@@ -916,28 +916,28 @@ def image_type(self, p):
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a_ell = self ._E .ap (ell )
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u = k (a_ell )** 2 * k (ell )** (- 1 )
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if u == 3 :
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- verbose ("found an element of order 6" ,2 )
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+ verbose ("found an element of order 6" , level = 2 )
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# found an element of order 6:
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self .__image_type [p ] = non_split_str
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return self .__image_type [p ]
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if u == 2 and not has_an_el_order_4 :
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# found an element of order 4
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- verbose ("found an element of order 4" ,2 )
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+ verbose ("found an element of order 4" , level = 2 )
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has_an_el_order_4 = True
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if has_an_el_order_3 :
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self .__image_type [p ] = s4_str
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return self .__image_type [p ]
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if u == 1 and not has_an_el_order_3 :
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# found an element of order 3
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- verbose ("found an element of order 3" ,2 )
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+ verbose ("found an element of order 3" , level = 2 )
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has_an_el_order_3 = True
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if has_an_el_order_4 :
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self .__image_type [p ] = s4_str
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return self .__image_type [p ]
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- verbose ("p=5 and we could not determine the image, yet" , 2 )
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+ verbose ("p=5 and we could not determine the image, yet" , level = 2 )
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# we have not yet determined the image, there are only the following possible subgroups of PGL_2
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# (unless we were unlucky and none of the elements of order 6 showed up above, for instance)
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# A_4 of order 12 with elements of order 2 and 3
@@ -995,15 +995,15 @@ def image_type(self, p):
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u = k (a_ell )** 2 * k (ell )** (- 1 )
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if (u not in ex_setp ) and could_be_exc == 1 :
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# it can not be in the exceptional
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- verbose ("the image cannot be exceptional, found u=%s" % u ,2 )
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+ verbose ("the image cannot be exceptional, found u=%s" % u , level = 2 )
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could_be_exc = 0
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if a_ell != 0 and arith .kronecker (a_ell ** 2 - 4 * ell ,p ) == 1 and could_be_non_split == 1 :
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# it can not be in the normalizer of the non-split Cartan
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- verbose ("the image cannot be non-split, found u=%s" % u ,2 )
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+ verbose ("the image cannot be non-split, found u=%s" % u , level = 2 )
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could_be_non_split = 0
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if a_ell != 0 and arith .kronecker (a_ell ** 2 - 4 * ell ,p ) == - 1 and could_be_split == 1 :
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# it can not be in the normalizer of the split Cartan
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- verbose ("the image cannot be split, found u=%s" % u ,2 )
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+ verbose ("the image cannot be split, found u=%s" % u , level = 2 )
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could_be_split = 0
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assert could_be_exc + could_be_split + could_be_non_split > 0 , "bug in image_type."
@@ -1064,7 +1064,7 @@ def image_type(self, p):
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K = self ._E .division_field (p , 'z' )
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d = K .absolute_degree ()
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- verbose ("field of degree %s. try to compute Galois group" % (d ),2 )
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+ verbose ("field of degree %s. try to compute Galois group" % (d ), level = 2 )
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# If the degree is too big, we have no chance at the Galois
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# group. K.galois_group calls is_galois which used to rely on
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# pari's Galois group computations, so degree < 12
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