1gap> #Constructing form: QuadraticFormByPolynomial
2gap> r := PolynomialRing( GF(8), 3);
3GF(2^3)[x_1,x_2,x_3]
4gap> poly := r.1^2 + r.2^2 + r.3^2;
5x_1^2+x_2^2+x_3^2
6gap> form := QuadraticFormByPolynomial(poly, r);
7< quadratic form >
8gap> RadicalOfForm(form);
9<vector space over GF(2^3), with 63 generators>
10gap> r := PolynomialRing(GF(9),4);
11GF(3^2)[x_1,x_2,x_3,x_4]
12gap> poly := Z(3)^2*r.1^2+r.2^2+r.3*r.4;
13x_1^2+x_2^2+x_3*x_4
14gap> qform := QuadraticFormByPolynomial(poly,r);
15< quadratic form >
16gap> Display(qform);
17Quadratic form
18Gram Matrix:
19 1 . . .
20 . 1 . .
21 . . . 1
22 . . . .
23Polynomial: x_1^2+x_2^2+x_3*x_4
24
25gap> quit;
26