Strict transform of an ideal in Cox ring #4154
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TODO: tests, docstrings, documentation
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| @assert grading_group(cox_ring(Y)) === class_group(Y) | ||
| G = class_group(Y) |
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First define G as the class_group(Y) and then use G in the assert, since you need G afterwards anyway and in the case of failure of the assert, you did not loose anything.
| n = number_of_generators(G) | ||
| new_var = cox_ring(Y)[index_of_new_ray(f)] | ||
| M = generator_degrees(cox_ring(Y)) | ||
| @assert M[index_of_new_ray(f)][n] < 0 "Assuming the blowup adds a new column vector to `Oscar.generator_degrees(cox_ring(codomain(f)))`, the entry of that vector corresponding to the new ray should be negative. If not, multiply by -1." |
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Your error messages in case of failing asserts seem pretty long to me. Please try to make them shorter and maybe add appropriate notes to the documentation instead.
| for i in 1:n_rays(Y) | ||
| i == index_of_new_ray(f) || @assert M[i][n] >= 0 "Assuming the blowup adds a new column vector to `Oscar.generator_degrees(cox_ring(codomain(f)))` for which the entry corresponding to the new ray is negative, the entries corresponding to all the other rays should be nonnegative. If not, add integer multiples of the other columns until it is." |
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Do you want to say
@assert findfirst(M[i][n] < 0 && i != index_of_new_ray(f) , 1:n_rays(Y)) === nothing
| function strict_transform(f::ToricBlowupMorphism, I::MPolyIdeal) | ||
| F, ind = _cox_ring_homomorphism(f) | ||
| Y = domain(f) |
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Thanks for looking into this!
This is to compute the strict transform of an ideal in the cox ring of the codomain, correct? I would probably insert an @assert here, or something.
Once this is done, I would be curious to compare performance with the chart-based approach!
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@paemurru : Just a question, because this has been sitting here for 2 weeks now. What is the status here? Are you making progress on this? Are you waiting for comments from someone else? If so, please ping this person. |
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@afkafkafk13 I am working on this, this will probably stay as a draft pull request for quite some time. The current code only handles simple examples, the general case is a bit more complicated. The proof that it works uses a lot of notation, so is not suitable for a docstring or comment and must be typed in LaTeX. So it probably should be included in a research paper, unless an existing reference is found. Essentially, we have an abelian group homomorphism, in general not a C-algebra homomorphism and in general not unique, between the Cox rings that takes homogeneous ideals to homogeneous ideals. And the image of a homogeneous ideal is its total transform. |
TODO: tests, docstrings, documentation