@@ -171,11 +171,7 @@ def _isogeny_determine_algorithm(E, kernel):
171171
172172 raise ValueError ("invalid parameters to EllipticCurveIsogeny constructor" )
173173
174-
175- from sage .misc .superseded import deprecated_function_alias
176- isogeny_determine_algorithm = deprecated_function_alias (33619 , _isogeny_determine_algorithm )
177-
178- def isogeny_codomain_from_kernel (E , kernel , degree = None ):
174+ def isogeny_codomain_from_kernel (E , kernel ):
179175 r"""
180176 Compute the isogeny codomain given a kernel.
181177
@@ -210,28 +206,13 @@ def isogeny_codomain_from_kernel(E, kernel, degree=None):
210206 Elliptic Curve defined by y^2 + x*y + y = x^3 + 5*x + 2
211207 over Finite Field of size 7
212208
209+ sage: # needs sage.rings.finite_rings
213210 sage: E = EllipticCurve(GF(19), [1,2,3,4,5])
214211 sage: kernel_list = [E((15,10)), E((10,3)), E((6,5))]
215212 sage: isogeny_codomain_from_kernel(E, kernel_list)
216213 Elliptic Curve defined by y^2 + x*y + 3*y = x^3 + 2*x^2 + 3*x + 15
217214 over Finite Field of size 19
218-
219- TESTS:
220-
221- Test deprecation warning for obsolete argument::
222-
223- sage: isogeny_codomain_from_kernel(E, kernel_list, degree=4)
224- doctest:warning
225- ...
226- DeprecationWarning: The "degree" argument to isogeny_codomain_from_kernel() does nothing and will be removed.
227- ...
228- Elliptic Curve defined by y^2 + x*y + 3*y = x^3 + 2*x^2 + 3*x + 15
229- over Finite Field of size 19
230215 """
231- if degree is not None :
232- from sage .misc .superseded import deprecation
233- deprecation (33619 , 'The "degree" argument to isogeny_codomain_from_kernel() does nothing and will be removed.' )
234-
235216 algorithm = _isogeny_determine_algorithm (E , kernel )
236217
237218 if algorithm == 'velu' :
@@ -3456,47 +3437,6 @@ def compute_isogeny_stark(E1, E2, ell):
34563437from sage .misc .superseded import deprecated_function_alias
34573438compute_isogeny_starks = deprecated_function_alias (34871 , compute_isogeny_stark )
34583439
3459- def split_kernel_polynomial (poly ):
3460- r"""
3461- Obsolete internal helper function formerly used by
3462- :func:`compute_isogeny_kernel_polynomial`.
3463-
3464- Use
3465- :meth:`~sage.rings.polynomial.polynomial_element.Polynomial.radical`
3466- instead.
3467-
3468- INPUT:
3469-
3470- - ``poly`` -- a nonzero univariate polynomial
3471-
3472- OUTPUT:
3473-
3474- The maximum separable divisor of ``poly``. If the input is a full
3475- kernel polynomial where the roots which are `x`-coordinates of
3476- points of order greater than 2 have multiplicity 1, the output
3477- will be a polynomial with the same roots, all of multiplicity 1.
3478-
3479- EXAMPLES:
3480-
3481- Check that this behaves identically to ``.radical()``::
3482-
3483- sage: # needs sage.rings.finite_rings
3484- sage: from sage.schemes.elliptic_curves.ell_curve_isogeny import split_kernel_polynomial
3485- sage: q = next_prime(randrange(3,10^3))
3486- sage: e = randrange(1,5)
3487- sage: R = GF(q^e,'a')['x']
3488- sage: f = R.random_element(randrange(10,100)).monic()
3489- sage: split_kernel_polynomial(f) == f.radical()
3490- doctest:warning ...
3491- DeprecationWarning: ...
3492- True
3493- """
3494- from sage .misc .superseded import deprecation
3495- deprecation (33619 , 'The split_kernel_polynomial() function is obsolete. '
3496- 'Use .radical() instead.' )
3497- from sage .misc .misc_c import prod
3498- return prod ([p for p ,e in poly .squarefree_decomposition ()])
3499-
35003440def compute_isogeny_kernel_polynomial (E1 , E2 , ell , algorithm = "stark" ):
35013441 r"""
35023442 Return the kernel polynomial of an isogeny of degree ``ell``
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