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set caching of polynomial rings to false in AG #4371

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set caching of polynomial rings to false in AG #4371

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a741683
sets poly ring caching to false for algebraic geometry
ederc Sep 16, 2024
cbf60fa
Fix == to ===.
HechtiDerLachs Sep 20, 2024
e1aec2a
Attempt for first round of fixes.
HechtiDerLachs Nov 29, 2024
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51 changes: 39 additions & 12 deletions src/AlgebraicGeometry/Schemes/AffineSchemes/Morphisms/Methods.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -18,7 +18,7 @@ function fiber_product(
)
Y = domain(f)
X = codomain(f)
X == codomain(g) || error("maps need to have the same codomain")
X === codomain(g) || error("maps need to have the same codomain")
Z = domain(g)
YxZ, pY, pZ = product(Y, Z)
RX = ambient_coordinate_ring(X)
Expand Down Expand Up @@ -315,7 +315,7 @@ function product(X::AbsAffineScheme{BRT, RT}, Y::AbsAffineScheme{BRT, RT};
else
new_symb = vcat(new_symb, Symbol.([change_var_names_to[2]*"$i" for i in 1:ngens(L)]))
end
KL, z = polynomial_ring(k, new_symb)
KL, z = polynomial_ring(k, new_symb; cached=false)
XxY = spec(KL)
pr1 = morphism(XxY, X, gens(KL)[1:m], check=false)
pr2 = morphism(XxY, Y, gens(KL)[m+1:m+n], check=false)
Expand Down Expand Up @@ -371,7 +371,7 @@ function product(X::StdAffineScheme, Y::StdAffineScheme;
else
new_symb = vcat(new_symb, Symbol.([change_var_names_to[2]*"$i" for i in 1:ngens(S)]))
end
RS, z = polynomial_ring(k, new_symb)
RS, z = polynomial_ring(k, new_symb; cached=false)
inc1 = hom(R, RS, gens(RS)[1:m], check=false)
inc2 = hom(S, RS, gens(RS)[m+1:m+n], check=false)
IX = ideal(RS, inc1.(gens(modulus(underlying_quotient(OO(X))))))
Expand Down Expand Up @@ -478,9 +478,36 @@ The optional arguments `domain_map` and `codomain_map` can be used
to specify the morphisms `b₁` and `b₂`, respectively.
"""
function base_change(phi::Any, f::AbsAffineSchemeMor;
domain_map::AbsAffineSchemeMor=base_change(phi, domain(f))[2],
codomain_map::AbsAffineSchemeMor=base_change(phi, codomain(f))[2]
domain_map::Union{AbsAffineSchemeMor, Nothing} = nothing,
codomain_map::Union{AbsAffineSchemeMor, Nothing} = nothing
)
# We need to cater for the case where `phi` is a natural inclusion.
# In that case, we have the same `ambient_coordinate_ring` for domain and codomain
# and we need to make sure, its base change is performed only once.
if domain_map === nothing
ambient_coordinate_map = nothing # initialize the variable
if codomain_map !== nothing && ambient_coordinate_ring(domain(f)) === ambient_coordinate_ring(codomain(f))
# The `ambient_coordinate_ring` is already determined by the map on the codomain
R = ambient_coordinate_ring(domain(f))
R_red = ambient_coordinate_ring(domain(codomain_map))
ambient_ring_map_domain = hom(R, R_red, phi, gens(R_red))
else
_, ambient_ring_map_domain = _change_base_ring(phi, ambient_coordinate_ring(domain(f)))
end
_, domain_map = base_change(phi, domain(f); ambient_ring_map=ambient_ring_map_domain)
end
if codomain_map === nothing
ambient_ring_map_codomain = nothing # initialize the variable
if ambient_coordinate_ring(domain(f)) === ambient_coordinate_ring(codomain(f))
# The `ambient_ring` is already determined by the map on the domain
R = ambient_coordinate_ring(domain(f))
R_red = ambient_coordinate_ring(domain(domain_map))
ambient_ring_map_codomain = hom(R, R_red, phi, gens(R_red))
else
ambient_ring_map_codomain = _change_base_ring(phi, ambient_coordinate_ring(codomain(f)))
end
_, codomain_map = base_change(phi, codomain(f); ambient_ring_map=ambient_ring_map_codomain)
end
X = domain(f)
Y = codomain(f)
XX = domain(domain_map)
Expand All @@ -503,20 +530,20 @@ function base_change(phi::Any, f::AbsAffineSchemeMor;
end

