Use IsZero instead of comparing with 0*x in the library

lib/algebra.gi

@@ -3599,7 +3599,7 @@ InstallMethod( CentralIdempotentsOfAlgebra,
             g:= GcdRepresentation( p, facs[j] );
             gcd:= g[1]*p+g[2]*facs[j];
             qq:= g[1]*(cf[j]-c)/gcd;
-            if qq<>0*qq then
+            if not IsZero( qq ) then
               c:= p*EuclideanRemainder( qq, facs[j] )
                               + c;
             fi;

lib/alglie.gi

@@ -2964,12 +2964,12 @@ InstallMethod( RootSystem,
        local s,t,rt;
        s:=0; t:=0;
        rt:=a-b;
-       while (rt in R) or (rt=0*R[1]) do
+       while (rt in R) or IsZero( rt ) do
          rt:=rt-b;
          s:=s+1;
        od;
        rt:=a+b;
-       while (rt in R) or (rt=0*R[1]) do
+       while (rt in R) or IsZero( rt ) do
          rt:=rt+b;
          t:=t+1;
        od;
@@ -4399,7 +4399,7 @@ local ReductionModuloTable,   #
        n:= Length( r );
 
        for i in [1..n-1] do
-         if r[i][2]=0*r[i][2] or
+         if IsZero( r[i][2] ) or
                     (Length(r[i][1])>1 and r[i][1][1]=r[i][1][2]) then
 
            #the thing is zero; get rid of it.
@@ -4413,7 +4413,7 @@ local ReductionModuloTable,   #
            Unbind(r[i]);
          fi;
        od;
-       if r[n][2]=0*r[n][2] or
+       if IsZero( r[n][2] ) or
                (Length(r[n][1])>1 and r[n][1][1]=r[n][1][2]) then
 
           #the thing is zero; get rid of it.

lib/algliess.gi

@@ -285,7 +285,7 @@ BindGlobal( "SimpleLieAlgebraTypeA_G", function( type, n, F )
                 # We take care of the commutation relations of the form
                 # [h_j,x_{\beta_i}]= < \beta_i, \alpha_j > x_{\beta_i}.
                 cc:= LinearCombination( R[i], C[j] );
-                if cc <> 0*cc then
+                if not IsZero( cc ) then
 
                     posR[i][j]:= One(F)*cc;
 
@@ -593,7 +593,7 @@ BindGlobal( "SimpleLieAlgebraTypeA_G", function( type, n, F )
                     cc:= d*cc;
                 fi;
 
-                if cc <> 0*cc then
+                if not IsZero( cc ) then
 
                     posR[i][j]:= One(F)*cc;
 

lib/algrep.gi

@@ -1852,7 +1852,7 @@ InstallMethod( ConvertToNormalFormMonomialElement,
 
             is_replaced:= false;
             for j in [1..Length(cf)] do
-                if cf[j] <> 0*cf[j] then
+                if not IsZero( cf[j] ) then
                     if not is_replaced then
                         tt1:= ShallowCopy( tt );
                         tt1[i]:= bases[i][j];
@@ -1885,7 +1885,7 @@ InstallMethod( ConvertToNormalFormMonomialElement,
     for i in [1..Length(tensors)] do
         if len > 0 and tensors[i] = res[len-1] then
             res[len]:= res[len]+cfts[i];
-            if res[len] = 0*res[len] then
+            if IsZero( res[len] ) then
                 Unbind( res[len-1] );
                 Unbind( res[len] );
                 len:= len-2;
@@ -2233,7 +2233,7 @@ InstallMethod( ConvertToNormalFormMonomialElement,
 
             is_replaced:= false;
             for j in [1..Length(cf)] do
-                if cf[j] <> 0*cf[j] then
+                if not IsZero( cf[j] ) then
                     if not is_replaced then
                         tt1:= ShallowCopy( tt );
                         tt1[i]:= basis[j];
@@ -2297,7 +2297,7 @@ InstallMethod( ConvertToNormalFormMonomialElement,
 
