implement given divisor as a specific hyperelliptic curve divisor
I get the values of a divisor for a hyperelliptic curve from a research paper to ensure (u, v) are the divisor is correct and i want to use this divisor on calculation.
so Idid the following:
A Secured Cloud System using Hyper Elliptic Curve
and in sage:
p = 4112543547855339322343814790708185367671872426434747235319998473455582535888229747778325047393413053
K = GF(p)
R.<x> = K[]
f = x^5 + 7943193*x^4 + 6521255*x^3 + 1065528*x^2 + 3279922*x + 3728927
C = HyperellipticCurve( f )
J = C.jacobian()
X = J(K)
u, v = x^2 + 22457213658579645161*x + 62960708771725664757, 65279057408798633572*x + 32004384923913711271
D = X( [u,v] )
"error"
verbose 0 (3324:
multi_polynomial_ideal.py,
groebner_basis) Warning: falling back
to very slow toy implementation.
verbose 0 (1083:
multi_polynomial_ideal.py, dimension)
Warning: falling back to very slow toy
implementation. Error in lines 9-9
Traceback (most recent call last):
File
"/cocalc/lib/python2.7/site-packages/smc_sagews/sage_server.py",
line 1013, in execute
exec compile(block+'\n', '', 'single') in namespace, locals File
"", line 1, in <module> File
"/ext/sage/sage-8.1/local/lib/python2.7/site-packages/sage/schemes/hyperelliptic_curves/jacobian_homset.py",
line 145, in __call__
return JacobianMorphism_divisor_class_field(self,
tuple(P)) File
"/ext/sage/sage-8.1/local/lib/python2.7/site-packages/sage/schemes/hyperelliptic_curves/jacobian_morphism.py",
line 388, in __init__
polys, C)) ValueError: Argument polys (= (x^2 + 22457213658579645161x
+ 62960708771725664757, 65279057408798633572x +
32004384923913711271)) must be divisor
on curve Hyperelliptic Curve over
Finite Field of size
4112543547855339322343814790708185367671872426434747235319998473455582535888229747778325047393413053
defined by y^2 = x^5 + 7943193x^4 +
6521255x^3 + 1065528x^2 + 3279922x
+ 3728927.
Does this mean the paper is wrong or I am at wrong.
and if so, how can I modify my work?
