require Ring on the second parameter.
(IntegerLinearDependence): Add similar requirement on the parameter.
Diffstat (limited to 'src/algebra')
| -rw-r--r-- | src/algebra/catdef.spad.pamphlet | 11 | ||||
| -rw-r--r-- | src/algebra/lindep.spad.pamphlet | 4 | ||||
| -rw-r--r-- | src/algebra/si.spad.pamphlet | 2 |
3 files changed, 11 insertions, 6 deletions
diff --git a/src/algebra/catdef.spad.pamphlet b/src/algebra/catdef.spad.pamphlet index 4c6317f3..0a1a435b 100644 --- a/src/algebra/catdef.spad.pamphlet +++ b/src/algebra/catdef.spad.pamphlet @@ -1013,7 +1013,7 @@ LeftModule(R:Rng):Category == Join(AbelianGroup, LeftLinearSet R) )abbrev category LINEXP LinearlyExplicitRingOver ++ Author: ++ Date Created: -++ Date Last Updated: +++ Date Last Updated: June 14, 2010 ++ Basic Functions: ++ Related Constructors: ++ Also See: @@ -1021,8 +1021,13 @@ LeftModule(R:Rng):Category == Join(AbelianGroup, LeftLinearSet R) ++ Keywords: ++ References: ++ Description: -++ An extension ring with an explicit linear dependence test. -LinearlyExplicitRingOver(R:Ring): Category == Ring with +++ An extension of left-module with an explicit linear dependence test. +LinearlyExplicitRingOver(R:Ring): Category == LeftModule R with + reducedSystem: Vector % -> Matrix R + ++ \spad{reducedSystem [v1,...,vn]} returns a matrix \spad{M} + ++ 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: 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/lindep.spad.pamphlet b/src/algebra/lindep.spad.pamphlet index 64c06067..d6a266e0 100644 --- a/src/algebra/lindep.spad.pamphlet +++ b/src/algebra/lindep.spad.pamphlet @@ -19,7 +19,7 @@ ++ Description: Test for linear dependence. LinearDependence(S, R): Exports == Implementation where S: IntegralDomain - R: LinearlyExplicitRingOver S + R: Join(Ring,LinearlyExplicitRingOver S) Q ==> Fraction S @@ -90,7 +90,7 @@ LinearDependence(S, R): Exports == Implementation where ++ Date Last Updated: 14 May 1991 ++ Description: Test for linear dependence over the integers. IntegerLinearDependence(R): Exports == Implementation where - R: LinearlyExplicitRingOver Integer + R: Join(Ring,LinearlyExplicitRingOver Integer) Z ==> Integer diff --git a/src/algebra/si.spad.pamphlet b/src/algebra/si.spad.pamphlet index 2321b60d..e9e5637c 100644 --- a/src/algebra/si.spad.pamphlet +++ b/src/algebra/si.spad.pamphlet @@ -262,7 +262,7 @@ SingleInteger(): Join(IntegerNumberSystem,OrderedFinite,BooleanLogic,Logic,OpenM if wholeObj then OMputEndObject(dev) - reducedSystem m == m pretend Matrix(Integer) + reducedSystem(m: Matrix %) == m pretend Matrix(Integer) coerce(x):OutputForm == rep(x)::OutputForm convert(x:%):Integer == rep x i:Integer * y:% == i::% * y |