Example 11.11::
sage: set_random_seed()
- sage: n = ZZ.random_element(1,10)
- sage: J = JordanSpinEJA(n)
+ sage: J = JordanSpinEJA.random_instance()
sage: x = J.random_element()
sage: while not x.is_invertible():
....: x = J.random_element()
aren't multiples of the identity are regular::
sage: set_random_seed()
- sage: n = ZZ.random_element(1,10)
- sage: J = JordanSpinEJA(n)
+ sage: J = JordanSpinEJA.random_instance()
sage: x = J.random_element()
sage: x == x.coefficient(0)*J.one() or x.degree() == 2
True
The minimal polynomial and the characteristic polynomial coincide
and are known (see Alizadeh, Example 11.11) for all elements of
the spin factor algebra that aren't scalar multiples of the
- identity::
+ 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: n = ZZ.random_element(2,10)
+ sage: n_max = max(2, JordanSpinEJA._max_test_case_size())
+ sage: n = ZZ.random_element(2, n_max)
sage: J = JordanSpinEJA(n)
sage: y = J.random_element()
sage: while y == y.coefficient(0)*J.one():
and in particular, a re-scaling of the basis::
sage: set_random_seed()
- sage: n = ZZ.random_element(1,5)
- sage: J1 = RealSymmetricEJA(n)
+ sage: n_max = RealSymmetricEJA._max_test_case_size()
+ sage: n = ZZ.random_element(1, n_max)
+ sage: J1 = RealSymmetricEJA(n,QQ)
sage: J2 = RealSymmetricEJA(n,QQ,False)
sage: X = random_matrix(QQ,n)
sage: X = X*X.transpose()
Alizadeh's Example 11.12::
sage: set_random_seed()
- sage: n = ZZ.random_element(1,10)
- sage: J = JordanSpinEJA(n)
- sage: x = J.random_element()
+ sage: x = JordanSpinEJA.random_instance().random_element()
sage: x_vec = x.to_vector()
+ sage: n = x_vec.degree()
sage: x0 = x_vec[0]
sage: x_bar = x_vec[1:]
sage: A = matrix(QQ, 1, [x_vec.inner_product(x_vec)])