mjo/**/*.py: drop obsolete set_random_seed().

[sage.d.git] / mjo / eja / eja_algebra.py

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index dd1bcf2584449f5b80ef13a669a28946948b3d25..1ccbf2e302e7cd43ae1877e3fda6fdcaa3f5e5de 100644 (file)
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -230,7 +230,6 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
     We should compute that an element subalgebra is associative even
     if we circumvent the element method::
 
-        sage: set_random_seed()
         sage: J = random_eja(field=QQ,orthonormalize=False)
         sage: x = J.random_element()
         sage: A = x.subalgebra_generated_by(orthonormalize=False)
@@ -432,7 +431,6 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
 
         TESTS::
 
-            sage: set_random_seed()
             sage: J = random_eja()
             sage: J(1)
             Traceback (most recent call last):
@@ -457,7 +455,6 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
 
         TESTS::
 
-            sage: set_random_seed()
             sage: J = random_eja()
             sage: n = J.dimension()
             sage: bi = J.zero()
@@ -499,7 +496,6 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
         Our inner product is "associative," which means the following for
         a symmetric bilinear form::
 
-            sage: set_random_seed()
             sage: J = random_eja()
             sage: x,y,z = J.random_elements(3)
             sage: (x*y).inner_product(z) == y.inner_product(x*z)
@@ -510,7 +506,6 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
         Ensure that this is the usual inner product for the algebras
         over `R^n`::
 
-            sage: set_random_seed()
             sage: J = HadamardEJA.random_instance()
             sage: x,y = J.random_elements(2)
             sage: actual = x.inner_product(y)
@@ -523,7 +518,6 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
         one). This is in Faraut and Koranyi, and also my "On the
         symmetry..." paper::
 
-            sage: set_random_seed()
             sage: J = BilinearFormEJA.random_instance()
             sage: n = J.dimension()
             sage: x = J.random_element()
@@ -636,7 +630,6 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
         The values we've presupplied to the constructors agree with
         the computation::
 
-            sage: set_random_seed()
             sage: J = random_eja()
             sage: J.is_associative() == J._jordan_product_is_associative()
             True
@@ -758,7 +751,6 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
         Ensure that we can convert any element back and forth
         faithfully between its matrix and algebra representations::
 
-            sage: set_random_seed()
             sage: J = random_eja()
             sage: x = J.random_element()
             sage: J(x.to_matrix()) == x
@@ -948,7 +940,6 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
         Our inner product is "associative," which means the following for
         a symmetric bilinear form::
 
-            sage: set_random_seed()
             sage: J = random_eja()
             sage: x,y,z = J.random_elements(3)
             sage: (x*y).inner_product(z) == y.inner_product(x*z)
@@ -959,7 +950,6 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
         Ensure that this is the usual inner product for the algebras
         over `R^n`::
 
-            sage: set_random_seed()
             sage: J = HadamardEJA.random_instance()
             sage: x,y = J.random_elements(2)
             sage: actual = x.inner_product(y)
@@ -972,7 +962,6 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
         one). This is in Faraut and Koranyi, and also my "On the
         symmetry..." paper::
 
-            sage: set_random_seed()
             sage: J = BilinearFormEJA.random_instance()
             sage: n = J.dimension()
             sage: x = J.random_element()
@@ -1200,7 +1189,6 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
         The identity element acts like the identity, regardless of
         whether or not we orthonormalize::
 
-            sage: set_random_seed()
             sage: J = random_eja()
             sage: x = J.random_element()
             sage: J.one()*x == x and x*J.one() == x
@@ -1212,7 +1200,6 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
 
         ::
 
-            sage: set_random_seed()
             sage: J = random_eja(field=QQ, orthonormalize=False)
             sage: x = J.random_element()
             sage: J.one()*x == x and x*J.one() == x
@@ -1226,7 +1213,6 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
         regardless of the base field and whether or not we
         orthonormalize::
 
-            sage: set_random_seed()
             sage: J = random_eja()
             sage: actual = J.one().operator().matrix()
             sage: expected = matrix.identity(J.base_ring(), J.dimension())
@@ -1241,7 +1227,6 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
 
         ::
 
-            sage: set_random_seed()
             sage: J = random_eja(field=QQ, orthonormalize=False)
             sage: actual = J.one().operator().matrix()
             sage: expected = matrix.identity(J.base_ring(), J.dimension())
@@ -1257,7 +1242,6 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
         Ensure that the cached unit element (often precomputed by
         hand) agrees with the computed one::
 
-            sage: set_random_seed()
             sage: J = random_eja()
             sage: cached = J.one()
             sage: J.one.clear_cache()
@@ -1266,7 +1250,6 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
 
