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7.10.2.26 fibonacciGroup
Procedure from library fpalgebras.lib (see fpalgebras_lib).
- Usage:
- fibonacciGroup(m,d); m an integer, d an integer
- Return:
- ring
- Note:
- - the ring contains the ideal I, which contains the required relations
- The Fibonacci group F(2, m) with the following presentation
< x_1, x_2, ... , x_m | x_i * x_(i + 1) = x_(i + 2) >
- d gives the degreebound for the Letterplace ring
- varying m produces a family of examples
Example:
| | LIB "fpalgebras.lib";
def R = fibonacciGroup(3,5); setring R;
I;
==> I[1]=x(1)*x(2)+x(3)
==> I[2]=x(1)*Y(1)+1
==> I[3]=Y(1)*x(1)+1
==> I[4]=x(2)*Y(2)+1
==> I[5]=Y(2)*x(2)+1
==> I[6]=x(3)*Y(3)+1
==> I[7]=Y(3)*x(3)+1
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