miguelmarco
commented
8 years ago Attachment: libsirocco-1.1.tar.gz
The sirocco library.
Closed miguelmarco closed 7 years ago
miguelmarco
commented
8 years ago Attachment: libsirocco-1.1.tar.gz
The sirocco library.
slel
commented
8 years ago Description changed:
---
+++
@@ -1,3 +1,5 @@
This ticket implements the computation of the fundamental group of the complement of a plane (affine or projective) curve over the rationals or number fields with an embedding in QQbar (in theory it could be done for more general fields, but most likely wouldn't be practical).
It relies on the SIROCCO library [1] that performs a certified root continuation method specifically tailored for this task.
+
+[1] https://github.com/miguelmarco/siroccoAdd link to Sirocco library in ticket description.
miguelmarco
commented
8 years ago miguelmarco
commented
8 years ago Author: Miguel Marco
miguelmarco
commented
8 years ago New commits:
20f7bb2 | Add sirocco package and zarisk-vankampen implementation |
miguelmarco
commented
8 years ago Commit: 20f7bb2
cheuberg
commented
7 years ago This does no longer merge with current sage releases.
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313
commented
7 years ago Branch pushed to git repo; I updated commit sha1. New commits:
6e26772 | Add sirocco package and zarisk-vankampen implementation |
4562507 | Update to sirocco version 2.0 |
fc3f6b3 | Adapt optional extension to c++ |
97a7598 | Fixed imports |
bb898e4 | Merge branch 'u/mmarco/implement_zariski_vankampen_method_to_compute_fundamental_groups_of_complements_of_plane_curves_' of git://trac.sagemath.org/sage into t/21045/implement_zariski_vankampen_method_to_compute_fundamental_groups_of_complements_of_plane_curves_ |
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313
commented
7 years ago miguelmarco
commented
7 years ago Description changed:
---
+++
@@ -1,5 +1,33 @@
This ticket implements the computation of the fundamental group of the complement of a plane (affine or projective) curve over the rationals or number fields with an embedding in QQbar (in theory it could be done for more general fields, but most likely wouldn't be practical).
-It relies on the SIROCCO library [1] that performs a certified root continuation method specifically tailored for this task.
-[1] https://github.com/miguelmarco/sirocco
+Some use examples:
+
+```
+sage: A.<x,y> = AffineSpace(QQ, 2)
+sage: C = A.curve(y^2 - x^3 - x^2)
+sage: C.fundamental_group()
+Finitely presented group < x0 | >
+```
+
+```
+sage: a = QQ[x](x^2+5).roots(QQbar)[0][0]
+sage: a
+-2.236067977499790?*I
+sage: F = NumberField(a.minpoly(), 'a', embedding=a)
+sage: P.<x,y,z> = ProjectiveSpace(F, 2)
+sage: F.inject_variables()
+Defining a
+sage: C = P.curve(x^2 + a * y^2)
+sage: C.fundamental_group()
+Finitely presented group < x0 | >
+```
+
+It relies on version 2 of the SIROCCO library [1] that performs a certified root continuation method specifically tailored for this task.
+
+This same ticket implements the inclusion of Sirocco as an optional package (so it must be installed in order for the functinality to be available). The tarball is available in [2].
+
+- [1] https://github.com/miguelmarco/SIROCCO2
+- [2] https://iuma.unizar.es/es/investigacion/software/sirocco
+
+I think it is ready for review.
Note that in order for the functionality to be available, the package sirocco 2 must be installed. The tarball must be downloaded and copied to the upstream directory.
Note also that currently the file name must be corrected (there is a superfluous underscore). I asked the webmaster to correct it.
tscrim
commented
7 years ago The quick comments:
For bullet points, you need to format them as:
- a really long line continues
at the same starting pointcontpath_mp and contpath are not cpdef? Subsequently, they could have a specified return type? For contpath_mp, you could fill in the list in a second for loop to avoid the list comprehension.contpath, do you want to force input types?j = <int>i; the range will give you int, especially if you cdef int i.res does not seem to be used in contpath_mp.RealField (in contpath_mp), but I don't remember how to do so offhand. You should also create the parent outside of the for loop.fundamental_group appears twice in affine_curve.py.7ed8c4ca-6d56-4ae9-953a-41e42b4ed313
commented
7 years ago 7ed8c4ca-6d56-4ae9-953a-41e42b4ed313
commented
7 years ago Branch pushed to git repo; I updated commit sha1. New commits:
f3d12bc | Some review fixes. |
miguelmarco
commented
7 years ago Thanks for the review.
Replying to @tscrim:
The quick comments:
For bullet points, you need to format them as:
- a really long line continues at the same starting point
Fixed (I think I didn't miss anyone).
