#5947: Coleman integrals of exact forms
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Reporter: jen | Owner: was
Type: defect | Status: new
Priority: major | Milestone: sage-3.4.2
Component: algebraic geometry | Keywords:
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Say I define a hyperelliptic curve and calculate the action of Frobenius
\phi on basis differentials w_i. Sage outputs the matrix and f_i such that
\phi* w_i = df_i + \sum A_ij w_j.
Then for f_i, int(df_i,P,Q) = f_i(Q)-f_i(P). However, it seems Sage is
computing f.diff() to be -df instead of df.
{{{
sage: R.<x> = QQ['x']
sage: H = HyperellipticCurve(x*(x-1)*(x+9))
sage: K = Qp(7,10)
sage: HK = H.change_ring(K)
sage: import sage.schemes.elliptic_curves.monsky_washnitzer as mw
sage: M_frob, forms = mw.matrix_of_frobenius_hyperelliptic(HK)
sage: f = forms[0]
sage: P = HK(9,36)
sage: Q = HK.teichmuller(P)
sage: HK.coleman_integral(f.diff(),P,Q)
6*7^2 + 5*7^3 + 7^4 + 7^5 + 7^6 + 3*7^7 + 5*7^9 + 4*7^10 + O(7^11)
}}}
However, it seems that f.diff() is actually -f.diff(), as the answer
should be
{{{
sage: f(Q[0],Q[1])-f(P[0],P[1])
7^2 + 7^3 + 5*7^4 + 5*7^5 + 5*7^6 + 3*7^7 + 6*7^8 + 7^9 + 2*7^10 + O(7^11)
}}}
which is in fact the negation of what it's computing:
{{{
sage: f(P[0],P[1])-f(Q[0],Q[1])
6*7^2 + 5*7^3 + 7^4 + 7^5 + 7^6 + 3*7^7 + 5*7^9 + 4*7^10 + O(7^11)
}}}
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5947>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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