#5396: [with patch, needs work] Wrapping lcalc library
---------------------------+------------------------------------------------
Reporter: rishi | Owner: Rishi
Type: enhancement | Status: new
Priority: major | Milestone: sage-4.1.2
Component: number theory | Keywords: lcalc
Reviewer: | Author:
Merged: |
---------------------------+------------------------------------------------
Comment(by rishi):
Here I am reproducing what the sage worksheet does.
{{{
sage: import sage.libs.lcalc.for_testing
sage: from sage.libs.lcalc.for_testing import *
sage: D=DirichletGroup(5)
sage: chi=D[1]
sage: chi.values()
[0, 1, zeta4, -zeta4, -1]
sage: L=dirLFuncGenerator(chi)
sage: L.find_zeros_via_N(5)
[-4.13290370521285,
6.18357819545085,
8.45722917442324,
-9.44293112972852,
-11.2828964415816]
#Following Code produces the lowest zeros of Dirichlet L functions of
Cubic Characters with modulus up to 10
sage: for k in srange(3,10):
for chi in DirichletGroup(k,CyclotomicField(3)):
if chi.is_primitive() and chi.order()==3:
L=dirLFuncGenerator(chi)
print k, L.find_zeros_via_N(1)[0]
....:
7 4.35640162473628
7 -4.35640162473628
9 -3.44409315514895
9 3.44409315514895
#Here we create a L function corresponding to Elliptic Curve and find its
zeros
sage: E=EllipticCurve('11a')
sage: L=elLFuncGenerator(E)
sage: L.find_zeros_via_N(5)
[6.36261389471309,
8.60353961929075,
10.0355090971811,
11.4512586103452,
13.5686390571300]
#Another example related to Elliptic Curves
sage: E=EllipticCurve('37')
sage: L2=elLFuncGenerator(E)
sage: print L2.value(.5), L2.value(.5,derivative=1)
0 0.305999824716000 elliptic curve
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5396#comment:12>
Sage <http://sagemath.org/>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--~--~---------~--~----~------------~-------~--~----~
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To post to this group, send email to [email protected]
To unsubscribe from this group, send email to
[email protected]
For more options, visit this group at
http://groups.google.com/group/sage-trac?hl=en
-~----------~----~----~----~------~----~------~--~---