- Is there a reason why
contpath_mpandcontpathare notcpdef? Subsequently, they could have a specified return type? Forcontpath_mp, you could fill in the list in a second for loop to avoid the list comprehension.
There is a reason for that: I didn't know about cpdef until now.
About the return type, it should be list[list[RealNumber]], but that doesn't seem to work. list[list] works though.
What is exactly the problem with list comprehension?
- For
contpath, do you want to force input types?
Done, but I don't see any advantage in doing so. If there is a speedup, it is negligible.
- Error messages should start with a lower case.
Fixed.
- Do you want to make zariski_vankampen.py a Cython file for speed?
I tried it, but got some error messages related to the use of parallel functions.
Anyways, I don't expect a significant speedup by compiling it: the bottlenecks are calls to external functions (mainly discriminant computation and contpath calls). The only part that could benefit from compilation is the braid reconstruction from the piecewise linear paths, but my experience shows that this time is very small compared to the computation of the paths themselves.
I could try to cythonize it, but would need some help.
- You don't need to do this
j = <int>i; therangewill give youint, especially if youcdef int i.
Fixed.
resdoes not seem to be used incontpath_mp.
Fixed.
- I think there are better ways to construct a new (unset)
RealField(incontpath_mp), but I don't remember how to do so offhand. You should also create the parent outside of the for loop.
I tried several ways and this was the one that worked. If you remember a better way, please let me know.
fundamental_groupappears twice inaffine_curve.py.
Fixed.
tscrim
commented
7 years ago I can do a first attempt at cythonizing. Do you have a good test case that is not too slow nor too fast to do profiling on to see where the current bottlenecks are?
The reason I bring up the list comprehension is Cython cannot handle them in c(p)def (maybe just cpdef) functions.
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313
commented
7 years ago 7ed8c4ca-6d56-4ae9-953a-41e42b4ed313
commented
7 years ago Branch pushed to git repo; I updated commit sha1. New commits:
e7796fb | Fixed some doctests, and bug when variables are not x,y |
miguelmarco
commented
7 years ago I fixed some doctest and a bug that prevented it to work when the variables where not x and y.
About nontrivial examples to test, here are two:
This one is a good example of the power of sirocco: this group is computed in a few seconds, and as far as I know, it has never been computed before (even though the curve has been explicitely studied)
sage: F = NumberField(QQ[x]('x^2+1'), 'I', embedding = QQbar(I))
sage: F.inject_variables()
Defining I
sage: P.<x,y,z> = ProjectiveSpace(F,2)
sage: c = P.curve((4131/160000*I + 20493/640000)*x^4*y^2 + (-21883/240000*I - 243083/4320000)*x^3*y^3 + (4301/60000*I + 22393/1440000)*x^2*y^4 + (-729/50000*I - 145071/1600000)*x^4*y*z + (4391/400000*I + 92699/800000)*x^3*y^2*z + (20251/100000*I + 50513/900000)*x^2*y^3*z + (-4301/18750*I - 22393/450000)*x*y^4*z + (-72171/4000000*I + 767637/16000000)*x^4*z^2 + (121131/1000000*I + 147717/1000000)*x^3*y*z^2 + (-42633/125000*I - 169493/375000)*x^2*y^2*z^2 + (6341/62500*I + 97183/562500)*x*y^3*z^2 + (8602/46875*I + 22393/562500)*y^4*z^2 + (1323/250000*I - 167481/1000000)*x^3*z^3 + (-3621/62500*I + 47037/250000)*x^2*y*z^3 + (5189/15625*I + 24559/125000)*x*y^2*z^3 + (-14404/46875*I - 80002/421875)*y^3*z^3 + (189/5000*I + 81/625)*x^2*z^4 + (-177/1250*I - 339/1250)*x*y*z^4 + (68/625*I + 253/1875)*y^2*z^4)
