Polynomials

Type R<x>:= PolynomialRing( Rationals(), 1 ); to define the variable $x$. It is necessary to define $x$ before you can type a polynomial in $x$ into MAGMA. Once you gave a polynomial, say f:=x^2-1;, you can use MAGMA to do several things: evaluate $f$ at a particular value of $x$, differentiate or integrate $f$, find the coefficients of $f$, factor $f$, and so on. Type Factorization( f ); to obtain the factorization of $f$ in $R$. For example, Factorization( x^2-1 ); gives the factorization

[<x - 1, 1>,<x + 1, 1>].