From: Michael Orlitzky <michael@orlitzky.com>
Date: Mon, 15 Nov 2021 18:53:29 +0000 (-0500)
Subject: mjo/**/*.py: drop obsolete set_random_seed().
X-Git-Url: http://gitweb.michael.orlitzky.com/?p=sage.d.git;a=commitdiff_plain;h=928b7d49fda98ff105c92293b5797bb7a2b9873a

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

We use a random random seed by default now finally.
---

diff --git a/mjo/basis_repr.py b/mjo/basis_repr.py
index 5c85998..9b9f15d 100644
--- a/mjo/basis_repr.py
+++ b/mjo/basis_repr.py
@@ -92,7 +92,6 @@ def basis_repr(M):
 
     The inverse is generally an inverse::
 
-        sage: set_random_seed()
         sage: n = ZZ.random_element(10)
         sage: M = MatrixSpace(QQ,n)
         sage: X = M.random_element()
diff --git a/mjo/cone/faces.py b/mjo/cone/faces.py
index acd9802..6c5843e 100644
--- a/mjo/cone/faces.py
+++ b/mjo/cone/faces.py
@@ -51,7 +51,6 @@ def face_generated_by(K,S):
 
     The face generated by <whatever> should be a face::
 
-        sage: set_random_seed()
         sage: K = random_cone(max_ambient_dim=8, max_rays=10)
         sage: S = ( K.random_element() for idx in range(5) )
         sage: F = face_generated_by(K, S)
@@ -60,7 +59,6 @@ def face_generated_by(K,S):
 
     The face generated by a set should always contain that set::
 
-        sage: set_random_seed()
         sage: K = random_cone(max_ambient_dim=8, max_rays=10)
         sage: S = ( K.random_element() for idx in range(5) )
         sage: F = face_generated_by(K, S)
@@ -70,7 +68,6 @@ def face_generated_by(K,S):
     The generators of a proper cone are all extreme vectors of the cone,
     and therefore generate their own faces::
 
-        sage: set_random_seed()
         sage: K = random_cone(max_ambient_dim=8,
         ....:                 max_rays=10,
         ....:                 strictly_convex=True,
@@ -82,7 +79,6 @@ def face_generated_by(K,S):
     that ``x`` is in the relative interior of ``F`` if and only if
     ``F`` is the face generated by ``x`` [Tam]_::
 
-        sage: set_random_seed()
         sage: K = random_cone(max_ambient_dim=8, max_rays=10)
         sage: x = K.random_element()
         sage: S = [x]
@@ -96,7 +92,6 @@ def face_generated_by(K,S):
     and ``G`` in the face lattice is equal to the face generated by
     ``F + G`` (in the Minkowski sense) [Tam]_::
 
-        sage: set_random_seed()
         sage: K = random_cone(max_ambient_dim=8, max_rays=10)
         sage: L = K.face_lattice()
         sage: F = L.random_element()
@@ -109,7 +104,6 @@ def face_generated_by(K,S):
     Combining Proposition 3.1 and Corollary 3.9 in [Tam]_ gives the
     following equality for any ``y`` in ``K``::
 
-        sage: set_random_seed()
         sage: K = random_cone(max_ambient_dim=8, max_rays=10)
         sage: y = K.random_element()
         sage: S = [y]
@@ -172,7 +166,6 @@ def dual_face(K,F):
     The dual face of ``K`` with respect to itself should be the
     lineality space of its dual [Tam]_::
 
-        sage: set_random_seed()
         sage: K = random_cone(max_ambient_dim=8, max_rays=10)
         sage: K_dual = K.dual()
         sage: lKd_gens = ( dir*l for dir in [1,-1] for l in K_dual.lines() )
@@ -183,7 +176,6 @@ def dual_face(K,F):
     If ``K`` is proper, then the dual face of its trivial face is the
     dual of ``K`` [Tam]_::
 
