X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_algebra.py;h=725cd7132343ee6f3ba5769d8053aaff32501560;hb=73ba2d67c0850074e655b4da61aa021e6d9b6816;hp=515e25f9c97de0ae102e8dc6bd7b29db89e39dd0;hpb=f0f0e4c8277496289e86ba97caceea496763870e;p=sage.d.git diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py index 515e25f..725cd71 100644 --- a/mjo/eja/eja_algebra.py +++ b/mjo/eja/eja_algebra.py @@ -16,12 +16,9 @@ from sage.misc.cachefunc import cached_method from sage.misc.prandom import choice from sage.misc.table import table from sage.modules.free_module import FreeModule, VectorSpace -from sage.rings.integer_ring import ZZ -from sage.rings.number_field.number_field import QuadraticField -from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing -from sage.rings.rational_field import QQ -from sage.rings.real_lazy import CLF, RLF - +from sage.rings.all import (ZZ, QQ, RR, RLF, CLF, + PolynomialRing, + QuadraticField) from mjo.eja.eja_element import FiniteDimensionalEuclideanJordanAlgebraElement from mjo.eja.eja_utils import _mat2vec @@ -40,11 +37,12 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule): rank, prefix='e', category=None, - natural_basis=None): + natural_basis=None, + check=True): """ SETUP:: - sage: from mjo.eja.eja_algebra import random_eja + sage: from mjo.eja.eja_algebra import (JordanSpinEJA, random_eja) EXAMPLES: @@ -56,7 +54,23 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule): sage: x*y == y*x True + TESTS: + + The ``field`` we're given must be real:: + + sage: JordanSpinEJA(2,QQbar) + Traceback (most recent call last): + ... + ValueError: field is not real + """ + if check: + if not field.is_subring(RR): + # Note: this does return true for the real algebraic + # field, and any quadratic field where we've specified + # a real embedding. + raise ValueError('field is not real') + self._rank = rank self._natural_basis = natural_basis @@ -237,7 +251,10 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule): """ (A_of_x, x, xr, detA) = self._charpoly_matrix_system() R = A_of_x.base_ring() - if i >= self.rank(): + + if i == self.rank(): + return R.one() + if i > self.rank(): # Guaranteed by theory return R.zero() @@ -364,8 +381,8 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule): r = self.rank() n = self.dimension() - # The list of coefficient polynomials a_1, a_2, ..., a_n. - a = [ self._charpoly_coeff(i) for i in range(n) ] + # The list of coefficient polynomials a_0, a_1, a_2, ..., a_n. + a = [ self._charpoly_coeff(i) for i in range(r+1) ] # We go to a bit of trouble here to reorder the # indeterminates, so that it's easier to evaluate the @@ -377,17 +394,6 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule): S = PolynomialRing(S, R.variable_names()) t = S(t) - # Note: all entries past the rth should be zero. The - # coefficient of the highest power (x^r) is 1, but it doesn't - # appear in the solution vector which contains coefficients - # for the other powers (to make them sum to x^r). - if (r < n): - a[r] = 1 # corresponds to x^r - else: - # When the rank is equal to the dimension, trying to - # assign a[r] goes out-of-bounds. - a.append(1) # corresponds to x^r - return sum( a[k]*(t**k) for k in xrange(len(a)) ) @@ -435,9 +441,6 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule): sage: J = ComplexHermitianEJA(3) sage: J.is_trivial() False - sage: A = J.zero().subalgebra_generated_by() - sage: A.is_trivial() - True """ return self.dimension() == 0 @@ -611,14 +614,6 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule): return self.linear_combination(zip(self.gens(), coeffs)) - def random_element(self): - # Temporary workaround for https://trac.sagemath.org/ticket/28327 - if self.is_trivial(): - return self.zero() - else: - s = super(FiniteDimensionalEuclideanJordanAlgebra, self) - return s.random_element() - def random_elements(self, count): """ Return ``count`` random elements as a tuple. @@ -683,11 +678,15 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule): TESTS: Ensure that every EJA that we know how to construct has a - positive integer rank:: + positive integer rank, unless the algebra is trivial in + which case its rank will be zero:: sage: set_random_seed() - sage: r = random_eja().rank() - sage: r in ZZ and r > 0 + sage: J = random_eja() + sage: r = J.rank() + sage: r in ZZ + True + sage: r > 0 or (r == 0 and J.is_trivial()) True """ @@ -838,7 +837,7 @@ class RealCartesianProductEJA(FiniteDimensionalEuclideanJordanAlgebra, return x.to_vector().inner_product(y.to_vector()) -def random_eja(): +def random_eja(field=QQ): """ Return a "random" finite-dimensional Euclidean Jordan Algebra. @@ -875,7 +874,7 @@ def random_eja(): """ classname = choice(KnownRankEJA.__subclasses__()) - return classname.random_instance() + return classname.random_instance(field=field) @@ -1223,15 +1222,17 @@ class ComplexMatrixEuclideanJordanAlgebra(MatrixEuclideanJordanAlgebra): n = M.nrows() if M.ncols() != n: raise ValueError("the matrix 'M' must be square") - field = M.base_ring() + + # We don't need any adjoined elements... + field = M.base_ring().base_ring() + blocks = [] for z in M.list(): - a = z.vector()[0] # real part, I guess - b = z.vector()[1] # imag part, I guess + a = z.list()[0] # real part, I guess + b = z.list()[1] # imag part, I guess blocks.append(matrix(field, 2, [[a,b],[-b,a]])) - # We can drop the imaginaries here. - return matrix.block(field.base_ring(), n, blocks) + return matrix.block(field, n, blocks) @staticmethod @@ -1338,6 +1339,16 @@ class ComplexHermitianEJA(ComplexMatrixEuclideanJordanAlgebra, KnownRankEJA): sage: from mjo.eja.eja_algebra import ComplexHermitianEJA + EXAMPLES: + + In theory, our "field" can be any subfield of the reals:: + + sage: ComplexHermitianEJA(2, AA) + Euclidean Jordan algebra of dimension 4 over Algebraic Real Field + sage: ComplexHermitianEJA(2, RR) + Euclidean Jordan algebra of dimension 4 over Real Field with + 53 bits of precision + TESTS: The dimension of this algebra is `n^2`:: @@ -1623,6 +1634,16 @@ class QuaternionHermitianEJA(QuaternionMatrixEuclideanJordanAlgebra, sage: from mjo.eja.eja_algebra import QuaternionHermitianEJA + EXAMPLES: + + In theory, our "field" can be any subfield of the reals:: + + sage: QuaternionHermitianEJA(2, AA) + Euclidean Jordan algebra of dimension 6 over Algebraic Real Field + sage: QuaternionHermitianEJA(2, RR) + Euclidean Jordan algebra of dimension 6 over Real Field with + 53 bits of precision + TESTS: The dimension of this algebra is `2*n^2 - n`::