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Change a test to use jldoctest for easier inspecting and fixing
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@fingolfin
fingolfin committed Nov 7, 2024
1 parent 14f1a85 commit 248b024
Showing 1 changed file with 88 additions and 37 deletions.
125 changes: 88 additions & 37 deletions test/Modules/ModulesGraded.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -1046,37 +1046,94 @@ end
@test degree(phi) == degree(element_to_homomorphism(phi)(v)) - degree(v)
end

@testset "minimal Betti tables" begin
# The Veronese surface in IP^4 due to Wolfram
F = GF(31991)
R, (x,y,z,u,v) = graded_polynomial_ring(F, [:x, :y, :z, :u, :v])
I = ideal([F(45)/16*x^3-8565*x^2*y-7937*x*y^2+14060*x^2*z+F(53)/113*x*y*z-F(125)/17*x*z^2-15712*x^2*u-5990*x*y*u-F(71)/88*x*z*u-6141*x*u^2+F(49)/104*x^2*v-194*x*y*v+F(63)/103*y^2*v+F(74)/103*x*z*v+11618*y*z*v+F(41)/111*z^2*v+14387*x*u*v-F(64)/9*y*u*v+13097*z*u*v+F(84)/101*u^2*v+12211*x*v^2+F(85)/63*y*v^2-F(119)/100*z*v^2-6247*u*v^2-F(74)/51*v^3,-F(45)/16*x^2*y+8565*x*y^2+7937*y^3-14060*x*y*z-F(53)/113*y^2*z+F(125)/17*y*z^2+15712*x*y*u+5990*y^2*u+F(71)/88*y*z*u+6141*y*u^2-x^2*v+3340*x*y*v+F(111)/40*y^2*v+F(22)/37*x*z*v-F(110)/29*y*z*v-F(71)/25*z^2*v-F(71)/87*x*u*v+F(112)/55*y*u*v+F(103)/80*z*u*v-F(100)/7*u^2*v-5013*x*v^2+15010*y*v^2+F(52)/51*z*v^2+F(126)/5*u*v^2-6580*v^3,-F(45)/16*x^2*z+8565*x*y*z+7937*y^2*z-14060*x*z^2-F(53)/113*y*z^2+F(125)/17*z^3+15712*x*z*u+5990*y*z*u+F(71)/88*z^2*u+6141*z*u^2+F(41)/79*x^2*v+F(121)/48*x*y*v+9621*y^2*v+F(105)/83*x*z*v+F(27)/26*y*z*v-649*z^2*v-12278*x*u*v+14655*y*u*v+10594*z*u*v+10462*u^2*v+F(76)/13*x*v^2+F(97)/50*y*v^2-7761*z*v^2+F(52)/31*u*v^2-6636*v^3,-F(45)/16*x^2*u+8565*x*y*u+7937*y^2*u-14060*x*z*u-F(53)/113*y*z*u+F(125)/17*z^2*u+15712*x*u^2+5990*y*u^2+F(71)/88*z*u^2+6141*u^3-F(40)/31*x^2*v+13297*x*y*v+F(126)/113*y^2*v-F(51)/100*x*z*v-F(97)/38*y*z*v+10372*z^2*v-F(4)/31*x*u*v+F(32)/9*y*u*v-F(1)/7*z*u*v+15473*u^2*v+F(101)/36*x*v^2+F(97)/109*y*v^2-14100*z*v^2+F(109)/32*u*v^2-F(5)/111*v^3,-F(40)/31*x^3+13297*x^2*y+F(126)/113*x*y^2-F(51)/100*x^2*z-F(97)/38*x*y*z+10372*x*z^2+F(26)/105