         if len > 0 and tensors[i] = res[len-1] then
             res[len]:= res[len]+cfts[i];
-            if res[len] = 0*res[len] then
+            if IsZero( res[len] ) then
                 Unbind( res[len-1] );
                 Unbind( res[len] );
                 len:= len-2;
@@ -2567,7 +2567,7 @@ InstallMethod( ConvertToNormalFormMonomialElement,
 
             is_replaced:= false;
             for j in [1..Length(cf)] do
-                if cf[j] <> 0*cf[j] then
+                if not IsZero( cf[j] ) then
                     if not is_replaced then
                         tt1:= ShallowCopy( tt );
                         tt1[i]:= basis[j];
@@ -2621,7 +2621,7 @@ InstallMethod( ConvertToNormalFormMonomialElement,
         wed:= tensors[i];
         if len > 0 and wed = res[len-1] then
             res[len]:= res[len]+cfts[i];
-            if res[len] = 0*res[len] then
+            if IsZero( res[len] ) then
                 Unbind( res[len-1] );
                 Unbind( res[len] );
                 len:= len-2;
@@ -3376,7 +3376,7 @@ InstallHandlingByNiceBasis( "IsDirectSumElementsSpace", rec(
           cf:= Coefficients( Basis(
                        FamilyObj(v)!.constituentModules[i] ), ev[i] );
           for k in [1..Length(cf)] do
-              if cf[k] <> 0*cf[k] then
+              if not IsZero( cf[k] ) then
                   Add( vec, num+k );
                   Add( vec, cf[k] );
               fi;

lib/autsr.gi

@@ -1402,7 +1402,7 @@ local
     D:=List(D,d->List([1..Length(ocr.generators)],i->ocr.generators[i]^-1*d[i]));
     D:=List(D,d->ocr.listToCocycle(d));
     TriangulizeMat(D);
-    D:=Filtered(D,x->x<>0*x);
+    D:=Filtered(D,x->not IsZero( x ));
 
     b:=BaseSteinitzVectors(b,D).factorspace;
 

lib/ctblgrp.gi

@@ -1006,13 +1006,13 @@ BindGlobal( "SplitTwoSpace", function(D,raum)
       for root in SquareRoots(D.field,(p/2)^2-q) do
         a1:=(-p/2+root);
         n:=v1v2+a1*v2v2;
-        if (n=0*o) then
+        if IsZero( n ) then
           # proceeding would force a division by zero
           NotFailed:=false;
         else
           a2:=-(v1v1+a1*v2v1)/n;
           n:=v1v1+a2*(v1v2+v2v1)+a2^2*v2v2;
-          if n<>0*o then
+          if not IsZero( n ) then
             deg2:=List(SquareRoots(D.field,o/(raum.dim-d)/n),Int);
             for d2 in deg2 do
               if d2 in mdeg2 then

lib/fieldfin.gi

@@ -613,7 +613,7 @@ InstallMethod( NormalBase,
     [ IsField and IsFinite, IsScalar ],
 function(F, b)
     local q, d, z, l, bas, i;
-    if b=0*b then
+    if IsZero( b ) then
         b := One(F);
     fi;
     q := Size(LeftActingDomain(F));

lib/grppcaut.gi

@@ -565,7 +565,7 @@ BindGlobal( "CocycleSQ", function( epi, field )
     od;
 
     # check
-    if c = 0 * c then return 0; fi;
+    if IsZero( c ) then return 0; fi;
     return c;
 end );
 

lib/grppccom.gi

@@ -497,7 +497,7 @@ local   z,K,N,zett,SN,B,L,tau,gens,imgs,A,T,heads,dim,s,v,j,i,root;
     od;
     while j <= dim and heads[j] <> 0  do
       z:=v[j] / B[heads[j]][j];
-      if z <> 0*z  then
+      if not IsZero( z ) then
         s:=s / A[heads[j]] ^ ocr.logTable[LogFFE(z,root)+1];
       fi;
       v:=v - v[j] / B[heads[j]][j] * B[heads[j]];

