#16773: Analytic Rank Bound
-------------------------------------+-------------------------------------
       Reporter:  spice              |        Owner:  spice
           Type:  enhancement        |       Status:  needs_work
       Priority:  major              |    Milestone:  sage-6.5
      Component:  elliptic curves    |   Resolution:
       Keywords:  elliptic curves,   |    Merged in:
  analytic rank, l-functions         |    Reviewers:  William Stein
        Authors:  Simon Spicer       |  Work issues:
Report Upstream:  N/A                |       Commit:
         Branch:                     |  4d5bbec0ebddce3b202d2ab9ff84463ecfdea094
  u/spice/analytic_rank_bound        |     Stopgaps:
   Dependencies:                     |
-------------------------------------+-------------------------------------
Changes (by vbraun):

 * status:  positive_review => needs_work


Comment:

 32-bit Linux:
 {{{
 sage -t --long src/sage/lfunctions/zero_sums.pyx
 **********************************************************************
 File "src/sage/lfunctions/zero_sums.pyx", line 198, in
 sage.lfunctions.zero_sums.LFunctionZeroSum_abstract.digamma
 Failed example:
     Z.digamma(3.2)
 Expected:
     0.9988388912865993
 Got:
     0.9988388912865995
 **********************************************************************
 File "src/sage/lfunctions/zero_sums.pyx", line 200, in
 sage.lfunctions.zero_sums.LFunctionZeroSum_abstract.digamma
 Failed example:
     Z.digamma(3.2,include_constant_term=False)
 Expected:
     1.576054556188132
 Got:
     1.5760545561881325
 **********************************************************************
 File "src/sage/lfunctions/zero_sums.pyx", line 202, in
 sage.lfunctions.zero_sums.LFunctionZeroSum_abstract.digamma
 Failed example:
     Z.digamma(1+I)
 Expected:
     0.09465032062247625 + 1.076674047468581*I
 Got:
     0.09465032062247693 + 1.076674047468581*I
 **********************************************************************
 File "src/sage/lfunctions/zero_sums.pyx", line 289, in
 sage.lfunctions.zero_sums.LFunctionZeroSum_abstract.logarithmic_derivative
 Failed example:
     Z.logarithmic_derivative(2.2,num_terms=50000) # long time
 Expected:
     (0.5751579645060139, 0.008988775519160675)
 Got:
     (0.5751579645060141, 0.008988775519160675)
 **********************************************************************
 File "src/sage/lfunctions/zero_sums.pyx", line 305, in
 sage.lfunctions.zero_sums.LFunctionZeroSum_abstract.logarithmic_derivative
 Failed example:
     Z.logarithmic_derivative(complex(3,-1))
 Expected:
     (0.04764548578052381 + 0.16513832809989326*I, 6.584671359095225e-06)
 Got:
     (0.0476454857805238 + 0.16513832809989318*I, 6.584671359095225e-06)
 **********************************************************************
 File "src/sage/lfunctions/zero_sums.pyx", line 502, in
 sage.lfunctions.zero_sums.LFunctionZeroSum_abstract.zerosum
 Failed example:
     Z.zerosum(Delta=1,tau=2.876,function="sincsquared")
 Expected:
     1.075551295651154
 Got:
     1.0755512956511541
 **********************************************************************
 File "src/sage/lfunctions/zero_sums.pyx", line 504, in
 sage.lfunctions.zero_sums.LFunctionZeroSum_abstract.zerosum
 Failed example:
     Z.zerosum(Delta=1,tau=1.2,function="sincsquared")
 Expected:
     0.10831555377490683
 Got:
     0.10831555377490693
 **********************************************************************
 File "src/sage/lfunctions/zero_sums.pyx", line 808, in
 sage.lfunctions.zero_sums.LFunctionZeroSum_abstract._zerosum_cauchy
 Failed example:
     Z._zerosum_cauchy(Delta=1,tau=6.36261389)
 Expected:
     2.180904626331156
 Got:
     2.1809046263311567
 **********************************************************************
 File "src/sage/lfunctions/zero_sums.pyx", line 815, in
 sage.lfunctions.zero_sums.LFunctionZeroSum_abstract._zerosum_cauchy
 Failed example:
     Z._zerosum_cauchy(Delta=1,tau=1.5)
 Expected:
     0.9827072037553375
 Got:
     0.9827072037553374
 **********************************************************************
 File "src/sage/lfunctions/zero_sums.pyx", line 824, in
 sage.lfunctions.zero_sums.LFunctionZeroSum_abstract._zerosum_cauchy
 Failed example:
     Z._zerosum_cauchy(Delta=1.5)
 Expected:
     12.93835258975716
 Got:
     12.938352589757159
 **********************************************************************
 File "src/sage/lfunctions/zero_sums.pyx", line 1180, in
 
sage.lfunctions.zero_sums.LFunctionZeroSum_EllipticCurve._zerosum_sincsquared_fast
 Failed example:
     print(E.rank(),Z._zerosum_sincsquared_fast(Delta=1.5))
 Expected:
     (0, 0.0104712060086507)
 Got:
     (0, 0.010471206008650728)
 **********************************************************************
 5 items had failures:
    1 of   7 in
 
sage.lfunctions.zero_sums.LFunctionZeroSum_EllipticCurve._zerosum_sincsquared_fast
    3 of  10 in
 sage.lfunctions.zero_sums.LFunctionZeroSum_abstract._zerosum_cauchy
    3 of   8 in sage.lfunctions.zero_sums.LFunctionZeroSum_abstract.digamma
    2 of  10 in
 sage.lfunctions.zero_sums.LFunctionZeroSum_abstract.logarithmic_derivative
    2 of  10 in sage.lfunctions.zero_sums.LFunctionZeroSum_abstract.zerosum
     [127 tests, 11 failures, 146.27 s]
 }}}

--
Ticket URL: <http://trac.sagemath.org/ticket/16773#comment:41>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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