*x^2*u-3745*x*y*u+F(63)/103*y^2*u-F(98)/61*x*z*u+11618*y*z*u+F(41)/111*z^2*u+F(26)/15*x*u^2-F(64)/9*y*u^2+13097*z*u^2+F(84)/101*u^3+F(101)/36*x^2*v+F(97)/109*x*y*v-14100*x*z*v-14778*x*u*v+F(85)/63*y*u*v-F(119)/100*z*u*v-6247*u^2*v-F(5)/111*x*v^2-F(74)/51*u*v^2,F(40)/31*x^2*y-13297*x*y^2-F(126)/113*y^3+F(51)/100*x*y*z+F(97)/38*y^2*z-10372*y*z^2-x^2*u+F(103)/30*x*y*u+2754*y^2*u+F(22)/37*x*z*u+F(126)/95*y*z*u-F(71)/25*z^2*u-F(71)/87*x*u^2-F(109)/7*y*u^2+F(103)/80*z*u^2-F(100)/7*u^3-F(101)/36*x*y*v-F(97)/109*y^2*v+14100*y*z*v-5013*x*u*v+10008*y*u*v+F(52)/51*z*u*v+F(126)/5*u^2*v+F(5)/111*y*v^2-6580*u*v^2,F(40)/31*x^2*z-13297*x*y*z-F(126)/113*y^2*z+F(51)/100*x*z^2+F(97)/38*y*z^2-10372*z^3+F(41)/79*x^2*u+F(121)/48*x*y*u+9621*y^2*u+5671*x*z*u-F(42)/71*y*z*u-5219*z^2*u-12278*x*u^2+14655*y*u^2+F(58)/59*z*u^2+10462*u^3-F(101)/36*x*z*v-F(97)/109*y*z*v+14100*z^2*v+F(76)/13*x*u*v+F(97)/50*y*u*v-12763*z*u*v+F(52)/31*u^2*v+F(5)/111*z*v^2-6636*u*v^2,F(41)/79*x^3+F(121)/48*x^2*y+9621*x*y^2-F(22)/109*x^2*z+F(25)/19*x*y*z+F(63)/103*y^2*z+F(23)/45*x*z^2+11618*y*z^2+F(41)/111*z^3-12278*x^2*u+14655*x*y*u+F(126)/73*x*z*u-F(64)/9*y*z*u+13097*z^2*u+10462*x*u^2+F(84)/101*z*u^2+F(76)/13*x^2*v+F(97)/50*x*y*v-F(106)/115*x*z*v+F(85)/63*y*z*v-F(119)/100*z^2*v+F(52)/31*x*u*v-6247*z*u*v-6636*x*v^2-F(74)/51*z*v^2,-F(41)/79*x^2*y-F(121)/48*x*y^2-9621*y^3-x^2*z-F(22)/89*x*y*z-F(32)/17*y^2*z+F(22)/37*x*z^2-F(86)/111*y*z^2-F(71)/25*z^3+12278*x*y*u-14655*y^2*u-F(71)/87*x*z*u+F(74)/47*y*z*u+F(103)/80*z^2*u-10462*y*u^2-F(100)/7*z*u^2-F(76)/13*x*y*v-F(97)/50*y^2*v-5013*x*z*v-9220*y*z*v+F(52)/51*z^2*v-F(52)/31*y*u*v+F(126)/5*z*u*v+6636*y*v^2-6580*z*v^2,x^3+11117*x^2*y+991*x*y^2-F(63)/103*y^3-F(22)/37*x^2*z-F(35)/13*x*y*z-11618*y^2*z+F(71)/25*x*z^2-F(41)/111*y*z^2+F(71)/87*x^2*u+F(68)/115*x*y*u+F(64)/9*y^2*u-F(103)/80*x*z*u-13097*y*z*u+F(100)/7*x*u^2-F(84)/101*y*u^2+5013*x^2*v-F(67)/114*x*y*v-F(85)/63*y^2*v-F(52)/51*x*z*v+F(119)/100*y*z*v-F(126)/5*x*u*v+6247*y*u*v+6580*x*v^2+F(74)/51*y*v^2])
I = ideal(R, minimal_generating_set(I))
F = graded_free_module(R, 1)
sub_F, inc = sub(F, [g*F[1] for g in gens(I)])
M = cokernel(inc)
A, _ = quo(R, I)
