Pensieve Header: Inverting R[1,1] in β-calculus and taking its square root.

SetDirectory["C:\\drorbn\\AcademicPensieve\\2012-01"];
<< betaCalculus.m

{ar[1,1], F[c[1]]ar[1,1]} // βForm

ar[1,1] ** (α ar[1,1]) // βForm

Solve[1+α+α c[1]==0, α]

{R[1,1], F[c[1]]ar[1,1]} // βForm

R[1,1] ** (F[c[1]]ar[1,1]) // βForm

R[1,1] ** (α ar[1,1]) // βForm

α /. First@Solve[((-1+(E^(c[1])) (1+α c[1]))/(c[1]))==0, α] // FullSimplify

{
R[1,1],
(α ar[1,1])**(α ar[1,1])
} // βForm

α /. First@Solve[((-1+(E^(c[1])))/(c[1])) == α (2+α c[1]), α]// FullSimplify

{
R[1,1,-1]**R[1,1],
R[1,1,1/2]**R[1,1,1/2]**R[1,1,-1],
R[1,1,-1/2]**R[1,1,1/2],
R[1,1,1/3]**R[1,1,1/3]**R[1,1,1/3] // FullSimplify
} // βForm