The Basis command computes the simplest common basis for the list of expressions exprs defined by the complexity with respect to the given variables vars.

A list of new expressions is returned such that every element of exprs can be written as a linear combination of these returned expressions with integer coefficients.

$\mathrm{with}\left(\mathrm{SolveTools}\right)\:$

$\mathrm{Basis}\left(\left[x+y\,x-y\right]\,\left\{x\,y\right\}\right)$

$\left[x\,y\right]$

$\mathrm{Basis}\left(\left[x+y\,x-y\right]\,\left\{x\right\}\right)$

$\left[x-y\,2y\right]$