# To reproduce the string on the right hand side, evaluate
# `"$(Oscar.minimal_betti_table(M))"`
# and insert the result here; after verification of the result!
@test "$(Oscar.minimal_betti_table(A))" == " 0 1 2 3 4\n---------------------\n0 : 1 - - - -\n1 : - - - - -\n2 : - 7 10 5 1\n---------------------\ntotal: 1 7 10 5 1"

@test "$(Oscar.minimal_betti_table(M))" == " 0 1 2 3 4\n---------------------\n0 : 1 - - - -\n1 : - - - - -\n2 : - 7 10 5 1\n---------------------\ntotal: 1 7 10 5 1"

@test "$(Oscar.minimal_betti_table(I))" == "$(Oscar.minimal_betti_table(sub_F))"

# small example due to Janko
R, x = graded_polynomial_ring(QQ, :x => 1:7)
I = ideal(R, [x[1]*x[2]*x[5], x[1]*x[2]*x[6], x[3]*x[4]*x[6], x[3]*x[4]*x[7], x[5]*x[7]])
A, _ = quo(R, I)
@test "$(Oscar.minimal_betti_table(A))" == " 0 1 2 3\n-----------------\n0 : 1 - - -\n1 : - 1 - -\n2 : - 4 4 -\n3 : - - 1 -\n4 : - - - 1\n-----------------\ntotal: 1 5 5 1"

# another example due to Wolfram
R, (x, y, z, w) = graded_polynomial_ring(QQ, [:x, :y, :z, :w])
I = ideal(R, [w^2 - x*z, w*x - y*z, x^2 - w*y, x*y - z^2, y^2 - w*z])
A, _ = quo(R, I)
@test "$(Oscar.minimal_betti_table(free_resolution(A)))" == " 0 1 2 3\n-----------------\n0 : 1 - - -\n1 : - 5 5 -\n2 : - - - 1\n-----------------\ntotal: 1 5 5 1"
end
Oscar.@_AuxDocTest "minimal Betti tables", (fix = false),
raw"""
# The Veronese surface in IP^4 due to Wolfram
```jldoctest; setup = :(using Oscar)
julia> F = GF(31991)
Prime field of characteristic 31991
julia> R, (x,y,z,u,v) = graded_polynomial_ring(F, [:x, :y, :z, :u, :v]);
julia> I = ideal([F(45)/16*x^3-8565*x^2*y-7937*x*y^2+14060*x^2*z+F(53)/113*x*y*z-F(125)/17*x*z^2-15712*x^2*u-5990*x*y*u-F(71)/88*x*z*u-6141*x*u^2+F(49)/104*x^2*v-194*x*y*v+F(63)/103*y^2*v+F(74)/103*x*z*v+11618*y*z*v+F(41)/111*z^2*v+14387*x*u*v-F(64)/9*y*u*v+13097*z*u*v+F(84)/101*u^2*v+12211*x*v^2+F(85)/63*y*v^2-F(119)/100*z*v^2-6247*u*v^2-F(74)/51*v^3,-F(45)/16*x^2*y+8565*x*y^2+7937*y^3-14060*x*y*z-F(53)/113*y^2*z+F(125)/17*y*z^2+15712*x*y*u+5990*y^2*u+F(71)/88*y*z*u+6141*y*u^2-x^2*v+3340*x*y*v+F(111)/40*y^2*v+F(22)/37*x*z*v-F(110)/29*y*z*v-F(71)/25*z^2*v-F(71)/87*x*u*v+F(112)/55*y*u*v+F(103)/80*z*u*v-F(100)/7*u^2*v-5013*x*v^2+15010*y*v^2+F(52)