Math Test

1 Limit

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

2 Numeration

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.

3 Parentheses

Some delimiters also taken from the Spanish Lyx User’s Guide. An array:
12 2 3 4 × yx
And an inline array a b c dio .
There are also big brackets: (a) [b] {c} d |e| f.
Aligned brackets can be present: (toText). One of them may be omitted: toText).

4 Fraction

A big recursive fraction:
(1)/((1 + ((1)/(1 + ((1)/(1 + 2x))))))
A nice fraction: 56.
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.

5 Roots

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:
(78((8)/(4)x))/(s + 5(((78x + 45y) × (Height))/(sin(x + 1)) + 5)).

6 Decorations

6.1 Cases

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 

6.2 Braces

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.

7 Spacing

The command \raisebox is useful to, surprisingly, raise a little box.
raisedoverloweredand back.
It can also be used just for spacing.
BV.
There are other spacing commands, like \hspace: " ", and \vspace: " ". Protected space can be used: a b.

8 Fonts

Fonts can be switched on and off.
By default, text in formulae is shown italicized. Variable: meters.
Some font styles. Roman: 1 mathrm. Sans serif: 2 mathsf. Typewriter: 3 mathtt. Bold: 4 mathbf.
Regular text. Normal text: 5 textfm. Literal text: 6 mbox text. Phonetic alphabet: 7abcde. Regular text can be embedded into formulae: regular text \command \another command \\no spaces allowed.
Units can be shown with or without a magnitude. Without: km. With: 57 km. Fractional units: 20 kmh. With a fraction before the units: 32 km, (7)/(16) s.
Some special fonts are supported: , F, 𝔽, 𝔉.
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.

9 Colors and Boxes

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

10 Macros

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.

11 Pathological 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.

12 Bye-bye

That’s all folks!