-        sage: set_random_seed()
         sage: K = random_cone(max_ambient_dim=8,
         ....:                 max_rays=10,
         ....:                 strictly_convex=True,
@@ -196,7 +188,6 @@ def dual_face(K,F):
     The dual of the cone of ``K`` at ``y`` is the dual face of the face
     of ``K`` generated by ``y`` ([Tam]_ Corollary 3.2)::
 
-        sage: set_random_seed()
         sage: K = random_cone(max_ambient_dim=8, max_rays=10)
         sage: y = K.random_element()
         sage: S = [y]
@@ -209,7 +200,6 @@ def dual_face(K,F):
     Since all faces of a polyhedral cone are exposed, the dual face of a
     dual face should be the original face [HilgertHofmannLawson]_::
 
-        sage: set_random_seed()
         sage: def check_prop(K,F):
         ....:     return dual_face(K.dual(), dual_face(K,F)).is_equivalent(F)
         sage: K = random_cone(max_ambient_dim=8, max_rays=10)
diff --git a/mjo/cone/nonnegative_orthant.py b/mjo/cone/nonnegative_orthant.py
index 8c6f5b5..2bd1b3c 100644
--- a/mjo/cone/nonnegative_orthant.py
+++ b/mjo/cone/nonnegative_orthant.py
@@ -48,7 +48,6 @@ def nonnegative_orthant(n, lattice=None):
 
     The nonnegative orthant is a proper cone::
 
-        sage: set_random_seed()
         sage: n = ZZ.random_element(10)
         sage: K = nonnegative_orthant(n)
         sage: K.is_proper()
diff --git a/mjo/cone/permutation_invariant.py b/mjo/cone/permutation_invariant.py
index faa39f7..d071586 100644
--- a/mjo/cone/permutation_invariant.py
+++ b/mjo/cone/permutation_invariant.py
@@ -65,7 +65,6 @@ def is_permutation_invariant(K):
 
     As is the nonnegative orthant::
 
-        sage: set_random_seed()
         sage: K = nonnegative_orthant(ZZ.random_element(5))
         sage: is_permutation_invariant(K)
         True
diff --git a/mjo/cone/rearrangement.py b/mjo/cone/rearrangement.py
index c65316e..0bbf95b 100644
--- a/mjo/cone/rearrangement.py
+++ b/mjo/cone/rearrangement.py
@@ -116,7 +116,6 @@ def rearrangement_cone(p,n,lattice=None):
     cone should sum to a nonnegative number (this tests that the
     generators really are what we think they are)::
 
-        sage: set_random_seed()
         sage: def _has_rearrangement_property(v,p):
         ....:     return sum( sorted(v)[0:p] ) >= 0
         sage: all( _has_rearrangement_property(
@@ -131,7 +130,6 @@ def rearrangement_cone(p,n,lattice=None):
     The rearrangenent cone of order ``p`` is contained in the rearrangement
     cone of order ``p + 1`` by [Jeong]_ Proposition 5.2.1::
 
-        sage: set_random_seed()
         sage: n = ZZ.random_element(2,10)
         sage: p = ZZ.random_element(1,n)
         sage: K1 = rearrangement_cone(p,n)
@@ -143,7 +141,6 @@ def rearrangement_cone(p,n,lattice=None):
     rearrangement cone of order ``n - p`` when ``p`` is less than ``n``,
     by [Jeong]_ Proposition 5.2.1::
 
-        sage: set_random_seed()
         sage: n = ZZ.random_element(2,10)
         sage: p = ZZ.random_element(1,n)
         sage: K1 = rearrangement_cone(p,n)
diff --git a/mjo/cone/schur.py b/mjo/cone/schur.py
index edf282d..1fa1e52 100644
--- a/mjo/cone/schur.py
+++ b/mjo/cone/schur.py
@@ -65,7 +65,6 @@ def schur_cone(n, lattice=None):
     [GourionSeeger]_, whose elements' entries are in non-increasing
     order::
 
-        sage: set_random_seed()
         sage: n = ZZ.random_element(10)
         sage: K = schur_cone(n).dual()
         sage: x = K.random_element()
@@ -81,7 +80,6 @@ def schur_cone(n, lattice=None):
 
