* algebra/aggcat.spad.pamphlet (FiniteLinearAggregate): Remove

	duplicate definition of reverse.
	* algebra/algcat.spad.pamphlet (FramedAlgebra): Remove duplicate
	definition of regularRepresentation.  Explicitly disambiguate
	the argument of coodinates.
	* algebra/efupxs.spad.pamphlet
	(ElementaryFunctionsUnivariatePuiseuxSeries):  Remove duplicate
	definition of asinhIfCan, acoshIfCan, asechIfCan, acshIfCan.
	* algebra/equation2.spad.pamphlet (Equation): Remove duplicate
	definition of *: (S,%) -> %.
	* algebra/fortpak.spad.pamphlet (MultiVariableCalculusFunctions):
	Remove duplicate definition of jacobian.
	* algebra/tree.spad.pamphlet (BinaryTree): Remove duplicate
	definition of empty.

6 files changed, 2 insertions, 14 deletions

diff --git a/src/algebra/aggcat.spad.pamphlet b/src/algebra/aggcat.spad.pamphlet
index 3ed7ceca..42a4f3fd 100644
--- a/src/algebra/aggcat.spad.pamphlet
+++ b/src/algebra/aggcat.spad.pamphlet
@@ -1956,7 +1956,6 @@ FiniteLinearAggregate(S:Type): Category == LinearAggregate S with
     if % has shallowlyMutable then
       reverse x	 == reverse_! copy x
       sort(f, l) == sort_!(f, copy l)
-      reverse x	 == reverse_! copy x
 
       if S has OrderedSet then
 	sort_! l == sort_!(_<$S, l)
diff --git a/src/algebra/algcat.spad.pamphlet b/src/algebra/algcat.spad.pamphlet
index d757de0f..94fde902 100644
--- a/src/algebra/algcat.spad.pamphlet
+++ b/src/algebra/algcat.spad.pamphlet
@@ -154,8 +154,7 @@ FramedAlgebra(R:CommutativeRing, UP:UnivariatePolynomialCategory R):
    convert(v:Vector R):%   == represents(v)
    traceMatrix()           == traceMatrix basis()
    discriminant()          == discriminant basis()
-   regularRepresentation x == regularRepresentation(x, basis())
-   coordinates x           == coordinates(x, basis())
+   coordinates(x:%)        == coordinates(x, basis())
    represents x            == represents(x, basis())
 
    coordinates(v:Vector %) ==
diff --git a/src/algebra/efupxs.spad.pamphlet b/src/algebra/efupxs.spad.pamphlet
index 277b0a85..97bf95c7 100644
--- a/src/algebra/efupxs.spad.pamphlet
+++ b/src/algebra/efupxs.spad.pamphlet
@@ -166,12 +166,8 @@ ElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS):_
     cothIfCan  upxs == applyIfCan(cothIfCan,upxs)
     sechIfCan  upxs == applyIfCan(sechIfCan,upxs)
     cschIfCan  upxs == applyIfCan(cschIfCan,upxs)
-    asinhIfCan upxs == applyIfCan(asinhIfCan,upxs)
-    acoshIfCan upxs == applyIfCan(acoshIfCan,upxs)
     atanhIfCan upxs == applyIfCan(atanhIfCan,upxs)
     acothIfCan upxs == applyIfCan(acothIfCan,upxs)
-    asechIfCan upxs == applyIfCan(asechIfCan,upxs)
-    acschIfCan upxs == applyIfCan(acschIfCan,upxs)
 
     asinIfCan upxs ==
       order(upxs,0) < 0 => "failed"
diff --git a/src/algebra/equation2.spad.pamphlet b/src/algebra/equation2.spad.pamphlet
index 4079a096..7aad51f6 100644
--- a/src/algebra/equation2.spad.pamphlet
+++ b/src/algebra/equation2.spad.pamphlet
@@ -189,8 +189,7 @@ Equation(S: Type): public == private where
         eq1 - eq2 == eq1.lhs - eq2.lhs = eq1.rhs - eq2.rhs
     if S has SemiGroup then
         eq1:$ * eq2:$ == eq1.lhs * eq2.lhs = eq1.rhs * eq2.rhs
-        l:S   * eqn:$ == l       * eqn.lhs = l       * eqn.rhs
-        l:S * eqn:$  ==  l * eqn.lhs    =    l * eqn.rhs
+        l:S * eqn:$ == l * eqn.lhs = l * eqn.rhs
         eqn:$ * l:S  ==  eqn.lhs * l    =    eqn.rhs * l
         -- We have to be a bit careful here: raising to a +ve integer is OK
         -- (since it's the equivalent of repeated multiplication)
diff --git a/src/algebra/fortpak.spad.pamphlet b/src/algebra/fortpak.spad.pamphlet
index 5f3fb1e6..b3ae68a3 100644
--- a/src/algebra/fortpak.spad.pamphlet
+++ b/src/algebra/fortpak.spad.pamphlet
@@ -588,10 +588,6 @@ MultiVariableCalculusFunctions(S,F,FLAF,FLAS) : Exports == Implementation where
          for j in 1 .. (n-iw+1) repeat (_
            setelt(bandM,iw,j,D(v,[xlist(j),xlist(j+iw-1)])) ) )
        bandM
-    jacobian(vf,xflas) ==
-       xlist:List(S) := parts(xflas)
-       i: PI
-       matrix([[D(vf(i),x) for x in xlist] for i in 1 .. maxIndex(vf)])
     bandedJacobian(vf,xflas,kl,ku) ==
        xlist:List(S) := parts(xflas)
        j,iw: PI
diff --git a/src/algebra/tree.spad.pamphlet b/src/algebra/tree.spad.pamphlet
index 27b0d061..a174308e 100644
--- a/src/algebra/tree.spad.pamphlet
+++ b/src/algebra/tree.spad.pamphlet
@@ -382,7 +382,6 @@ BinaryTree(S: SetCategory): Exports == Implementation where
      Rep := List Tree S
      t1 = t2 == (t1::Rep) =$Rep (t2::Rep)
      empty()== [] pretend %
-     empty()== [] pretend %
      node(l,v,r) == cons(tree(v,l:Rep),r:Rep)
      binaryTree(l,v,r) == node(l,v,r)
      binaryTree(v:S) == node(empty(),v,empty())