sage: c.fundamental_group()
Finitely presented group < x2, x56 | x2^-1*x56*(x2^-1*x56^-1)^3*x2*x56*x2^-1*x56^-1, (x56^-1*x2^-1)^2*x56*x2*x56^2*x2^-1*x56^-1*x2*x56*x2*x56^-1, x56^-1*x2^-1*(x56*x2)^2*x56^-1*x2^-1*x56^-1*x2*x56^2*x2*x56^-1*x2^-1*x56^-1 >
This other one takes a couple of minutes in my laptop. It was the motivation for the writing of GAP3's VKCURVE package (which computes it in almost half an hour in the same computer):
sage: A.<x,y> = AffineSpace(QQ,2)
sage: c = A.curve(746496+3732480*x-3111936*x*y^2-93281756/27*x*y^4+58341596/27*x*y^6+7464960*x^2-384*y^2-9334272*x^2*y^2 +17556484/27*x^2*y^4+43196/27*x^2*y^6+7464576*x^3-756138248/81*x^3*y^2+192792964/81*x^3*y^4+16/81*x^3*y^6+3730944*x^4 -139967996/81*y^4-84021416/27*x^4*y^2+82088/27*x^4*y^4+744192*x^5+43192/27*x^5*y^2-1720/27*x^5*y^4 -124412/81*x^6 +777600800*y^6+95896/81*x^6*y^2-8/81*x^6*y^4-10364/27*x^7-4/27*x^7*y^2+4/27*x^8-8/81*y^8-4/27*x^8*y^2+4/81*x^9)
Finitely presented group < x0, x21, x29, x41, x54 | x29^-1*x54^-1*x29*x54*x29*x54^-1, x41^-1*x29*x41*x29*x41^-1*x29^-1, x29^-1*x0*x29*x0*x29^-1*x0^-1, x21*x29*x21^-1*x29^-1*x21^-1*x29, x41^-1*x0^-1*x41^-1*x0*x41*x0, x54^-1*x21^-1*x54^-1*x21*x54*x21, x41*x21*x41^-1*x21^-1*x41^-1*x21, x21*x0*x21*x0^-1*x21^-1*x0^-1, x41*x54*x41*x54^-1*x41^-1*x54^-1, x54^-1*x0^-1*x54^-1*x0*x54*x0, x41*x21*x29*x21^-1*x41^-1*x21*x29^-1*x21^-1, x41*x54*x41^-1*x29*x54^-1*x41^-1*x54*x29^-1, x21^-1*x0*x54*x0^-1*x21*x0*x54^-1*x0^-1, x0^-1*x41*x21*x41^-1*x0*x41*x21^-1*x41^-1, x21^-1*x0*x41*x0^-1*x21*x0*x41^-1*x0^-1, x21^-1*x54^-1*x0*x54*x21*x54^-1*x0^-1*x54, x29^-1*x54^-1*x0^-1*x54*x29*x54^-1*x0*x54, x29^-1*x0*x54*x0^-1*x29*x0*x54^-1*x0^-1, x29*x0^2*x29^-1*x54^-1*x29*x0^-2*x29^-1*x54, x29^-1*x41*x54*x21*x41^-1*x29*x41*x21^-1*x54^-1*x41^-1, x0*x54^-1*x41*x54*x0^-1*x29^-1*x21^-1*x54^-1*x41^-1*x54*x21*x29, x29^-1*x21^-1*x29*x0*x41*x54*x21*x29*x21^-1*x54^-1*x41^-1*x0^-1, x41^-1*x0^-1*x21*x29*x0*x41*x54*x21*x0^-1*x29^-1*x21^-1*x54^-1, x0^-1*x29^-1*x21*x54^-1*x29*x0*x29*x41*x54*x21^-1*x29*x41^-1*x54^-1*x41^-1, x41^-1*x54^-1*x29*x0^-1*x41*x54*x21*x29*x21*x41^-1*x0*x29^-1*x21^-1*x54^-1, x21^-1*x54^-1*x29*x21^-1*x41^-1*x0*x41*x54*x0*x41^-1*x0^-1*x21*x29^-1*x54, x54*x21*x29*x0*x29^-1*x54*x21^-1*x54^-1*x41^-1*x0^-1*x29^-1*x0*x41*x21^-1, x41*x54*x21*x29*x0*x21^-1*x29*x41*x21*x29^2*x21*x29^-1*x21^-1*x41^-2*x0^-1*x29^-1*x21^-1*x54^-1*x41^-1*x21^-1, x29*x21^-1*x0*x54^2*x41*x54*x21*x0*x29^-1*x41*x0^-1*x21^-1*x0^-2*x54^-1*x41^-1*x0^-1*x29^-1*x21^-1*x29*x0^-1*x21^2, x29*x41^-1*x0*x41*(x21*x54)^2*x0*x54*x21*x0*x29^-1*x21^-1*x41*x54^-1*x41^-1*x29^-1*(x29^-1*x0^-1)^2*x29^-1*x54^-1*x0^-1*x21 >
I did some tests cythonizing some of the functions in zariski_vankampen.py, and I could not observe any speedup at all. I don't think it will be worth the effort.
Are you sure about the list comprehension problem? It seems to work fine in this cpdef'ed function.
tscrim
commented
7 years ago Reviewer: Travis Scrimshaw
tscrim
commented
7 years ago tscrim
commented
7 years ago I've hit that list comprehension problem before. shrugs
From doing some profiling, I agree that there is no real gain from the extra Cythonization.