/51*z*v^2+F(126)/5*u*v^2-6580*v^3,-F(45)/16*x^2*z+8565*x*y*z+7937*y^2*z-14060*x*z^2-F(53)/113*y*z^2+F(125)/17*z^3+15712*x*z*u+5990*y*z*u+F(71)/88*z^2*u+6141*z*u^2+F(41)/79*x^2*v+F(121)/48*x*y*v+9621*y^2*v+F(105)/83*x*z*v+F(27)/26*y*z*v-649*z^2*v-12278*x*u*v+14655*y*u*v+10594*z*u*v+10462*u^2*v+F(76)/13*x*v^2+F(97)/50*y*v^2-7761*z*v^2+F(52)/31*u*v^2-6636*v^3,-F(45)/16*x^2*u+8565*x*y*u+7937*y^2*u-14060*x*z*u-F(53)/113*y*z*u+F(125)/17*z^2*u+15712*x*u^2+5990*y*u^2+F(71)/88*z*u^2+6141*u^3-F(40)/31*x^2*v+13297*x*y*v+F(126)/113*y^2*v-F(51)/100*x*z*v-F(97)/38*y*z*v+10372*z^2*v-F(4)/31*x*u*v+F(32)/9*y*u*v-F(1)/7*z*u*v+15473*u^2*v+F(101)/36*x*v^2+F(97)/109*y*v^2-14100*z*v^2+F(109)/32*u*v^2-F(5)/111*v^3,-F(40)/31*x^3+13297*x^2*y+F(126)/113*x*y^2-F(51)/100*x^2*z-F(97)/38*x*y*z+10372*x*z^2+F(26)/105*x^2*u-3745*x*y*u+F(63)/103*y^2*u-F(98)/61*x*z*u+11618*y*z*u+F(41)/111*z^2*u+F(26)/15*x*u^2-F(64)/9*y*u^2+13097*z*u^2+F(84)/101*u^3+F(101)/36*x^2*v+F(97)/109*x*y*v-14100*x*z*v-14778*x*u*v+F(85)/63*y*u*v-F(119)/100*z*u*v-6247*u^2*v-F(5)/111*x*v^2-F(74)/51*u*v^2,F(40)/31*x^2*y-13297*x*y^2-F(126)/113*y^3+F(51)/100*x*y*z+F(97)/38*y^2*z-10372*y*z^2-x^2*u+F(103)/30*x*y*u+2754*y^2*u+F(22)/37*x*z*u+F(126)/95*y*z*u-F(71)/25*z^2*u-F(71)/87*x*u^2-F(109)/7*y*u^2+F(103)/80*z*u^2-F(100)/7*u^3-F(101)/36*x*y*v-F(97)/109*y^2*v+14100*y*z*v-5013*x*u*v+10008*y*u*v+F(52)/51*z*u*v+F(126)/5*u^2*v+F(5)/111*y*v^2-6580*u*v^2,F(40)/31*x^2*z-13297*x*y*z-F(126)/113*y^2*z+F(51)/100*x*z^2+F(97)/38*y*z^2-10372*z^3+F(41)/79*x^2*u+F(121)/48*x*y*u+9621*y^2*u+5671*x*z*u-F(42)/71*y*z*u-5219*z^2*u-12278*x*u^2+14655*y*u^2+F(58)/59*z*u^2+10462*u^3-F(101)/36*x*z*v-F(97)/109*y*z*v+14100*z^2*v+F(76)/13*x*u*v+F(97)/50*y*u*v-12763*z*u*v+F(52)/31*u^2*v+F(5)/111*z*v^2-6636*u*v^2,F(41)/79*x^3+F(121)/48*x^2*y+9621*x*y^2-F(22)/109*x^2*z+F(25)/19*x*y*z+F(63)/103*y^2*z+F(23)/45*x*z^2+11618*y*z^2+F(41)/111*z^3-12278*x^2*u+14655*x*y*u+F(126)/73*x*z*u-F(64)/9*y*z*u+13097*z^2*u+10462*x*u^2+F(84)/101*z*u^2+F(76)/13*x^2*v+F(97)/50*x*y*v-F(106)/115*x*z*v+F(85)/63*y*z*v-F(119)/100*z^2*v+F(52)/31*x*u*v-6247*z*u*v-6636*x*v^2-F(74)/51*z*v^2,-F(41)/79*x^2*y-F(121)/48*x*y^2-9621*y^3-x^2*z-F(22)/89*x*y*z-F(32)/17*y^2*z+F(22)/37*x*z^2-F(86)/111*y*z^2-F(71)/25*z^