Intent Examples

MathCAT Version: 0.6.7

MathML Documents Index

MathML MathML (default intents) MathML (explicit intents) TeX Comments
Numbers
1,234 + 1,234 
§
<math display='block'>
 <mn>1,234</mn>
 <mo>+</mo>
 <mn>1,234</mn>
</math>
1234 plus 1234
§
<math intent=':common' display='block'>
1234 plus 1234
§
<math intent=':literal' display='block'>
1234 plus 1234
 
§
<math display='block'>
 <mn intent='1.234:decimal-comma'>1,234</mn>
 <mo>+</mo>
 <mn intent='1.234:decimal-comma'>1,234</mn>
</math>
1.234 plus 1.234
§
<math display='block'>
 <mn intent=':decimal-comma'>1,234</mn>
 <mo>+</mo>
 <mn intent=':decimal-comma'>1,234</mn>
</math>
1234 plus 1234
 1,234+1{,}234 decimal comma
1,234 ; 1,234 ; 1,234,000 
§
<math display='block'>
 <mn>1,234</mn>
 <mo>;</mo>
 <mn>1,234</mn>
 <mo>;</mo>
 <mn>1,234,000</mn>
</math>
1234 semicolon 1234 semicolon 1234000
§
<math intent=':common' display='block'>
1234 semicolon 1234 semicolon 1234000
§
<math intent=':literal' display='block'>
1234 semicolon 1234 semicolon 1234000
 
§
<math display='block' mathbackground='yellow'>
 <mn intent='1234:thousands-comma'>1,234</mn>
 <mo>;</mo>
 <mn intent='1234:thousands-comma'>1,234</mn>
 <mo>;</mo>
 <mn intent='1234000:thousands-comma'>1,234,000</mn>
</math>
1234 semicolon 1234 semicolon 1234000
§
<math display='block' mathbackground='yellow'>
 <mn intent=':thousands-comma'>1,234</mn>
 <mo>;</mo>
 <mn intent=':thousands-comma'>1,234</mn>
 <mo>;</mo>
 <mn intent=':thousands-comma'>1,234,000</mn>
</math>
1234 semicolon 1234 semicolon 1234000
 1,234; 1,234; 1,234,000 grouping comma
−3 
§
<math display='block'>
 <mn>−3</mn>
</math>
negative 3
§
<math intent=':common' display='block'>
negative 3
§
<math intent=':literal' display='block'>
minus 3
 
§
<math display='block'>
 <mn intent='-3'>−3</mn>
</math>
minus 3
 -3 mn -3
− 3 
§
<math display='block'>
 <mrow>
  <mo>−</mo>
  <mn>3</mn>
 </mrow>
</math>
negative 3
§
<math intent=':common' display='block'>
negative 3
§
<math intent=':literal' display='block'>
minus 3
 
§
<math display='block'>
 <mrow intent='-3'>
  <mo>−</mo>
  <mn>3</mn>
 </mrow>
</math>
minus 3
 -3 mrow mo -3
X,XVI 
§
<math display='block'>
 <mn>X</mn><mo>,</mo><mn>XVI</mn>
</math>
10 comma 16
§
<math intent=':common' display='block'>
10 comma 16
§
<math intent=':literal' display='block'>
x comma XVI
 
§
<math display='block'>
 <mn intent=':roman-numeral'>X</mn><mo>,</mo><mn intent=':roman-numeral'>XVI</mn>
</math>
10 comma 16
 \text{X},\text{XVI} Roman Numerals
Super and Sub Scripts
x 2 
§
<math display='block'>
 <msup>
  <mi>x</mi>
  <mn>2</mn>
 </msup>
</math>
x squared
§
<math intent=':common' display='block'>
x squared
§
<math intent=':literal' display='block'>
x super 2 end super
 
§
<math display='block'>
 <msup>
  <mi>x</mi>
  <mn>2</mn>
 </msup>
</math>
x squared
 x^2 squared
x 3 
§
<math display='block'>
 <msup>
  <mi>x</mi>
  <mn>3</mn>
 </msup>
</math>
x cubed
§
<math intent=':common' display='block'>
x cubed
§
<math intent=':literal' display='block'>
x super 3 end super
 
§
<math display='block'>
 <msup>
  <mi>x</mi>
  <mn>3</mn>
 </msup>
</math>
x cubed
 x^3 cubed
H 2 
§
<math display='block'>
 <msup>
  <mi mathvariant='normal'>H</mi>
  <mn>2</mn>
 </msup>
</math>
h squared
§
<math intent=':common' display='block'>
h squared
§
<math intent=':literal' display='block'>
h super 2 end super
 
§
<math display='block'>
 <msup intent='index($H,$n)'>
  <mi arg='H' mathvariant='normal'>H</mi>
  <mn arg='n'>2</mn>
 </msup>
</math>
index of, h comma 2
§
<math display='block'>
 <msup intent='index:silent($H,$n)'>
  <mi arg='H' mathvariant='normal'>H</mi>
  <mn arg='n'>2</mn>
 </msup>
</math>
h 2
 \mathrm{H}^2 2nd Cohomology
ℝ 2 
§
<math display='block'>
 <msup>
  <mi>&#x211D;</mi>
  <mn>2</mn>
 </msup>
</math>
R 2
§
<math intent=':common' display='block'>
R 2
§
<math intent=':literal' display='block'>
double-struck r super 2 end super
 
§
<math display='block'>
 <msup intent='vector-space-power($R,$n)'>
  <mi arg='R'>&#x211D;</mi>
  <mn arg='n'>2</mn>
 </msup>
</math>
vector space power of, the real numbers comma 2
§
<math display='block'>
 <msup intent='vector-space-power:silent(_R,$n)'>
  <mi arg='R'>&#x211D;</mi>
  <mn arg='n'>2</mn>
 </msup>
</math>
R 2
 \mathbb{R}^2 R 2
x n 
§
<math display='block'>
 <msup>
  <mi>x</mi>
  <mi>n</mi>
 </msup>
</math>
x to the n-th
§
<math intent=':common' display='block'>
x to the n-th
§
<math intent=':literal' display='block'>
x super n end super
 
§
<math display='block'>
 <msup>
  <mi>x</mi>
  <mi>n</mi>
 </msup>
</math>
x to the n-th
 x^n x to nth
x † 
§
<math display='block'>
 <msup>
  <mi>x</mi>
  <mo>&#x2020;<!-- U+2020--></mo>
 </msup>
</math>
x dagger,
§
<math intent=':common' display='block'>
x dagger,
§
<math intent=':literal' display='block'>
x dagger
 
§
<math display='block'>
 <msup intent='x-dagger'>
  <mi>x</mi>
  <mo>&#x2020;<!-- U+2020--></mo>
 </msup>
</math>
x dagger
 x^\dagger dagger
x T 
§
<math display='block'>
 <msup>
  <mi>x</mi>
  <mi mathvariant='normal'>T</mi>
 </msup>
</math>
x transpose
§
<math intent=':common' display='block'>
x transpose
§
<math intent=':literal' display='block'>
x super t end super
 