I made some changes to improve the Cython generated code, removed trailing whitespace, cleaned up the documentation and imports, and some other misc tweaks. So the code should be slight improvement in speed, but likely marginal. Mainly it is cleaner code.
If my changes look good, then you can set a positive review (unless you can add an doctest to the functions in libs/sirocco.pyx, but this is preferable).
New commits:
a170d3b | Merge branch 'u/mmarco/implement_zariski_vankampen_method_to_compute_fundamental_groups_of_complements_of_plane_curves_' of git://trac.sagemath.org/sage into public/topology/zariski_van_kampen_plane_curves-21045 |
c55db60 | Improving Cython code, removing whitespace, doc improvements. |
miguelmarco
commented
7 years ago Thanks for the review!
vbraun
commented
7 years ago On 32-bit
sage -t --long src/sage/schemes/curves/zariski_vankampen.py
**********************************************************************
File "src/sage/schemes/curves/zariski_vankampen.py", line 196, in sage.schemes.curves.zariski_vankampen.segments
Failed example:
segments(disc)
Expected:
[(-2.84740787203333 - 2.84740787203333*I,
-2.14285714285714 + 1.11022302462516e-16*I),
(-2.84740787203333 + 2.84740787203333*I,
-2.14285714285714 + 1.11022302462516e-16*I),
(2.50000000000000 + 2.50000000000000*I,
1.26513881334184 + 2.19128470333546*I),
(2.50000000000000 + 2.50000000000000*I,
2.50000000000000 - 2.50000000000000*I),
(1.26513881334184 + 2.19128470333546*I, 0.000000000000000),
(0.000000000000000, 1.26513881334184 - 2.19128470333546*I),
(2.50000000000000 - 2.50000000000000*I,
1.26513881334184 - 2.19128470333546*I),
(-2.84740787203333 + 2.84740787203333*I,
1.26513881334184 + 2.19128470333546*I),
(-2.14285714285714 + 1.11022302462516e-16*I, 0.000000000000000),
(-2.84740787203333 - 2.84740787203333*I,
1.26513881334184 - 2.19128470333546*I)]
Got:
[(-2.84740787203333 - 2.84740787203333*I,
-2.14285714285714 + 8.65735434729675e-17*I),
(-2.84740787203333 + 2.84740787203333*I,
-2.14285714285714 + 8.65735434729675e-17*I),
(2.50000000000000 + 2.50000000000000*I,
1.26513881334184 + 2.19128470333546*I),
(2.50000000000000 + 2.50000000000000*I,
2.50000000000000 - 2.50000000000000*I),
(1.26513881334184 + 2.19128470333546*I, 1.97324795392362e-17),
(1.97324795392362e-17, 1.26513881334184 - 2.19128470333546*I),
(2.50000000000000 - 2.50000000000000*I,
1.26513881334184 - 2.19128470333546*I),
(-2.84740787203333 + 2.84740787203333*I,
1.26513881334184 + 2.19128470333546*I),
(-2.14285714285714 + 8.65735434729675e-17*I, 1.97324795392362e-17),
(-2.84740787203333 - 2.84740787203333*I,
1.26513881334184 - 2.19128470333546*I)]
**********************************************************************
1 item had failures:
1 of 6 in sage.schemes.curves.zariski_vankampen.segments
[37 tests, 1 failure, 1.29 s]Branch pushed to git repo; I updated commit sha1. New commits:
f88a9db | Fixed optional doctests |
f502374 | Merge branch 'public/topology/zariski_van_kampen_plane_curves-21045' of git://trac.sagemath.org/sage into t/21045/implement_zariski_vankampen_method_to_compute_fundamental_groups_of_complements_of_plane_curves_ |
d0b297e | Stablish numerical tolerance for doctests |
miguelmarco
commented
7 years ago I guess that is a discrpancy on the rounding unit. Added some tolerance to the doctest.
vbraun
commented
7 years ago Changed branch from public/topology/zariski_van_kampen_plane_curves-21045 to d0b297e
This ticket implements the computation of the fundamental group of the complement of a plane (affine or projective) curve over the rationals or number fields with an embedding in QQbar (in theory it could be done for more general fields, but most likely wouldn't be practical).
Some use examples:
It relies on version 2 of the SIROCCO library [1] that performs a certified root continuation method specifically tailored for this task.
This same ticket implements the inclusion of Sirocco as an optional package (so it must be installed in order for the functinality to be available). The tarball is available in [2].
CC: @sagetrac-gjorgenson @bhutz @sagetrac-caravantes @tscrim
Component: algebraic geometry
Author: Miguel Marco
Branch/Commit:
d0b297eReviewer: Travis Scrimshaw
Issue created by migration from https://trac.sagemath.org/ticket/21045