3+12278*x*y*u-14655*y^2*u-F(71)/87*x*z*u+F(74)/47*y*z*u+F(103)/80*z^2*u-10462*y*u^2-F(100)/7*z*u^2-F(76)/13*x*y*v-F(97)/50*y^2*v-5013*x*z*v-9220*y*z*v+F(52)/51*z^2*v-F(52)/31*y*u*v+F(126)/5*z*u*v+6636*y*v^2-6580*z*v^2,x^3+11117*x^2*y+991*x*y^2-F(63)/103*y^3-F(22)/37*x^2*z-F(35)/13*x*y*z-11618*y^2*z+F(71)/25*x*z^2-F(41)/111*y*z^2+F(71)/87*x^2*u+F(68)/115*x*y*u+F(64)/9*y^2*u-F(103)/80*x*z*u-13097*y*z*u+F(100)/7*x*u^2-F(84)/101*y*u^2+5013*x^2*v-F(67)/114*x*y*v-F(85)/63*y^2*v-F(52)/51*x*z*v+F(119)/100*y*z*v-F(126)/5*x*u*v+6247*y*u*v+6580*x*v^2+F(74)/51*y*v^2]);
julia> I = ideal(R, minimal_generating_set(I));
julia> F = graded_free_module(R, 1);
julia> sub_F, inc = sub(F, [g*F[1] for g in gens(I)]);
julia> M = cokernel(inc);
julia> A, _ = quo(R, I);
julia> minimal_betti_table(A)
degree: 0 1 2 3 4
----------------------
0: 1 - - - -
1: - - - - -
2: - 7 10 5 1
----------------------
total: 1 7 10 5 1
julia> minimal_betti_table(M)
degree: 0 1 2 3 4
----------------------
0: 1 - - - -
1: - - - - -
2: - 7 10 5 1
----------------------
total: 1 7 10 5 1
julia> minimal_betti_table(I)
degree: 0 1 2 3
-------------------
3: 7 10 5 1
-------------------
total: 7 10 5 1
```
# small example due to Janko
```jldoctest; setup = :(using Oscar)
julia> R, x = graded_polynomial_ring(QQ, :x => 1:7);
julia> I = ideal(R, [x[1]*x[2]*x[5], x[1]*x[2]*x[6], x[3]*x[4]*x[6], x[3]*x[4]*x[7], x[5]*x[7]]);
julia> A, _ = quo(R, I);
julia> minimal_betti_table(A)
degree: 0 1 2 3
------------------
0: 1 - - -
1: - 1 - -
2: - 4 4 -
3: - - 1 -
4: - - - 1
------------------
total: 1 5 5 1
```
# another example due to Wolfram
```jldoctest; setup = :(using Oscar)
julia> R, (x, y, z, w) = graded_polynomial_ring(QQ, [:x, :y, :z, :w]);
julia> I = ideal(R, [w^2 - x*z, w*x - y*z, x^2 - w*y, x*y - z^2, y^2 - w*z]);
julia> A, _ = quo(R, I);
julia> minimal_betti_table(free_resolution(A))
degree: 0 1 2 3
------------------
0: 1 - - -
1: - 5 5 -
2: - - - 1
------------------
total: 1 5 5 1
```
"""

@testset "sheaf cohomology" begin
S, _ = graded_polynomial_ring(QQ, :x => 1:4)
Expand Down Expand Up @@ -1264,9 +1321,3 @@ end
ideal_as_module(J)
quotient_ring_as_module(J)
end






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