Trac #16773: Analytic Rank Bound

Implement functionality to bound from above the analytic rank of a rational elliptic curve. This uses the zero sum method as described in [http://msp.org/obs/2013/1-1/obs-v1-n1-p07-s.pdf]. Because this avoids computing with the curve's L-function directly, it is often faster than traditional analytic rank techniques. The enhancement also includes functionality to compute more general zero sums for an elliptic curve L-function, as well as computing with the logarithmic derivative. The elliptic_curves object in Sage has also been modified to contain examples of elliptic curves up to rank 28. To this end the elliptic_curves spkg has been updated to version 0.8. The zipped data file for the spkg can be obtained at [http://www.math.washington.edu/~mlungu/files/elliptic_curves-0.8.tar.bz 2] Complete working sage install with docs built: [https://cloud.sagemath.com/projects/8499bab7-d4a5-4956-acd2-248b5550731 d/files/sage/] Built HTML documentation files (as public, this will work later this week, but not now...) [https://cloud.sagemath.com/8499bab7-d4a5-4956-acd2-248b5550731d/raw/sag e/src/doc/output/html/en/reference/lfunctions/sage/lfunctions/zero_sums. html#sage.lfunctions.zero_sums.LFunctionZeroSum] [https://cloud.sagemath.com/8499bab7-d4a5-4956-acd2-248b5550731d/raw/sag e/src/doc/output/html/en/reference/plane_curves/sage/schemes/elliptic_cu rves/ell_rational_field.html#sage.schemes.elliptic_curves.ell_rational_f ield.EllipticCurve_rational_field.analytic_rank_upper_bound] URL: http://trac.sagemath.org/16773 Reported by: spice Ticket author(s): Simon Spicer Reviewer(s): William Stein
sagemath · Jul 14, 2015 · 18f22f6 · 18f22f6
2 parents eddb17d + 7056dd9
commit 18f22f6
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diff --git a/build/pkgs/elliptic_curves/SPKG.txt b/build/pkgs/elliptic_curves/SPKG.txt
@@ -33,6 +33,9 @@ Includes two databases:
 
 == Changelog ==
 
+=== elliptic_curves-0.8 (Simon Spicer, 2014-10-24) ===
+ * #16773: add more examples of high rank curves
+
 === elliptic_curves-0.7 (R. Andrew Ohana, 2012-05-17) ===
  * #13123: move SAGE_DATA to SAGE_LOCAL/share
 

diff --git a/build/pkgs/elliptic_curves/checksums.ini b/build/pkgs/elliptic_curves/checksums.ini
@@ -1,4 +1,4 @@
 tarball=elliptic_curves-VERSION.tar.bz2
-sha1=779a6abd34b7f33d28f5242c36d6494970dc5136
-md5=6f00374117140c04f23f50a9cb420e97
-cksum=1728958122
+sha1=4de409b03002f5cb7b97f62a6797e33aa968bb80
+md5=fd9beee5a0e4a5ae330ffd6f1ab12112
+cksum=291102768
diff --git a/build/pkgs/elliptic_curves/package-version.txt b/build/pkgs/elliptic_curves/package-version.txt
@@ -1 +1 @@
-0.7
+0.8
diff --git a/src/doc/en/reference/lfunctions/index.rst b/src/doc/en/reference/lfunctions/index.rst
@@ -10,5 +10,6 @@ with :math:`L`-functions.
    sage/lfunctions/lcalc
    sage/lfunctions/sympow
    sage/lfunctions/dokchitser
+   sage/lfunctions/zero_sums
 
 .. include:: ../footer.txt
diff --git a/src/module_list.py b/src/module_list.py
@@ -488,6 +488,16 @@ def uname_specific(name, value, alternative):
 
     Extension('*', ['sage/interfaces/*.pyx']),
 
+    ################################
+    ##
+    ## sage.lfunctions
+    ##
+    ################################
+
+    Extension('sage.lfunctions.zero_sums',
+              sources = ['sage/lfunctions/zero_sums.pyx'],
+              libraries = ["m","flint"]),
+
     ################################
     ##
     ## sage.libs

diff --git a/src/sage/lfunctions/all.py b/src/sage/lfunctions/all.py
@@ -4,3 +4,4 @@
 
 from sympow import sympow
 
+from zero_sums import LFunctionZeroSum