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Improve IsSubset for cyclotomic domains (such as Integers, PositiveIntegers, GaussianRationals etc.) #6265

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Improve IsSubset for cyclotomic domains (such as Integers, PositiveIntegers, GaussianRationals etc.) #6265

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948667b
fix: Fix IsSubset for cyclotomic domains
limakzi Mar 11, 2026
6cf0efb
Fix IsSubset implementation
limakzi Mar 12, 2026
0b71ca1
Simplify tests for IsSubset
limakzi Mar 12, 2026
95febd7
Add IsSubset method for a range and a cyclotomic
limakzi Mar 15, 2026
d997254
Add IsSubset method for a list and a cyclotomic semiring
limakzi Mar 15, 2026
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14 changes: 14 additions & 0 deletions lib/cyclotom.gi
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Original file line number Diff line number Diff line change
Expand Up @@ -2065,6 +2065,20 @@ function (A,B)
end );


InstallMethod( IsSubset, "for a cyclotomic semiring and a range",
[IsCyclotomicCollection and IsSemiringWithOne,
IsRange],
function (D, R)
if IsEmpty(R) then return true; fi;
# Since D is a semiring-with-one, and thus in particular an additive magma,
# it suffices to check whether the start and end point of the given range
# are contained in it. Actually it suffices if the smaller one is contained
# in it, but figuring out which end is smaller is more work than just
# directly checking both end points.
return First(R) in D and Last(R) in D;
end );


InstallMethod( Intersection2, "for certain cyclotomic semirings",
[IsCyclotomicCollection and IsSemiringWithOne,
IsCyclotomicCollection and IsSemiringWithOne],
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13 changes: 12 additions & 1 deletion tst/testinstall/cyclotom.tst
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@@ -1,4 +1,4 @@
#@local a,cyc,gm,i,l1,l2,l3,mat,n,r,x,y,z,sets
#@local a,b,cyc,gm,i,l1,l2,l3,mat,n,r,ranges,s,x,y,z,sets
gap> START_TEST("cyclotom.tst");

# Check basic arithmetic operations.
Expand Down Expand Up @@ -352,5 +352,16 @@ gap> SetX(r, r, {i,j} -> IsSubset(sets[i],sets[j]) = (i>=j));
gap> SetX(r, r, {i,j} -> (sets[i]=sets[j]) = (i=j));
[ true ]

#
# IsSubset for cyclotomic semirings and ranges for large bounds
#
gap> sets:=[ PositiveIntegers, NonnegativeIntegers, Integers, GaussianIntegers, GaussianRationals, Cyclotomics ];;
gap> b:=2^(8*GAPInfo.BytesPerVariable - 6);;
gap> ranges:=[ [-2..-1], [-1..0], [-1..1], [0..1], [1..2], [-b..-1], [-b..0], [-b..1], [-1..b], [0..b], [1..b], [-b,b]];;
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@limakzi limakzi Mar 15, 2026 •
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Note test contains a test for a list as well.
The cyclotomics must not be subset of finite list.
My concern is whether we should split this test case.

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@fingolfin fingolfin Mar 17, 2026

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I am confused as to what you are talking about here.

Ah -- is it maybe the [-b,b] at the end? That's a typo, what I meant is this:

Suggested change
gap> ranges:=[ [-2..-1], [-1..0], [-1..1], [0..1], [1..2], [-b..-1], [-b..0], [-b..1], [-1..b], [0..b], [1..b], [-b,b]];;
gap> ranges:=[ [-2..-1], [-1..0], [-1..1], [0..1], [1..2], [-b..-1], [-b..0], [-b..1], [-1..b], [0..b], [1..b], [-b..b]];;

gap> SetX(ranges, sets, {r,s} -> IsSubset(s,r) = (IsEmpty(r) or (First(r) in s and Last(r) in s)));
[ true ]
gap> SetX(ranges, sets, {r,s} -> not IsSubset(r,s));
[ true ]

#
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@fingolfin fingolfin Mar 19, 2026

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When I wrote that I'd suggest to keep the tests for ranges and lists apart, my idea was to insert something like this, here below the ranges tests:

Suggested change
#
#
gap> lists:=[ [-2,-1], [], [-1,0,1], [0,1], [1,2], [-b,-1], [-b,0], [-b,1], [-1,b], [0,b], [1,b], [-b,b]];;
#
gap> SetX(ranges, lists, {r,s} -> IsSubset(s,r) = (IsEmpty(r) or (First(r) in s and Last(r) in s)));
[ true ]
gap> SetX(ranges, lists, {r,s} -> not IsSubset(r,s));
[ true ]

gap> STOP_TEST("cyclotom.tst");
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