§
<math display='block'>
 <msup intent='$op($arg)'>
  <mi arg='arg'>x</mi>
  <mi arg='op'
      intent='transpose'
      mathvariant='normal'>T</mi>
 </msup>
</math>
x transpose
§
<math display='block' mathbackground='yellow'>
 <msup intent='$op:function($arg)'>
  <mi arg='arg'>x</mi>
  <mi arg='op'
      intent='transpose'
      mathvariant='normal'>T</mi>
 </msup>
</math>
transpose of, x
§
<math display='block' mathbackground='yellow'>
 <msup intent='transpose:function($arg)'>
  <mi arg='arg'>x</mi>
  <mi arg='op'
      intent='transpose'
      mathvariant='normal'>T</mi>
 </msup>
</math>
transpose of, x
§
<math display='block'>
 <msup intent='_($op, _of, $arg)'>
  <mi arg='arg'>x</mi>
  <mi arg='op'
      intent='transpose'
      mathvariant='normal'>T</mi>
 </msup>
</math>
transpose of x
§
<math display='block'>
  <msup intent='_:silent($op, _of, $arg)'>
  <mi arg='arg'>x</mi>
  <mi arg='op'
      intent='transpose'
      mathvariant='normal'>T</mi>
 </msup>
</math>
transpose of x
§
<math display='block' mathbackground='yellow'>
 <msup intent='_transpose($arg)'>
  <mi arg='arg'>x</mi>
  <mi arg='op'
      intent='transpose'
      mathvariant='normal'>T</mi>
 </msup>
</math>
transpose of, x
 x^{\mathrm{T}} x transpose
x T 
§
<math display='block'>
 <mmultiscripts>
  <mi>x</mi>
  <mprescripts/>
  <mrow/>
  <mi mathvariant='normal'>T</mi>
 </mmultiscripts>
</math>
x pre superscript t,
§
<math intent=':common' display='block'>
x pre superscript t,
§
<math intent=':literal' display='block'>
x pre superscript t,
 
§
<math display='block'>
 <mmultiscripts intent='$op($arg)'>
  <mi arg='arg'>x</mi>
  <mprescripts/>
  <mrow/>
  <mi arg='op'
      intent='transpose'
      mathvariant='normal'>T</mi>
 </mmultiscripts>
</math>
x transpose
§
<math display='block' mathbackground='yellow'>
 <mmultiscripts intent='$op:function($arg)'>
  <mi arg='arg'>x</mi>
  <mprescripts/>
  <mrow/>
  <mi arg='op'
      intent='transpose'
      mathvariant='normal'>T</mi>
 </mmultiscripts>
</math>
transpose of, x
§
<math display='block'>
 <mmultiscripts intent='_($op, _of, $arg)'>
  <mi arg='arg'>x</mi>
  <mprescripts/>
  <mrow/>
  <mi arg='op'
      intent='transpose'
      mathvariant='normal'>T</mi>
 </mmultiscripts>
</math>
transpose of x
§
<math display='block'>
 <mmultiscripts intent='_:silent($op, _of, $arg)'>
  <mi arg='arg'>x</mi>
  <mprescripts/>
  <mrow/>
  <mi arg='op'
      intent='transpose'
      mathvariant='normal'>T</mi>
 </mmultiscripts>
</math>
transpose of x
 {}^{\mathrm{T}}x x transpose pre-sup
x i j T 
§
<math display='block'>
 <msubsup>
  <mi>x</mi>
  <mrow>
   <mi>i</mi>
   <mi>j</mi>
  </mrow>
  <mi mathvariant='normal'>T</mi>
 </msubsup>
</math>
x sub i j end subscript, to the t-th
§
<math intent=':common' display='block'>
x sub i j end subscript, to the t-th
§
<math intent=':literal' display='block'>
x sub i j super t end super
 
§
<math display='block'>
 <msubsup intent='transpose(index:silent($x,$sub))'>
  <mi arg='x'>x</mi>
  <mrow arg='sub' intent=':index'>
   <mi>i</mi>
   <mi>j</mi>
  </mrow>
  <mi mathvariant='normal'>T</mi>
 </msubsup>
</math>
x i j transpose
§
<math display='block'>
 <msubsup>
  <mi>x</mi>
  <mrow arg='sub' intent=':index'>
   <mi>i</mi>
   <mi>j</mi>
  </mrow>
  <mi intent='transpose:postfix' mathvariant='normal'>T</mi>
 </msubsup>
</math>
x sub i j end subscript, to the transpose
§
<math display='block'>
 <msubsup intent='transpose(sub:infix($base, $sub))'>
  <mi arg='base'>x</mi>
  <mrow arg='sub' intent=':index'>
   <mi>i</mi>
   <mi>j</mi>
  </mrow>
  <mi>T</mi>
 </msubsup>
</math>
, x sub i j, transpose
 x_{ij}^{\mathrm{T}} x sub transpose
4 th 
§
<math display='block'>
 <msup>
  <mn>4</mn>
  <mi>th</mi>
 </msup>
</math>
4 to the th
§
<math intent=':common' display='block'>
4 to the th
§
<math intent=':literal' display='block'>
4 super th end super
 
§
<math display='block'>
 <msup>
  <mn>4</mn>
  <mi intent='ordinal-mark'>th</mi>
 </msup>
</math>
4 to the ordinal mark
§
<math display='block'>
 <msup intent='ordinal-mark:silent($n,$th)'>
  <mn arg='n'>4</mn>
  <mi arg='th'>th</mi>
 </msup>
</math>
4 th
§
<math display='block'>
 <msup intent='_4th'>
  <mn>4</mn>
  <mi>th</mi>
 </msup>
</math>
4th
 4{\mathrm{th} ordinal 4th
A = ∑ n = 0 ∞ a n X n ∈ R ⟦ X ⟧ 
§
<math display='block'>
 <mrow>
  <mi>A</mi>
  <mo>=</mo>
  <munderover>
   <mo>∑</mo>
   <mrow>
    <mi>n</mi>
    <mo>=</mo>
    <mn>0</mn>
   </mrow>
   <mi>∞</mi>
   </munderover>
   <msub>
    <mi>a</mi>
    <mi>n</mi>
   </msub>
   <msup>
    <mi>X</mi>
    <mi>n</mi>
   </msup>
   <mo>∈</mo>
   <mrow>
    <mi>R</mi>
    <mo>⟦</mo>
    <mi>X</mi>
    <mo>⟧</mo>
   </mrow>
 </mrow>
</math>
eigh is equal to; the sum from n is equal to 0 to infinity of; eigh sub n x to the n-th; is an element of; r, left white square bracket, x right white square bracket
§
<math intent=':common' display='block'>
eigh is equal to; the sum from n is equal to 0 to infinity of; eigh sub n x to the n-th; is an element of; r, left white square bracket, x right white square bracket
§
<math intent=':literal' display='block'>
eigh is equal to; sum with n is equal to 0 below and infinity above; eigh sub n x super n end super; is an element of; r, left white square bracket, x right white square bracket
 