     The Schur cone induces the majorization ordering::
 
-        sage: set_random_seed()
         sage: def majorized_by(x,y):
         ....:     return (all(sum(x[0:i]) <= sum(y[0:i])
         ....:                 for i in range(x.degree()-1))
diff --git a/mjo/cone/symmetric_pd.py b/mjo/cone/symmetric_pd.py
index e396bbc..607df2a 100644
--- a/mjo/cone/symmetric_pd.py
+++ b/mjo/cone/symmetric_pd.py
@@ -38,7 +38,6 @@ def random_symmetric_pd(V):
 
     Well, it doesn't crash at least::
 
-        sage: set_random_seed()
         sage: V = VectorSpace(QQ, 2)
         sage: A = random_symmetric_pd(V)
         sage: A.matrix_space()
diff --git a/mjo/cone/symmetric_psd.py b/mjo/cone/symmetric_psd.py
index 89eba53..d711773 100644
--- a/mjo/cone/symmetric_psd.py
+++ b/mjo/cone/symmetric_psd.py
@@ -191,7 +191,6 @@ def random_symmetric_psd(V, accept_zero=True, rank=None):
 
     Well, it doesn't crash at least::
 
-        sage: set_random_seed()
         sage: V = VectorSpace(QQ, 2)
         sage: A = random_symmetric_psd(V)
         sage: A.matrix_space()
@@ -201,7 +200,6 @@ def random_symmetric_psd(V, accept_zero=True, rank=None):
 
     A matrix with the desired rank is returned::
 
-        sage: set_random_seed()
         sage: V = VectorSpace(QQ, 5)
         sage: A = random_symmetric_psd(V,False,1)
         sage: A.rank()
@@ -221,7 +219,6 @@ def random_symmetric_psd(V, accept_zero=True, rank=None):
 
     If the user asks for a rank that's too high, we fail::
 
-        sage: set_random_seed()
         sage: V = VectorSpace(QQ, 2)
         sage: A = random_symmetric_psd(V,False,3)
         Traceback (most recent call last):
diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index dd1bcf2..1ccbf2e 100644
--- 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
diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index 47f6ff0..0fd1c5f 100644
--- a/mjo/eja/eja_element.py
+++ b/mjo/eja/eja_element.py
@@ -43,14 +43,12 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
 
         The definition of `x^2` is the unambiguous `x*x`::
 
-            sage: set_random_seed()
             sage: x = random_eja().random_element()
             sage: x*x == (x^2)
             True
 
         A few examples of power-associativity::
 
-            sage: set_random_seed()
             sage: x = random_eja().random_element()
             sage: x*(x*x)*(x*x) == x^5
             True
@@ -60,7 +58,6 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
         We also know that powers operator-commute (Koecher, Chapter
         III, Corollary 1)::
 
-            sage: set_random_seed()
             sage: x = random_eja().random_element()
             sage: m = ZZ.random_element(0,10)
             sage: n = ZZ.random_element(0,10)
@@ -107,7 +104,6 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
 
         We should always get back an element of the algebra::
 
-            sage: set_random_seed()
             sage: p = PolynomialRing(AA, 't').random_element()
             sage: J = random_eja()
             sage: x = J.random_element()
@@ -157,7 +153,6 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
         The characteristic polynomial of an element should evaluate
         to zero on that element::
 
-            sage: set_random_seed()
             sage: x = random_eja().random_element()
             sage: p = x.characteristic_polynomial()
             sage: x.apply_univariate_polynomial(p).is_zero()
@@ -239,7 +234,6 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
         Ensure that we can always compute an inner product, and that
         it gives us back a real number::
 
-            sage: set_random_seed()
             sage: J = random_eja()
             sage: x,y = J.random_elements(2)
             sage: x.inner_product(y) in RLF
@@ -267,7 +261,6 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
         The definition of a Jordan algebra says that any element
         operator-commutes with its square::
 
-            sage: set_random_seed()
             sage: x = random_eja().random_element()
             sage: x.operator_commutes_with(x^2)
             True
@@ -276,7 +269,6 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
 
