ToBoxes

The boxes an expression's traditional notation is made of, after evaluating it.

✓ checked against that system · ! checked, with disagreements (hover a chip)Wolfram LanguageToBoxes!↗

ToBoxes(expr)The boxes an expression's traditional notation is made of, after evaluating it.

Typed signatures

Type	Package	Applies
(any) -> boxes	boxes	always

Domain: Boxes

Details

• Wolfram's ToBoxes[expr] gives StandardForm boxes by default; ours are the traditional notation, ToBoxes[expr, TraditionalForm] without its FormBox wrapper and with templates expanded.
• The result is typed boxes.

Examples

Basic #

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In$\mathrm{ToBoxes}(x^2)$Out$\mathrm{SuperscriptBox}(\text{x}, \text{2})$

evaluates its argument first; see MakeBoxes

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In$\mathrm{ToBoxes}(2+3)$Out$\text{5}$

a binomial coefficient: a fraction without its bar, in parentheses

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In$\mathrm{ToBoxes}(\binom{n}{k})$Out$\mathrm{RowBox}(\bigl\lbrack\text{(}, \mathrm{FractionBox}(\text{n}, \text{k}, (\mathrm{FractionLine},\mathrm{False})), \text{)}\bigr\rbrack)$

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In$\mathrm{ToBoxes}(\frac{\sqrt{x}}{y})$Out$\mathrm{FractionBox}(\mathrm{SqrtBox}(\text{x}), \text{y})$

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In$\mathrm{ToBoxes}(b^2+a)$Out$\mathrm{RowBox}(\bigl\lbrack\mathrm{SuperscriptBox}(\text{b}, \text{2}), \text{+}, \text{a}\bigr\rbrack)$

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In$\mathrm{ToBoxes}(\mathrm{B}(a, b))$Out$\mathrm{RowBox}(\bigl\lbrack\text{Beta}, \text{⁡}, \mathrm{RowBox}(\bigl\lbrack\text{(}, \text{a}, \text{,}, \text{b}, \text{)}\bigr\rbrack)\bigr\rbrack)$

Scope #

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In$\mathrm{Map}(\mathrm{ToBoxes}, \bigl\lbrack i, π, e\bigr\rbrack)$Out$\bigl\lbrack\text{i}, \text{$\pi$}, \text{e}\bigr\rbrack$

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In$\mathrm{ToBoxes}(\bigl\lbrack\bigl\lbrack a, b, c\bigr\rbrack, \bigl\lbrack d, e, f\bigr\rbrack\bigr\rbrack)$Out$\mathrm{RowBox}(\bigl\lbrack\text{[}, \mathrm{RowBox}(\bigl\lbrack\text{[}, \text{a}, \text{,}, \text{b}, \text{,}, \text{c}, \text{]}\bigr\rbrack), \text{,}, \mathrm{RowBox}(\bigl\lbrack\text{[}, \text{d}, \text{,}, \text{e}, \text{,}, \text{f}, \text{]}\bigr\rbrack), \text{]}\bigr\rbrack)$

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In$\mathrm{Map}(\mathrm{ToBoxes}, N(\bigl\lbrack\frac{10}{3}, 10/3i\bigr\rbrack, 20))$Out$\bigl\lbrack\text{3.3333333333333333333}, \mathrm{RowBox}(\bigl\lbrack\text{3.3333333333333333333}, \text{⁢}, \text{i}\bigr\rbrack)\bigr\rbrack$

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In$\mathrm{Map}(\mathrm{ToBoxes}, \bigl\lbrack a^{x}, a^{x}, \sqrt{a}, \sqrt{a}, \sqrt[3]{a}, e^{x}, \frac{1}{x}, \frac{1}{x}\bigr\rbrack)$Out$\bigl\lbrack\mathrm{SuperscriptBox}(\text{a}, \text{x}), \mathrm{SuperscriptBox}(\text{a}, \text{x}), \mathrm{SqrtBox}(\text{a}), \mathrm{SqrtBox}(\text{a}), \mathrm{RadicalBox}(\text{a}, \text{3}), \mathrm{SuperscriptBox}(\text{e}, \text{x}), \mathrm{FractionBox}(\text{1}, \text{x}), \mathrm{FractionBox}(\text{1}, \text{x})\bigr\rbrack$

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In$\mathrm{ToBoxes}(\bigl\lbrack1, 2, 3\bigr\rbrack)$Out$\mathrm{RowBox}(\bigl\lbrack\text{[}, \text{1}, \text{,}, \text{2}, \text{,}, \text{3}, \text{]}\bigr\rbrack)$

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In$\mathrm{Map}(\mathrm{ToBoxes}, \bigl\lbrack\text{a}, \text{$\alpha$}, \text{⊕}\bigr\rbrack)$Out$\bigl\lbrack\mathrm{TextBox}(\text{a}, (\mathrm{ShowStringCharacters},\mathrm{True})), \mathrm{TextBox}(\text{$\alpha$}, (\mathrm{ShowStringCharacters},\mathrm{True})), \mathrm{TextBox}(\text{⊕}, (\mathrm{ShowStringCharacters},\mathrm{True}))\bigr\rbrack$

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In$\mathrm{ToBoxes}(\bigl\lbrack\bigl\lbrack a, b, c\bigr\rbrack, \bigl\lbrack d, k, f\bigr\rbrack\bigr\rbrack)$Out$\mathrm{RowBox}(\bigl\lbrack\text{[}, \mathrm{RowBox}(\bigl\lbrack\text{[}, \text{a}, \text{,}, \text{b}, \text{,}, \text{c}, \text{]}\bigr\rbrack), \text{,}, \mathrm{RowBox}(\bigl\lbrack\text{[}, \text{d}, \text{,}, \text{k}, \text{,}, \text{f}, \text{]}\bigr\rbrack), \text{]}\bigr\rbrack)$

Properties #

A rational becomes a fraction box of numerator and denominator

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In$\mathrm{ToBoxes}(\frac{1}{10})$Out$\mathrm{FractionBox}(\text{1}, \text{10})$

About

Examples	14
Checked against	Wolfram Language 4 agree10 differ
Crosswalk	Wolfram Language

See also: MakeBoxes, DisplayForm, RawBoxes