sagemathgh-38923: remove some deprecated functionality

    
These should all be older than a year.
    
URL: sagemath#38923
Reported by: Lorenz Panny
Reviewer(s): Frédéric Chapoton

src/sage/rings/finite_rings/element_base.pyx

@@ -22,7 +22,6 @@ from sage.structure.element cimport Element
 from sage.structure.parent cimport Parent
 from sage.rings.integer_ring import ZZ
 from sage.rings.integer import Integer
-from sage.misc.superseded import deprecated_function_alias
 
 
 def is_FiniteFieldElement(x):
@@ -1104,8 +1103,6 @@ cdef class FinitePolyExtElement(FiniteRingElement):
             f = f.reverse(self.parent().degree() - 1)
         return f(p)
 
-    integer_representation = deprecated_function_alias(33941, to_integer)
-
     def to_bytes(self, byteorder='big'):
         r"""
         Return an array of bytes representing an integer.

src/sage/rings/finite_rings/finite_field_base.pyx

@@ -41,7 +41,6 @@ from sage.misc.cachefunc import cached_method
 from sage.misc.prandom import randrange
 from sage.rings.integer cimport Integer
 import sage.rings.abc
-from sage.misc.superseded import deprecation_cython as deprecation, deprecated_function_alias
 
 # Copied from sage.misc.fast_methods, used in __hash__() below.
 cdef int SIZEOF_VOID_P_SHIFT = 8*sizeof(void *) - 4
@@ -457,8 +456,6 @@ cdef class FiniteField(Field):
             r = r * g + self(d)
         return r
 
-    fetch_int = deprecated_function_alias(33941, from_integer)
-
     def _is_valid_homomorphism_(self, codomain, im_gens, base_map=None):
         """
         Return ``True`` if the map from ``self`` to codomain sending

src/sage/rings/finite_rings/finite_field_givaro.py

@@ -23,7 +23,6 @@
 from sage.rings.integer import Integer
 from sage.rings.finite_rings.element_givaro import Cache_givaro
 from sage.libs.pari.all import pari
-from sage.misc.superseded import deprecated_function_alias
 
 
 class FiniteField_givaro(FiniteField):
@@ -488,8 +487,6 @@ def from_integer(self, n):
         """
         return self._cache.fetch_int(n)
 
-    fetch_int = deprecated_function_alias(33941, from_integer)
-
     def _pari_modulus(self):
         """
         Return the modulus of ``self`` in a format for PARI.

src/sage/rings/finite_rings/finite_field_ntl_gf2e.py

@@ -18,7 +18,6 @@
 from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.libs.pari.all import pari
 from sage.rings.integer import Integer
-from sage.misc.superseded import deprecated_function_alias
 
 
 def late_import():
@@ -289,8 +288,6 @@ def from_integer(self, number):
         """
         return self._cache.fetch_int(number)
 
-    fetch_int = deprecated_function_alias(33941, from_integer)
-
     def _pari_modulus(self):
         """
         Return PARI object which is equivalent to the

src/sage/schemes/elliptic_curves/ell_curve_isogeny.py

@@ -3580,10 +3580,6 @@ def compute_isogeny_stark(E1, E2, ell):
     return qn
 
 
-from sage.misc.superseded import deprecated_function_alias
-compute_isogeny_starks = deprecated_function_alias(34871, compute_isogeny_stark)
-
-
 def compute_isogeny_kernel_polynomial(E1, E2, ell, algorithm=None):
     r"""
     Return the kernel polynomial of a cyclic, separable, normalized
@@ -3650,11 +3646,6 @@ def compute_isogeny_kernel_polynomial(E1, E2, ell, algorithm=None):
         sage: poly.factor()
         (x + 10) * (x + 12) * (x + 16)
     """
-    if algorithm == 'starks':
-        from sage.misc.superseded import deprecation
-        deprecation(34871, 'The "starks" algorithm is being renamed to "stark".')
-        algorithm = 'stark'
-
     if algorithm is None:
         char = E1.base_ring().characteristic()
         if char != 0 and char < 4*ell + 4:

src/sage/schemes/elliptic_curves/ell_generic.py

@@ -2511,121 +2511,58 @@ def multiplication_by_m(self, m, x_only=False):
 
         return mx, my
 
-    def multiplication_by_m_isogeny(self, m):
+    def scalar_multiplication(self, m):
         r"""
-        Return the ``EllipticCurveIsogeny`` object associated to the
-        multiplication-by-`m` map on this elliptic curve.
-
-        The resulting isogeny will
-        have the associated rational maps (i.e., those returned by
-        :meth:`multiplication_by_m`) already computed.
-
-        NOTE: This function is currently *much* slower than the
-        result of ``self.multiplication_by_m()``, because
-        constructing an isogeny precomputes a significant amount
-        of information. See :issue:`7368` and :issue:`8014` for the
-        status of improving this situation.
-
-        INPUT:
-
-        - ``m`` -- nonzero integer
+        Return the scalar-multiplication map `[m]` on this elliptic
+        curve as a
+        :class:`sage.schemes.elliptic_curves.hom_scalar.EllipticCurveHom_scalar`
+        object.
 