§
<math display='block'>
 <mrow>
  <mi>A</mi>
  <mo>=</mo>
  <munderover>
   <mo>∑</mo>
   <mrow>
    <mi>n</mi>
    <mo>=</mo>
    <mn>0</mn>
   </mrow>
   <mi>∞</mi>
   </munderover>
   <msub>
    <mi>a</mi>
    <mi>n</mi>
   </msub>
   <msup>
    <mi>X</mi>
    <mi>n</mi>
   </msup>
   <mo>∈</mo>
   <mrow intent='power-series($r,$x)'>
    <mi arg='r'>R</mi>
    <mo>⟦</mo>
    <mi arg='x'>X</mi>
    <mo>⟧</mo>
   </mrow>
 </mrow>
</math>
eigh is equal to; the sum from n is equal to 0 to infinity of; eigh sub n x to the n-th; is an element of, power series of, r comma x
§
<math display='block'>
 <mrow>
  <mi>A</mi>
  <mo>=</mo>
  <munderover>
   <mo>∑</mo>
   <mrow intent='_(0)'>
    <mi>n</mi>
    <mo>=</mo>
    <mn>0</mn>
   </mrow>
   <mi>∞</mi>
   </munderover>
   <msub>
    <mi>a</mi>
    <mi>n</mi>
   </msub>
   <msup intent='_power:silent($x,_to_the,$n)'>
    <mi arg='x'>X</mi>
    <mi arg='n'>n</mi>
   </msup>
   <mo>∈</mo>
   <mrow intent='power-series:silent(
                 $r,_power_series,_over,$x)'>
    <mi arg='r'>R</mi>
    <mo>⟦</mo>
    <mi arg='x'>X</mi>
    <mo>⟧</mo>
   </mrow>
 </mrow>
</math>
eigh is equal to; the sum from 0 to infinity of; eigh sub n x to the n; is an element of, r power series over x
 A=\sum_0^\infty a_n X^n \in R\lBrack X \rBrack formal power series
sin 2 ⁡ 𝜃 + cos 2 ⁡ 𝜃 = 1 
§
<math display='block'>
 <mrow>
  <msup>
   <mi>sin</mi>
   <mn>2</mn>
  </msup>
  <mo>&#x2061;</mo>
  <mi>𝜃</mi>
 </mrow>
 <mo>+</mo>
 <mrow>
  <msup>
   <mi>cos</mi>
   <mn>2</mn>
  </msup>
  <mo>&#x2061;</mo>
  <mi>𝜃</mi>
 </mrow>
 <mo>=</mo>
 <mn>1</mn>
</math>
sine squared of theta, plus cosine squared of theta; is equal to 1
§
<math intent=':common' display='block'>
sine squared of theta, plus cosine squared of theta; is equal to 1
§
<math intent=':literal' display='block'>
sine super 2 end super of theta, plus, cosine super 2 end super of theta; is equal to 1
 
§
<math display='block'>
 <mrow>
  <msup>
   <mi>sin</mi>
   <mn>2</mn>
  </msup>
  <mo intent='apply:silent'>&#x2061;</mo>
  <mi intent='theta'>𝜃</mi>
 </mrow>
 <mo>+</mo>
 <mrow>
  <msup>
   <mi>cos</mi>
   <mn>2</mn>
  </msup>
  <mo intent='apply:silent'>&#x2061;</mo>
  <mi intent='theta'>𝜃</mi>
 </mrow>
 <mo>=</mo>
 <mn>1</mn>
</math>
sine squared theta, plus cosine squared theta; is equal to 1
 \sin^2\theta + \cos^2\theta=1 sin squared plus cos squared
Combinations and Permutations
( n k ) 
§
<math display='block'>
 <mrow>
  <mo>(</mo>
  <mfrac linethickness='0pt'>
   <mi>n</mi>
   <mi>k</mi>
  </mfrac>
  <mo>)</mo>
 </mrow>
</math>
n choose k
§
<math intent=':common' display='block'>
n choose k
§
<math intent=':literal' display='block'>
open paren n over k, close paren
 
§
<math display='block'>
 <mrow intent='binomial($n,$k)'>
  <mo>(</mo>
  <mfrac linethickness='0pt'>
   <mi arg='n'>n</mi>
   <mi arg='k'>k</mi>
  </mfrac>
  <mo>)</mo>
 </mrow>
</math>
n choose k
§
<math display='block'>
 <mrow intent='binomial:infix($n,$k)'>
  <mo>(</mo>
  <mfrac linethickness='0pt'>
   <mi arg='n'>n</mi>
   <mi arg='k'>k</mi>
  </mfrac>
  <mo>)</mo>
 </mrow>
</math>
, n binomial k,
 \binom{n}{k} binom n k
C k n 
§
<math display='block'>
 <mmultiscripts>
  <mi>C</mi>
  <mi>k</mi>
  <mrow/>
  <mprescripts/>
  <mrow/>
  <mi>n</mi>
 </mmultiscripts>
</math>
n choose k
§
<math intent=':common' display='block'>
n choose k
§
<math intent=':literal' display='block'>
c pre superscript n, subscript k
 
§
<math display='block'>
 <mmultiscripts intent='binomial($n,$k)'>
  <mi>C</mi>
  <mi arg='k'>k</mi>
  <mrow/>
  <mprescripts/>
  <mrow/>
  <mi arg='n'>n</mi>
 </mmultiscripts>
</math>
n choose k
§
<math display='block'>
 <mmultiscripts intent='binomial:infix($n,$k)'>
  <mi>C</mi>
  <mi arg='k'>k</mi>
  <mrow/>
  <mprescripts/>
  <mrow/>
  <mi arg='n'>n</mi>
 </mmultiscripts>
</math>
, n binomial k,
 {}^n C_k binom sup n C sub k
C k n 
§
<math display='block'>
 <msubsup>
  <mi>C</mi>
  <mi>k</mi>
  <mi>n</mi>
 </msubsup>
</math>
c sub k, to the n-th
§
<math intent=':common' display='block'>
c sub k, to the n-th
§
<math intent=':literal' display='block'>
c sub k super n end super
 
§
<math display='block'>
 <msubsup intent='binomial($n,$k)'>
  <mi>C</mi>
  <mi arg='k'>k</mi>
  <mi arg='n'>n</mi>
 </msubsup>
</math>
n choose k
§
<math display='block'>
 <msubsup intent='binomial:infix($n,$k)'>
  <mi>C</mi>
  <mi arg='k'>k</mi>
  <mi arg='n'>n</mi>
 </msubsup>
</math>
, n binomial k,
 C^n_k binom C sup n sub k
C ( n , k ) 
§
<math display='block'>
 <mrow>
  <mi>C</mi>
  <mo>(</mo>
  <mi>n</mi>
  <mo>,</mo>
  <mi>k</mi>
  <mo>)</mo>
 </mrow>
</math>
c of, open paren n comma k, close paren
§
<math intent=':common' display='block'>
c of, open paren n comma k, close paren
§
<math intent=':literal' display='block'>
c, open paren n comma k, close paren
 