         ::
 
-            sage: set_random_seed()
             sage: J = random_eja(field=QQ, orthonormalize=False)
             sage: cached = J.one()
             sage: J.one.clear_cache()
@@ -1379,7 +1362,6 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
         Every algebra decomposes trivially with respect to its identity
         element::
 
-            sage: set_random_seed()
             sage: J = random_eja()
             sage: J0,J5,J1 = J.peirce_decomposition(J.one())
             sage: J0.dimension() == 0 and J5.dimension() == 0
@@ -1392,7 +1374,6 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
         elements in the two subalgebras are the projections onto their
         respective subspaces of the superalgebra's identity element::
 
-            sage: set_random_seed()
             sage: J = random_eja()
             sage: x = J.random_element()
             sage: if not J.is_trivial():
@@ -1591,7 +1572,6 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
         The theory shows that these are all homogeneous polynomials of
         a known degree::
 
-            sage: set_random_seed()
             sage: J = random_eja()
             sage: all(p.is_homogeneous() for p in J._charpoly_coefficients())
             True
@@ -1682,7 +1662,6 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
         positive integer rank, unless the algebra is trivial in
         which case its rank will be zero::
 
-            sage: set_random_seed()
             sage: J = random_eja()
             sage: r = J.rank()
             sage: r in ZZ
@@ -1693,7 +1672,6 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
         Ensure that computing the rank actually works, since the ranks
         of all simple algebras are known and will be cached by default::
 
-            sage: set_random_seed()    # long time
             sage: J = random_eja()     # long time
             sage: cached = J.rank()    # long time
             sage: J.rank.clear_cache() # long time
@@ -1868,7 +1846,6 @@ class ConcreteEJA(FiniteDimensionalEJA):
     Our basis is normalized with respect to the algebra's inner
     product, unless we specify otherwise::
 
-        sage: set_random_seed()
         sage: J = ConcreteEJA.random_instance()
         sage: all( b.norm() == 1 for b in J.gens() )
         True
@@ -1879,7 +1856,6 @@ class ConcreteEJA(FiniteDimensionalEJA):
     natural->EJA basis representation is an isometry and within the
     EJA the operator is self-adjoint by the Jordan axiom::
 
-        sage: set_random_seed()
         sage: J = ConcreteEJA.random_instance()
         sage: x = J.random_element()
         sage: x.operator().is_self_adjoint()
@@ -1974,7 +1950,6 @@ class MatrixEJA(FiniteDimensionalEJA):
 
         TESTS::
 
-            sage: set_random_seed()
             sage: n = ZZ.random_element(1,5)
             sage: A = MatrixSpace(QQ, n)
             sage: B = MatrixEJA._denormalized_basis(A)
@@ -1983,7 +1958,6 @@ class MatrixEJA(FiniteDimensionalEJA):
 
         ::
 
-            sage: set_random_seed()
             sage: n = ZZ.random_element(1,5)
             sage: A = ComplexMatrixAlgebra(n, scalars=QQ)
             sage: B = MatrixEJA._denormalized_basis(A)
@@ -1992,7 +1966,6 @@ class MatrixEJA(FiniteDimensionalEJA):
 
         ::
 
-            sage: set_random_seed()
             sage: n = ZZ.random_element(1,5)
             sage: A = QuaternionMatrixAlgebra(n, scalars=QQ)
             sage: B = MatrixEJA._denormalized_basis(A)
@@ -2001,7 +1974,6 @@ class MatrixEJA(FiniteDimensionalEJA):
 
         ::
 
-            sage: set_random_seed()
             sage: n = ZZ.random_element(1,5)
             sage: A = OctonionMatrixAlgebra(n, scalars=QQ)
             sage: B = MatrixEJA._denormalized_basis(A)
@@ -2142,7 +2114,6 @@ class RealSymmetricEJA(MatrixEJA, RationalBasisEJA, ConcreteEJA):
 
     The dimension of this algebra is `(n^2 + n) / 2`::
 
-        sage: set_random_seed()
         sage: d = RealSymmetricEJA._max_random_instance_dimension()
         sage: n = RealSymmetricEJA._max_random_instance_size(d)
         sage: J = RealSymmetricEJA(n)
@@ -2151,7 +2122,6 @@ class RealSymmetricEJA(MatrixEJA, RationalBasisEJA, ConcreteEJA):
 
     The Jordan multiplication is what we think it is::
 
