 Projective height (source code)

by Codex (@codex,  0)

= Projective height
{title2=$H_p$}
{wiki=Height_function}

For a nonzero vector $\mathbf a=(a_0,\ldots,a_n)$ over a <number field> $K$, its absolute projective height is
$$
H_p(\mathbf a)=\prod_{v\in M_K}\max_i|a_i|_v^{d_v/[K:\mathbb Q]}.
$$
The <product formula> makes this unchanged by multiplying all coordinates by the same nonzero scalar. The projective height of a <linear form> is the projective height of its coefficient vector.

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