3030from sage .matrix .matrix_space import MatrixSpace
3131from sage .misc .functional import denominator , is_even
3232from sage .misc .lazy_import import lazy_import
33- from sage .misc .superseded import deprecated_function_alias , deprecation
33+ from sage .misc .superseded import deprecated_function_alias
3434from sage .modules .free_module_element import vector
3535from sage .quadratic_forms .quadratic_form__evaluate import (
3636 QFEvaluateMatrix ,
4646from sage .structure .sage_object import SageObject
4747
4848
49- def is_QuadraticForm (Q ):
50- """
51- Determine if the object ``Q`` is an element of the :class:`QuadraticForm` class.
52-
53- This function is deprecated.
54-
55- EXAMPLES::
56-
57- sage: Q = QuadraticForm(ZZ, 2, [1,2,3])
58- sage: from sage.quadratic_forms.quadratic_form import is_QuadraticForm
59- sage: is_QuadraticForm(Q)
60- doctest:...: DeprecationWarning: the function is_QuadraticForm is deprecated;
61- use isinstance(x, sage.quadratic_forms.quadratic_form.QuadraticForm) instead...
62- True
63- sage: is_QuadraticForm(2)
64- False
65- """
66- deprecation (35305 ,
67- "the function is_QuadraticForm is deprecated; use "
68- "isinstance(x, sage.quadratic_forms.quadratic_form.QuadraticForm) instead" )
69- return isinstance (Q , QuadraticForm )
70-
71-
7249def quadratic_form_from_invariants (F , rk , det , P , sminus ):
7350 r"""
7451 Return a rational quadratic form with given invariants.
@@ -521,7 +498,7 @@ def __init__(
521498 unsafe_initialization = False ,
522499 number_of_automorphisms = None ,
523500 determinant = None ,
524- ):
501+ ) -> None :
525502 """
526503 EXAMPLES::
527504
@@ -721,7 +698,7 @@ def __pari__(self):
721698 """
722699 return self .matrix ().__pari__ ()
723700
724- def _pari_init_ (self ):
701+ def _pari_init_ (self ) -> str :
725702 """
726703 Return a PARI-formatted Hessian matrix for Q, as string.
727704
@@ -733,7 +710,7 @@ def _pari_init_(self):
733710 """
734711 return self .matrix ()._pari_init_ ()
735712
736- def _repr_ (self ):
713+ def _repr_ (self ) -> str :
737714 """
738715 Give a text representation for the quadratic form given as an upper-triangular matrix of coefficients.
739716
@@ -758,7 +735,7 @@ def _repr_(self):
758735 out_str += "]"
759736 return out_str
760737
761- def _latex_ (self ):
738+ def _latex_ (self ) -> str :
762739 """
763740 Give a LaTeX representation for the quadratic form given as an upper-triangular matrix of coefficients.
764741
@@ -847,7 +824,7 @@ def __setitem__(self, ij, coeff):
847824 except Exception :
848825 raise RuntimeError ("this coefficient cannot be coerced to an element of the base ring for the quadratic form" )
849826
850- def __hash__ (self ):
827+ def __hash__ (self ) -> int :
851828 r"""
852829 TESTS::
853830
@@ -861,7 +838,7 @@ def __hash__(self):
861838 """
862839 return hash (self .__base_ring ) ^ hash (tuple (self .__coeffs ))
863840
864- def __eq__ (self , right ):
841+ def __eq__ (self , right ) -> bool :
865842 """
866843 Determines if two quadratic forms are equal.
867844
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