function base_change(phi::Any, f::ClosedEmbedding;
domain_map::AbsAffineSchemeMor=base_change(phi, domain(f))[2],
codomain_map::AbsAffineSchemeMor=base_change(phi, codomain(f))[2]
domain_map::Union{AbsAffineSchemeMor, Nothing} = nothing,
codomain_map::Union{AbsAffineSchemeMor, Nothing} = nothing
)
@assert codomain(codomain_map) === codomain(f)
@assert codomain(domain_map) === domain(f)
codomain_map !== nothing && @req codomain(codomain_map) === codomain(f) "incompatible map"
domain_map !== nothing && @req codomain(domain_map) === domain(f) "incompatible map"
g = underlying_morphism(f)
_, bc_g, _ = base_change(phi, g; domain_map, codomain_map)
domain_map, bc_g, codomain_map = base_change(phi, g; domain_map, codomain_map)
I = image_ideal(f)
@assert base_ring(I) === OO(codomain(f))
@assert base_ring(I) === OO(codomain(f))
#bc_I = ideal(OO(codomain(bc_g)), pullback(codomain_map).(gens(I)))
bc_I = pullback(codomain_map)(I)
@assert domain(bc_g) === domain(domain_map)
@assert codomain(bc_g) === domain(codomain_map)
domain_map !== nothing && @req domain(bc_g) === domain(domain_map) "incompatible map"
codomain_map !== nothing && @req codomain(bc_g) === domain(codomain_map) "incompatible map"
return domain_map, ClosedEmbedding(bc_g, bc_I; check=false), codomain_map
end

Expand Down
57 changes: 33 additions & 24 deletions src/AlgebraicGeometry/Schemes/AffineSchemes/Objects/Methods.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -412,45 +412,54 @@ For an affine scheme `X` over a `base_ring` ``𝕜`` and a morphism
``φ : 𝕜 → 𝕂`` this computes ``Y = X × Spec(𝕂)`` and returns a pair
`(Y, psi)` where `psi` is the canonical map ``Y → X``.
"""
function base_change(phi::Any, X::AbsAffineScheme)
kk = base_ring(X)
kk_red = parent(phi(zero(kk)))
function base_change(
phi::Any, X::AbsAffineScheme;
ambient_ring_map::Map=_change_base_ring(phi, ambient_coordinate_ring(X))[2]
)
R = OO(X)
R_red, Phi = _change_base_ring(phi, R)
R_red, Phi = _change_base_ring(phi, R; ambient_ring_map)
Y = spec(R_red)
return Y, morphism(Y, X, Phi; check=false)
end

### Some helper functions
function _change_base_ring(phi::Any, R::MPolyRing)
K = coefficient_ring(R)
kk = parent(phi(zero(K)))
P, _ = polynomial_ring(kk, symbols(R))
Phi = hom(R, P, phi, gens(P); check=false)
return P, Phi
function _change_base_ring(
phi::Any, R::MPolyRing;
ambient_ring_map::Map=begin
K = coefficient_ring(R)
kk = parent(phi(zero(K)))
P, _ = polynomial_ring(kk, symbols(R); cached=false)
Phi = hom(R, P, phi, gens(P); check=false)
Phi
end
)
return codomain(ambient_ring_map), ambient_ring_map
end

