Implement Union(Rationals,Integers) and more, add tests

Resolves #657

lib/cyclotom.gi

@@ -2002,8 +2002,8 @@ BindGlobal("CompareCyclotomicCollectionHelper_Filters", [
 BindGlobal("CompareCyclotomicCollectionHelper_Proxies", [
  [ 1 ], [ 0, 1 ],
  [ -1, 0, 1 ], [ -1, 0, 1, E(4) ],
- [ -1, 0, 1/2, 1 ], [ -1, 0, 1, 1/2, E(4) ],
- [ -1, 0, 1, 1/2, E(4), E(9) ], fail
+ [ -1, 0, 1/2, 1 ], [ -1, 0, 1/2, 1, E(4), 1/2+E(4) ],
+ [ -1, 0, 1/2, 1, E(4), 1/2+E(4), E(9) ], fail
 ] );
 
 if IsHPCGAP then
@@ -2033,6 +2033,7 @@ function (A,B)
  return ab[1] = ab[2];
 end );
 
+
 InstallMethod( IsSubset, "for certain cyclotomic semirings",
  [IsCyclotomicCollection and IsSemiringWithOne,
  IsCyclotomicCollection and IsSemiringWithOne],
@@ -2058,6 +2059,20 @@ function (A,B)
 end );
 
 
+InstallMethod( Union2, "for certain cyclotomic semirings",
+ [IsCyclotomicCollection and IsSemiringWithOne,
+ IsCyclotomicCollection and IsSemiringWithOne],
+function (A,B)
+ local ab, i;
+ ab := CompareCyclotomicCollectionHelper(A, B);
+ # Verify that we recognized both A and B, otherwise give up.
+ if fail in ab then TryNextMethod(); fi;
+ i := Position( CompareCyclotomicCollectionHelper_Proxies, Union2( ab[1], ab[2] ) );
+ if i = fail then TryNextMethod(); fi;
+ return CompareCyclotomicCollectionHelper_Semirings[i];
+end );
+
+
 #############################################################################
 ##
 #E

tst/testinstall/cyclotom.tst

@@ -317,6 +317,35 @@ Error, COEFFSCYC: <cyc> must be a cyclotomic (not a boolean or fail)
 gap> CycList([1,fail]);
 Error, CycList: each entry must be a rational (not a boolean or fail)
 
+#
+# Some tests for some operations on certain pre-defined infinite collections
+# of cyclotomics, which are implemented using CompareCyclotomicCollectionHelper.
+# For the tests, we exploit that the supported collections can be grouped into
+# two totally ordered chains.
+#
+gap> sets:=[ PositiveIntegers, NonnegativeIntegers, Integers, Rationals, GaussianRationals, Cyclotomics ];;
+gap> r:=[1..Length(sets)];;
+gap> SetX(r, r, {i,j} -> Intersection(sets[i],sets[j]) = sets[Minimum(i,j)]);
+[ true ]
+gap> SetX(r, r, {i,j} -> Union(sets[i],sets[j]) = sets[Maximum(i,j)]);
+[ true ]
+gap> SetX(r, r, {i,j} -> IsSubset(sets[i],sets[j]) = (i>=j));
+[ true ]
+gap> SetX(r, r, {i,j} -> (sets[i]=sets[j]) = (i=j));
+[ true ]
+
+#
+gap> sets:=[ PositiveIntegers, NonnegativeIntegers, Integers, GaussianIntegers, GaussianRationals, Cyclotomics ];;
+gap> r:=[1..Length(sets)];;
+gap> SetX(r, r, {i,j} -> Intersection(sets[i],sets[j]) = sets[Minimum(i,j)]);
+[ true ]
+gap> SetX(r, r, {i,j} -> Union(sets[i],sets[j]) = sets[Maximum(i,j)]);
+[ true ]
+gap> SetX(r, r, {i,j} -> IsSubset(sets[i],sets[j]) = (i>=j));
+[ true ]
+gap> SetX(r, r, {i,j} -> (sets[i]=sets[j]) = (i=j));
+[ true ]
+
 #
 gap> STOP_TEST( "cyclotom.tst", 1);