The i-th Steenrod operation Pi(f) of f, which must be a multivariate polynomial with coefficients in a finite field, and i must be a non-negative integer.
> K:=GF(3); > F4:=MatrixGroup<4,K | > [-1,0,0,0, 1,1,0,0, 0,0,1,0, 0,0,0,1], > [1,1,0,0, 0,-1,0,0, 0,1,1,0, 0,0,0,1], > [1,0,0,0, 0,1,-1,0, 0,0,-1,0, 0,0,1,1], > [1,0,0,0, 0,1,0,0, 0,0,1,1, 0,0,0,-1] >; > R := InvariantRing(F4); > f2 := InvariantsOfDegree(R, 2)[1]; > f4 := SteenrodOperation(f2, 1); > f10 := SteenrodOperation(f4, 3); > f4; 2*x1^4 + x1^3*x3 + 2*x1^3*x4 + x1*x3^3 + 2*x1*x4^3 + 2*x2^3*x3 + x2^3*x4 + 2*x2*x3^3 + x2*x4^3 + x4^4 > f10; 2*x1^10 + x1^9*x3 + 2*x1^9*x4 + x1*x3^9 + 2*x1*x4^9 + 2*x2^9*x3 + x2^9*x4 + 2*x2*x3^9 + x2*x4^9 + x4^10 > f4 in R; true > f10 in R; true