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A longstanding problem... (related: #1861) The columns in AMS math environments have a fixed alignment (colAlign() in InsetMathGrid.cpp). We set this alignment for display (Georg's displayColAlign()) in InsetMathHull and InsetMathSplit. This is done according to tests and documentation for the various environments. There is also some mechanical code factoring via colAlign(). Finally, I disable setting the horizontal alignment in InsetMathSplit, which has no impact on the LaTeX output, and has no longer any impact on the screen. (As for vertical alignment I discovered that it was in fact customisable for \aligned & friends! I hope that the more faithful interface will let other users discover that too.)
Inset 'Xyz' is implemented by 'MathXyzInset' in 'math_xyzinset.[hC]' Inset hierarchy: MathInset (abstract base) / | \ Dim Char Symbol, Space, ... (thing that need (for things formerly the width_/ascent_ known as characters) /descent_ cache) / \ Nest Dots, Func, ... (for thing with nested content) | \ Grid Decoration Delim Frac Macro Root Script Sqrt / \ Array Hull (base for eqnarray/align/...)