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# Representing Textual Forms by Boxes

All textual and graphical forms in Mathematica are ultimately represented in terms of nested collections of boxes. Typically the elements of these boxes correspond to objects that are to be placed at definite relative positions in two dimensions.
Here are the boxes corresponding to the expression a+b.
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DisplayForm shows how these boxes would be displayed.
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 DisplayForm[boxes] show boxes as they would be displayed

Showing the displayed form of boxes.

This displays three strings in a row.
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This displays one string as a subscript of another.
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This puts two subscript boxes in a row.
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 "text" literal text RowBox[{a,b,...}] a row of boxes or strings a, b, ... GridBox[{{a1,b1,...},{a2,b2,...},...}] a grid of boxes SubscriptBox[a,b] subscript ab SuperscriptBox[a,b] superscript ab SubsuperscriptBox[a,b,c] subscript and superscript UnderscriptBox[a,b] underscript OverscriptBox[a,b] overscript UnderoverscriptBox[a,b,c] underscript and overscript FractionBox[a,b] fraction SqrtBox[a] square root RadicalBox[a,b] bth root

Some basic box types.

This nests a fraction inside a radical.
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This puts a superscript on a subscripted object.
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This puts both a subscript and a superscript on the same object.
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 FrameBox[box] render box with a frame drawn around it GridBox[list,RowLines->True] put lines between rows in a GridBox GridBox[list,ColumnLines->True] put lines between columns GridBox[list,RowLines->{True,False}] put a line below the first row, but not subsequent ones

Inserting frames and grid lines.

This shows a fraction with a frame drawn around it.
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This puts lines between rows and columns of an array.
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And this also puts a frame around the outside.
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 StyleBox[boxes,options] render boxes with the specified option settings StyleBox[boxes,"style"] render boxes in the specified style

Modifying the appearance of boxes.

StyleBox takes the same options as Style. The difference is that Style is a high-level function that applies to an expression to determine how it will be displayed, while StyleBox is the corresponding low-level function in the underlying box structure.
This shows the string "name" in italics.
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This shows "name" in the style used for section headings in your current notebook.
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This uses section heading style, but with characters shown in gray.
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If you use a notebook front end for Mathematica, then you will be able to change the style and appearance of what you see on the screen directly by using menu items. Internally, however, these changes will still be recorded by the insertion of appropriate StyleBox objects.
 FormBox[boxes,form] interpret boxes using rules associated with the specified form InterpretationBox[boxes,expr] interpret boxes as representing the expression expr TagBox[boxes,tag] use tag to guide the interpretation of boxes ErrorBox[boxes] indicate an error and do not attempt further interpretation of boxes

Controlling the interpretation of boxes.

This prints as x with a superscript.
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It is normally interpreted as a power.
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This again prints as x with a superscript.
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But now it is interpreted as vec[x, 2], following the specification given in the InterpretationBox.
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If you edit the boxes given in an InterpretationBox, then there is no guarantee that the interpretation specified by the interpretation box will still be correct. As a result, Mathematica provides various options that allow you to control the selection and editing of InterpretationBox objects.
 option default value Editable Automatic whether to allow the contents to be edited Selectable True whether to allow the contents to be selected Deletable True whether to allow the box to be deleted DeletionWarning False whether to issue a warning if the box is deleted BoxAutoDelete False whether to strip the box if its contents are modified StripWrapperBoxes False whether to remove StyleBox etc. from within boxes in TagBox[boxes, ...]

Options for InterpretationBox and related boxes.

TagBox objects are used to store information that will not be displayed but which can nevertheless be used by the rules that interpret boxes. Typically the tag in TagBox[boxes, tag] is a symbol which gives the head of the expression corresponding to boxes. If you edit only the arguments of this expression then there is a good chance that the interpretation specified by the TagBox will still be appropriate. As a result, is effectively the default setting for a TagBox.
The rules that Mathematica uses for interpreting boxes are in general set up to ignore details of formatting, such as those defined by StyleBox objects. Thus, unless StripWrapperBoxes->False, a red x, for example, will normally not be distinguished from an ordinary black x.
A red x is usually treated as identical to an ordinary one.
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