X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_element.py;h=107603ce712ecf79d6de89a2e4fd573f17738798;hb=9c35b8d70e384cd98b8ec7eb7a84cf84db1d1137;hp=00a15a1c56897172f57aeec2d43a391f3b367a45;hpb=a7cf81951d0cb51ea40d9362a75385204596df42;p=sage.d.git diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py index 00a15a1..107603c 100644 --- a/mjo/eja/eja_element.py +++ b/mjo/eja/eja_element.py @@ -1,6 +1,6 @@ -from sage.algebras.finite_dimensional_algebras.finite_dimensional_algebra_element import FiniteDimensionalAlgebraElement from sage.matrix.constructor import matrix from sage.modules.free_module import VectorSpace +from sage.modules.with_basis.indexed_element import IndexedFreeModuleElement # TODO: make this unnecessary somehow. from sage.misc.lazy_import import lazy_import @@ -10,7 +10,7 @@ lazy_import('mjo.eja.eja_subalgebra', from mjo.eja.eja_operator import FiniteDimensionalEuclideanJordanAlgebraOperator from mjo.eja.eja_utils import _mat2vec -class FiniteDimensionalEuclideanJordanAlgebraElement(FiniteDimensionalAlgebraElement): +class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement): """ An element of a Euclidean Jordan algebra. """ @@ -25,7 +25,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(FiniteDimensionalAlgebraEle dir(self.__class__) ) - def __init__(self, A, elt=None): + def __init__(self, A, elt): """ SETUP:: @@ -60,7 +60,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(FiniteDimensionalAlgebraEle sage: set_random_seed() sage: J = random_eja() sage: v = J.vector_space().random_element() - sage: J(v).vector() == v + sage: J(v).to_vector() == v True """ @@ -75,8 +75,9 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(FiniteDimensionalAlgebraEle # already fits into the algebra, but also happens to live # in the parent's "natural ambient space" (this happens with # vectors in R^n). + ifme = super(FiniteDimensionalEuclideanJordanAlgebraElement, self) try: - FiniteDimensionalAlgebraElement.__init__(self, A, elt) + ifme.__init__(A, elt) except ValueError: natural_basis = A.natural_basis() if elt in natural_basis[0].matrix_space(): @@ -85,8 +86,9 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(FiniteDimensionalAlgebraEle # natural-basis coordinates ourselves. V = VectorSpace(elt.base_ring(), elt.nrows()**2) W = V.span( _mat2vec(s) for s in natural_basis ) - coords = W.coordinates(_mat2vec(elt)) - FiniteDimensionalAlgebraElement.__init__(self, A, coords) + coords = W.coordinate_vector(_mat2vec(elt)) + ifme.__init__(A, coords) + def __pow__(self, n): """ @@ -228,7 +230,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(FiniteDimensionalAlgebraEle """ p = self.parent().characteristic_polynomial() - return p(*self.vector()) + return p(*self.to_vector()) def inner_product(self, other): @@ -437,7 +439,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(FiniteDimensionalAlgebraEle # -1 to ensure that _charpoly_coeff(0) is really what # appears in front of t^{0} in the charpoly. However, # we want (-1)^r times THAT for the determinant. - return ((-1)**r)*p(*self.vector()) + return ((-1)**r)*p(*self.to_vector()) def inverse(self): @@ -465,7 +467,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(FiniteDimensionalAlgebraEle sage: x = J.random_element() sage: while not x.is_invertible(): ....: x = J.random_element() - sage: x_vec = x.vector() + sage: x_vec = x.to_vector() sage: x0 = x_vec[0] sage: x_bar = x_vec[1:] sage: coeff = ~(x0^2 - x_bar.inner_product(x_bar)) @@ -765,8 +767,8 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(FiniteDimensionalAlgebraEle sage: y = J.random_element() sage: while y == y.coefficient(0)*J.one(): ....: y = J.random_element() - sage: y0 = y.vector()[0] - sage: y_bar = y.vector()[1:] + sage: y0 = y.to_vector()[0] + sage: y_bar = y.to_vector()[1:] sage: actual = y.minimal_polynomial() sage: t = PolynomialRing(J.base_ring(),'t').gen(0) sage: expected = t^2 - 2*y0*t + (y0^2 - norm(y_bar)^2) @@ -783,7 +785,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(FiniteDimensionalAlgebraEle """ A = self.subalgebra_generated_by() - return A(self).operator().minimal_polynomial() + return A.element_class(A,self).operator().minimal_polynomial() @@ -837,7 +839,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(FiniteDimensionalAlgebraEle """ B = self.parent().natural_basis() W = B[0].matrix_space() - return W.linear_combination(zip(self.vector(), B)) + return W.linear_combination(zip(B,self.to_vector())) def operator(self): @@ -862,11 +864,10 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(FiniteDimensionalAlgebraEle """ P = self.parent() - fda_elt = FiniteDimensionalAlgebraElement(P, self) return FiniteDimensionalEuclideanJordanAlgebraOperator( P, P, - fda_elt.matrix().transpose() ) + self.to_matrix() ) def quadratic_representation(self, other=None): @@ -887,7 +888,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(FiniteDimensionalAlgebraEle sage: n = ZZ.random_element(1,10) sage: J = JordanSpinEJA(n) sage: x = J.random_element() - sage: x_vec = x.vector() + sage: x_vec = x.to_vector() sage: x0 = x_vec[0] sage: x_bar = x_vec[1:] sage: A = matrix(QQ, 1, [x_vec.inner_product(x_vec)]) @@ -1070,7 +1071,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(FiniteDimensionalAlgebraEle # Our FiniteDimensionalAlgebraElement superclass uses rows. u_next = u**(s+1) A = u_next.operator().matrix() - c = J(A.solve_right(u_next.vector())) + c = J(A.solve_right(u_next.to_vector())) # Now c is the idempotent we want, but it still lives in the subalgebra. return c.superalgebra_element() @@ -1116,7 +1117,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(FiniteDimensionalAlgebraEle # -1 to ensure that _charpoly_coeff(r-1) is really what # appears in front of t^{r-1} in the charpoly. However, # we want the negative of THAT for the trace. - return -p(*self.vector()) + return -p(*self.to_vector()) def trace_inner_product(self, other):