         Test Lemma 1 from Chapter III of Koecher::
 
-            sage: set_random_seed()
             sage: u,v = random_eja().random_elements(2)
             sage: lhs = u.operator_commutes_with(u*v)
             sage: rhs = v.operator_commutes_with(u^2)
@@ -286,7 +278,6 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
         Test the first polarization identity from my notes, Koecher
         Chapter III, or from Baes (2.3)::
 
-            sage: set_random_seed()
             sage: x,y = random_eja().random_elements(2)
             sage: Lx = x.operator()
             sage: Ly = y.operator()
@@ -298,7 +289,6 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
         Test the second polarization identity from my notes or from
         Baes (2.4)::
 
-            sage: set_random_seed()
             sage: x,y,z = random_eja().random_elements(3)
             sage: Lx = x.operator()
             sage: Ly = y.operator()
@@ -312,7 +302,6 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
         Test the third polarization identity from my notes or from
         Baes (2.5)::
 
-            sage: set_random_seed()
             sage: u,y,z = random_eja().random_elements(3)
             sage: Lu = u.operator()
             sage: Ly = y.operator()
@@ -377,7 +366,6 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
         An element is invertible if and only if its determinant is
         non-zero::
 
-            sage: set_random_seed()
             sage: x = random_eja().random_element()
             sage: x.is_invertible() == (x.det() != 0)
             True
@@ -385,7 +373,6 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
         Ensure that the determinant is multiplicative on an associative
         subalgebra as in Faraut and Korányi's Proposition II.2.2::
 
-            sage: set_random_seed()
             sage: J = random_eja().random_element().subalgebra_generated_by()
             sage: x,y = J.random_elements(2)
             sage: (x*y).det() == x.det()*y.det()
@@ -393,7 +380,6 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
 
         The determinant in real matrix algebras is the usual determinant::
 
-            sage: set_random_seed()
             sage: X = matrix.random(QQ,3)
             sage: X = X + X.T
             sage: J1 = RealSymmetricEJA(3)
@@ -450,7 +436,6 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
         The inverse in the spin factor algebra is given in Alizadeh's
         Example 11.11::
 
-            sage: set_random_seed()
             sage: J = JordanSpinEJA.random_instance()
             sage: x = J.random_element()
             sage: while not x.is_invertible():
@@ -475,14 +460,12 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
 
         The identity element is its own inverse::
 
-            sage: set_random_seed()
             sage: J = random_eja()
             sage: J.one().inverse() == J.one()
             True
 
         If an element has an inverse, it acts like one::
 
-            sage: set_random_seed()
             sage: J = random_eja()
             sage: x = J.random_element()
             sage: (not x.is_invertible()) or (x.inverse()*x == J.one())
@@ -490,7 +473,6 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
 
         The inverse of the inverse is what we started with::
 
-            sage: set_random_seed()
             sage: J = random_eja()
             sage: x = J.random_element()
             sage: (not x.is_invertible()) or (x.inverse().inverse() == x)
@@ -500,7 +482,6 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
         of an element is the inverse of its left-multiplication operator
         applied to the algebra's identity, when that inverse exists::
 
-            sage: set_random_seed()
             sage: J = random_eja()
             sage: x = J.random_element()
             sage: (not x.operator().is_invertible()) or (
@@ -510,7 +491,6 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
         Check that the fast (cached) and slow algorithms give the same
         answer::
 
-            sage: set_random_seed()                              # long time
             sage: J = random_eja(field=QQ, orthonormalize=False) # long time
             sage: x = J.random_element()                         # long time
             sage: while not x.is_invertible():                   # long time
@@ -562,14 +542,12 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
 
         The identity element is always invertible::
 
-            sage: set_random_seed()
             sage: J = random_eja()
             sage: J.one().is_invertible()
             True
 
         The zero element is never invertible in a non-trivial algebra::
 
