> <\body> <\tmdoc-title> Polynomial rings Rings of polynomials are defined from a coefficient ring. <\session|mathemagix|default> <\input> <|input> use "realroot" <\textput> \; Here is the ring of polynomials with coefficients in >; the first variable is , the second : <\unfolded-io> <|unfolded-io> R := ZZ['x,'y] <|unfolded-io> > <\textput> Notice that in the example above, and to any value. If we want to use the name eg. of an assigned variable, we quote it: <\unfolded-io> <|unfolded-io> z:= 3; R := ZZ['x,'y,'z] <|unfolded-io> > <\textput> The number of variables is unlimited. If the > variable has no name, it is represented by >. Here is an how to access to the corresponding polynomials in the ring :\ <\unfolded-io> <|unfolded-io> \ [R[0], R[1], R[2], R[100]] <|unfolded-io> x,y,z,x100> <\textput> Variable names can be full names:\ <\unfolded-io> <|unfolded-io> QQ[xi, mu] <|unfolded-io> ,\>> <\textput> The set of named variables can be extended: <\unfolded-io> <|unfolded-io> R := R[u] <|unfolded-io> > <\textput> The set of named variables can be redefined:\ <\unfolded-io> <|unfolded-io> R := ZZ[a,b] <|unfolded-io> > <\input> <|input> \; <\initial> <\collection>