-        OUTPUT:
+        EXAMPLES::
 
-        - An ``EllipticCurveIsogeny`` object associated to the
-          multiplication-by-`m` map on this elliptic curve.
+            sage: E = EllipticCurve('77a1')
+            sage: m = E.scalar_multiplication(-7); m
+            Scalar-multiplication endomorphism [-7]
+             of Elliptic Curve defined by y^2 + y = x^3 + 2*x over Rational Field
+            sage: m.degree()
+            49
+            sage: P = E(2,3)
+            sage: m(P)
+            (-26/225 : -2132/3375 : 1)
+            sage: m.rational_maps() == E.multiplication_by_m(-7)
+            True
 
-        EXAMPLES::
+        ::
 
             sage: E = EllipticCurve('11a1')
-            sage: E.multiplication_by_m_isogeny(7)
-            doctest:warning ... DeprecationWarning: ...
-            Isogeny of degree 49
-             from Elliptic Curve defined by y^2 + y = x^3 - x^2 - 10*x - 20
-                   over Rational Field
-             to   Elliptic Curve defined by y^2 + y = x^3 - x^2 - 10*x - 20
-                   over Rational Field
+            sage: E.scalar_multiplication(7)
+            Scalar-multiplication endomorphism [7]
+             of Elliptic Curve defined by y^2 + y = x^3 - x^2 - 10*x - 20 over Rational Field
 
         TESTS:
 
         Tests for :issue:`32490`::
 
             sage: E = EllipticCurve(QQbar, [1,0])                                       # needs sage.rings.number_field
-            sage: E.multiplication_by_m_isogeny(1).rational_maps()                      # needs sage.rings.number_field
+            sage: E.scalar_multiplication(1).rational_maps()                      # needs sage.rings.number_field
             (x, y)
 
         ::
 
             sage: E = EllipticCurve_from_j(GF(31337).random_element())                  # needs sage.rings.finite_rings
             sage: P = E.random_point()                                                  # needs sage.rings.finite_rings
-            sage: [E.multiplication_by_m_isogeny(m)(P) == m*P for m in (1,2,3,5,7,9)]   # needs sage.rings.finite_rings
+            sage: [E.scalar_multiplication(m)(P) == m*P for m in (1,2,3,5,7,9)]   # needs sage.rings.finite_rings
             [True, True, True, True, True, True]
 
         ::
 