-            sage: set_random_seed()
             sage: J = random_eja()
             sage: (not J.is_trivial()) and J.zero().is_invertible()
             False
@@ -577,7 +555,6 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
         Test that the fast (cached) and slow algorithms give the same
         answer::
 
-            sage: set_random_seed()                              # long time
             sage: J = random_eja(field=QQ, orthonormalize=False) # long time
             sage: x = J.random_element()                         # long time
             sage: slow = x.is_invertible()                       # long time
@@ -660,14 +637,12 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
 
         The identity element is minimal only in an EJA of rank one::
 
-            sage: set_random_seed()
             sage: J = random_eja()
             sage: J.rank() == 1 or not J.one().is_primitive_idempotent()
             True
 
         A non-idempotent cannot be a minimal idempotent::
 
-            sage: set_random_seed()
             sage: J = JordanSpinEJA(4)
             sage: x = J.random_element()
             sage: (not x.is_idempotent()) and x.is_primitive_idempotent()
@@ -677,7 +652,6 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
         idempotent if and only if it's idempotent with trace equal to
         unity::
 
-            sage: set_random_seed()
             sage: J = JordanSpinEJA(4)
             sage: x = J.random_element()
             sage: expected = (x.is_idempotent() and x.trace() == 1)
@@ -687,7 +661,6 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
 
         Primitive idempotents must be non-zero::
 
-            sage: set_random_seed()
             sage: J = random_eja()
             sage: J.zero().is_idempotent()
             True
@@ -744,14 +717,12 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
 
         The identity element is never nilpotent, except in a trivial EJA::
 
-            sage: set_random_seed()
             sage: J = random_eja()
             sage: J.one().is_nilpotent() and not J.is_trivial()
             False
 
         The additive identity is always nilpotent::
 
-            sage: set_random_seed()
             sage: random_eja().zero().is_nilpotent()
             True
 
@@ -794,7 +765,6 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
         The zero element should never be regular, unless the parent
         algebra has dimension less than or equal to one::
 
-            sage: set_random_seed()
             sage: J = random_eja()
             sage: J.dimension() <= 1 or not J.zero().is_regular()
             True
@@ -802,7 +772,6 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
         The unit element isn't regular unless the algebra happens to
         consist of only its scalar multiples::
 
-            sage: set_random_seed()
             sage: J = random_eja()
             sage: J.dimension() <= 1 or not J.one().is_regular()
             True
@@ -837,7 +806,6 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
         In the spin factor algebra (of rank two), all elements that
         aren't multiples of the identity are regular::
 
-            sage: set_random_seed()
             sage: J = JordanSpinEJA.random_instance()
             sage: n = J.dimension()
             sage: x = J.random_element()
@@ -849,7 +817,6 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
         The zero and unit elements are both of degree one in nontrivial
         algebras::
 
-            sage: set_random_seed()
             sage: J = random_eja()
             sage: d = J.zero().degree()
             sage: (J.is_trivial() and d == 0) or d == 1
@@ -860,7 +827,6 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
 
         Our implementation agrees with the definition::
 
-            sage: set_random_seed()
             sage: x = random_eja().random_element()
             sage: x.degree() == x.minimal_polynomial().degree()
             True
@@ -969,7 +935,6 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
         always the same, except in trivial algebras where the minimal
         polynomial of the unit/zero element is ``1``::
 
-            sage: set_random_seed()
             sage: J = random_eja()
             sage: mu = J.one().minimal_polynomial()
             sage: t = mu.parent().gen()
@@ -983,7 +948,6 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
         The degree of an element is (by one definition) the degree
         of its minimal polynomial::
 
-            sage: set_random_seed()
             sage: x = random_eja().random_element()
             sage: x.degree() == x.minimal_polynomial().degree()
             True
@@ -994,7 +958,6 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
         identity. We require the dimension of the algebra to be at least
         two here so that said elements actually exist::
 
-            sage: set_random_seed()
             sage: d_max = JordanSpinEJA._max_random_instance_dimension()
             sage: n = ZZ.random_element(2, max(2,d_max))
             sage: J = JordanSpinEJA(n)
@@ -1011,7 +974,6 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
 
