@@ -187,7 +187,7 @@ class SchemeMorphism_polynomial_projective_space(SchemeMorphism_polynomial):
187187 y,
188188 x
189189 """
190- def __init__ (self , parent , polys , check = True ):
190+ def __init__ (self , parent , polys , check = True ) -> None :
191191 """
192192 Initialize.
193193
@@ -557,7 +557,7 @@ def __eq__(self, right):
557557 return all (self ._polys [i ] * right ._polys [j ] == self ._polys [j ] * right ._polys [i ]
558558 for i in range (n ) for j in range (i + 1 , n ))
559559
560- def __ne__ (self , right ):
560+ def __ne__ (self , right ) -> bool :
561561 """
562562 Test the inequality of two projective morphisms.
563563
@@ -961,7 +961,7 @@ def normalize_coordinates(self, **kwds):
961961 ideal = ZZ (ideal )
962962 if self .base_ring () != QQ :
963963 raise ValueError ('ideal was an integer, but the base ring of this ' +
964- 'morphism is %s' % self .base_ring ())
964+ 'morphism is %s' % self .base_ring ())
965965 if not ideal .is_prime ():
966966 raise ValueError ('ideal must be a prime, not %s' % ideal )
967967 uniformizer = ideal
@@ -980,7 +980,7 @@ def normalize_coordinates(self, **kwds):
980980 raise TypeError ('valuation must be a valuation on a number field, not %s' % valuation )
981981 if valuation .domain () != self .base_ring ():
982982 raise ValueError ('the domain of valuation must be the base ring of this morphism ' +
983- 'not %s' % valuation .domain ())
983+ 'not %s' % valuation .domain ())
984984 uniformizer = valuation .uniformizer ()
985985 ramification_index = 1 / valuation (uniformizer )
986986 valuations = []
@@ -1805,7 +1805,7 @@ def _number_field_from_algebraics(self):
18051805 for t in exps :
18061806 G = 0
18071807 for e in t :
1808- G += C [j ]* prod ([R .gen (i )** e [i ] for i in range (N + 1 )])
1808+ G += C [j ] * prod ([R .gen (i )** e [i ] for i in range (N + 1 )])
18091809 j += 1
18101810 F .append (G )
18111811 return H (F )
@@ -1888,8 +1888,6 @@ def indeterminacy_locus(self):
18881888 sage: H = End(P)
18891889 sage: f = H([x^2, y^2, z^2])
18901890 sage: f.indeterminacy_locus() # needs sage.libs.singular
1891- ... DeprecationWarning: The meaning of indeterminacy_locus() has changed.
1892- Read the docstring. See https://github.com/sagemath/sage/issues/29145 for details.
18931891 Closed subscheme of Projective Space of dimension 2 over Rational Field defined by:
18941892 z,
18951893 y,
@@ -1905,7 +1903,7 @@ def indeterminacy_locus(self):
19051903 z,
19061904 x^2 - y^2
19071905
1908- There is related :meth:`base_indeterminacy_locus()` method. This
1906+ There is a related :meth:`base_indeterminacy_locus()` method. This
19091907 computes the indeterminacy locus only from the defining polynomials of
19101908 the map::
19111909
@@ -1918,11 +1916,9 @@ def indeterminacy_locus(self):
19181916 x^2 - y^2,
19191917 z^2
19201918 """
1921- from sage .misc .superseded import deprecation
1922- deprecation (29145 , "The meaning of indeterminacy_locus() has changed. Read the docstring." )
19231919 P = self .domain ()
19241920 X = P .subscheme (0 ) # projective space as a subscheme
1925- return (self * X .hom (P .gens (), P )).indeterminacy_locus ()
1921+ return (self * X .hom (P .gens (), P )).indeterminacy_locus ()
19261922
19271923 def indeterminacy_points (self , F = None , base = False ):
19281924 r"""
@@ -1944,8 +1940,6 @@ def indeterminacy_points(self, F=None, base=False):
19441940 sage: H = End(P)
19451941 sage: f = H([x*z - y*z, x^2 - y^2, z^2])
19461942 sage: f.indeterminacy_points() # needs sage.libs.singular
1947- ... DeprecationWarning: The meaning of indeterminacy_locus() has changed.
1948- Read the docstring. See https://github.com/sagemath/sage/issues/29145 for details.
