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graeffe --
graeffe transformation (squares the roots)
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graeffe(F RINGELEM): RINGELEM
graeffe3(F RINGELEM): RINGELEM
GraeffeN(F RINGELEM, N INT): RINGELEM |
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 a polynomial whose roots
are the cubes of the roots of
F.
For more general cases,
GraeffeN produces a polynomial whose roots
are the
N-th powers of the roots of
F.
/**/ 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
/**/ GraeffeN(f, 7);
x^3 -115*x^2 -24187*x -823543
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