Fixed typos and function name that were admonished.

doc/ref/algfld.xml

@@ -102,7 +102,7 @@ gap> m^2;
 <Section Label="Finding Subfields">
 <Heading>Finding Subfields</Heading>
 
-<#Include Label="DecomPoly">
+<#Include Label="IdealDecompositionsOfPolynomial">
 
 </Section>
 </Chapter>

lib/algfld.gd

@@ -190,19 +190,19 @@ DeclareGlobalFunction("AlgExtSquareHensel");
 
 #############################################################################
 ##
-#F  DecomPoly( <f> [:"onlyone"] )  finds ideal decompositions of rational f
+#F  IdealDecompositionsOfPolynomial( <f> [:"onlyone"] )  finds ideal decompositions of rational f
 ##
-##  <#GAPDoc Label="DecomPoly">
+##  <#GAPDoc Label="IdealDecompositionsOfPolynomial">
 ##  <ManSection>
-##  <Func Name="DecomPoly" Arg='pol'/>
+##  <Func Name="IdealDecompositionsOfPolynomial" Arg='pol'/>
 ##
 ##  <Description>
 ##  Let <M>f</M> be a univariate, rational, irreducible, polynomial. A
 ##  pair <M>g</M>,<M>h</M> of polynomials of degree strictly
 ##  smaller than that of <M>f</M>, such that <M>f(x)|g(h(x))</M> is
 ##  called an ideal decomposition. In the context of field
 ##  extensions, if <M>\alpha</M> is a root of <M>f</M> in a suitable extension
-##  and <M>Q</M> the field of rational numbers, such a decomposition corresponds
+##  and <M>Q</M> the field of rational numbers. Such decompositions correspond
 ##  to (proper) subfields <M>Q\lt Q(\beta)\lt Q(\alpha)</M>, where <M>g</M> is the
 ##  minimal polynomial of <M>\beta</M>.
 ##  This function determines such decompositions up to equality of the subfields
@@ -212,21 +212,21 @@ DeclareGlobalFunction("AlgExtSquareHensel");
 ##  most one such decomposition (and performs faster).
 ##  <Example><![CDATA[
 ##  gap> x:=X(Rationals,"x");;pol:=x^8-24*x^6+144*x^4-288*x^2+144;;
-##  gap> l:=DecomPoly(pol);
+##  gap> l:=IdealDecompositionsOfPolynomial(pol);
 ##  [ [ x^2+72*x+144, x^6-20*x^4+60*x^2-36 ],
 ##    [ x^2-48*x+144, x^6-21*x^4+84*x^2-48 ],
 ##    [ x^2+288*x+17280, x^6-24*x^4+132*x^2-288 ],
 ##    [ x^4-24*x^3+144*x^2-288*x+144, x^2 ] ]
 ##  gap> List(l,x->Value(x[1],x[2])/pol);
 ##  [ x^4-16*x^2-8, x^4-18*x^2+33, x^4-24*x^2+120, 1 ]
-##  gap> DecomPoly(pol:onlyone);
+##  gap> IdealDecompositionsOfPolynomial(pol:onlyone);
 ##  [ [ x^2+72*x+144, x^6-20*x^4+60*x^2-36 ] ]
 ##  ]]></Example>
 ##  In this example the given polynomial is regular with Galois group
-##  <M>Q_8</M>, thus exposing the four proper subfields.
+##  <M>Q_8</M>, as expected we get four proper subfields.
 ##  </Description>
 ##  </ManSection>
 ##  <#/GAPDoc>
 ##
-DeclareGlobalFunction("DecomPoly");
-
+DeclareGlobalFunction("IdealDecompositionsOfPolynomial");
+DeclareSynonym("DecomPoly",IdealDecompositionsOfPolynomial);

lib/algfld.gi

@@ -2194,10 +2194,10 @@ end);
 
 #############################################################################
 ##
-#F  DecomPoly( <f> [,"onlyone"] )  finds ideal decompositions of rational f
+#F  IdealDecompositionsOfPolynomial( <f> [,"onlyone"] )  finds ideal decompositions of rational f
 ##                       This is equivalent to finding subfields of K(alpha).
 ##
-InstallGlobalFunction(DecomPoly,function(f)
+InstallGlobalFunction(IdealDecompositionsOfPolynomial,function(f)
 local n,e,ff,p,ffp,ffd,roots,allroots,nowroots,fm,fft,comb,combi,k,h,i,j,
       gut,avoid,blocks,g,m,decom,z,R,scale,allowed,hp,hpc,a,kfam,only;
 

lib/grp.gd

@@ -4543,14 +4543,17 @@ DeclareOperation( "LowIndexSubgroups",
 ##  provided only as a separate function, and not as method for the operation
 ##  <C>Normalizer</C>, as it can often be slower than other built-in routines.
 ##  In certain hard cases (non-solvable groups with nontrivial radical), however
-##  its performance is substantially superior.  The function thus provided as a
+##  its performance is substantially superior.
+##  The function thus is provided as a
 ##  non-automated tool for advanced users.
 ##  <Example><![CDATA[
 ##  gap> g:=TransitiveGroup(30,2030);;
 ##  gap> s:=SylowSubgroup(g,5);;
 ##  gap> Size(NormalizerViaRadical(g,s));
 ##  28800
 ##  ]]></Example>
+##  Note that this example only demonstartes usage, but that in this case
+##  in fact the ordinary <C>Normalizer</C> routine performs faster.
 ##  </Description>
 ##  </ManSection>
 ##  <#/GAPDoc>