@@ -944,35 +944,27 @@ def basic_j_invariant_parameters(self, coeff_indices=None, nonzero=False):
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((1, 2), (12, 29, 6)),
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((1, 2), (31, 31, 7))]
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- One can specify the list of coefficients indices to be
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- considered in the computation ::
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+ Use the ``nonzero=True`` flag to display only the parameters
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+ whose `j`-invariant value is nonzero ::
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- sage: A = GF(3)['T']
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- sage: K.<T> = Frac(A)
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- sage: phi = DrinfeldModule(A, [T, T, 2, T, 2*T, T^3, T^4 + T^2 + 1])
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- sage: phi.basic_j_invariant_parameters([1, 5])
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- [((1, 5), (273, 91, 31)),
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- ((1, 5), (297, 163, 55)),
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- ((1, 5), (295, 157, 53)),
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- ((1, 5), (265, 67, 23)),
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- ((1, 5), (357, 343, 115)),
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- ...
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- ((1, 5), (146, 74, 25))]
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+ sage: phi.basic_j_invariant_parameters(nonzero=True)
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+ [((2,), (31, 6))]
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- Use ``nonzero=True`` to speed up the computations for Drinfeld
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- modules having multiple zero coefficients::
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- sage: A = GF(5)['T']
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+ One can specify the list of coefficients indices to be
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+ considered in the computation::
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+
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+ sage: A = GF(2)['T']
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sage: K.<T> = Frac(A)
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- sage: phi = DrinfeldModule(A, [T, 0, T+1, 0, 1, 0 , T])
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- sage: phi.basic_j_invariant_parameters(nonzero=True )
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- [((2, 4 ), (260, 641, 26 )),
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- ((2, 4 ), (157, 19 , 1)),
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- ((2, 4 ), (27, 24 , 1)),
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- ((2, 4 ), (188, 143, 6 )),
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- ((2, 4 ), (401, 260, 11 )),
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- ...
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- ((2, 4 ), (288, 39, 2 ))]
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+ sage: phi = DrinfeldModule(A, [T, T, 1 , T])
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+ sage: phi.basic_j_invariant_parameters([1, 2] )
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+ [((1, 2 ), (1, 2, 1 )),
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+ ((1, 2 ), (4, 1 , 1)),
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+ ((1, 2 ), (7, 0 , 1)),
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+ ((1, 2 ), (5, 3, 2 )),
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+ ((1, 2 ), (0, 7, 3 )),
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+ ((1, 2), (6, 5, 3)),
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+ ((1, 2 ), (7, 7, 4 ))]
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TESTS::
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