# Math Test

# 1Limits

A limit:
limx→ ∞f(x),
which should appear as x→ ∞ in italics, and «lim» in plain style. Inlined: limx→ ∞f(x).
And why not, a sum:
∞⎲⎳i= 1ai,
where the sum’s limits should appear below (i= 1) and above (∞) the ∑ but to the right. Inlined: ∑∞i= 1ai. Integral: ∫∞x=ax dx. Display mode:
∞⌠⌡x=ax dx.
We can also integrate without limits: ∫A dx.
A sum inside another element (red color):
∞⎲⎳i= 1ai.
The placing of limits can be cofigured with the `\limits` and `\nolimits` macros:
limx→ ∞f(x),⎲⎳∞i= 1x,∞⌠⌡0f(x) dx

## 1.1Super- and Subscript

When any element has both super- and subscript, they should appear like inlined limits, one above the other: a34. Also before an element: 32He. In display mode:
⎲⎳i,jaij+ ⎲⎳i,jaji= ⎲⎳iaii,
21H+21H→32He+10n.

# 2Numeration

Equations can be numbered, like 1↓.
(1) y=x
And also like 2↓.
(2) x= 3
Notice that eq. 2↑ comes after eq. 1↑.
Some equations can also be numbered, even if they don’t have a label.
(3) x= 2y
Other equations that contain * should not numbered, but perhaps aligned:
left right
Some environments allow for multiple labels:
(4) a = b×c (5) c×d×e = i.
Now a random environment: x y.

# 3Brackets

An array:
⎡⎢⎣ 12 2 3 4 ×yx ⎤⎥⎦
And an inline array ⎡⎢⎣ a b c dio ⎤⎥⎦.
Arrays are separated by variable-size brackets: ⎛⎜⎝ a b c d ⎞⎟⎠ ⎡⎢⎣ a b c d ⎤⎥⎦ ⎧⎨⎩ a b c d ⎫⎬⎭ ⟨ a b c d ⟩ ||| a b c d |||which might also differ on right and left ⎛⎜⎝ a b c d ⎞⎟⎠ or use the empty opening ⎧⎨⎩ a b c d or closing: a b c d |||. There are also fixed-size big brackets: (a) [b] {c} ⟨d⟩ |e| ⟨f⟩.
Aligned brackets can be present: (toText). One of them may be omitted: toText).
Aligned brackets can be applied to complex items:
s×⎛⎜⎜⎜⎝1 +⎛⎜⎝ a11 a21 a12 a22 ⎞⎟⎠×⎛⎜⎝ 1 − 1 − 1 − 1 ⎞⎟⎠+∥∥∥∥∥ 1 − 1 0 − 1 1 0 0 0 r ∥∥∥∥∥⎞⎟⎟⎟⎠.
Math brackets should not be mistaken for TeX brackets: (ℱ{s(x)})/(2).

# 4Fraction

A big recursive fraction:
(1)/(⎛⎜⎝1 +⎛⎜⎝(1)/(1 +⎛⎝(1)/(1 + 2x)⎞⎠)⎞⎟⎠⎞⎟⎠)
A nice fraction: 5⁄6.
A non-diminishing fraction containing alignments:
(1)/(1 +⎛⎝(1)/(1 +x)×(1)/(1 +x)⎞⎠).
A similar concept is a binomial coefficient: (A+ 1B). It can be prettily presented:
⎛⎜⎝A B+ 1⎞⎟⎠.
A symbol can be stacked over another using `\stackrel`: xR→y. Anything can be stacked: headheels.

# 5Roots

A square root: √(3). A root in a fraction: √(((78x+ 45y) ×√(Height))/(sin(x+ 1))+ 5).
A more complex square root in a fraction:
(1)/(⎛⎝1 +√(2)⎛⎝(1)/(1 +√(2))⎞⎠+√((1)/(2))⎞⎠).
Higher order roots: 3√(x+y), x+ 1√(Weight). In a fraction:
(7⁄8√((8)/(4)x))/(s+ 5√(((78x+ 45y) ×√(Height))/(sin(x+ 1))+ 5)).

# 6Decorations

## 6.1Cases

Used to switch several values.
y=⎧⎨⎩ x i= 0, x+ 1 i< 3
Cases may have more than two rows:
f(x) =⎧⎪⎨⎪⎩ 0 x< 0, ∞ x= 0, 0 x> 0

## 6.2Braces

Values can be underbraced or overbraced.
a−b=c+d+e+f.
Underbraces and overbraces can contain text.
a−bover=c+d+eover+funder+g.
They can also be inlined: a+bover.

# 7Spacing

The command `\raisebox` is useful to, surprisingly, raise a little box,
raisedoverlowered and back.
Like `\mbox`, it puts its content in a text box. It can also be used just for spacing:
BV.
There are other spacing commands: `\hspace` a b, protected space a b, and at “block level”`\vspace`: a b.
There should be 1 cm of vertical space above this paragraph.

# 8Fonts

This section tests font support.

## 8.1Variables and Functions

By default, letters denote variables and are taken from the `\mathnormal` font, which is italic: αx+αy=α(x+y), with the exception of upright capital Greek letters, G≠ Γ. Letters run together represent different variables: abcd=a×b×c×d.
There has been some trouble over some commands like Greek letters; some of them should be italicized, as in: μ or Å. Others should not, as in Ω. Upright Greek letters are also available: μ ≠μ. An example from the LyX math guide:
π+→ μ++ νμ.
Functions names should be upright: sin(2π), log(x), tanδ.

## 8.2Mathematical Fonts

Mathematical fonts used in equations include Roman (`\mathrm`), Sans Serif (`\mathsf`), `Typewriter` (`\mathtt`), Bold (`\mathbf`), SCRIPT (`\mathscr`), CALLIGRAPHIC (`\mathcal`), BLACKBOARD BOLD (`\mathbb`), and Fraktur (`\mathfrak`). For the latter, some single characters are translated to their Unicode equivalents: ℱ, 𝔽, 𝔉.
Regular text in a formula can be achieved via text font commands like `\textrm`: 5to10, via boxes like \mbox (prevents line breaks): 6is more than 5, or the AMSmath `\text` macro (scales like math symbols) basesupersub. The content of an mbox is processed in LaTeX text mode. This allows text font commands, e.g. a switch to sans-serif-bold-italic, or the phonetic alphabet: sfbfit, tipa.

## 8.3Units

Units should be written upright, either with `\mathrm` or with macros from the `units` package, e.g. as simple unit, km, with magnitude, 57km, with fractional unit, 200km⁄h, or with a fraction before the units, 3⁄2km, (7)/(16)s.

## 8.4Sizes

Sizes can be specified in formulas: display,text,script,scriptscript.

# 9Colors and Boxes

A colored box: aaa.
A framed box: box. It can be aligned left: box or right: box.

# 10Macros

Definitions can be added as macros. Then they can be used in formulae: √(12)+1√(2).
Macro definitions can accept default parameters. Again, useful in formulae: 4√(5). Default parameters can then be overriden: 5√(y)+x√(4).
Other definitions from the preamble can be used: 3√(4).
Definitions on the fly are also possible: 7√(8), and used with different values: a√(b).
Macros may contain a literal parameter. It should parse correctly: t.
A macro with four parameters from the LyX detailed math guide. Now in use: 1 +x1,  2=  −((1 −x))/(2)±√(((1 −x)2)/(4)− 5)−B.

# 11Pathological Cases

Empty equations have been known to fail: .
An equation with an mbox containing a comment: text more, and a comment inside textrm: text more. Finally, a comment at the end of a text function: only text.

# 12Bye-bye

That’s all folks!