§
<math display='block'>
 <mrow intent='binomial($n,$k)'>
  <mi>C</mi>
  <mo>(</mo>
  <mi arg='n'>n</mi>
  <mo>,</mo>
  <mi arg='k'>k</mi>
  <mo>)</mo>
 </mrow>
</math>
n choose k
§
<math display='block'>
 <mrow intent='binomial:infix($n,$k)'>
  <mi>C</mi>
  <mo>(</mo>
  <mi arg='n'>n</mi>
  <mo>,</mo>
  <mi arg='k'>k</mi>
  <mo>)</mo>
 </mrow>
</math>
, n binomial k,
 C(n,k) binom C n k
P k n 
§
<math display='block'>
 <mmultiscripts>
  <mi>P</mi>
  <mi>k</mi>
  <mrow/>
  <mprescripts/>
  <mrow/>
  <mi>n</mi>
 </mmultiscripts>
</math>
k permutations of n
§
<math intent=':common' display='block'>
k permutations of n
§
<math intent=':literal' display='block'>
p pre superscript n, subscript k
 
§
<math display='block'>
 <mmultiscripts
     intent='permutation($n,$k)'>
  <mi>P</mi>
  <mi arg='k'>k</mi>
  <mrow/>
  <mprescripts/>
  <mrow/>
  <mi arg='n'>n</mi>
 </mmultiscripts>
</math>
permutation of, n comma k
§
<math display='block'>
 <mmultiscripts
     intent='permutation:prefix($n,$k)'>
  <mi>P</mi>
  <mi arg='k'>k</mi>
  <mrow/>
  <mprescripts/>
  <mrow/>
  <mi arg='n'>n</mi>
 </mmultiscripts>
</math>
permutation n k,
§
<math display='block'>
 <mmultiscripts
     intent='_permutation:prefix(_of,$k,_from,$n)'>
  <mi>P</mi>
  <mi arg='k'>k</mi>
  <mrow/>
  <mprescripts/>
  <mrow/>
  <mi arg='n'>n</mi>
 </mmultiscripts>
</math>
permutation of k from n,
 {}^n P_k permutations sup n P sub k
P k n 
§
<math display='block'>
 <msubsup>
  <mi>P</mi>
  <mi>k</mi>
  <mi>n</mi>
 </msubsup>
</math>
k permutations of n
§
<math intent=':common' display='block'>
k permutations of n
§
<math intent=':literal' display='block'>
p sub k super n end super
 
§
<math display='block'>
 <msubsup
     intent='P($n,$k)'>
  <mi>P</mi>
  <mi arg='k'>k</mi>
  <mi arg='n'>n</mi>
 </msubsup>
</math>
p of, n comma k
§
<math display='block'>
 <msubsup
     intent='permutation-symbol($n,$k)'>
  <mi>P</mi>
  <mi arg='k'>k</mi>
  <mi arg='n'>n</mi>
 </msubsup>
</math>
k permutations of n
§
<math display='block'>
 <msubsup
     intent='permutation:prefix($n,$k)'>
  <mi>P</mi>
  <mi arg='k'>k</mi>
  <mi arg='n'>n</mi>
 </msubsup>
</math>
permutation n k,
§
<math display='block'>
 <msubsup
     intent='_permutation:prefix(_of,$k,_from,$n)'>
  <mi>P</mi>
  <mi arg='k'>k</mi>
  <mi arg='n'>n</mi>
 </msubsup>
</math>
permutation of k from n,
 P^n_k permutations P sup n sub k
P ( n , k ) 
§
<math display='block'>
 <mrow>
  <mi>P</mi>
  <mo>(</mo>
  <mi>n</mi>
  <mo>,</mo>
  <mi>k</mi>
  <mo>)</mo>
 </mrow>
</math>
p of, open paren n comma k, close paren
§
<math intent=':common' display='block'>
p of, open paren n comma k, close paren
§
<math intent=':literal' display='block'>
p, open paren n comma k, close paren
 
§
<math display='block'>
 <mrow
     intent='permutation-symbol($n,$k)'>
  <mi>P</mi>
  <mo>(</mo>
  <mi arg='n'>n</mi>
  <mo>,</mo>
  <mi arg='k'>k</mi>
  <mo>)</mo>
 </mrow>
</math>
k permutations of n
§
<math display='block'>
 <mrow
     intent='permutation:prefix($n,$k)'>
  <mi>P</mi>
  <mo>(</mo>
  <mi arg='n'>n</mi>
  <mo>,</mo>
  <mi arg='k'>k</mi>
  <mo>)</mo>
 </mrow>
</math>
permutation n k,
§
<math display='block'>
 <mrow
     intent='_permutation:prefix(_of,$k,_from, $n)'>
  <mi>P</mi>
  <mo>(</mo>
  <mi arg='n'>n</mi>
  <mo>,</mo>
  <mi arg='k'>k</mi>
  <mo>)</mo>
 </mrow>
</math>
permutation of k from n,
 P(n,k) permutations P n k
Infix
x ⊂ y 
§
<math display='block'>
 <mrow>
  <mi>x</mi>
  <mo>&#x2282;</mo>
  <mi>y</mi>
 </mrow>
</math>
x is a subset of y
§
<math intent=':common' display='block'>
x is a subset of y
§
<math intent=':literal' display='block'>
x is a subset of y
 
§
<math display='block'>
 <mrow>
  <mi>x</mi>
  <mo intent='subset'>&#x2282;</mo>
  <mi>y</mi>
 </mrow>
</math>
x subset y
§
<math display='block'>
 <mrow intent='_is_a_subset_of:infix($x,$y)'>
  <mi arg='x'>x</mi>
  <mo>&#x2282;</mo>
  <mi arg='y'>y</mi>
 </mrow>
</math>
, x is a subset of y,
 x \subset y subset
x ‖ y 
§
<math display='block'>
 <mrow>
  <mi>x</mi>
  <mo intent='parallel'>‖</mo>
  <mi>y</mi>
 </mrow>
</math>
x parallel y
§
<math intent=':common' display='block'>
x parallel y
§
<math intent=':literal' display='block'>
x parallel y
 
