From 82929c32be58e92dccd449f8a874dc1419980f50 Mon Sep 17 00:00:00 2001
From: dos-reis <gdr@axiomatics.org>
Date: Mon, 14 Jun 2010 15:46:03 +0000
Subject: 	* 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.

---
 src/algebra/catdef.spad.pamphlet | 11 ++++++++---
 1 file changed, 8 insertions(+), 3 deletions(-)

(limited to 'src/algebra/catdef.spad.pamphlet')

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.
-- 
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