function _change_base_ring(phi::Any, A::MPolyQuoRing)
R = base_ring(A)
function _change_base_ring(
phi::Any, A::MPolyQuoRing;
ambient_ring_map::Map=_change_base_ring(phi, base_ring(A))[2]
)
I = modulus(A)
P, Phi = _change_base_ring(phi, R)
I_red = ideal(P, Phi.(gens(I)))
P = codomain(ambient_ring_map)
I_red = ideal(P, ambient_ring_map.(gens(I)))
Q, pr = quo(P, I_red)
Phi_bar = hom(A, Q, phi, gens(Q), check=false)
return Q, Phi_bar
end

function _change_base_ring(phi::Any,
function _change_base_ring(
phi::Any,
W::MPolyLocRing{<:Any, <:Any, <:Any, <:Any,
<:MPolyPowersOfElement}
<:MPolyPowersOfElement};
ambient_ring_map::Map=_change_base_ring(phi, base_ring(W))[2]
)
R = base_ring(W)
P, Phi = _change_base_ring(phi, R)
@assert _has_coefficient_map(Phi)
P = codomain(ambient_ring_map)
@assert _has_coefficient_map(ambient_ring_map)
U = inverted_set(W)
U_red = MPolyPowersOfElement(P, Phi.(denominators(U)))
U_red = MPolyPowersOfElement(P, ambient_ring_map.(denominators(U)))
W_red, loc_map = localization(P, U_red)
comp = hom(R, W_red, phi, gens(W_red); check=false)
comp = hom(base_ring(W), W_red, phi, gens(W_red); check=false)
@assert _has_coefficient_map(comp)
res_map = hom(W, W_red, comp, check=false)
@assert _has_coefficient_map(res_map)
Expand All @@ -459,11 +468,11 @@ end

function _change_base_ring(phi::Any,
L::MPolyQuoLocRing{<:Any, <:Any, <:Any, <:Any,
<:MPolyPowersOfElement}
<:MPolyPowersOfElement};
ambient_ring_map::Map=_change_base_ring(phi, base_ring(L))[2]
)
R = base_ring(L)
W = localized_ring(L)
W_red, Phi_W = _change_base_ring(phi, W)
W_red, Phi_W = _change_base_ring(phi, W; ambient_ring_map)
I = modulus(L)
I_red = ideal(W_red, Phi_W.(gens(I)))
L_red, pr = quo(W_red, I_red)
Expand Down
18 changes: 13 additions & 5 deletions test/AlgebraicGeometry/Schemes/AffineSchemes.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -267,20 +267,28 @@ end
P = OO(IA2)
x, y = gens(P)

X = subscheme(IA2, x^2 + y^2)
X, inc_X = sub(IA2, x^2 + y^2)

U = hypersurface_complement(IA2, x)
inc_U = inclusion_morphism(U, IA2)

V = hypersurface_complement(X, x)
inc_V = inclusion_morphism(V, X)

kk, pr = quo(ZZ, 5)
IA2_red, phi1 = base_change(pr, IA2)
X_red, phi2 = base_change(pr, X)
U_red, phi3 = base_change(pr, U)
V_red, phi4 = base_change(pr, V)
red_X, phi2, _ = base_change(pr, inc_X; codomain_map=phi1)
X_red = domain(red_X)
@test ambient_coordinate_ring(IA2_red) === ambient_coordinate_ring(X_red)
red_U, phi3, _ = base_change(pr, inc_U; codomain_map=phi1)
U_red = domain(red_U)
@test ambient_coordinate_ring(IA2_red) === ambient_coordinate_ring(U_red)
red_V, phi4, _ = base_change(pr, inc_V; codomain_map=red_X)
V_red = domain(red_V)
@test ambient_coordinate_ring(IA2_red) === ambient_coordinate_ring(V_red)

m1 = compose(inclusion_morphism(V_red, IA2_red), phi1);
m2 = compose(phi4, inclusion_morphism(V, IA2));
m2 = compose(red_V, inclusion_morphism(V, IA2));
@test m1 == m2

# Testing morphisms
Expand Down
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