X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_algebra.py;h=79ccc7904830dc739e4af0a532c1bace2a801936;hb=9528af011cbb4d5e6a38ef972e0d14e7928d5eef;hp=ae5baa0eff4a64dac97944bbdaf5a8ec132495bd;hpb=1adac51be4b18c6045d69bea652d8f2059e09b26;p=sage.d.git diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py index ae5baa0..79ccc79 100644 --- a/mjo/eja/eja_algebra.py +++ b/mjo/eja/eja_algebra.py @@ -5,7 +5,7 @@ are used in optimization, and have some additional nice methods beyond what can be supported in a general Jordan Algebra. """ -from itertools import repeat +from itertools import izip, repeat from sage.algebras.quatalg.quaternion_algebra import QuaternionAlgebra from sage.categories.magmatic_algebras import MagmaticAlgebras @@ -61,9 +61,6 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule): self._rank = rank self._natural_basis = natural_basis - # TODO: HACK for the charpoly.. needs redesign badly. - self._basis_normalizers = None - if category is None: category = MagmaticAlgebras(field).FiniteDimensional() category = category.WithBasis().Unital() @@ -259,19 +256,6 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule): store the trace/determinant (a_{r-1} and a_{0} respectively) separate from the entire characteristic polynomial. """ - if self._basis_normalizers is not None: - # Must be a matrix class? - # WARNING/TODO: this whole mess is mis-designed. - n = self.natural_basis_space().nrows() - field = self.base_ring().base_ring() # yeeeeaaaahhh - J = self.__class__(n, field, False) - (_,x,_,_) = J._charpoly_matrix_system() - p = J._charpoly_coeff(i) - # p might be missing some vars, have to substitute "optionally" - pairs = zip(x.base_ring().gens(), self._basis_normalizers) - substitutions = { v: v*c for (v,c) in pairs } - return p.subs(substitutions) - (A_of_x, x, xr, detA) = self._charpoly_matrix_system() R = A_of_x.base_ring() if i >= self.rank(): @@ -425,7 +409,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule): # assign a[r] goes out-of-bounds. a.append(1) # corresponds to x^r - return sum( a[k]*(t**k) for k in range(len(a)) ) + return sum( a[k]*(t**k) for k in xrange(len(a)) ) def inner_product(self, x, y): @@ -507,7 +491,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule): """ M = list(self._multiplication_table) # copy - for i in range(len(M)): + for i in xrange(len(M)): # M had better be "square" M[i] = [self.monomial(i)] + M[i] M = [["*"] + list(self.gens())] + M @@ -694,7 +678,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule): # not worry about it. raise NotImplementedError - n = ZZ.random_element(1, cls._max_test_case_size()) + n = ZZ.random_element(cls._max_test_case_size()) + 1 return cls(n, field, **kwargs) @@ -815,8 +799,8 @@ class RealCartesianProductEJA(FiniteDimensionalEuclideanJordanAlgebra): """ def __init__(self, n, field=QQ, **kwargs): V = VectorSpace(field, n) - mult_table = [ [ V.gen(i)*(i == j) for j in range(n) ] - for i in range(n) ] + mult_table = [ [ V.gen(i)*(i == j) for j in xrange(n) ] + for i in xrange(n) ] fdeja = super(RealCartesianProductEJA, self) return fdeja.__init__(field, mult_table, rank=n, **kwargs) @@ -899,7 +883,7 @@ class MatrixEuclideanJordanAlgebra(FiniteDimensionalEuclideanJordanAlgebra): def _max_test_case_size(): # Play it safe, since this will be squared and the underlying # field can have dimension 4 (quaternions) too. - return 3 + return 2 @classmethod def _denormalized_basis(cls, n, field): @@ -908,6 +892,9 @@ class MatrixEuclideanJordanAlgebra(FiniteDimensionalEuclideanJordanAlgebra): def __init__(self, n, field=QQ, normalize_basis=True, **kwargs): S = self._denormalized_basis(n, field) + # Used in this class's fast _charpoly_coeff() override. + self._basis_normalizers = None + if n > 1 and normalize_basis: # We'll need sqrt(2) to normalize the basis, and this # winds up in the multiplication table, so the whole @@ -932,6 +919,30 @@ class MatrixEuclideanJordanAlgebra(FiniteDimensionalEuclideanJordanAlgebra): **kwargs) + @cached_method + def _charpoly_coeff(self, i): + """ + Override the parent method with something that tries to compute + over a faster (non-extension) field. + """ + if self._basis_normalizers is None: + # We didn't normalize, so assume that the basis we started + # with had entries in a nice field. + return super(MatrixEuclideanJordanAlgebra, self)._charpoly_coeff(i) + else: + # If we didn't unembed first, this number would be wrong + # by a power-of-two factor for complex/quaternion matrices. + n = self.real_unembed(self.natural_basis_space().zero()).nrows() + field = self.base_ring().base_ring() # yeeeeaaaahhh + J = self.__class__(n, field, False) + (_,x,_,_) = J._charpoly_matrix_system() + p = J._charpoly_coeff(i) + # p might be missing some vars, have to substitute "optionally" + pairs = izip(x.base_ring().gens(), self._basis_normalizers) + substitutions = { v: v*c for (v,c) in pairs } + return p.subs(substitutions) + + @staticmethod def multiplication_table_from_matrix_basis(basis): """ @@ -953,9 +964,9 @@ class MatrixEuclideanJordanAlgebra(FiniteDimensionalEuclideanJordanAlgebra): V = VectorSpace(field, dimension**2) W = V.span_of_basis( _mat2vec(s) for s in basis ) n = len(basis) - mult_table = [[W.zero() for j in range(n)] for i in range(n)] - for i in range(n): - for j in range(n): + mult_table = [[W.zero() for j in xrange(n)] for i in xrange(n)] + for i in xrange(n): + for j in xrange(n): mat_entry = (basis[i]*basis[j] + basis[j]*basis[i])/2 mult_table[i][j] = W.coordinate_vector(_mat2vec(mat_entry)) @@ -1138,7 +1149,7 @@ class RealSymmetricEJA(RealMatrixEuclideanJordanAlgebra): @staticmethod def _max_test_case_size(): - return 5 # Dimension 10 + return 4 # Dimension 10 @@ -1726,9 +1737,9 @@ class JordanSpinEJA(FiniteDimensionalEuclideanJordanAlgebra): """ def __init__(self, n, field=QQ, **kwargs): V = VectorSpace(field, n) - mult_table = [[V.zero() for j in range(n)] for i in range(n)] - for i in range(n): - for j in range(n): + mult_table = [[V.zero() for j in xrange(n)] for i in xrange(n)] + for i in xrange(n): + for j in xrange(n): x = V.gen(i) y = V.gen(j) x0 = x[0]