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graeffe

graeffe transformation (squares the roots)

Syntax
graeffe(R RINGELEM): RINGELEM
graeffe3(R RINGELEM): RINGELEM

Description
The function graeffe applies the graeffe transformation to the univariate polynomial F . The result is a univariate polynomial whose roots are the squares of the roots of F .

The similar function graeffe3 produces the polynomial whose roots are the cubes of the roots of F

Example
/**/  use P ::= QQ[x];
/**/  f := x^3-3*x^2+5*x-7;
/**/  graeffe(f);
x^3 +x^2 -17*x -49
/**/  graeffe3(f);
x^3 -3*x^2 -43*x -343

See Also