X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_element_subalgebra.py;h=34a63afdc0be38fb34ab95bb211df6d926d9be57;hb=95ae8e7b0ddca840da9631603a2f37cca888468b;hp=7bc4b3a9a79c5cae8dbd60db3f63d581d215fc23;hpb=d96de12813f0403a0ca7ca1c57c75c732cf13612;p=sage.d.git diff --git a/mjo/eja/eja_element_subalgebra.py b/mjo/eja/eja_element_subalgebra.py index 7bc4b3a..34a63af 100644 --- a/mjo/eja/eja_element_subalgebra.py +++ b/mjo/eja/eja_element_subalgebra.py @@ -2,66 +2,24 @@ from sage.matrix.constructor import matrix from sage.misc.cachefunc import cached_method from sage.rings.all import QQ -from mjo.eja.eja_subalgebra import FiniteDimensionalEuclideanJordanSubalgebra - - -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() - - # 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). - powers = [ elt**k for k in range(V.dimension()) ] - power_vectors = [ p.to_vector() for p in powers ] - P = matrix(field, power_vectors) - - if orthonormalize_basis == False: - # Echelonize the matrix ourselves, because otherwise the - # call to P.pivot_rows() below can choose a non-optimal - # row-reduction algorithm. In particular, scaling can - # help over AA because it avoids the RecursionError that - # gets thrown when we have to look too hard for a root. - # - # Beware: QQ supports an entirely different set of "algorithm" - # keywords than do AA and RR. - algo = None - if field is not QQ: - algo = "scaled_partial_pivoting" - P.echelonize(algorithm=algo) - - # In this case, we just need to figure out which elements - # of the "powers" list are redundant... First compute the - # vector subspace spanned by the powers of the given - # element. - - # Figure out which powers form a linearly-independent set. - ind_rows = P.pivot_rows() - - # Pick those out of the list of all powers. - superalgebra_basis = tuple(map(powers.__getitem__, ind_rows)) - else: - # If we're going to orthonormalize the basis anyway, we - # might as well just do Gram-Schmidt on the whole list of - # powers. The redundant ones will get zero'd out. If this - # looks like a roundabout way to orthonormalize, it is. - # But converting everything from algebra elements to vectors - # to matrices and then back again turns out to be about - # as fast as reimplementing our own Gram-Schmidt that - # works in an EJA. - G,_ = P.gram_schmidt(orthonormal=True) - basis_vectors = [ g for g in G.rows() if not g.is_zero() ] - superalgebra_basis = [ self._superalgebra.from_vector(b) - for b in basis_vectors ] - - fdeja = super(FiniteDimensionalEuclideanJordanElementSubalgebra, self) - fdeja.__init__(self._superalgebra, - superalgebra_basis, - category=category, - check_axioms=False) +from mjo.eja.eja_subalgebra import FiniteDimensionalEJASubalgebra + + +class FiniteDimensionalEJAElementSubalgebra(FiniteDimensionalEJASubalgebra): + def __init__(self, elt, **kwargs): + superalgebra = elt.parent() + + # TODO: going up to the superalgebra dimension here is + # overkill. We should append p vectors as rows to a matrix + # and continually rref() it until the rank stops going + # up. When n=10 but the dimension of the algebra is 1, that + # can save a shitload of time (especially over AA). + powers = tuple( elt**k for k in range(elt.degree()) ) + + super().__init__(superalgebra, + powers, + associative=True, + **kwargs) # The rank is the highest possible degree of a minimal # polynomial, and is bounded above by the dimension. We know @@ -94,7 +52,7 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide sage: J.one() e0 + e1 + e2 + e3 + e4 sage: x = sum(J.gens()) - sage: A = x.subalgebra_generated_by() + sage: A = x.subalgebra_generated_by(orthonormalize=False) sage: A.one() f0 sage: A.one().superalgebra_element() @@ -105,7 +63,7 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide The identity element acts like the identity over the rationals:: sage: set_random_seed() - sage: x = random_eja(field=QQ).random_element() + sage: x = random_eja(field=QQ,orthonormalize=False).random_element() sage: A = x.subalgebra_generated_by() sage: x = A.random_element() sage: A.one()*x == x and x*A.one() == x @@ -116,7 +74,7 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide sage: set_random_seed() sage: x = random_eja().random_element() - sage: A = x.subalgebra_generated_by(orthonormalize_basis=True) + sage: A = x.subalgebra_generated_by() sage: x = A.random_element() sage: A.one()*x == x and x*A.one() == x True @@ -125,8 +83,8 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide the rationals:: sage: set_random_seed() - sage: x = random_eja(field=QQ).random_element() - sage: A = x.subalgebra_generated_by() + sage: x = random_eja(field=QQ,orthonormalize=False).random_element() + sage: A = x.subalgebra_generated_by(orthonormalize=False) sage: actual = A.one().operator().matrix() sage: expected = matrix.identity(A.base_ring(), A.dimension()) sage: actual == expected @@ -137,7 +95,7 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide sage: set_random_seed() sage: x = random_eja().random_element() - sage: A = x.subalgebra_generated_by(orthonormalize_basis=True) + sage: A = x.subalgebra_generated_by() sage: actual = A.one().operator().matrix() sage: expected = matrix.identity(A.base_ring(), A.dimension()) sage: actual == expected