         The minimal polynomial should always kill its element::
 
-            sage: set_random_seed()
             sage: x = random_eja().random_element()
             sage: p = x.minimal_polynomial()
             sage: x.apply_univariate_polynomial(p)
@@ -1020,7 +982,6 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
         The minimal polynomial is invariant under a change of basis,
         and in particular, a re-scaling of the basis::
 
-            sage: set_random_seed()
             sage: d_max = RealSymmetricEJA._max_random_instance_dimension()
             sage: d = ZZ.random_element(1, d_max)
             sage: n = RealSymmetricEJA._max_random_instance_size(d)
@@ -1167,7 +1128,6 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
 
         TESTS::
 
-            sage: set_random_seed()
             sage: J = random_eja()
             sage: x,y = J.random_elements(2)
             sage: x.operator()(y) == x*y
@@ -1196,7 +1156,6 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
         The explicit form in the spin factor algebra is given by
         Alizadeh's Example 11.12::
 
-            sage: set_random_seed()
             sage: x = JordanSpinEJA.random_instance().random_element()
             sage: x_vec = x.to_vector()
             sage: Q = matrix.identity(x.base_ring(), 0)
@@ -1216,7 +1175,6 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
 
         Test all of the properties from Theorem 11.2 in Alizadeh::
 
-            sage: set_random_seed()
             sage: J = random_eja()
             sage: x,y = J.random_elements(2)
             sage: Lx = x.operator()
@@ -1410,7 +1368,6 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
 
         This subalgebra, being composed of only powers, is associative::
 
-            sage: set_random_seed()
             sage: x0 = random_eja().random_element()
             sage: A = x0.subalgebra_generated_by()
             sage: x,y,z = A.random_elements(3)
@@ -1420,7 +1377,6 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
         Squaring in the subalgebra should work the same as in
         the superalgebra::
 
-            sage: set_random_seed()
             sage: x = random_eja().random_element()
             sage: A = x.subalgebra_generated_by()
             sage: A(x^2) == A(x)*A(x)
@@ -1431,7 +1387,6 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
         element... unless the original algebra was trivial, in which
         case the subalgebra is trivial too::
 
-            sage: set_random_seed()
             sage: A = random_eja().zero().subalgebra_generated_by()
             sage: (A.is_trivial() and A.dimension() == 0) or A.dimension() == 1
             True
@@ -1462,7 +1417,6 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
         where there are non-nilpotent elements, or that we get the dumb
         solution in the trivial algebra::
 
-            sage: set_random_seed()
             sage: J = random_eja()
             sage: x = J.random_element()
             sage: while x.is_nilpotent() and not J.is_trivial():
@@ -1546,14 +1500,12 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
 
         The trace of an element is a real number::
 
-            sage: set_random_seed()
             sage: J = random_eja()
             sage: J.random_element().trace() in RLF
             True
 
         The trace is linear::
 
-            sage: set_random_seed()
             sage: J = random_eja()
             sage: x,y = J.random_elements(2)
             sage: alpha = J.base_ring().random_element()
@@ -1589,7 +1541,6 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
 
         The trace inner product is commutative, bilinear, and associative::
 
-            sage: set_random_seed()
             sage: J = random_eja()
             sage: x,y,z = J.random_elements(3)
             sage: # commutative
diff --git a/mjo/eja/eja_operator.py b/mjo/eja/eja_operator.py
index 7100ea6..a8beed6 100644
--- a/mjo/eja/eja_operator.py
+++ b/mjo/eja/eja_operator.py
@@ -470,7 +470,6 @@ class FiniteDimensionalEJAOperator(Map):
         The left-multiplication-by-zero operation on a given algebra
         is its zero map::
 
-            sage: set_random_seed()
             sage: J = random_eja()
             sage: J.zero().operator().is_zero()
             True
@@ -510,7 +509,6 @@ class FiniteDimensionalEJAOperator(Map):
 
         The identity operator is its own inverse::
 
