X-Git-Url: https://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Fhurwitz.py;h=ff84b51f8e3923ef7a8a93cb7d42ea1cfe6e3d32;hb=928b7d49fda98ff105c92293b5797bb7a2b9873a;hp=10b308d2bfa602373e0924e390e7e10453eff221;hpb=a9a40bcc98ebf4e4821a068c7b6273430a2b459a;p=sage.d.git diff --git a/mjo/hurwitz.py b/mjo/hurwitz.py index 10b308d..ff84b51 100644 --- a/mjo/hurwitz.py +++ b/mjo/hurwitz.py @@ -23,7 +23,6 @@ class Octonion(IndexedFreeModuleElement): Conjugating twice gets you the original element:: - sage: set_random_seed() sage: O = Octonions() sage: x = O.random_element() sage: x.conjugate().conjugate() == x @@ -58,7 +57,6 @@ class Octonion(IndexedFreeModuleElement): This method is idempotent:: - sage: set_random_seed() sage: O = Octonions() sage: x = O.random_element() sage: x.real().real() == x.real() @@ -91,7 +89,6 @@ class Octonion(IndexedFreeModuleElement): This method is idempotent:: - sage: set_random_seed() sage: O = Octonions() sage: x = O.random_element() sage: x.imag().imag() == x.imag() @@ -121,7 +118,6 @@ class Octonion(IndexedFreeModuleElement): The norm is nonnegative and belongs to the base field:: - sage: set_random_seed() sage: O = Octonions() sage: n = O.random_element().norm() sage: n >= 0 and n in O.base_ring() @@ -129,7 +125,6 @@ class Octonion(IndexedFreeModuleElement): The norm is homogeneous:: - sage: set_random_seed() sage: O = Octonions() sage: x = O.random_element() sage: alpha = O.base_ring().random_element() @@ -167,7 +162,6 @@ class Octonion(IndexedFreeModuleElement): TESTS:: - sage: set_random_seed() sage: O = Octonions() sage: x = O.random_element() sage: x.is_zero() or ( x*x.inverse() == O.one() ) @@ -241,7 +235,6 @@ class Octonions(CombinatorialFreeModule): This gives the correct unit element:: - sage: set_random_seed() sage: O = Octonions() sage: x = O.random_element() sage: x*O.one() == x and O.one()*x == x @@ -529,7 +522,6 @@ class OctonionMatrixAlgebra(HurwitzMatrixAlgebra): TESTS:: - sage: set_random_seed() sage: A = OctonionMatrixAlgebra(ZZ.random_element(10)) sage: x = A.random_element() sage: x*A.one() == x and A.one()*x == x @@ -622,7 +614,6 @@ class QuaternionMatrixAlgebra(HurwitzMatrixAlgebra): TESTS:: - sage: set_random_seed() sage: A = QuaternionMatrixAlgebra(ZZ.random_element(10)) sage: x = A.random_element() sage: x*A.one() == x and A.one()*x == x @@ -732,7 +723,6 @@ class ComplexMatrixAlgebra(HurwitzMatrixAlgebra): TESTS:: - sage: set_random_seed() sage: A = ComplexMatrixAlgebra(ZZ.random_element(10)) sage: x = A.random_element() sage: x*A.one() == x and A.one()*x == x