# Arithmetic, normalization and the three standard orders.
ring grevlex x y z
show (x + y)^3
show (x + y)*(x - y) - x^2 + y^2
show (x - 2*y + 3/4*z)^2
show x*y^2 + y^3*z^0 + x^3 + z^2*x + 7
order lex
show x*y^2 + y^3 + x^3 + z^2*x + 7
order grlex
show x*y^2 + y^3 + x^3 + z^2*x + 7
order elim 1
show x*y^2 + y^3 + x^3 + z^2*x + 7
order weighted
show x*y*z + x^2*z + y^3
eval (x + y)^3 - z ; 1 ; 2 ; 1/2
subst x^2*y + x*z - y ; x ; 3
show 1/(2*3) * (6*x - 12)