lib/lierep.gi

@@ -199,7 +199,7 @@ InstallMethod( \+,
                i:= i+1;
             fi;
           od;
-          list:= Filtered( list, x -> x[2]<>0*x[2] );
+          list:= Filtered( list, x -> not IsZero( x[2] ) );
           l[k]:= list;
         fi;
       od;
@@ -433,7 +433,7 @@ InstallHandlingByNiceBasis( "IsCochainsSpace", rec(
       while j <> Length( vec ) do
         l[k]:= [ ];
         for i in [j+1..j+Length(tt)] do
-          if vec[i] <> 0*vec[i] then
+          if not IsZero( vec[i] ) then
             Add( l[k], [ tt[i-j], vec[i] ] );
           fi;
         od;
@@ -494,7 +494,7 @@ InstallGlobalFunction( ValueCochain,
            cfs1:= [ ];
            for i in [1..Length(cfs)] do
              for j in [1..Length(cfs[i][k])]  do
-               if cfs[i][k][j] <> 0*cfs[i][k][j] then
+               if not IsZero( cfs[i][k][j] ) then
                   cf:= ShallowCopy( cfs[i] );
                   cf[k] := [ cf[k][j], j ];
                   Add( cfs1, cf );
@@ -603,7 +603,7 @@ InstallGlobalFunction( LieCoboundaryOperator,
 
          cfs:= Coefficients( Basis(V), val );
          for k in [1..Length(cfs)] do
-           if cfs[k] <> 0*cfs[k] then
+           if not IsZero( cfs[k] ) then
              Add( list[k], [ t, cfs[k] ] );
            fi;
          od;
@@ -873,7 +873,7 @@ BindGlobal( "NextIterator_WeylOrbit", function( it )
     if it!.status = 1 then
         it!.status:= 2;
         mu:= it!.currentWeight;
-        if mu = 0*mu then
+        if IsZero( mu ) then
             it!.isDone:= true;
         fi;
         return mu;
@@ -1642,7 +1642,7 @@ InstallGlobalFunction( CollectUEALatticeElement,
          od;
          Append( res, WriteAsLCOfBinoms( vars, q ) );
          for k in [2,4..Length(res)] do
-             if res[k] = 0*res[k] then
+             if IsZero( res[k] ) then
                  Unbind( res[k-1] ); Unbind( res[k] );
              fi;
          od;
@@ -2194,7 +2194,7 @@ InstallMethod( \*,
     for i in [1..Length( mons )] do
         if len > 0 and lst[len-1] = mons[i] then
             lst[len]:= lst[len]+cfs[i];
-            if lst[len] = 0*lst[len] then
+            if IsZero( lst[len] ) then
                 Remove( lst, len-1 );
                 Remove( lst, len-1 );
                 len:= len-2;
@@ -2673,7 +2673,7 @@ InstallGlobalFunction( LeftReduceUEALatticeElement,
     rem:= p;
     res:= 0*p;
 
-    while rem <> 0*rem do
+    while not IsZero( rem ) do
 
         m1:= LeadingUEALatticeMonomial( novar, rem );
         k:= 1;
@@ -2806,7 +2806,7 @@ InstallMethod(\+,
             lu:= lu0;
         else
             cf:= lu[2*p]+lv[k+1];
-            if cf = 0*cf then
+            if IsZero( cf ) then
                 Remove( lu, 2*p-1 );
                 Remove( lu, 2*p-1 );
                 Remove( vecs, p );
@@ -2980,14 +2980,14 @@ InstallOtherMethod(\^,
                 for k in [j,j+2..len] do
                     cf:= cf*Binomial( hw[ em[i][k]-2*n ], em[i][k+1] );
                 od;
-                if cf <> 0*cf then
+                if not IsZero( cf ) then
                     mon:= em[i]{[1..j-1]};
                     pos:= Position( er, mon );
                     if pos = fail then
                         Add( er, mon ); Add( er, cf );
                     else
                         er[pos+1]:= er[pos+1]+cf;
-                        if er[pos+1] = 0*er[pos+1] then
+                        if IsZero( er[pos+1] ) then
                             Remove( er, pos );
                             Remove( er, pos );
                         fi;
@@ -3002,7 +3002,7 @@ InstallOtherMethod(\^,
                 Add( er, mon ); Add( er, cf );
             else
                 er[pos+1]:= er[pos+1]+cf;
-                if er[pos+1] = 0*er[pos+1] then
+                if IsZero( er[pos+1] ) then
                     Remove( er, pos );
                     Remove( er, pos );
                 fi;
@@ -3296,7 +3296,7 @@ InstallMethod( HighestWeightModule,
         # divide by their greatest common divisor.
 
