X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_element.py;h=e8c183b51d522efd14aba57b779b4b5ebfa4b896;hb=45f207f28a8396426469fedb026b4da82e30fbf5;hp=c2f2b7c12ff92dbc0a57036057afad55acd63ddd;hpb=a4f0908c2216ff989161d33873102805d1c6aabd;p=sage.d.git diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py index c2f2b7c..e8c183b 100644 --- a/mjo/eja/eja_element.py +++ b/mjo/eja/eja_element.py @@ -4,7 +4,7 @@ from sage.modules.free_module import VectorSpace from sage.modules.with_basis.indexed_element import IndexedFreeModuleElement from mjo.eja.eja_operator import FiniteDimensionalEJAOperator -from mjo.eja.eja_utils import _mat2vec +from mjo.eja.eja_utils import _mat2vec, _scale class FiniteDimensionalEJAElement(IndexedFreeModuleElement): """ @@ -664,7 +664,7 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement): element should always be in terms of minimal idempotents:: sage: J = JordanSpinEJA(4) - sage: x = sum( i*J.gens()[i] for i in range(len(J.gens())) ) + sage: x = sum( i*J.monomial(i) for i in range(len(J.gens())) ) sage: x.is_regular() True sage: [ c.is_primitive_idempotent() @@ -910,7 +910,7 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement): M = matrix([(self.parent().one()).to_vector()]) old_rank = 1 - # Specifying the row-reduction algorithm can e.g. help over + # Specifying the row-reduction algorithm can e.g. help over # AA because it avoids the RecursionError that gets thrown # when we have to look too hard for a root. # @@ -1077,7 +1077,9 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement): SETUP:: sage: from mjo.eja.eja_algebra import (ComplexHermitianEJA, - ....: QuaternionHermitianEJA) + ....: HadamardEJA, + ....: QuaternionHermitianEJA, + ....: RealSymmetricEJA) EXAMPLES:: @@ -1107,14 +1109,36 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement): [0 0 0 0 0 0 1 0] [0 0 0 0 0 0 0 1] + This also works in Cartesian product algebras:: + + sage: J1 = HadamardEJA(1) + sage: J2 = RealSymmetricEJA(2) + sage: J = cartesian_product([J1,J2]) + sage: x = sum(J.gens()) + sage: x.to_matrix()[0] + [1] + sage: x.to_matrix()[1] + [ 1 0.7071067811865475?] + [0.7071067811865475? 1] + """ B = self.parent().matrix_basis() W = self.parent().matrix_space() - # This is just a manual "from_vector()", but of course - # matrix spaces aren't vector spaces in sage, so they - # don't have a from_vector() method. - return W.linear_combination( zip(B, self.to_vector()) ) + if self.parent()._matrix_basis_is_cartesian: + # Aaaaand linear combinations don't work in Cartesian + # product spaces, even though they provide a method + # with that name. This is special-cased because the + # _scale() function is slow. + pairs = zip(B, self.to_vector()) + return sum( ( _scale(b, alpha) for (b,alpha) in pairs ), + W.zero()) + else: + # This is just a manual "from_vector()", but of course + # matrix spaces aren't vector spaces in sage, so they + # don't have a from_vector() method. + return W.linear_combination( zip(B, self.to_vector()) ) + def norm(self): @@ -1379,7 +1403,20 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement): SETUP:: - sage: from mjo.eja.eja_algebra import random_eja + sage: from mjo.eja.eja_algebra import (random_eja, + ....: HadamardEJA, + ....: RealSymmetricEJA) + + EXAMPLES: + + We can create subalgebras of Cartesian product EJAs that are not + themselves Cartesian product EJAs (they're just "regular" EJAs):: + + sage: J1 = HadamardEJA(3) + sage: J2 = RealSymmetricEJA(2) + sage: J = cartesian_product([J1,J2]) + sage: J.one().subalgebra_generated_by() + Euclidean Jordan algebra of dimension 1 over Algebraic Real Field TESTS: @@ -1412,12 +1449,12 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement): True """ - from mjo.eja.eja_subalgebra import FiniteDimensionalEJASubalgebra powers = tuple( self**k for k in range(self.degree()) ) - A = FiniteDimensionalEJASubalgebra(self.parent(), - powers, - associative=True, - **kwargs) + A = self.parent().subalgebra(powers, + associative=True, + check_field=False, + check_axioms=False, + **kwargs) A.one.set_cache(A(self.parent().one())) return A