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