         res:= LeftReduceUEALatticeElement( novar, G, lms, lmtab, p );
-        if res <> 0*res then
+        if not IsZero( res ) then
             cf:= res![1]{[2,4..Length(res![1])]};
             res:= (Lcm(List(cf,DenominatorRat))/
                                  Gcd(List(cf,NumeratorRat)))*res;
@@ -3640,7 +3640,7 @@ InstallMethod( HighestWeightModule,
                            LeadingUEALatticeMonomial(novar,fac1)[3]*fac2;
                     comp:= NormalizedLeftReduction( novar, GB, lms, lmtab,
                                    comp );
-                    if comp <> 0*comp then
+                    if not IsZero( comp ) then
 
                         vec:= ListWithIdenticalEntries( Length( sortmn[pp] ),
                                       0 );
@@ -3684,7 +3684,7 @@ InstallMethod( HighestWeightModule,
                     ecomp:= [ ];
                     cfsc:= [ ];
                     for i in [1..Length(vecs[l])] do
-                        if vecs[l][i] <> 0*vecs[l][i] then
+                        if not IsZero( vecs[l][i] ) then
 
                             Add( ecomp, sortmn[j][i] );
                             Add( cfsc, vecs[l][i] );
@@ -3995,7 +3995,7 @@ InstallGlobalFunction( ExtendRepresentation,
            for s in [1..Length(cij[1])] do
              M:= M - cij[2][s]*mm[cij[1][s]];
            od;
-           if M <> 0*M then return false; fi;
+           if not IsZero( M ) then return false; fi;
          od;
        od;
        return true;

lib/matrix.gi

@@ -3792,7 +3792,7 @@ InstallGlobalFunction( BasisNullspaceModN, function( M, n )
     # nullM is also the nullspace for M
 
     nullM := null*snf.rowtrans mod n;
-    Assert (1, ForAll (nullM, v -> v*M mod n =0*M[1]));
+    Assert (1, ForAll (nullM, v -> IsZero( v*M mod n )));
     return nullM;
 end);
 
@@ -4506,7 +4506,7 @@ function( mat )
   w:= GcdRepresentation( g, Derivative( g ) )[2];
   w:= w*g;
   B:= ShallowCopy( mat );
-  while Value( g, B ) <> 0*B do
+  while not IsZero( Value( g, B ) ) do
     B:= B - Value( w, B );
   od;
 

lib/meatauto.gi

@@ -768,7 +768,7 @@ local nv, nw, F, zero, minusone, zeroW, gV, gW, k, U, echu, r, homs, s, work, an
         Add(hom, image);
       od;
       hom:=ImmutableMatrix(F,hom);
-      Assert(1,hom<>0*hom);
+      Assert(1,not IsZero( hom ));
       Add(newhoms, hom);
     od;
 

lib/polyrat.gi

@@ -2029,7 +2029,7 @@ local x,xd,er,i,j,k,m,p,sel,xi,gamma,G,g,loop,zero,add;
             if k>xi/2 then
               k:=k - xi; #symmetric rep
             fi;
-            if k<>0*k then
+            if not IsZero( k ) then
               Add(g,gamma[j-1]);
               Add(g,k);
             fi;