§
<math display='block'>
 <mrow>
  <mi>x</mi>
  <mo intent='parallel'>‖</mo>
  <mi>y</mi>
 </mrow>
</math>
x parallel y
§
<math display='block'>
 <mrow>
  <mi>x</mi>
  <mo intent='_is_parallel_to'>‖</mo>
  <mi>y</mi>
 </mrow>
</math>
x is parallel to y
§
<math display='block'>
 <mrow intent='_($x,_is,$op,_to,$y)'>
  <mi arg='x'>x</mi>
  <mo arg='op' intent='parallel'>‖</mo>
  <mi arg='y'>y</mi>
 </mrow>
</math>
x is parallel to y
§
<math display='block'>
 <mrow intent='_:silent($x,_is,$op,_to,$y)'>
  <mi arg='x'>x</mi>
  <mo arg='op' intent='parallel'>‖</mo>
  <mi arg='y'>y</mi>
 </mrow>
</math>
x is parallel to y
 x \parallel y parallel
Functions
A ⁡ ( n , m ) 
§
<math display='block'>
 <mrow>
  <mi>A</mi>
  <mo>&#x2061;</mo>
  <mrow>
   <mo>(</mo>
   <mi>n</mi>
   <mo>,</mo>
   <mi>m</mi>
   <mo>)</mo>
  </mrow>
 </mrow>
</math>
eigh of, open paren n comma m, close paren
§
<math intent=':common' display='block'>
eigh of, open paren n comma m, close paren
§
<math intent=':literal' display='block'>
eigh of, open paren n comma m, close paren
 
§
<math display='block'>
 <mrow intent='$A($n,$m)'>
  <mi arg='A' intent='Ackerman'>A</mi>
  <mo>&#x2061;</mo>
  <mrow>
   <mo>(</mo>
   <mi arg='n'>n</mi>
   <mo>,</mo>
   <mi arg='m'>m</mi>
   <mo>)</mo>
  </mrow>
 </mrow>
</math>
Ackerman of, n comma m
§
<math display='block'>
 <mrow>
  <mi intent='Ackerman'>A</mi>
  <mo>&#x2061;</mo>
  <mrow>
   <mo>(</mo>
   <mi>n</mi>
   <mo>,</mo>
   <mi>m</mi>
   <mo>)</mo>
  </mrow>
 </mrow>
</math>
Ackerman of, open paren n comma m, close paren
§
<math display='block'>
 <mrow>
  <mi intent='A:Ackerman'>A</mi>
  <mo>&#x2061;</mo>
  <mrow>
   <mo>(</mo>
   <mi>n</mi>
   <mo>,</mo>
   <mi>m</mi>
   <mo>)</mo>
  </mrow>
 </mrow>
</math>
eigh of, open paren n comma m, close paren
 A(m,n) Ackerman or A
Higher Order Functions
( g ∘ h ) ′ ( x ) 
§
<math display='block'>
 <mrow>
  <msup>
   <mrow>
    <mo>(</mo>
    <mi>g</mi>
    <mo>∘</mo>
    <mi>h</mi>
    <mo>)</mo>
   </mrow>
   <mo>′</mo>
  </msup>
  <mo>(</mo>
  <mi>x</mi>
  <mo>)</mo>
 </mrow>
</math>
open paren, g composed with h, close paren prime; times x
§
<math intent=':common' display='block'>
open paren, g composed with h, close paren prime; times x
§
<math intent=':literal' display='block'>
open paren, g composed with h, close paren prime; open paren x close paren
 
§
<math display='block'>
 <mrow intent='$op3($x)'>
  <msup arg='op3' intent='$op2($composed)'>
   <mrow arg='composed' intent='$op1:infix($g,$h)'>
    <mo>(</mo>
    <mi arg='g'>g</mi>
    <mo arg='op1' intent='function-composition'>∘</mo>
    <mi arg='h'>h</mi>
    <mo>)</mo>
   </mrow>
   <mo arg='op2' intent='first-derivative'>′</mo>
  </msup>
  <mo>(</mo>
  <mi arg='x'>x</mi>
  <mo>)</mo>
 </mrow>
</math>
first derivative of; g function composition h, applied to x
 (g∘h)′(x) low (g∘h)′(x)
( g ∘ h ) ′ ( x ) 
§
<math display='block'>
 <mrow>
  <mo>(</mo>
  <mi>g</mi>
  <mo>∘</mo>
  <mi>h</mi>
  <mo>)</mo>
  <mo>′</mo>
  <mo>(</mo>
  <mi>x</mi>
  <mo>)</mo>
 </mrow>
</math>
open paren, g composed with h, close paren prime; times x
§
<math intent=':common' display='block'>
open paren, g composed with h, close paren prime; times x
§
<math intent=':literal' display='block'>
open paren, g composed with h, close paren prime; open paren x close paren
 
§
<math display='block'>
 <mrow intent='first-derivative(function-composition:infix(g,h))(x)'>
  <mo>(</mo>
  <mi>g</mi>
  <mo>∘</mo>
  <mi>h</mi>
  <mo>)</mo>
  <mo>′</mo>
  <mo>(</mo>
  <mi>x</mi>
  <mo>)</mo>
 </mrow>
</math>
first derivative of; g function composition h, applied to x
 (g∘h)′(x) high (g∘h)′(x)
( g ∘ h ) ′ ( x ) 
§
<math display='block'>
 <mrow>
  <msup>
   <mrow>
    <mo>(</mo>
    <mi>g</mi>
    <mo>∘</mo>
    <mi>h</mi>
    <mo>)</mo>
   </mrow>
   <mo>′</mo>
  </msup>
  <mo>(</mo>
  <mi>x</mi>
  <mo>)</mo>
 </mrow>
</math>
open paren, g composed with h, close paren prime; times x
§
<math intent=':common' display='block'>
open paren, g composed with h, close paren prime; times x
§
<math intent=':literal' display='block'>
open paren, g composed with h, close paren prime; open paren x close paren
 
§
<math display='block'>
 <mrow intent='apply($op3,$x)'>
  <msup arg='op3' intent='apply($op2,$composed)'>
   <mrow arg='composed' intent='apply:infix($op1,$g,$h)'><!-- ?-->
    <mo>(</mo>
    <mi arg='g'>g</mi>
    <mo arg='op1' intent='function-composition'>∘</mo>
    <mi arg='h'>h</mi>
    <mo>)</mo>
   </mrow>
   <mo arg='op2' intent='first-derivative'>′</mo>
  </msup>
  <mo>(</mo>
  <mi arg='x'>x</mi>
  <mo>)</mo>
 </mrow>
</math>
apply of, apply of, first derivative comma; function composition apply g apply h, comma x
 (g∘h)′(x) apply (g∘h)′(x)
( g ∘ h ) ′ ⁡ ( x ) 
§
<math display='block'>
 <mrow>
  <msup>
   <mrow>
    <mo>(</mo>
    <mi>g</mi>
    <mo>∘</mo>
    <mi>h</mi>
    <mo>)</mo>
   </mrow>
   <mo>′</mo>
  </msup>
  <mo>&#x2061;</mo>
  <mo>(</mo>
  <mi>x</mi>
  <mo>)</mo>
 </mrow>
</math>
open paren, g composed with h, close paren prime, of x
§
<math intent=':common' display='block'>
open paren, g composed with h, close paren prime, of x
§
<math intent=':literal' display='block'>
open paren, g composed with h, close paren prime of open paren x close paren
 
