+define gf_gcd(a, b)
+{
+ local swap = 0;
+ local g, x = 1, X = 0, y = 0, Y = 1, q, r, t;
+ if (a.x < b.x) {
+ t = a; a = b; b = t;
+ swap = 1;
+ }
+ if (b == gf(0))
+ g = a;
+ else {
+ while (b != gf(0)) {
+ q = gf_div(a, b); r = gf_mod(a, b);
+ t = X * q + x; x = X; X = t;
+ t = Y * q + y; y = Y; Y = t;
+ a = b; b = r;
+ }
+ g = a;
+ }
+ if (swap) {
+ t = x; x = y; y = t;
+ }
+ return list(g, x, y);
+}
+
+define gf_inv(a, b)
+{
+ local l = gf_gcd(b, a);
+ if (l[[0]] != gf(1)) quit "not coprime in gf_inv";
+ return l[[2]];
+}
+