From 685cabdd4d9264c959bedde818db2122e446448b Mon Sep 17 00:00:00 2001
From: Max Horn <max@quendi.de>
Date: Thu, 27 Jul 2023 13:21:41 +0200
Subject: [PATCH] Unify tests for quadratic field sizes

... and some related cleanup
---
 lib/correlations.gi    | 2 +-
 lib/enumerators.gi     | 6 +++---
 lib/gpolygons.gi       | 2 +-
 lib/group.gi           | 2 +-
 lib/polaritiesps.gi    | 2 +-
 lib/polarspace.gi      | 6 +++---
 lib/projectivespace.gi | 2 +-
 7 files changed, 11 insertions(+), 11 deletions(-)

diff --git a/lib/correlations.gi b/lib/correlations.gi
index 8294b370..bc0bd9f7 100644
--- a/lib/correlations.gi
+++ b/lib/correlations.gi
@@ -1648,7 +1648,7 @@ InstallMethod(HermitianPolarityOfProjectiveSpace,
   if Rank(matrix) <> NrRows(matrix) then
     Error("<matrix> must not be singular");
   fi;
-  if not IsInt(Sqrt(Size(field))) then
+  if IsOddInt(DegreeOverPrimeField(field)) then
     Error("Size of <field> must be a square" );
   fi;
   form := HermitianFormByMatrix(matrix,field);  
diff --git a/lib/enumerators.gi b/lib/enumerators.gi
index bc6dbe36..4dae505d 100644
--- a/lib/enumerators.gi
+++ b/lib/enumerators.gi
@@ -1580,7 +1580,7 @@ InstallGlobalFunction( HermElementNumber,
     a2 := a - 1;
     v := ListWithIdenticalEntries(d+1,Z(q)^0);
 	n := Int((d+1) / 2);
-	FG_herm_Sbar_unrank(RootInt(q,2),v,1,d+1,a2);
+	FG_herm_Sbar_unrank(Sqrt(q),v,1,d+1,a2);
     return v;
 end );
 
@@ -1594,11 +1594,11 @@ InstallGlobalFunction( HermNumberElement,
 	v := StructuralCopy(var!.obj);        
 	y := v[PositionNonZeroFromRight(v)];
 	if IsOddInt(q) then
-	  y := y/(Z(q)^((RootInt(q,2)-1)/2)); #Strange Anton normalization...
+	  y := y/(Z(q)^((Sqrt(q)-1)/2)); #Strange Anton normalization...
 	fi;
 	v := v/y;
     #wittindex := (d+1)/2;
-    a := FG_herm_Sbar_rank(RootInt(q,2), v, 1, d+1);
+    a := FG_herm_Sbar_rank(Sqrt(q), v, 1, d+1);
     return a + 1; ## adjustment for lists beginning at 1
 end );
 
diff --git a/lib/gpolygons.gi b/lib/gpolygons.gi
index 6707f324..84dd7c75 100644
--- a/lib/gpolygons.gi
+++ b/lib/gpolygons.gi
@@ -3577,7 +3577,7 @@ InstallMethod( FisherqClan,
 	nonsquares := Difference(AsList(GF(q)),squares);;
 	n := First(nonsquares, t -> t-1 in squares);
 
-	zeta := PrimitiveRoot(GF(q^2));
+	zeta := Z(q^2);
 	omega := zeta^(q+1);
 	i := zeta^((q+1)/2);
 	z := zeta^(q-1);
diff --git a/lib/group.gi b/lib/group.gi
index 098d25c1..1202213d 100644
--- a/lib/group.gi
+++ b/lib/group.gi
@@ -2379,7 +2379,7 @@ InstallMethod( CanonicalGramMatrix,
     
       # Unitary Gram matrix      
 		elif type = "hermitian" then
-			if IsOddInt(PrimePowersInt(Size(f))[2]) then
+			if IsOddInt(DegreeOverPrimeField(f)) then
 				Error("field order must be a square");
 			fi;
 			m := IdentityMat(d, f);
diff --git a/lib/polaritiesps.gi b/lib/polaritiesps.gi
index 733f14f6..9ea29c4e 100644
--- a/lib/polaritiesps.gi
+++ b/lib/polaritiesps.gi
@@ -151,7 +151,7 @@ InstallMethod(HermitianPolarityOfProjectiveSpace,
   if Rank(matrix) <> NrRows(matrix) then
     Error("<matrix> must not be singular");
   fi;
-  if not IsInt(Sqrt(Size(field))) then
+  if IsOddInt(DegreeOverPrimeField(field)) then
     Error("Size of <field> must be a square" );
   fi;
   form := HermitianFormByMatrix(matrix,field);  
diff --git a/lib/polarspace.gi b/lib/polarspace.gi
index d507ac65..1a0c13d7 100644
--- a/lib/polarspace.gi
+++ b/lib/polarspace.gi
@@ -763,7 +763,7 @@ InstallMethod( HermitianPolarSpace,
 	[ IsPosInt, IsField ],
 	function( d, f )
 		local h,m,types,max,reps,q,creps,degree;
-		if PrimePowersInt(Size(f))[2] mod 2 <> 0 then
+		if IsOddInt(DegreeOverPrimeField(f)) then
 			Error("field order must be a square");
 			return;
 		fi;
@@ -2141,9 +2141,9 @@ InstallMethod( NumberOfTotallySingularSubspaces,
 		elif type = "hyperbolic" then e:= 0; qe := q^e;
 		elif type = "parabolic" or type = "symplectic" then e:=1; qe := q^e;
 		elif type = "hermitian" and IsEvenInt(ps!.dimension) then e:=3; 
-			qe := RootInt(q,2)^e;
+			qe := Sqrt(q)^e;
 		elif type = "hermitian" and IsOddInt(ps!.dimension) then e:=1; 
-			qe := RootInt(q,2)^e;
+			qe := Sqrt(q)^e;
 		else Error("Polar space doesn't know its type!");
 		fi;
 
diff --git a/lib/projectivespace.gi b/lib/projectivespace.gi
index f81c4c85..a44cedc0 100644
--- a/lib/projectivespace.gi
+++ b/lib/projectivespace.gi
@@ -2225,7 +2225,7 @@ InstallMethod( BaerSublineOnThreePoints,
 	fi;
 	geo := AmbientSpace(x);
 	gfq2 := geo!.basefield;
-	if RootInt(Size(gfq2),2)^2 <> Size(gfq2) then
+	if IsOddInt(DegreeOverPrimeField(gfq2)) then
 		Error( "the order of the basefield must be a square" );
 	fi;
 	gfq := GF(Sqrt(Size(gfq2)));