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	NoncommutativePolynomials
ExampleSkewPolynomial ←	↑	→ SandboxFactoringNoncommutativePolynomials

NonCommutativeLaurentPolynomials

Edit detail for NonCommutativeLaurentPolynomials revision 1 of 1

	1
Editor: Bill Page Time: 2011/03/29 17:32:49 GMT-7
Note: example

changed:
-
Consider a noncommutative group ring over commuting polynomials
\begin{axiom}
NPOLY:=MonoidRing(Polynomial(Fraction(Integer)),FreeGroup(Symbol))
\end{axiom}

Generators
\begin{axiom}
x:NPOLY:='x::FreeGroup Symbol
y:NPOLY:='y::FreeGroup Symbol
x':NPOLY:=('x::FreeGroup Symbol)^(-1)
y':NPOLY:=('y::FreeGroup Symbol)^(-1)
a:POLY FRAC INT := 'a::Symbol
\end{axiom}

Example
\begin{axiom}
p:=x*y*x+y
(p+3*a+1)*x'
\end{axiom}

Consider a noncommutative group ring over commuting polynomials

fricas

(1) -> NPOLY:=MonoidRing(Polynomial(Fraction(Integer)),FreeGroup(Symbol))

$\label{eq1}\hbox{\axiomType{MonoidRing}\ } \left({{\hbox{\axiomType{Polynomial}\ } \left({\hbox{\axiomType{Fraction}\ } \left({\hbox{\axiomType{Integer}\ }}\right)}\right)}, \:{\hbox{\axiomType{FreeGroup}\ } \left({\hbox{\axiomType{Symbol}\ }}\right)}}\right)$