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The Trace function is a placeholder for representing the trace of an algebraic number (or function), that is the sum of its conjugates. It is used in conjunction with evala.

The call evala(Trace(a, L, K)) computes the trace of a over the algebraic number (or function) field represented by K. In case K is not specified and a is an algebraic number, the trace over the rational is computed. In case K is not specified and a is an algebraic function, the smallest possible transcendental extension of the rational numbers is chosen. The expression a is viewed as an element of the smallest field containing a and the RootOfs in L.

The RootOfs in K must form a subset of the RootOfs occurring in L and in a. In other words, K must be a 'syntactic' subfield of the field generated by L and the RootOfs in a.

$\mathrm{alias}\left(\mathrm{sqrt2}=\mathrm{RootOf}\left(x^2-2\right)\right)\:$

$\mathrm{alias}\left(\mathrm{\alpha }=\mathrm{RootOf}\left(y^2-x+\mathrm{RootOf}\left(x^2-2\right)y\,y\right)\right)\:$

$\mathrm{evala}\left(\mathrm{Trace}\left(\mathrm{\alpha }\right)\right)$

$0$

$\mathrm{evala}\left(\mathrm{Trace}\left(\mathrm{\alpha }\,\varnothing \,\mathrm{sqrt2}\right)\right)$

$-\mathrm{sqrt2}$

$\mathrm{evala}\left(\mathrm{Trace}\left(z-\frac{\mathrm{\alpha }}{z}\right)\right)$

$4z$