             sage: E = EllipticCurve('99.a1')
-            sage: E.multiplication_by_m_isogeny(5)
-            Isogeny of degree 25 from Elliptic Curve defined by y^2 + x*y + y = x^3 - x^2 - 17*x + 30 over Rational Field to Elliptic Curve defined by y^2 + x*y + y = x^3 - x^2 - 17*x + 30 over Rational Field
-            sage: E.multiplication_by_m_isogeny(2).rational_maps()
-            ((1/4*x^4 + 33/4*x^2 - 121/2*x + 363/4)/(x^3 - 3/4*x^2 - 33/2*x + 121/4),
-             (-1/256*x^7 + 1/128*x^6*y - 7/256*x^6 - 3/256*x^5*y - 105/256*x^5 - 165/256*x^4*y + 1255/256*x^4 + 605/128*x^3*y - 473/64*x^3 - 1815/128*x^2*y - 10527/256*x^2 + 2541/128*x*y + 4477/32*x - 1331/128*y - 30613/256)/(1/16*x^6 - 3/32*x^5 - 519/256*x^4 + 341/64*x^3 + 1815/128*x^2 - 3993/64*x + 14641/256))
-
-        Test for :issue:`34727`::
-
-            sage: E = EllipticCurve([5,5])
-            sage: E.multiplication_by_m_isogeny(-1)
-            Isogeny of degree 1
-             from Elliptic Curve defined by y^2 = x^3 + 5*x + 5 over Rational Field
-             to Elliptic Curve defined by y^2 = x^3 + 5*x + 5 over Rational Field
-            sage: E.multiplication_by_m_isogeny(-2)
-            Isogeny of degree 4
-             from Elliptic Curve defined by y^2 = x^3 + 5*x + 5 over Rational Field
-             to Elliptic Curve defined by y^2 = x^3 + 5*x + 5 over Rational Field
-            sage: E.multiplication_by_m_isogeny(-3)
-            Isogeny of degree 9
-             from Elliptic Curve defined by y^2 = x^3 + 5*x + 5 over Rational Field
-             to Elliptic Curve defined by y^2 = x^3 + 5*x + 5 over Rational Field
-            sage: mu = E.multiplication_by_m_isogeny
-            sage: all(mu(-m) == -mu(m) for m in (1,2,3,5,7))
-            True
-        """
-        from sage.misc.superseded import deprecation
-        deprecation(32826, 'The .multiplication_by_m_isogeny() method is superseded by .scalar_multiplication().')
-
-        mx, my = self.multiplication_by_m(m)
-
-        torsion_poly = self.torsion_polynomial(abs(m)).monic()
-        phi = self.isogeny(torsion_poly, codomain=self)
-        phi._EllipticCurveIsogeny__initialize_rational_maps(precomputed_maps=(mx, my))
-
-        # trac 32490: using codomain=self can give a wrong isomorphism
-        for aut in self.automorphisms():
-            psi = aut * phi
-            if psi.rational_maps() == (mx, my):
-                return psi
-
-        assert False, 'bug in multiplication_by_m_isogeny()'
-
-    def scalar_multiplication(self, m):
-        r"""
-        Return the scalar-multiplication map `[m]` on this elliptic
-        curve as a
-        :class:`sage.schemes.elliptic_curves.hom_scalar.EllipticCurveHom_scalar`
-        object.
-
-        EXAMPLES::
-
-            sage: E = EllipticCurve('77a1')
-            sage: m = E.scalar_multiplication(-7); m
-            Scalar-multiplication endomorphism [-7]
-            of Elliptic Curve defined by y^2 + y = x^3 + 2*x over Rational Field
-            sage: m.degree()
-            49
-            sage: P = E(2,3)
-            sage: m(P)
-            (-26/225 : -2132/3375 : 1)
-            sage: m.rational_maps() == E.multiplication_by_m(-7)
-            True
+            sage: E.scalar_multiplication(5)
+            Scalar-multiplication endomorphism [5]
+             of Elliptic Curve defined by y^2 + x*y + y = x^3 - x^2 - 17*x + 30 over Rational Field
+            sage: E.scalar_multiplication(2).rational_maps()
+            ((x^4 + 33*x^2 - 242*x + 363)/(4*x^3 - 3*x^2 - 66*x + 121),
+             (-4*x^7 + 8*x^6*y - 28*x^6 - 12*x^5*y - 420*x^5 - 660*x^4*y + 5020*x^4 + 4840*x^3*y - 7568*x^3 - 14520*x^2*y - 42108*x^2 + 20328*x*y + 143264*x - 10648*y - 122452)/(64*x^6 - 96*x^5 - 2076*x^4 + 5456*x^3 + 14520*x^2 - 63888*x + 58564))
         """
         from sage.schemes.elliptic_curves.hom_scalar import EllipticCurveHom_scalar
         return EllipticCurveHom_scalar(self, m)

src/sage/schemes/elliptic_curves/hom.py

@@ -238,12 +238,10 @@ def _richcmp_(self, other, op):
             sage: wE = identity_morphism(E)
             sage: wF = identity_morphism(F)
             sage: mE = E.scalar_multiplication(1)
-            sage: mF = F.multiplication_by_m_isogeny(1)
-            doctest:warning ... DeprecationWarning: ...
-            sage: [mE == wE, mF == wF]
-            [True, True]
-            sage: [a == b for a in (wE,mE) for b in (wF,mF)]
-            [False, False, False, False]
+            sage: mE == wE
+            True
+            sage: [a == wF for a in (wE,mE)]
+            [False, False]
 
         .. SEEALSO::
 

src/sage/schemes/elliptic_curves/hom_scalar.py

@@ -396,8 +396,7 @@ def scaling_factor(self):
             sage: u = phi.scaling_factor()
             sage: u == phi.formal()[1]
             True
-            sage: u == E.multiplication_by_m_isogeny(5).scaling_factor()
-            doctest:warning ... DeprecationWarning: ...
+            sage: u == 5
             True
 
         The scaling factor lives in the base ring::