Free algebra elements¶
AUTHORS:
- David Kohel (2005-09)
TESTS:
sage: R.<x,y> = FreeAlgebra(QQ,2)
sage: x == loads(dumps(x))
True
sage: x*y
x*y
sage: (x*y)^0
1
sage: (x*y)^3
x*y*x*y*x*y
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class
sage.algebras.free_algebra_element.
FreeAlgebraElement
(A, x)¶ Bases:
sage.structure.element.AlgebraElement
,sage.combinat.free_module.CombinatorialFreeModuleElement
A free algebra element.
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to_pbw_basis
()¶ Return
self
in the Poincare-Birkhoff-Witt (PBW) basis.EXAMPLES:
sage: F.<x,y,z> = FreeAlgebra(ZZ, 3) sage: p = x^2*y + 3*y*x + 2 sage: p.to_pbw_basis() 2*PBW[1] + 3*PBW[y]*PBW[x] + PBW[x^2*y] + PBW[x*y]*PBW[x] + PBW[y]*PBW[x]^2
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variables
()¶ Return the variables used in
self
.EXAMPLES:
sage: A.<x,y,z> = FreeAlgebra(ZZ,3) sage: elt = x + x*y + x^3*y sage: elt.variables() [x, y] sage: elt = x + x^2 - x^4 sage: elt.variables() [x] sage: elt = x + z*y + z*x sage: elt.variables() [x, y, z]
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