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