Now regarding issue 2:
On Saturday, July 2, 2016 at 9:42:53 PM UTC-7, Rob Harron wrote:
>
> (2) An arithmetic error. For example,
>
> sage: chi = kronecker_character(3*61379)
> sage: M = ModularSymbols(chi, 2, sign=1, base_ring=GF(3))
> ...
> File
> "/projects/sage/sage-6.10/local/lib/python2.7/site-packages/sage/modular/modsym/relation_matrix.py",
>
> line 125, in modS_relations
> j, s = syms.apply_S(i)
> File
> "/projects/sage/sage-6.10/local/lib/python2.7/site-packages/sage/modular/modsym/manin_symbol_list.py",
>
> line 1062, in apply_S
> k, s = self.index((self._weight-2-i, v, -u))
> File
> "/projects/sage/sage-6.10/local/lib/python2.7/site-packages/sage/modular/modsym/manin_symbol_list.py",
>
> line 1255, in index
> x, s = self.normalize(x)
> File
> "/projects/sage/sage-6.10/local/lib/python2.7/site-packages/sage/modular/modsym/manin_symbol_list.py",
>
> line 1290, in normalize
> u,v,s = self.__P1.normalize_with_scalar(x[1],x[2])
> File "sage/modular/modsym/p1list.pyx", line 1160, in
> sage.modular.modsym.p1list.P1List.normalize_with_scalar
> (/projects/sage/sage-6.10/src/build/cythonized/sage/modular/modsym/p1list.c:8566)
> self.__normalize(self.__N, u, v, &uu, &vv, &ss, 1)
> File "sage/modular/modsym/p1list.pyx", line 363, in
> sage.modular.modsym.p1list.c_p1_normalize_llong
> (/projects/sage/sage-6.10/src/build/cythonized/sage/modular/modsym/p1list.c:2997)
> ss[0] = <int> (arith_llong.c_inverse_mod_longlong(s*min_t, N) % ll_N)
> File "sage/rings/fast_arith.pyx", line 381, in
> sage.rings.fast_arith.arith_llong.c_inverse_mod_longlong
> (/projects/sage/sage-6.10/src/build/cythonized/sage/rings/fast_arith.c:5546)
> raise ArithmeticError("The inverse of %s modulo %s is not
> defined."%(a,m))
> ArithmeticError: The inverse of -2142142713 modulo 184137 is not defined.
>
>
This appears to be the underlying issue:
sage: import sage.modular.modsym.p1list as p1list
sage: N = 3*61379
sage: p1 = p1list.P1List(N)
sage: p1.normalize_with_scalar(21, -1)
...
ArithmeticError: The inverse of -2142142713 modulo 184137 is not defined.
The offending subroutine appears to be c_p1_normalize_llong, in case this
helps.
Kiran
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