@@ -409,7 +409,7 @@ def lfun_genus2(C):
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sage: L(3)
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0.965946926261520
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- sage: C = HyperellipticCurve(x^2+ x, x^3+ x^2+ 1)
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+ sage: C = HyperellipticCurve(x^2 + x, x^3 + x^2 + 1)
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sage: L = LFunction(lfun_genus2(C))
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sage: L(2)
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0.364286342944359
@@ -445,11 +445,11 @@ class LFunction(SageObject):
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0.000000000000000
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sage: L.derivative(1)
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0.305999773834052
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- sage: L.derivative(1,2)
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+ sage: L.derivative(1, 2)
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0.373095594536324
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sage: L.num_coeffs()
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- sage: L.taylor_series(1,4)
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+ sage: L.taylor_series(1, 4)
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0.000000000000000 + 0.305999773834052*z + 0.186547797268162*z^2 - 0.136791463097188*z^3 + O(z^4)
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sage: L.check_functional_equation() # abs tol 4e-19
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1.08420217248550e-19
@@ -463,9 +463,9 @@ class LFunction(SageObject):
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sage: L = E.lseries().dokchitser(algorithm="pari")
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sage: L.num_coeffs()
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- sage: L.derivative(1,E.rank())
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+ sage: L.derivative(1, E.rank())
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1.51863300057685
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- sage: L.taylor_series(1,4)
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+ sage: L.taylor_series(1, 4)
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...e-19 + (...e-19)*z + 0.759316500288427*z^2 - 0.430302337583362*z^3 + O(z^4)
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.. RUBRIC:: Number field
@@ -481,15 +481,15 @@ class LFunction(SageObject):
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sage: L(2)
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1.10398438736918
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- sage: L.taylor_series(2,3)
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+ sage: L.taylor_series(2, 3)
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1.10398438736918 - 0.215822638498759*z + 0.279836437522536*z^2 + O(z^3)
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.. RUBRIC:: Ramanujan `\Delta` L-function
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The coefficients are given by Ramanujan's tau function::
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sage: from sage.lfunctions.pari import lfun_generic, LFunction
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- sage: lf = lfun_generic(conductor=1, gammaV=[0,1], weight=12, eps=1)
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+ sage: lf = lfun_generic(conductor=1, gammaV=[0, 1], weight=12, eps=1)
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sage: tau = pari('k->vector(k,n,(5*sigma(n,3)+7*sigma(n,5))*n/12 - 35*sum(k=1,n-1,(6*k-4*(n-k))*sigma(k,3)*sigma(n-k,5)))')
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sage: lf.init_coeffs(tau)
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sage: L = LFunction(lf)
@@ -498,7 +498,7 @@ class LFunction(SageObject):
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sage: L(1)
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0.0374412812685155
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- sage: L.taylor_series(1,3)
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+ sage: L.taylor_series(1, 3)
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0.0374412812685155 + 0.0709221123619322*z + 0.0380744761270520*z^2 + O(z^3)
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"""
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def __init__ (self , lfun , prec = None ):
@@ -608,7 +608,7 @@ def Lambda(self, s):
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sage: L = LFunction(lfun_number_field(QQ))
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sage: L.Lambda(2)
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0.523598775598299
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- sage: L.Lambda(1- 2)
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+ sage: L.Lambda(1 - 2)
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0.523598775598299
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"""
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s = self ._CCin (s )
@@ -630,7 +630,7 @@ def hardy(self, t):
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TESTS::
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- sage: L.hardy(.4+ .3*I)
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+ sage: L.hardy(.4 + .3*I)
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Traceback (most recent call last):
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...
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PariError: incorrect type in lfunhardy (t_COMPLEX)
@@ -694,7 +694,7 @@ def taylor_series(self, s, k=6, var='z'):
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sage: E = EllipticCurve('389a')
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sage: L = E.lseries().dokchitser(200,algorithm="pari")
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- sage: L.taylor_series(1,3)
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+ sage: L.taylor_series(1, 3)
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2...e-63 + (...e-63)*z + 0.75931650028842677023019260789472201907809751649492435158581*z^2 + O(z^3)
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Check that :trac:`25402` is fixed::
@@ -757,7 +757,7 @@ def __call__(self, s):
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sage: L = E.lseries().dokchitser(100, algorithm="pari")
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sage: L(1)
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0.00000000000000000000000000000
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- sage: L(1+ I)
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+ sage: L(1 + I)
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-1.3085436607849493358323930438 + 0.81298000036784359634835412129*I
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"""
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s = self ._CC (s )
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