§
<math display='block'>
 <mrow>
  <msup intent='first-derivative($composed)'>
   <mrow arg='composed'>
    <mo>(</mo>
    <mi>g</mi>
    <mo intent='composed-with'>∘</mo>
    <mi>h</mi>
    <mo>)</mo>
   </mrow>
   <mo>′</mo>
  </msup>
  <mo>&#x2061;</mo> <!-- apply function -->
  <mo>(</mo>
  <mi>x</mi>
  <mo>)</mo>
 </mrow>
</math>
first derivative of, open paren, g composed with h, close paren of x
 (g∘h)′(x) leaf (g∘h)′(x)
f * ⁡ ( p ) 
§
<math display='block'>
 <mrow>
  <msup>
   <mi>f</mi>
   <mo>*</mo>
  </msup>
  <mo>&#x2061;</mo>
  <mrow>
   <mo>(</mo>
   <mi>p</mi>
   <mo>)</mo>
  </mrow>
 </mrow>
</math>
f star, of p
§
<math intent=':common' display='block'>
f star, of p
§
<math intent=':literal' display='block'>
f star of open paren p close paren
 
§
<math display='block'>
 <mrow intent='convex-conjugate(f)(p)'>
  <msup>
   <mi>f</mi>
   <mo>*</mo>
  </msup>
  <mo>&#x2061;</mo>
  <mrow>
   <mo>(</mo>
   <mi>p</mi>
   <mo>)</mo>
  </mrow>
 </mrow>
</math>
convex conjugate of, f applied to p
§
<math display='block'>
 <mrow intent='$fs($p)'>
  <msup arg='fs' intent='convex-conjugate($f)'>
   <mi arg='f'>f</mi>
   <mo>*</mo>
  </msup>
  <mo>&#x2061;</mo>
  <mrow>
   <mo>(</mo>
   <mi arg='p'>p</mi>
   <mo>)</mo>
  </mrow>
 </mrow>
</math>
convex conjugate of, f applied to p
§
<math display='block'>
 <mrow>
  <msup intent=':decorated-function'>
   <mi>f</mi>
   <mo intent='convex-conjugate'>*</mo>
  </msup>
  <mo>&#x2061;</mo>
  <mrow>
   <mo>(</mo>
   <mi>p</mi>
   <mo>)</mo>
  </mrow>
 </mrow>
</math>
f convex conjugate, of p
 f^*(p) hof convex conjugate
Hints
🐇 X 
§
<math display='block'>
 <mrow>
  <mo>&#x1F407;</mo>
  <mi>X</mi>
 </mrow>
</math>
🐇 x
§
<math intent=':common' display='block'>
🐇 x
§
<math intent=':literal' display='block'>
🐇 x
 
§
<math display='block'>
 <mrow>
  <mo intent='my-function'>&#x1F407;</mo>
  <mi>X</mi>
 </mrow>
</math>
my function x
§
<math display='block'>
 <mrow>
  <mo intent='my-function:function'>&#x1F407;</mo>
  <mi>X</mi>
 </mrow>
</math>
my function x
§
<math display='block'>
 <mrow>
  <mo intent='my-function:silent'>&#x1F407;</mo>
  <mi>X</mi>
 </mrow>
</math>
x
 🐇 X intent on prefix mo
🐇 X 
§
<math display='block'>
 <mrow>
  <mo>&#x1F407;</mo>
  <mi>X</mi>
 </mrow>
</math>
🐇 x
§
<math intent=':common' display='block'>
🐇 x
§
<math intent=':literal' display='block'>
🐇 x
 
§
<math display='block'>
 <mrow intent='my-function($X)'>
  <mo>&#x1F407;</mo>
  <mi arg='X'>X</mi>
 </mrow>
</math>
my function of, x
§
<math display='block'>
 <mrow intent='my-function:function($X)'>
  <mo>&#x1F407;</mo>
  <mi arg='X'>X</mi>
 </mrow>
</math>
my function of, x
§
<math display='block'>
 <mrow intent='my-function:prefix($X)'>
  <mo>&#x1F407;</mo>
  <mi arg='X'>X</mi>
 </mrow>
</math>
my function x,
§
<math display='block'>
 <mrow intent='my-function:postfix($X)'>
  <mo>&#x1F407;</mo>
  <mi arg='X'>X</mi>
 </mrow>
</math>
, x my function
§
<math display='block'>
 <mrow intent='my-function:silent(
               _rabbit_function_applied_to,$X)'>
  <mo>&#x1F407;</mo>
  <mi arg='X'>X</mi>
 </mrow>
</math>
rabbit function applied to x
 🐇 X intent on mrow of prefix mo
x ⨯ y 
§
<math display='block'>
 <mrow>
  <mi>x</mi>
  <mo>⨯</mo>
  <mi>y</mi>
 </mrow>
</math>
x cross product y
§
<math intent=':common' display='block'>
x cross product y
§
<math intent=':literal' display='block'>
x cross product y
 
§
<math display='block'>
 <mrow>
  <mi arg='x'>x</mi>
  <mo arg='prod'
      intent='cross-product'>⨯</mo>
  <mi arg='y'>y</mi>
 </mrow>
</math>
x cross product y
§
<math display='block'>
 <mrow intent='$prod($x,$y)'>
  <mi arg='x'>x</mi>
  <mo arg='prod'
      intent='cross-product'>⨯</mo>
  <mi arg='y'>y</mi>
 </mrow>
</math>
cross product of, x comma y
§
<math display='block'>
 <mrow intent='$prod:infix($x,$y)'>
  <mi arg='x'>x</mi>
  <mo arg='prod'
      intent='cross-product'>⨯</mo>
  <mi arg='y'>y</mi>
 </mrow>
</math>
, x cross product y,
§
<math display='block'>
 <mrow intent='$prod:function($x,$y)'>
  <mi arg='x'>x</mi>
  <mo arg='prod'
      intent='cross-product'>⨯</mo>
  <mi arg='y'>y</mi>
 </mrow>
</math>
cross product of, x comma y
§
<math display='block'>
 <mrow intent='$prod:silent(
               _vector_product, _of, $x, _with, $y)'>
  <mi arg='x'>x</mi>
  <mo arg='prod'
      intent='cross-product'>⨯</mo>
  <mi arg='y'>y</mi>
 </mrow>
</math>
vector product of x with y
 x \vectimes y vectimes hints
x ⊞ y 
§
<math display='block'>
 <mrow>
  <mi>x</mi>
  <mo>&#x229e;</mo>
  <mi>y</mi>
 </mrow>
</math>
x squared plus y
§
<math intent=':common' display='block'>
x squared plus y
§
<math intent=':literal' display='block'>
x squared plus y
 
