Dear Forum, Dear Maycon Carneiro, > I creat an AlgebraicExtension over GF(2) using the polynomial x^3+x^2+1, > > gap>z2:=GF(2); > x:=X(z2,"x"); > pol:=x^3+x^2+1; > F8:=AlgebraicExtension(z2,pol); > a:=RootOfDefiningPolynomial(F8); > > now, i'd like to get the solutions over F8 of the equation: > > z^2+z*y+a*y^2= c, where c is an especified element of F8, say a^2.. and z, > y are variables in F8 > > how can i do this? or at least in one variable, say z, and i'll put an > especified element for y..
There is no general polynomial equations solver. in GAP. Basically you’ll need to do the same as in the answer I already gave you in https://math.stackexchange.com/questions/2563103/how-to-solve-a-quadratic-equation-over-finite-fields-with-gap Note that by using `Algebraic Extension’ your calculation will be a magnitude slower than if you use the built-in GF(8). I’ve also shown you in https://math.stackexchange.com/questions/2565387/how-to-work-in-gap-with-finite-fields-given-by-a-particular-polynomial how you can represent elements of (in this case) GF(8) in terms of roots of your original polynomial. Regards, Alexander Hulpke -- Colorado State University, Department of Mathematics, Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA email: hul...@colostate.edu, Phone: ++1-970-4914288 http://www.math.colostate.edu/~hulpke _______________________________________________ Forum mailing list Forum@gap-system.org https://mail.gap-system.org/mailman/listinfo/forum