19491943 [(-1 : 1 : 0), (1 : 1 : 0)]
19501944
19511945 ::
@@ -2114,7 +2108,7 @@ def reduce_base_field(self):
21142108 if K in NumberFields () or isinstance (K , sage .rings .abc .AlgebraicField ):
21152109 return self ._number_field_from_algebraics ()
21162110 if K in FiniteFields ():
2117- #find the degree of the extension containing the coefficients
2111+ # find the degree of the extension containing the coefficients
21182112 c = [v for g in self for v in g .coefficients ()]
21192113 d = lcm ([a .minpoly ().degree () for a in c ])
21202114 if d == 1 :
@@ -2138,7 +2132,7 @@ def reduce_base_field(self):
21382132 self .domain ().variable_names ())
21392133 new_R = new_domain .coordinate_ring ()
21402134 u = phi (L .gen ()) # gen of L in terms of gen of K
2141- g = R (str (u ).replace (K .variable_name (), R .variable_names ()[0 ])) # converted to R
2135+ g = R (str (u ).replace (K .variable_name (), R .variable_names ()[0 ])) # converted to R
21422136 new_f = []
21432137 for fi in self :
21442138 mon = fi .monomials ()
@@ -2148,17 +2142,17 @@ def reduce_base_field(self):
21482142 for c in coef :
21492143 # for each coefficient do the elimination
21502144 w = R (str (c ).replace (K .variable_name (), R .variable_names ()[0 ]))
2151- I = R .ideal ([b - g , w ])
2145+ I = R .ideal ([b - g , w ])
21522146 v = I .elimination_ideal ([a ]).gen (0 )
21532147 # elimination can change scale the result, so correct the leading coefficient
21542148 # and convert back to L
2155- if v .subs ({b :g }).lc () == w .lc ():
2149+ if v .subs ({b : g }).lc () == w .lc ():
21562150 new_c .append (L (str (v ).replace (R .variable_names ()[1 ], L .variable_name ())))
21572151 else :
2158- new_c .append (L (str (w .lc ()* v ).replace (R .variable_names ()[1 ], L .variable_name ())))
2152+ new_c .append (L (str (w .lc () * v ).replace (R .variable_names ()[1 ], L .variable_name ())))
21592153 # reconstruct as a poly in the new domain
2160- new_f .append (sum (new_c [i ]* prod (new_R .gen (j )** mon_deg [i ][j ]
2161- for j in range (new_R .ngens ()))
2154+ new_f .append (sum (new_c [i ] * prod (new_R .gen (j )** mon_deg [i ][j ]
2155+ for j in range (new_R .ngens ()))
21622156 for i in range (len (mon ))))
21632157 # return the correct type of map
21642158 if self .is_endomorphism ():
@@ -2194,7 +2188,7 @@ def reduce_base_field(self):
21942188 if M .degree () == da :
21952189 break
21962190 c = M (str (c ).replace (c .as_finite_field_element ()[0 ].variable_name (),
2197- M .variable_name ()))
2191+ M .variable_name ()))
21982192 new_c .append (M_to_L (c ))
21992193 # reconstruct as a poly in the new domain
22002194 new_f .append (sum ([new_c [i ] * prod (new_R .gen (j )** mon_deg [i ][j ]
@@ -2238,7 +2232,7 @@ def image(self):
22382232 """
22392233 X = self .domain ().subscheme (0 )
22402234 e = X .embedding_morphism ()
2241- return (self * e ).image ()
2235+ return (self * e ).image ()
22422236
22432237
22442238class SchemeMorphism_polynomial_projective_space_finite_field (SchemeMorphism_polynomial_projective_space_field ):
@@ -2305,7 +2299,7 @@ def __call__(self, x):
23052299 pass
23062300 raise ValueError ('the morphism is not defined at this point' )
23072301
2308- def __eq__ (self , other ):
2302+ def __eq__ (self , other ) -> bool :
23092303 """
23102304 EXAMPLES::
23112305
@@ -2435,7 +2429,7 @@ def representatives(self):
24352429 emb = Y .projective_embedding (0 )
24362430 hom = self .parent ()
24372431 reprs = []
2438- for r in (emb * self ).representatives ():
2432+ for r in (emb * self ).representatives ():
24392433 f0 = r [0 ]
24402434 reprs .append (hom ([f / f0 for f in r [1 :]]))
24412435 return reprs
@@ -2566,7 +2560,7 @@ def indeterminacy_locus(self):
25662560 components = X .irreducible_components ()
25672561
25682562 def self_with_domain (C ):
2569- return self * C .hom (Amb .gens (), X )
2563+ return self * C .hom (Amb .gens (), X )
25702564
25712565 locus = self_with_domain (components [0 ]).indeterminacy_locus ()
25722566 for C in components [1 :]:
@@ -2647,13 +2641,13 @@ def image(self):
26472641 D = PolynomialRing (k , names = dummy_names )
26482642
26492643 names = list (S .variable_names ()) + dummy_names # this order of variables is important
2650- R = PolynomialRing (k , names = names , order = 'degrevlex({}),degrevlex({})' .format (m ,n ))
2644+ R = PolynomialRing (k , names = names , order = 'degrevlex({}),degrevlex({})' .format (m , n ))
26512645
26522646 # compute the ideal of the image by elimination
26532647 i = R .ideal (list (X .defining_ideal ().gens ()) + [self ._polys [i ] - R .gen (n + i ) for i in range (m )])
26542648 j = [g for g in i .groebner_basis () if g in D ]
26552649
2656- gens = [g .subs (dict (zip (R .gens ()[n :],T .gens ()))) for g in j ]
2650+ gens = [g .subs (dict (zip (R .gens ()[n :], T .gens ()))) for g in j ]
26572651 return AY .subscheme (gens )
26582652
26592653 @cached_method
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