-            sage: set_random_seed()
             sage: J = random_eja()
             sage: idJ = J.one().operator()
             sage: idJ.inverse() == idJ
@@ -518,7 +516,6 @@ class FiniteDimensionalEJAOperator(Map):
 
         The inverse of the inverse is the operator we started with::
 
-            sage: set_random_seed()
             sage: x = random_eja().random_element()
             sage: L = x.operator()
             sage: not L.is_invertible() or (L.inverse().inverse() == L)
@@ -561,14 +558,12 @@ class FiniteDimensionalEJAOperator(Map):
 
         The identity operator is always invertible::
 
-            sage: set_random_seed()
             sage: J = random_eja()
             sage: J.one().operator().is_invertible()
             True
 
         The zero operator is never invertible in a nontrivial algebra::
 
-            sage: set_random_seed()
             sage: J = random_eja()
             sage: not J.is_trivial() and J.zero().operator().is_invertible()
             False
diff --git a/mjo/eja/eja_subalgebra.py b/mjo/eja/eja_subalgebra.py
index c8bf548..1286a16 100644
--- a/mjo/eja/eja_subalgebra.py
+++ b/mjo/eja/eja_subalgebra.py
@@ -15,7 +15,6 @@ class FiniteDimensionalEJASubalgebraElement(FiniteDimensionalEJAElement):
     The matrix representation of an element in the subalgebra is
     the same as its matrix representation in the superalgebra::
 
-        sage: set_random_seed()
         sage: x = random_eja(field=QQ,orthonormalize=False).random_element()
         sage: A = x.subalgebra_generated_by(orthonormalize=False)
         sage: y = A.random_element()
@@ -28,7 +27,6 @@ class FiniteDimensionalEJASubalgebraElement(FiniteDimensionalEJAElement):
     works like it does in the superalgebra, even if we orthonormalize
     our basis::
 
-        sage: set_random_seed()
         sage: x = random_eja(field=AA).random_element()
         sage: A = x.subalgebra_generated_by(orthonormalize=True)
         sage: y = A.random_element()
@@ -71,7 +69,6 @@ class FiniteDimensionalEJASubalgebraElement(FiniteDimensionalEJAElement):
 
         We can convert back and forth faithfully::
 
-            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)
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
diff --git a/mjo/matrix_algebra.py b/mjo/matrix_algebra.py
index 69d9aeb..bc46c2a 100644
--- a/mjo/matrix_algebra.py
+++ b/mjo/matrix_algebra.py
@@ -148,7 +148,6 @@ class MatrixAlgebraElement(IndexedFreeModuleElement):
 
         TESTS::
 
-            sage: set_random_seed()
             sage: entries = QuaternionAlgebra(QQ,-1,-1)
             sage: M = MatrixAlgebra(3, entries, QQ)
             sage: M.random_element().matrix_space() == M
diff --git a/mjo/polynomial.py b/mjo/polynomial.py
index 55ada9a..e50fece 100644
--- a/mjo/polynomial.py
+++ b/mjo/polynomial.py
@@ -135,7 +135,6 @@ def multidiv(f, gs):
     If we get a zero remainder, then the numerator should belong to
     the ideal generated by the denominators::
 
-        sage: set_random_seed()
         sage: R = PolynomialRing(QQ, 'x,y,z')
         sage: x,y,z = R.gens()
         sage: s = ZZ.random_element(1,5).abs()
@@ -150,7 +149,6 @@ def multidiv(f, gs):
     times the denominators, and the remainder's monomials aren't divisible
     by the leading term of any denominator::
 
-        sage: set_random_seed()
         sage: R = PolynomialRing(QQ, 'x,y,z')
         sage: s = ZZ.random_element(1,5).abs()
         sage: gs = [ R.random_element() for idx in range(s) ]
@@ -167,7 +165,6 @@ def multidiv(f, gs):
     should always get a zero remainder if we divide an element of a
     monomial ideal by its generators::
 
-        sage: set_random_seed()
         sage: R = PolynomialRing(QQ,'x,y,z')
         sage: gs = R.random_element().monomials()
         sage: I = R.ideal(gs)