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lines changed Original file line number Diff line number Diff line change @@ -1078,29 +1078,6 @@ def invariants(self):
10781078 """
10791079 return self ._a , self ._b
10801080
1081- def is_definite (self ):
1082- """
1083- Checks whether the quaternion algebra ``self`` is definite, i.e. whether it ramifies at the
1084- unique Archimedean place of its base field QQ. This is the case if and only if both
1085- invariants of ``self`` are negative.
1086-
1087- EXAMPLES::
1088-
1089- sage: QuaternionAlgebra(QQ,-5,-2).is_definite()
1090- True
1091- sage: QuaternionAlgebra(1).is_definite()
1092- False
1093-
1094- sage: QuaternionAlgebra(RR(2.),1).is_definite()
1095- Traceback (most recent call last):
1096- ...
1097- ValueError: base field must be rational numbers
1098- """
1099- if not isinstance (self .base_ring (), RationalField ):
1100- raise ValueError ("base field must be rational numbers" )
1101- a , b = self .invariants ()
1102- return a < 0 and b < 0
1103-
11041081 def __eq__ (self , other ):
11051082 """
11061083 Compare self and other.
@@ -1248,7 +1225,7 @@ def is_definite(self):
12481225 ...
12491226 ValueError: base field must be rational numbers
12501227 """
1251- if not is_RationalField (self .base_ring ()):
1228+ if not isinstance (self .base_ring (), RationalField ):
12521229 raise ValueError ("base field must be rational numbers" )
12531230 a , b = self .invariants ()
12541231 return a < 0 and b < 0
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