Various minor tweaks (#61)

* Use NrRows instead of Length

* MaximalVectorMat: more readable by avoiding nfmPolCoeffs

* Use function shorthand syntax in some places

... for better readability of the code.

* nfmPrimaryDecompositionforJNFCyclic: simplify code

Don't use Matrix(F,A) to rewrite A -- the calling code should take
care of using an "efficient" matrix representation.

Also remove the unused variable v, and directly iterate over minpolfacs
instead of using an index variable, for tighter (and thus more readable)
code.

Author: fingolfin

gap/nofoma.gi

@@ -169,12 +169,12 @@ InstallGlobalFunction(CyclicChainMat,function(mat)
   A:=ImmutableMatrix(DefaultFieldOfMatrix(mat),mat);
   idm:=OneMutable(A);
   if IsLowerTriangularMat(A) then 
-    return [idm,idm,[1..Length(A)+1],[1..Length(A)]];
+    return [idm,idm,[1..NrRows(A)+1],[1..NrRows(A)]];
   fi;
   sp:=SpinMatVector1(A,idm[1],[],[],[],[]);
   svec:=[1,Length(sp[1])+1];
   j:=1;
-  while Length(sp[1])<Length(A) do
+  while Length(sp[1])<NrRows(A) do
     while j in sp[5] do
       j:=j+1;
     od;
@@ -230,23 +230,21 @@ end);
 # Returns vector that has the same minimal polynomial as mat. 
 # For details about this function, see nofoma.gd.
 InstallGlobalFunction(MaximalVectorMat,function(mat)
-  local A,M,k,idm,sp,l,np,i,v1,z,one,f,rpols,svec,lm;
+  local A,M,k,idm,sp,l,np,i,v1,z,one,f,rpols,svec,lm,x;
   k:=DefaultFieldOfMatrix(mat);
   A:=ImmutableMatrix(k,mat);
   one:=One(k);
   idm:=OneMutable(A);
+  x:=Indeterminate(k);
   if IsDiagonalMat(A) then       # first deal with diagonal matrix
-    if ForAll([2..Length(A)],i->A[i,i]=A[1,1]) then
+    if ForAll([2..NrRows(A)],i->A[i,i]=A[1,1]) then
       v1:=idm[1];
-      np:=nfmPolCoeffs([-A[1,1],one]);
+      np:=x-A[1,1];
     else
-      v1:=ListWithIdenticalEntries(Length(A),one);
+      v1:=ListWithIdenticalEntries(NrRows(A),one);
       ConvertToVectorRepNC(v1,k);
-      l:=Set([1..Length(A)],i->A[i,i]);
-      np:=nfmPolCoeffs([-l[1],one]);
-      for i in [2..Length(l)] do
-        np:=nfmPolCoeffs([-l[i],one])*np;
-      od;
+      l:=Set([1..NrRows(A)],i->A[i,i]);
+      np:=Product(l, a -> x-a);
     fi;
     Info(Infonofoma,2,"#I Degree of minimal polynomial is ",Degree(np)," \n");
     return [v1,np];
@@ -296,7 +294,7 @@ InstallGlobalFunction(JacobMatComplement,function(T,d)
       fi;
     od;
   od;
-  for i in [d+1..Length(T)] do
+  for i in [d+1..NrRows(T)] do
     for j in [1..d] do 
       base[i,j]:=-F[d+1-j][i];
     od;
@@ -308,7 +306,7 @@ end);
 BindGlobal("BuildBlockDiagonalMat1",function(d,B)
   local neu,n,k;
   k:=DefaultFieldOfMatrix(B);
-  n:=d+Length(B);
+  n:=d+NrRows(B);
   neu:=IdentityMat(n,k);
   neu{[d+1..n]}{[d+1..n]}:=B;
   ConvertToMatrixRepNC(neu);
@@ -321,7 +319,7 @@ InstallGlobalFunction(RatFormStep1,function(A,v)
   sp:=SpinMatVector1(A,v,[],[],[],[]);
   t:=sp[2];
   d:=Length(t);
-  Append(t,idm{Difference([1..Length(A)],sp[5])});
+  Append(t,idm{Difference([1..NrRows(A)],sp[5])});
   ConvertToMatrixRepNC(t);
   A1:=t*A*t^(-1);
   minp:=-ShallowCopy(A1[d]{[1..d]});
@@ -335,14 +333,14 @@ InstallGlobalFunction(RatFormStep1J,function(A,v)
   sp:=SpinMatVector1(A,v,[],[],[],[]);
   t:=sp[2];
   d:=Length(t);
-  Append(t,idm{Difference([1..Length(A)],sp[5])});
+  Append(t,idm{Difference([1..NrRows(A)],sp[5])});
   ConvertToMatrixRepNC(t);
   A1:=t*A*t^(-1);
   minp:=-ShallowCopy(A1[d]{[1..d]});
   Add(minp,minp[1]^0);
   j:=JacobMatComplement(A1,Length(minp)-1);
   #return [j*A1*j^-1,j*t,minp];
-  return [A1{[d+1..Length(A1)]}{[d+1..Length(A1)]},j*t,minp];
+  return [A1{[d+1..NrRows(A1)]}{[d+1..NrRows(A1)]},j*t,minp];
 end);
 