§
<math display='block'>
 <mrow intent='foo:infix($x,$y)'>
  <mi arg='x'>x</mi>
  <mo>&#x229e;</mo>
  <mi arg='y'>y</mi>
 </mrow>
</math>
, x foo y,
§
<math display='block'>
 <mrow>
  <mi>x</mi>
  <mo intent='foo'>&#x229e;</mo>
  <mi>y</mi>
 </mrow>
</math>
x foo y
 x \boxplus y x foo/boxplus y
Delimiters
| x | 
§
<math display='block'>
 <mrow>
  <mo>|</mo>
  <mi>x</mi>
  <mo>|</mo>
 </mrow>
</math>
the absolute value of x,
§
<math intent=':common' display='block'>
the absolute value of x,
§
<math intent=':literal' display='block'>
vertical line x vertical line
 
§
<math display='block'>
 <mrow intent='absolute-value($x)'>
  <mo>|</mo>
  <mi arg='x'>x</mi>
  <mo>|</mo>
 </mrow>
</math>
the absolute value of x,
 \lvert x\rvert vert x abs
| x | 2 
§
<math display='block'>
 <msub>
  <mrow>
   <mo>|</mo>
   <mi>x</mi>
   <mo>|</mo>
  </mrow>
  <mn>2</mn>
 </msub>
</math>
the absolute value of x, sub 2
§
<math intent=':common' display='block'>
the absolute value of x, sub 2
§
<math intent=':literal' display='block'>
vertical line x vertical line sub 2
 
§
<math display='block'>
 <msub intent='l2-norm($x)'>
  <mrow>
   <mo>|</mo>
   <mi arg='x'>x</mi>
   <mo>|</mo>
  </mrow>
  <mn>2</mn>
 </msub>
</math>
l2 norm of, x
 \lvert x\rvert_2 l2 norm x
| M | 
§
<math display='block'>
 <mrow>
  <mo>|</mo>
  <mi>M</mi>
  <mo>|</mo>
 </mrow>
</math>
the determinant of m
§
<math intent=':common' display='block'>
the determinant of m
§
<math intent=':literal' display='block'>
vertical line m vertical line
 
§
<math display='block'>
 <mrow intent='determinant($M)'>
  <mo>|</mo>
  <mi arg='M'>M</mi>
  <mo>|</mo>
 </mrow>
</math>
the determinant of m
 \lvert M\rvert vert M determinant
| a b c d | 
§
<math display='block'>
 <mrow>
  <mo>|</mo>
  <mtable>
   <mtr>
    <mtd><mi>a</mi></mtd>
    <mtd><mi>b</mi></mtd>
   </mtr>
   <mtr>
    <mtd><mi>c</mi></mtd>
    <mtd><mi>d</mi></mtd>
   </mtr>
  </mtable>
  <mo>|</mo>
 </mrow>
</math>
the 2 by 2 determinant; row 1; eigh, b; row 2; c, d; end determinant
§
<math intent=':common' display='block'>
the 2 by 2 determinant; row 1; eigh, b; row 2; c, d; end determinant
§
<math intent=':literal' display='block'>
vertical line; table with 2 rows and 2 columns; row 1;
column 1; eigh,
column 2; b; row 2;
column 1; c,
column 2; d; vertical line
 
§
<math display='block'>
 <mrow intent='determinant($M)'>
  <mo>|</mo>
  <mtable arg='M' intent=':matrix'>
   <mtr>
    <mtd><mi>a</mi></mtd>
    <mtd><mi>b</mi></mtd>
   </mtr>
   <mtr>
    <mtd><mi>c</mi></mtd>
    <mtd><mi>d</mi></mtd>
   </mtr>
  </mtable>
  <mo>|</mo>
 </mrow>
</math>
the determinant of the 2 by 2 matrix; row 1; eigh, b; row 2; c, d; end matrix end determinant
§
<math display='block'>
 <mrow intent='$M'>
  <mo>|</mo>
  <mtable arg='M' intent=':determinant'>
   <mtr>
    <mtd><mi>a</mi></mtd>
    <mtd><mi>b</mi></mtd>
   </mtr>
   <mtr>
    <mtd><mi>c</mi></mtd>
    <mtd><mi>d</mi></mtd>
   </mtr>
  </mtable>
  <mo>|</mo>
 </mrow>
</math>
the 2 by 2 determinant; row 1; eigh, b; row 2; c, d; end determinant
 \begin{vmatrix}a&b\\c&d\end{vmatrix} vert abcd determinant
‖ x ‖ 
§
<math display='block'>
 <mrow>
  <mo>‖</mo>
  <mi>x</mi>
  <mo>‖</mo>
 </mrow>
</math>
magnitude of, x
§
<math intent=':common' display='block'>
magnitude of, x
§
<math intent=':literal' display='block'>
double vertical line x double vertical line
 
§
<math display='block'>
 <mrow intent='magnitude($x)'>
  <mo>‖</mo>
  <mi arg='x'>x</mi>
  <mo>‖</mo>
 </mrow>
</math>
magnitude of, x
 \lVert x\rVert Vert x magnitude
] x , y [ 
§
<math display='block'>
 <mrow>
  <mo>]</mo>
  <mi>x</mi>
  <mo>,</mo>
  <mi>y</mi>
  <mo>[</mo>
 </mrow>
</math>
close bracket, x comma y open bracket
§
<math intent=':common' display='block'>
close bracket, x comma y open bracket
§
<math intent=':literal' display='block'>
close bracket, x comma y open bracket
 
§
<math display='block'>
 <mrow intent='open-interval($x,$y)'>
  <mo>]</mo>
  <mi arg='x'>x</mi>
  <mo>,</mo>
  <mi arg='y'>y</mi>
  <mo>[</mo>
 </mrow>
</math>
the open interval from x to y
 \mathopen] x,y\mathclose[\rVert open-open inverted bracket
( x , y ) 
§
<math display='block'>
 <mrow>
  <mo>(</mo>
  <mi>x</mi>
  <mo>,</mo>
  <mi>y</mi>
  <mo>)</mo>
 </mrow>
</math>
open paren x comma y, close paren
§
<math intent=':common' display='block'>
open paren x comma y, close paren
§
<math intent=':literal' display='block'>
open paren x comma y, close paren
 
§
<math display='block'>
 <mrow intent='open-interval($x,$y)'>
  <mo>(</mo>
  <mi arg='x'>x</mi>
  <mo>,</mo>
  <mi arg='y'>y</mi>
  <mo>)</mo>
 </mrow>
</math>
the open interval from x to y
 (x,y) open-open
( x , y ] 
§
<math display='block'>
 <mrow>
  <mo>(</mo>
  <mi>x</mi>
  <mo>,</mo>
  <mi>y</mi>
  <mo>]</mo>
 </mrow>
</math>
the open closed interval from x to y
§
<math intent=':common' display='block'>
the open closed interval from x to y
§
<math intent=':literal' display='block'>
open paren x comma y, close bracket
 
