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Grading + caching for affine algebra of torus invariants #3469

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merged 4 commits into from
Feb 29, 2024
Merged

Grading + caching for affine algebra of torus invariants #3469

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a655be1
TorGrpInvRing to attributes, added test for affine_algebra for tori
Lax202 Feb 28, 2024
21f31d3
Merge branch 'master' into lr/torus
Lax202 Feb 29, 2024
4b73d10
graded affine algebra ring
Lax202 Feb 29, 2024
a62fd50
fix to doctest
Lax202 Feb 29, 2024
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23 changes: 10 additions & 13 deletions experimental/InvariantTheory/src/TorusInvariantsFast.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -159,15 +159,13 @@ end
#Setting up invariant ring for fast torus algorithm.
#####################

mutable struct TorGrpInvRing
@attributes mutable struct TorGrpInvRing
field::Field
poly_ring::MPolyDecRing #graded

group::TorusGroup
representation::RepresentationTorusGroup

fundamental::Vector{MPolyDecRingElem}

#Invariant ring of reductive group G (in representation R), no other input.
function TorGrpInvRing(R::RepresentationTorusGroup) #here G already contains information n and rep_mat
n = length(weights(R))
Expand Down Expand Up @@ -264,14 +262,9 @@ julia> fundamental_invariants(RT)
X[2]^2*X[3]
```
"""
function fundamental_invariants(z::TorGrpInvRing)
if isdefined(z, :fundamental)
return z.fundamental
else
R = z.representation
z.fundamental = torus_invariants_fast(weights(R), polynomial_ring(z))
return z.fundamental
end
@attr function fundamental_invariants(z::TorGrpInvRing)
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Suggested change
@attr function fundamental_invariants(z::TorGrpInvRing)
@attr SomeType function fundamental_invariants(z::TorGrpInvRing)

Please add the return type here to make the attribute lookup type stable

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I don't know what type to use here other than Vector{MPolyRingElem} or Vector{MPolyDecRingElem} - which are not concrete types.

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Faced the same issue with the other file - InvariantTheory.jl

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That's true. In most other places, we would add the field type as a type parameter to the invariant ring, which would then allow something smarter here.
But I think this is out of scope for this PR.

@fingolfin can you keep this in mind for some future refactoring?

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Sorry, I typed to slow. We can keep this here as is and I look into it in #3442.

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@lgoettgens sure, I actually had pointed out the same issue on a prior PR. We'll get there eventually ;-)

R = z.representation
return torus_invariants_fast(weights(R), polynomial_ring(z))
end

function Base.show(io::IO, R::TorGrpInvRing)
Expand Down Expand Up @@ -399,10 +392,14 @@ julia> affine_algebra(RT)
(Quotient of multivariate polynomial ring by ideal (-t[1]*t[3] + t[2]^2), Hom: quotient of multivariate polynomial ring -> graded multivariate polynomial ring)
```
"""
function affine_algebra(R::TorGrpInvRing)
@attr function affine_algebra(R::TorGrpInvRing)
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Suggested change
@attr function affine_algebra(R::TorGrpInvRing)
@attr SomeType function affine_algebra(R::TorGrpInvRing)

Here as well

V = fundamental_invariants(R)
s = length(V)
S,t = polynomial_ring(field(group(representation(R))), "t"=>1:s)
weights_ = zeros(Int, s)
for i in 1:s
weights_[i] = total_degree(V[i])
end
S,_ = graded_polynomial_ring(field(group(representation(R))), "t"=>1:s; weights = weights_)
R_ = polynomial_ring(R)
StoR = hom(S,R_,V)
I = kernel(StoR)
Expand Down
6 changes: 6 additions & 0 deletions experimental/InvariantTheory/test/runtests.jl
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Expand Up @@ -57,4 +57,10 @@
f = fundamental_invariants(I)
@test f == [X[1]*X[2]*X[3], X[1]^2*X[3]*X[4]]

#another example, with affine algebra computation
T = torus_group(QQ,2)
r = representation_from_weights(T, [-1 1; -1 1; 2 -2; 0 -1])
RT = invariant_ring(r)
A, _ = affine_algebra(RT)
@test ngens(modulus(A)) == 1
end
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