Talk:Mahler measure
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Calculating the Mahler measure of a polynomial via its roots is usually easier than performing the integration.
To calculate the Mahler measure of a polynomial in Maple You can do this:
>Mahler := proc( f ) > local r, n, i, m; > n := degree( f ); > r := solve( f=0, x ); > m := abs(coeff( f, x ) ); > for i from 1 to n do > m := m * max(1,abs(r[i])); > od; > end proc:
> f := -x^9-x^8-x^7-x^6-x^5 + x^4 + x^3+x^2-x-1;
9 8 7 6 5 4 3 2 f := -x - x - x - x - x + x + x + x - x - 1
> evalf( Mahler( f ) );
2.294787065
???
[edit]What is lα supposed to be? Polynomials are functions, not sequences. Reading it as Lα(X), where X is presumably the unit circle, does not work either, as then
which is hopelessly different from .
And what does If p is an irreducible polynomial with and , then p is a cyclotomic polynomial mean? Irreducible over which field? Certainly not the complex numbers. In any case, any polynomial can be normalized to M(p)=1 just by multiplying it with a suitable constant. -- EJ 03:45, 18 January 2006 (UTC)
- Right on both counts. According to Borwein it's the L0 "norm" (p.3), and irreducible monic integer polynomials (p.15). I have edited accordingly. Richard Pinch (talk) 19:11, 29 July 2008 (UTC)
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