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For an equation which contains a series, solving for the series variable achieves a generalized inversion of series.

The result, usually a series, will be in one of the remaining indeterminates. The indeterminate which produces the simplest answer is usually chosen.

The global variable Order will be used to determine the order of the series result.

Formally, if t = solve(f(series_in_x, y), x) is a series in y with sufficient terms, then substituting t for x in $f$ will result in 0 or $\mathrm{O}\left(y^{\mathrm{Order}}\right)$.

$\mathrm{Order}≔3$

$\mathrm{Order}≔3$

$\mathrm{solve}\left(\mathrm{series}\left(x\exp \left(x\right)\,x\right)=y\,x\right)$

$y-y^2+O\left(y^3\right)$

$\mathrm{solve}\left(\mathrm{series}\left(\exp \left(x\right)\,x\right)=a+b\,x\right)$

$\left(a-1+b\right)-\frac{1}{2}{\left(a-1+b\right)}^2+O\left({\left(a-1+b\right)}^3\right)$