Docu invariants lin. red. groups (Lakshmi Ramesh and Wolfram Decker) #3443
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…d Wolfram Decker)
wdecker
changed the title
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What is the status quo here?
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| @doc raw""" | ||
| linearly_reductive_group(sym::Symbol, m::Int, R::MPolyRing) | ||
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| If `sym` stands for implementing the special linear group, return SL$(m, K)$, where $K$ is the base field |
| function affine_algebra(R::RedGrpInvRing) | ||
| V = fundamental_invariants(R) | ||
| s = length(V) | ||
| S,t = polynomial_ring(field(group(representation(R))), "t"=>1:s) |
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Assuming the fundamental invariants are homogeneous, we could/should grade this polynomial ring appropriately.
Also, the presentation as affine algebra should be cached in the invariant ring.
This can be filed under "future improvements".
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@joschmitt As far as I can see, the ring is NOT graded for finite groups. Or?
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It is graded:
julia> RG = invariant_ring(matrix_group(QQ[-1 0 ; 0 -1]));
julia> A, AtoR = affine_algebra(RG);
julia> A
Quotient
of multivariate polynomial ring in 3 variables over QQ graded by
y1 -> [2]
y2 -> [2]
y3 -> [2]
by ideal (-y1*y3 + y2^2)
| characteristic(fld) == 0 || error("Characteristic should be 0 for linearly reductive groups") | ||
| G.field = fld | ||
| @req m^2 == ngens(pring) "ring not compatible" | ||
| G.group = (sym,m) | ||
| G.reynolds_operator = reynolds_slm | ||
| M = matrix(pring, m, m, gens(pring)) | ||
| M = transpose(matrix(pring, m, m, gens(pring))) |
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That's not a docu change but a change in behavior. Is this covered by a test? What is it fixing?
(Not arguing against this, I have no idea, but I also don't want this to accidentally slip through)
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This is correct now and fits with what we write in the book.
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It also fits with Sturmfels' book.
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And, it fits with the Disquisitiones Arithmetica.
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As discussed: I am happy to trust you this is correct as in: fits what we document and fits our book.
That it fits other books or papers only is relevant if we establish that they use exact same conventions as we and hence are supposed to give identical results. I had a look at that a few months ago, but I didn't keep my notes, and don't have time to repeat this right now. Anyway, as I already wrote, I am happy to trust you, I just want it to be explicit and not "by oversight" ;-).
BTW, if we verified it fits with the convention in those publications, but does not fit with the conventions in Derksen and Kemper; then I think we should actually point that out in the documentation, perhaps even with an example, as this is of course highly relevant for users of our code. And since we refer to e.g. Derksen/Derksen-Kemper in there, this is doubly important as a user might expect the reverse, or not even be aware of the differences in conventions.
(Ideally we would also state how it compares to Singular and Magma conventions, I guess?)
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(That's not a blocker for this PR, of course, just something "nice to have")
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@fingolfin, @joschmitt: We believe that we adressed all your remarks. Please check. |
…3443) Co-authored-by: Johannes Schmitt <[email protected]> (cherry picked from commit 73ba787)
benlorenz
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backport 1.0.x
- Add QQBar docs to the manual #3423 - do not show the OscarInterface banner #3422 - fix bugs in all_OD_infos #3419 - Ep/ Rename Spec to AffineScheme #3345 #3425 - Remove two mentions of Arb_jll #3431 - Tweak epimorphism_from_free_group #3430 - CI: re-enable nightly #3435 - support gen(G::GAPGroup, 0) #3332 - Align all_*_groups methods some more #3433 - Add all_perfect_groups #3434 - Add all_primitive_groups and all_transitive_groups variants taking a single int or int range #3404 - fix a docstring #3436 - Fixes multivariate division #3396 - Docu invariants tori #3428 - Improve docstrings for is_conjugate/is_conjugate_with_data. #3384 - Fix ambient_module(M::SubquoModule) #3448 - Bugfix for printing of affine schemes #3437 - Bugfix for bugfix for printing of affine schemes #3445 - Update OSCAR banner #3410 - Docu invariants lin. red. groups (Lakshmi Ramesh and Wolfram Decker) #3443 - add od_from_atlas_group, od_from_p_subgroup, and helpers #3444 - Unexport normalise #3453 - support group properties for character tables #3449 - add docstrings for acting_group and action_function #3432 (exports are used in new groups code for the book) - Adjust to renaming of rank(A::FinGenAbGroup) to torsion_free_rank(A::FinGenAbGroup) #3457 - Ensure fp_group(G) transfers group attributes #3464 - Added comment on convention #3467 - Export weierstrass_chart_on_minimal_model and patch transform_to_weierstrass #3458 - Fix a doc signature #3466 - Grading + caching for affine algebra of torus invariants #3469
…d Wolfram Decker)