Hasse-Schmidt derivatives #3912
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…ianBruns/Oscar.jl into kb/hasse_schmidt_derivatives
…ianBruns/Oscar.jl into kb/hasse_schmidt_derivatives
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@KilianBruns : Thank you for your contribution. One hint: |
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We usually don't add methods of the form I would suggest to remove those. |
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In all the examples, expressions like should be replaced by |
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Thank you for the changes. They look good. The test-file still seems to be in the wrong place. The error message reads: And still one more small request: Please add a small paragraph in the documentation stating briefly what Hasse-Derivatives are and where to find the mathematical background. If you need help with this, let me know by mail and we can look at this together. |
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to be reopened |
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reopen |
Codecov ReportAttention: Patch coverage is
Additional details and impacted files@@ Coverage Diff @@
## master #3912 +/- ##
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- Coverage 83.99% 81.38% -2.61%
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Lines 81358 92691 +11333
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+ Hits 68333 75439 +7106
- Misses 13025 17252 +4227
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| ### Implementation of Hasse-Schmidt derivatives as seen in | ||
| ### | ||
| ### Fruehbis-Krueger, Ristau, Schober: 'Embedded desingularization for arithmetic surfaces -- toward a parallel implementation' |
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Perhaps add this to our .bib file so it can be properly referenced in docstrings? (See https://docs.oscar-system.org/stable/DeveloperDocumentation/documentation/#Updating-the-bibliography for hints on how to do that)
| @doc raw""" | ||
| hasse_derivatives(f::MPolyRingElem) | ||
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| Return a list of Hasse-Schmidt derivatives of `f`, each with a multiindex `[a_1, ..., a_n]`, where `a_i` describes the number of times `f` was derived w.r.t. the `i`-th variable. |
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It would be nice "Hasse-Schmidt derivatives" were either defined or a citation added to a place defining it.
| Rtemp, _ = polynomial_ring(R, "y" => 1:n, "t" => 1:n) | ||
| # replace f(x_i) -> f(y_i + t_i) | ||
| F = evaluate(f, gens(Rtemp)[1:n] + gens(Rtemp)[n+1:2n]) |
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| Rtemp, _ = polynomial_ring(R, "y" => 1:n, "t" => 1:n) | |
| # replace f(x_i) -> f(y_i + t_i) | |
| F = evaluate(f, gens(Rtemp)[1:n] + gens(Rtemp)[n+1:2n]) | |
| Rtemp, (y, t) = polynomial_ring(R, :y => 1:n, :t => 1:n) | |
| # replace f(x_i) -> f(y_i + t_i) | |
| F = evaluate(f, y + t) |
This avoids allocations.
First generating the polynomial ring is cheaper with symbols instead of strings:
julia> n=2; R=QQ ; @time S,_ = polynomial_ring(R, "y" => 1:n, "t" => 1:n);
0.000070 seconds (85 allocations: 3.562 KiB)
julia> n=2; R=QQ ; @time S,_ = polynomial_ring(R, :y => 1:n, :t => 1:n);
0.000059 seconds (53 allocations: 2.328 KiB)
Secondly, gens(Rtemp) is not free either, it allocates a fresh vector and a fresh bunch of generator polynomials each time. E.g. if the coefficient ring is QQ, then gens(S) above performs
| return hasse_derivatives(lift(f)) | ||
| end | ||
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| # Oscar.MPolyLocRingElem (internal, expert use only) |
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Why expert use only? Presumably there is a pitfall, perhaps at least a hint could be added so what that is?
| @@ -0,0 +1,119 @@ | |||
| ###### Stil missing ################################################ | |||
| R, (x, y, z) = polynomial_ring(ZZ, ["x", "y", "z"]); | ||
| I = ideal(R, [x^2 - 1]); | ||
| RQ, _ = quo(R, I); |
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No need for those semicolons here and elsewhere in this test file
| R, (x, y, z) = polynomial_ring(ZZ, ["x", "y", "z"]); | |
| I = ideal(R, [x^2 - 1]); | |
| RQ, _ = quo(R, I); | |
| R, (x, y, z) = polynomial_ring(ZZ, ["x", "y", "z"]) | |
| I = ideal(R, [x^2 - 1]) | |
| RQ, _ = quo(R, I) |
Added
(Implemented at the request of @afkafkafk13)