1gap> #test_forms7: forms by polynomials
2gap> r := PolynomialRing( GF(7), 6);
3GF(7)[x_1,x_2,x_3,x_4,x_5,x_6]
4gap> vars := IndeterminatesOfPolynomialRing( r );
5[ x_1, x_2, x_3, x_4, x_5, x_6 ]
6gap> pol := (Z(7)^4)*vars[1]^2-vars[2]*vars[3]-vars[4]*vars[6]+vars[5]^2;
7Z(7)^4*x_1^2-x_2*x_3-x_4*x_6+x_5^2
8gap> form := BilinearFormByPolynomial(pol, r);
9< bilinear form >
10gap> IsEllipticForm(form);
11true
12gap> Display(form);
13Elliptic bilinear form
14Gram Matrix:
15 4 . . . . .
16 . . 3 . . .
17 . 3 . . . .
18 . . . . . 3
19 . . . . 1 .
20 . . . 3 . .
21Polynomial: Z(7)^4*x_1^2-x_2*x_3-x_4*x_6+x_5^2
22
23Witt Index: 2
24gap> quit;
25