doc: don't document Integers as filter (#1157)

* doc: don't document Integers as filter

This should resolve #1155

* maxplusmat: fix doc typo

* Fix maxplus matrix docs

---------

Co-authored-by: Codex <codex@openai.com>

Author: james-d-mitchell

doc/maxplusmat.xml

@@ -20,11 +20,10 @@
     <!-- <Filt Name = "IsProjectiveMaxPlusMatrix" Arg = "obj" Type =
          "Category"/> -->
     <Filt Name = "IsNTPMatrix"               Arg = "obj" Type = "Category"/>
-    <Filt Name = "Integers"           Arg = "obj" Type = "Category"/>
     <Returns><K>true</K> or <K>false</K>.</Returns>
     <Description>
       Every matrix over a semiring in &SEMIGROUPS; is a member of one of these
-      categories, which are subcategory of <Ref Filt = "IsMatrixOverSemiring"/>.
+      categories, which are subcategories of <Ref Filt = "IsMatrixOverSemiring"/>.
       <P/>
 
       <C>IsTropicalMatrix</C> is a supercategory of
@@ -37,7 +36,7 @@
         BookName="ref"/>, the underlying list of lists used to create the
       matrix can be accessed using <Ref Attr = "AsList"/>, the rows of
       <C>mat</C> can be accessed using <C>mat[i]</C> where <C>i</C> is between
-      <C>1</C> and the dimension of the matrix, it also possible to loop over
+      <C>1</C> and the dimension of the matrix, it is also possible to loop over
       the rows of a matrix; for tropical matrices <Ref
         Attr = "ThresholdTropicalMatrix"/>; for ntp matrices <Ref
         Attr = "ThresholdNTPMatrix"/> and <Ref Attr = "PeriodNTPMatrix"/>.
@@ -180,13 +179,14 @@ gap> PeriodNTPMatrix(mat);
     <Oper Name = "InverseOp" Arg = "mat" Label = "for an integer matrix"/>
     <Returns>An integer matrix.</Returns>
     <Description>
-      If <A>mat</A> is an integer matrix (i.e. belongs to the category
-      <Ref Filt = "Integers"/>) whose inverse (if it exists) is also an
-      integer matrix, then <C>InverseOp</C> returns the inverse of <A>mat</A>.
+      If <A>mat</A> is an integer matrix whose inverse (if it exists) is also
+      an integer matrix (i.e. a matrix whose <Ref Attr="BaseDomain"
+      BookName="ref"/> is <Ref Var= "Integers" BookName="ref"/>), then
+      <C>InverseOp</C> returns the inverse of <A>mat</A>.
       <P/>
 
       An integer matrix has an integer matrix inverse if and only if it
-      has determinant one.
+      has determinant <M>\pm 1</M>.
       <Example><![CDATA[
 gap> mat := Matrix(Integers, [[0, 0, -1],
 >                             [0, 1, 0],
@@ -206,9 +206,10 @@ true
     <Attr Name = "IsTorsion" Arg = "mat" Label = "for an integer matrix"/>
     <Returns><K>true</K> or <K>false</K></Returns>
     <Description>
-      If <A>mat</A> is an integer matrix (i.e. belongs to the
-      category <Ref Filt = "Integers"/>), then <C>IsTorsion</C> returns
-      <K>true</K> if <A>mat</A> is torsion and <K>false</K> otherwise. <P/>
+      If <A>mat</A> is an integer matrix (i.e. a matrix whose <Ref
+      Attr="BaseDomain" BookName="ref"/> is <Ref Var= "Integers"
+      BookName="ref"/>), then <C>IsTorsion</C> returns <K>true</K> if
+      <A>mat</A> is torsion and <K>false</K> otherwise. <P/>
 
       An integer matrix <A>mat</A> is torsion if and only if there exists an
       integer <C>n</C> such that <A>mat</A> to the power of <C>n</C> is
@@ -238,7 +239,7 @@ false
     <Attr Name = "Order" Arg = "mat"/>
     <Returns>An integer or <C>infinity</C>.</Returns>
     <Description>
-      If <A>mat</A> is an integer matrix, then <C>InverseOp</C> returns the
+      If <A>mat</A> is an integer matrix, then <C>Order</C> returns the
       order of <A>mat</A>. The order of <A>mat</A> is the smallest integer
       power of <A>mat</A> equal to the identity. If no such integer exists, the
       order is equal to <C>infinity</C>.