 #TODO: replace by CompanionMat
@@ -382,14 +380,14 @@ InstallGlobalFunction(FrobeniusNormalForm,function(mat)
   local A,P,invf,i,k,mv,step1,rest,d,piv;
   k:=DefaultFieldOfMatrix(mat);
   A:=ImmutableMatrix(k,mat);
-  if IsDiagonalMat(A) and ForAll([2..Length(A)],i->A[i,i]=A[1,1]) then
+  if IsDiagonalMat(A) and ForAll([2..NrRows(A)],i->A[i,i]=A[1,1]) then
     mv:=nfmPolCoeffs([-A[1,1],A[1,1]^0]);
-    return [ListWithIdenticalEntries(Length(A),mv),A^0,[1..Length(A)]];
+    return [ListWithIdenticalEntries(NrRows(A),mv),A^0,[1..NrRows(A)]];
   fi;
   mv:=MaximalVectorMat(A);
   invf:=[mv[2]];
   d:=Degree(mv[2]);
-  if d=Length(A) then      # cyclic space: only one companion block
+  if d=NrRows(A) then      # cyclic space: only one companion block
     step1:=[mv[1]];        # create base change
     for i in [2..d] do
       Add(step1,step1[i-1]*A);
@@ -416,7 +414,7 @@ InstallGlobalFunction(InvariantFactorsMat,function(mat)
   local A,A1,i,d,np,k,f,n,p;
   k:=DefaultFieldOfMatrix(mat);
   A:=ImmutableMatrix(k,mat);
-  n:=Length(A);
+  n:=NrRows(A);
   np:=MaximalVectorMat(A);
   d:=Degree(np[2]);
   f:=[np[2]];
@@ -491,7 +489,7 @@ InstallGlobalFunction(JordanChevalleyDecMatF,function(mat)
   local f,jc,p,N,D;
   f:=FrobeniusNormalForm(mat);
   Info(Infonofoma,2,"Frobenius normal form complete\n");
-  Add(f[3],Length(mat)+1);
+  Add(f[3],NrRows(mat)+1);
   jc:=List(f[1],p->JordanChevalleyDecMat(nfmCompanionMat1(CoefficientsOfUnivariatePolynomial(p)),p));
   N:=0*f[2];
   D:=0*f[2];
@@ -709,7 +707,7 @@ InstallGlobalFunction(PrimaryDecomp, function(A)
     for i in [1..Size(gs)] do 
       Add(combined, [gens[i],gs[i]]); 
     od;
-    Sort(combined, function(v,w) return v[2] < w[2]; end);
+    Sort(combined, {v,w} -> v[2] < w[2]);
     k := 0;
     dims := [];
     for i in [1..Size(gs)] do 
@@ -833,19 +831,16 @@ end);
 #Primary Decomposition for cyclic matrices 
 #Jordan normal form will call this function if a cyclic matrix is detected
 BindGlobal("nfmPrimaryDecompositionforJNFCyclic", function(A, minpol, minpolfacs)
-    local vspan,F,n,w,i,wspan,qi,k,v,COB,dims;
+    local vspan,n,w,mf,wspan,qi,k,COB,dims;
     n := NrRows(A);
-    F := DefaultFieldOfMatrix(A);
-    A := Matrix(F,A);
     vspan := nfmFindCyclicVectorNC(A);
-    v := vspan[1];
     dims := [];
     COB := ZeroMutable(A);
     k := 0;
-    for i in [1..Size(minpolfacs)] do 
-        qi := (minpolfacs[i][1])^(minpolfacs[i][2]);
+    for mf in minpolfacs do 
+        qi := (mf[1])^(mf[2]);
         w := nfmPolyEvalFromSpan(vspan,Quotient(minpol,qi));
-        wspan := nfmSpinUntil(w,A,Degree(minpolfacs[i][1])*minpolfacs[i][2]);
+        wspan := nfmSpinUntil(w,A,Degree(mf[1])*mf[2]);
         CopySubMatrix(wspan, COB, [1..NrRows(wspan)], [k+1..k+NrRows(wspan)], [1..n], [1..n]);
         Add(dims, NrRows(wspan));
         k := k + NrRows(wspan);
@@ -932,8 +927,8 @@ BindGlobal("CyclicDecompositionOfPrimarySubspace", function (A, p, m)
     dims := []; #dimensions of my cyclic subspaces
     sumdim := 0; #dimension of my direct sum
     conj := ZeroMutable(A);
-    while not Sum(minpolpowers, function(v) return v[2]*d; end) = n do #generally bigger than n, working our way down  
-        SortBy(minpolpowers, function(v) return v[2]; end); #Sort ws by their A-length (ascending)
+    while not Sum(minpolpowers, v -> v[2]*d) = n do #generally bigger than n, working our way down
+        SortBy(minpolpowers, v -> v[2]); #Sort ws by their A-length (ascending)
         vecs := ZeroVector(F,Length(minpolpowers));
         for i in [1..Length(minpolpowers)] do
             vecs[i] := minpolpowers[i][3]; #p(A)^(r-1)(w)
@@ -964,7 +959,7 @@ BindGlobal("CyclicDecompositionOfPrimarySubspace", function (A, p, m)
         fi;
     od;
     currdim := 1;
-    SortBy(minpolpowers, function(v) return v[2]; end); #sort by A-length
+    SortBy(minpolpowers, v -> v[2]); #sort by A-length
     for i in [1..Length(minpolpowers)] do
         wtrip := minpolpowers[i];
         conj{[currdim..currdim+(wtrip[2]*d)-1]}{[1..n]} := nfmSpinUntil(wtrip[1],A,wtrip[2]*d);