X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_element_subalgebra.py;h=7cf3f3702adb5832a7ef4bb86a80b24431d87a54;hb=008446f3a13b4fc117e1adfbc66f86784a6495c9;hp=2a82940f51c47c44aea0efdc47a202c243319ba6;hpb=d6d7353ccdcd1ab58c5f0e4621cb114e4a8c65ed;p=sage.d.git diff --git a/mjo/eja/eja_element_subalgebra.py b/mjo/eja/eja_element_subalgebra.py index 2a82940..7cf3f37 100644 --- a/mjo/eja/eja_element_subalgebra.py +++ b/mjo/eja/eja_element_subalgebra.py @@ -1,132 +1,15 @@ from sage.matrix.constructor import matrix -from mjo.eja.eja_algebra import FiniteDimensionalEuclideanJordanAlgebra -from mjo.eja.eja_element import FiniteDimensionalEuclideanJordanAlgebraElement +from mjo.eja.eja_subalgebra import FiniteDimensionalEuclideanJordanSubalgebra -class FiniteDimensionalEuclideanJordanElementSubalgebraElement(FiniteDimensionalEuclideanJordanAlgebraElement): - """ - SETUP:: - sage: from mjo.eja.eja_algebra import random_eja - - TESTS:: - - The natural representation of an element in the subalgebra is - the same as its natural representation in the superalgebra:: - - sage: set_random_seed() - sage: A = random_eja().random_element().subalgebra_generated_by() - sage: y = A.random_element() - sage: actual = y.natural_representation() - sage: expected = y.superalgebra_element().natural_representation() - sage: actual == expected - True - - The left-multiplication-by operator for elements in the subalgebra - works like it does in the superalgebra, even if we orthonormalize - our basis:: - - sage: set_random_seed() - sage: x = random_eja(AA).random_element() - sage: A = x.subalgebra_generated_by(orthonormalize_basis=True) - sage: y = A.random_element() - sage: y.operator()(A.one()) == y - True - - """ - - def superalgebra_element(self): - """ - Return the object in our algebra's superalgebra that corresponds - to myself. - - SETUP:: - - sage: from mjo.eja.eja_algebra import (RealSymmetricEJA, - ....: random_eja) - - EXAMPLES:: - - sage: J = RealSymmetricEJA(3) - sage: x = sum(J.gens()) - sage: x - e0 + e1 + e2 + e3 + e4 + e5 - sage: A = x.subalgebra_generated_by() - sage: A(x) - f1 - sage: A(x).superalgebra_element() - e0 + e1 + e2 + e3 + e4 + e5 - - TESTS: - - We can convert back and forth faithfully:: - - sage: set_random_seed() - sage: J = random_eja() - sage: x = J.random_element() - sage: A = x.subalgebra_generated_by() - sage: A(x).superalgebra_element() == x - True - sage: y = A.random_element() - sage: A(y.superalgebra_element()) == y - True - - """ - return self.parent().superalgebra().linear_combination( - zip(self.parent()._superalgebra_basis, self.to_vector()) ) - - - - -class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclideanJordanAlgebra): - """ - The subalgebra of an EJA generated by a single element. - - SETUP:: - - sage: from mjo.eja.eja_algebra import (ComplexHermitianEJA, - ....: JordanSpinEJA) - - TESTS: - - Ensure that our generator names don't conflict with the superalgebra:: - - sage: J = JordanSpinEJA(3) - sage: J.one().subalgebra_generated_by().gens() - (f0,) - sage: J = JordanSpinEJA(3, prefix='f') - sage: J.one().subalgebra_generated_by().gens() - (g0,) - sage: J = JordanSpinEJA(3, prefix='b') - sage: J.one().subalgebra_generated_by().gens() - (c0,) - - Ensure that we can find subalgebras of subalgebras:: - - sage: A = ComplexHermitianEJA(3).one().subalgebra_generated_by() - sage: B = A.one().subalgebra_generated_by() - sage: B.dimension() - 1 - - """ +class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclideanJordanSubalgebra): def __init__(self, elt, orthonormalize_basis): self._superalgebra = elt.parent() category = self._superalgebra.category().Associative() V = self._superalgebra.vector_space() field = self._superalgebra.base_ring() - # A half-assed attempt to ensure that we don't collide with - # the superalgebra's prefix (ignoring the fact that there - # could be super-superelgrbas in scope). If possible, we - # try to "increment" the parent algebra's prefix, although - # this idea goes out the window fast because some prefixen - # are off-limits. - prefixen = [ 'f', 'g', 'h', 'a', 'b', 'c', 'd' ] - try: - prefix = prefixen[prefixen.index(self._superalgebra.prefix()) + 1] - except ValueError: - prefix = prefixen[0] - # This list is guaranteed to contain all independent powers, # because it's the maximal set of powers that could possibly # be independent (by a dimension argument). @@ -165,17 +48,6 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide for b in basis_vectors ] W = V.span_of_basis( V.from_vector(v) for v in basis_vectors ) - n = len(superalgebra_basis) - mult_table = [[W.zero() for i in range(n)] for j in range(n)] - for i in range(n): - for j in range(n): - product = superalgebra_basis[i]*superalgebra_basis[j] - # product.to_vector() might live in a vector subspace - # if our parent algebra is already a subalgebra. We - # use V.from_vector() to make it "the right size" in - # that case. - product_vector = V.from_vector(product.to_vector()) - mult_table[i][j] = W.coordinate_vector(product_vector) # The rank is the highest possible degree of a minimal # polynomial, and is bounded above by the dimension. We know @@ -185,21 +57,11 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide # its rank too. rank = W.dimension() - natural_basis = tuple( b.natural_representation() - for b in superalgebra_basis ) - - - self._vector_space = W - self._superalgebra_basis = superalgebra_basis - - fdeja = super(FiniteDimensionalEuclideanJordanElementSubalgebra, self) - return fdeja.__init__(field, - mult_table, - rank, - prefix=prefix, - category=category, - natural_basis=natural_basis) + return fdeja.__init__(self._superalgebra, + superalgebra_basis, + rank=rank, + category=category) def _a_regular_element(self): @@ -386,5 +248,3 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide """ return self._vector_space - - Element = FiniteDimensionalEuclideanJordanElementSubalgebraElement