MakeBoxes[expr, form] is the low-level function used in Mathematica sessions to convert expressions into boxes.
MakeBoxes does not evaluate expr.
form can be StandardForm, TraditionalForm, or any other output form.
You can give definitions for MakeBoxes[expr, form] to specify your own rules for how expressions should be converted to boxes.
MakeBoxes is not automatically called on the results it generates. This means that explicit MakeBoxes calls must typically be inserted into definitions that are given.
If you change the output format for an expression by giving a definition for MakeBoxes, there is no guarantee that output you get will subsequently be able to be interpreted by Mathematica.
Definitions you give for MakeBoxes will override built-in Mathematica rules for generating output.
See The Mathematica Book: Section 2.8.17.
See also: MakeExpression, ToBoxes, Format.
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