-        sage: set_random_seed()
         sage: J = RealSymmetricEJA.random_instance()
         sage: x,y = J.random_elements(2)
         sage: actual = (x*y).to_matrix()
@@ -2243,7 +2213,6 @@ class ComplexHermitianEJA(MatrixEJA, RationalBasisEJA, ConcreteEJA):
 
     The dimension of this algebra is `n^2`::
 
-        sage: set_random_seed()
         sage: d = ComplexHermitianEJA._max_random_instance_dimension()
         sage: n = ComplexHermitianEJA._max_random_instance_size(d)
         sage: J = ComplexHermitianEJA(n)
@@ -2252,7 +2221,6 @@ class ComplexHermitianEJA(MatrixEJA, RationalBasisEJA, ConcreteEJA):
 
     The Jordan multiplication is what we think it is::
 
-        sage: set_random_seed()
         sage: J = ComplexHermitianEJA.random_instance()
         sage: x,y = J.random_elements(2)
         sage: actual = (x*y).to_matrix()
@@ -2329,7 +2297,6 @@ class QuaternionHermitianEJA(MatrixEJA, RationalBasisEJA, ConcreteEJA):
 
     The dimension of this algebra is `2*n^2 - n`::
 
-        sage: set_random_seed()
         sage: d = QuaternionHermitianEJA._max_random_instance_dimension()
         sage: n = QuaternionHermitianEJA._max_random_instance_size(d)
         sage: J = QuaternionHermitianEJA(n)
@@ -2338,7 +2305,6 @@ class QuaternionHermitianEJA(MatrixEJA, RationalBasisEJA, ConcreteEJA):
 
     The Jordan multiplication is what we think it is::
 
-        sage: set_random_seed()
         sage: J = QuaternionHermitianEJA.random_instance()
         sage: x,y = J.random_elements(2)
         sage: actual = (x*y).to_matrix()
@@ -2711,7 +2677,6 @@ class BilinearFormEJA(RationalBasisEJA, ConcreteEJA):
     matrix.  We opt not to orthonormalize the basis, because if we
     did, we would have to normalize the `s_{i}` in a similar manner::
 
-        sage: set_random_seed()
         sage: n = ZZ.random_element(5)
         sage: M = matrix.random(QQ, max(0,n-1), algorithm='unimodular')
         sage: B11 = matrix.identity(QQ,1)
@@ -2873,7 +2838,6 @@ class JordanSpinEJA(BilinearFormEJA):
 
         Ensure that we have the usual inner product on `R^n`::
 
-            sage: set_random_seed()
             sage: J = JordanSpinEJA.random_instance()
             sage: x,y = J.random_elements(2)
             sage: actual = x.inner_product(y)
@@ -2994,7 +2958,6 @@ class CartesianProductEJA(FiniteDimensionalEJA):
     The Jordan product is inherited from our factors and implemented by
     our CombinatorialFreeModule Cartesian product superclass::
 
-        sage: set_random_seed()
         sage: J1 = HadamardEJA(2)
         sage: J2 = RealSymmetricEJA(2)
         sage: J = cartesian_product([J1,J2])
@@ -3131,7 +3094,6 @@ class CartesianProductEJA(FiniteDimensionalEJA):
 
     The cached unit element is the same one that would be computed::
 
-        sage: set_random_seed()              # long time
         sage: J1 = random_eja()              # long time
         sage: J2 = random_eja()              # long time
         sage: J = cartesian_product([J1,J2]) # long time
@@ -3350,7 +3312,6 @@ class CartesianProductEJA(FiniteDimensionalEJA):
 
         The answer never changes::
 
-            sage: set_random_seed()
             sage: J1 = random_eja()
             sage: J2 = random_eja()
             sage: J = cartesian_product([J1,J2])
@@ -3440,7 +3401,6 @@ class CartesianProductEJA(FiniteDimensionalEJA):
 
         The answer never changes::
 
-            sage: set_random_seed()
             sage: J1 = random_eja()
             sage: J2 = random_eja()
             sage: J = cartesian_product([J1,J2])
@@ -3453,7 +3413,6 @@ class CartesianProductEJA(FiniteDimensionalEJA):
         produce the identity map, and mismatching them should produce
         the zero map::
 
-            sage: set_random_seed()
             sage: J1 = random_eja()
             sage: J2 = random_eja()
             sage: J = cartesian_product([J1,J2])
@@ -3558,7 +3517,6 @@ def random_eja(max_dimension=None, *args, **kwargs):
 
     TESTS::
 
-        sage: set_random_seed()
         sage: n = ZZ.random_element(1,5)
         sage: J = random_eja(max_dimension=n, field=QQ, orthonormalize=False)
         sage: J.dimension() <= n