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7.7.8.0. 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
This is a family
Example:
| LIB "fpalgebras.lib";
def R = fibonacciGroup(3,5); setring R;
I;
==> I[1]=x(1)(1)*x(2)(2)+x(3)(1)
==> I[2]=x(1)(1)*Y(1)(2)+1
==> I[3]=Y(1)(1)*x(1)(2)+1
==> I[4]=x(2)(1)*Y(2)(2)+1
==> I[5]=Y(2)(1)*x(2)(2)+1
==> I[6]=x(3)(1)*Y(3)(2)+1
==> I[7]=Y(3)(1)*x(3)(2)+1
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