equal
deleted
inserted
replaced
32 sq(x1*y3 - x2*y4 + x3*y1 + x4*y2) + |
32 sq(x1*y3 - x2*y4 + x3*y1 + x4*y2) + |
33 sq(x1*y4 + x2*y3 - x3*y2 + x4*y1)" |
33 sq(x1*y4 + x2*y3 - x3*y2 + x4*y1)" |
34 by(simp add: sq_def ring_eq_simps) |
34 by(simp add: sq_def ring_eq_simps) |
35 |
35 |
36 |
36 |
37 (* A challenge by John Harrison. Takes about 4 mins on a 3GHz machine. |
37 text{*A challenge by John Harrison. Takes about 74s on a 2.5GHz Apple G5.*} |
38 |
38 |
|
39 (* |
39 lemma "!!p1::'a::comm_ring. |
40 lemma "!!p1::'a::comm_ring. |
40 (sq p1 + sq q1 + sq r1 + sq s1 + sq t1 + sq u1 + sq v1 + sq w1) * |
41 (sq p1 + sq q1 + sq r1 + sq s1 + sq t1 + sq u1 + sq v1 + sq w1) * |
41 (sq p2 + sq q2 + sq r2 + sq s2 + sq t2 + sq u2 + sq v2 + sq w2) |
42 (sq p2 + sq q2 + sq r2 + sq s2 + sq t2 + sq u2 + sq v2 + sq w2) |
42 = sq (p1*p2 - q1*q2 - r1*r2 - s1*s2 - t1*t2 - u1*u2 - v1*v2 - w1*w2) + |
43 = sq (p1*p2 - q1*q2 - r1*r2 - s1*s2 - t1*t2 - u1*u2 - v1*v2 - w1*w2) + |
43 sq (p1*q2 + q1*p2 + r1*s2 - s1*r2 + t1*u2 - u1*t2 - v1*w2 + w1*v2) + |
44 sq (p1*q2 + q1*p2 + r1*s2 - s1*r2 + t1*u2 - u1*t2 - v1*w2 + w1*v2) + |