-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
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.
"""
dir(self.__class__) )
- def __init__(self, A, elt=None):
+ def __init__(self, A, elt):
"""
SETUP::
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
"""
# 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():
# 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):
"""
"""
p = self.parent().characteristic_polynomial()
- return p(*self.vector())
+ return p(*self.to_vector())
def inner_product(self, other):
# -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):
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))
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)
"""
A = self.subalgebra_generated_by()
- return A(self).operator().minimal_polynomial()
+ return A.element_class(A,self).operator().minimal_polynomial()
"""
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):
"""
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):
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)])
# 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()
# -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):
projects / sage.d.git / blobdiff