§
<math display='block'>
 <mrow intent='open-closed-interval($x,$y)'>
  <mo>(</mo>
  <mi arg='x'>x</mi>
  <mo>,</mo>
  <mi arg='y'>y</mi>
  <mo>]</mo>
 </mrow>
</math>
the open closed interval from x to y
 (x,y] open-closed
[ x , y ) 
§
<math display='block'>
 <mrow>
  <mo>[</mo>
  <mi>x</mi>
  <mo>,</mo>
  <mi>y</mi>
  <mo>)</mo>
 </mrow>
</math>
the closed open interval from x to y
§
<math intent=':common' display='block'>
the closed open interval from x to y
§
<math intent=':literal' display='block'>
open bracket x comma y, close paren
 
§
<math display='block'>
 <mrow intent='closed-open-interval($x,$y)'>
  <mo>[</mo>
  <mi arg='x'>x</mi>
  <mo>,</mo>
  <mi arg='y'>y</mi>
  <mo>)</mo>
 </mrow>
</math>
the closed open interval from x to y
 [x,y) closed-open
[ x , y ] 
§
<math display='block'>
 <mrow>
  <mo>[</mo>
  <mi>x</mi>
  <mo>,</mo>
  <mi>y</mi>
  <mo>]</mo>
 </mrow>
</math>
the closed interval from x to y
§
<math intent=':common' display='block'>
the closed interval from x to y
§
<math intent=':literal' display='block'>
open bracket x comma y, close bracket
 
§
<math display='block'>
 <mrow intent='closed-interval($x,$y)'>
  <mo>[</mo>
  <mi arg='x'>x</mi>
  <mo>,</mo>
  <mi arg='y'>y</mi>
  <mo>]</mo>
 </mrow>
</math>
the closed interval from x to y
§
<math display='block'>
 <mrow intent='closed-interval:prefix($x,$y)'>
  <mo>[</mo>
  <mi arg='x'>x</mi>
  <mo>,</mo>
  <mi arg='y'>y</mi>
  <mo>]</mo>
 </mrow>
</math>
closed interval x y,
 [x,y] closed-closed
( x   y   c   d ) 
§
<math display='block'>
 <mrow>
  <mo>(</mo>
  <mi>x</mi>
  <mo>&#x2009;</mo>
  <mi>y</mi>
  <mo>&#x2009;</mo>
  <mi>c</mi>
  <mo>&#x2009;</mo>
  <mi>d</mi>
  <mo>)</mo>
 </mrow>
</math>
open paren, x y c d, close paren
§
<math intent=':common' display='block'>
open paren, x y c d, close paren
§
<math intent=':literal' display='block'>
open paren, x y c d, close paren
 
§
<math display='block'>
 <mrow intent='vector($x,$y,$c,$d)'>
  <mo>(</mo>
  <mi arg='x'>x</mi>
  <mo>&#x2009;</mo>
  <mi arg='y'>y</mi>
  <mo>&#x2009;</mo>
  <mi arg='c'>c</mi>
  <mo>&#x2009;</mo>
  <mi arg='d'>d</mi>
  <mo>)</mo>
 </mrow>
</math>
vector of, x comma y comma c comma d
§
<math display='block'>
 <mrow intent='cycle($x,$y,$c,$d)'>
  <mo>(</mo>
  <mi arg='x'>x</mi>
  <mo>&#x2009;</mo>
  <mi arg='y'>y</mi>
  <mo>&#x2009;</mo>
  <mi arg='c'>c</mi>
  <mo>&#x2009;</mo>
  <mi arg='d'>d</mi>
  <mo>)</mo>
 </mrow>
</math>
cycle of, x comma y comma c comma d
§
<math display='block'>
 <mrow intent='vector:prefix($x,$y,$c,$d)'>
  <mo>(</mo>
  <mi arg='x'>x</mi>
  <mo>&#x2009;</mo>
  <mi arg='y'>y</mi>
  <mo>&#x2009;</mo>
  <mi arg='c'>c</mi>
  <mo>&#x2009;</mo>
  <mi arg='d'>d</mi>
  <mo>)</mo>
 </mrow>
</math>
vector x y c d,
§
<math display='block'>
 <mrow intent='cycle:prefix($x,$y,$c,$d)'>
  <mo>(</mo>
  <mi arg='x'>x</mi>
  <mo>&#x2009;</mo>
  <mi arg='y'>y</mi>
  <mo>&#x2009;</mo>
  <mi arg='c'>c</mi>
  <mo>&#x2009;</mo>
  <mi arg='d'>d</mi>
  <mo>)</mo>
 </mrow>
</math>
cycle x y c d,
 (a\,b\,c\,d) cycle thin space
Tables
[ a b x y ] 
§
<math display='block'>
 <mrow>
  <mo>[</mo>
  <mtable>
   <mtr>
    <mtd><mi>a</mi></mtd>
    <mtd><mi>b</mi></mtd>
   </mtr>
   <mtr>
    <mtd><mi>x</mi></mtd>
    <mtd><mi>y</mi></mtd>
   </mtr>
  </mtable>
  <mo>]</mo>
 </mrow>
</math>
the 2 by 2 matrix; row 1; eigh, b; row 2; x, y; end matrix
§
<math intent=':common' display='block'>
the 2 by 2 matrix; row 1; eigh, b; row 2; x, y; end matrix
§
<math intent=':literal' display='block'>
open bracket; table with 2 rows and 2 columns; row 1;
column 1; eigh,
column 2; b; row 2;
column 1; x,
column 2; y; close bracket
 
§
<math display='block'>
 <mrow intent='$m'>
  <mo>[</mo>
  <mtable arg='m' intent=':matrix'>
   <mtr>
    <mtd><mi>a</mi></mtd>
    <mtd><mi>b</mi></mtd>
   </mtr>
   <mtr>
    <mtd><mi>x</mi></mtd>
    <mtd><mi>y</mi></mtd>
   </mtr>
  </mtable>
  <mo>]</mo>
 </mrow>
</math>
the 2 by 2 matrix; row 1; eigh, b; row 2; x, y; end matrix
§
<math display='block'>
 <mrow intent='$m'>
  <mo>[</mo>
  <mtable arg='m' intent=':array'>
   <mtr>
    <mtd><mi>a</mi></mtd>
    <mtd><mi>b</mi></mtd>
   </mtr>
   <mtr>
    <mtd><mi>x</mi></mtd>
    <mtd><mi>y</mi></mtd>
   </mtr>
  </mtable>
  <mo>]</mo>
 </mrow>
</math>
array of, row 1;
column 1; eigh,
column 2; b; comma, row 2;
column 1; x,
column 2; y;
 \begin{bmatrix} a&b\\ x&y \end{bmatrix} bmatrix
( a b x y ) 
§
<math display='block'>
 <mrow>
  <mo>(</mo>
  <mtable>
   <mtr>
    <mtd><mi>a</mi></mtd>
    <mtd><mi>b</mi></mtd>
   </mtr>
   <mtr>
    <mtd><mi>x</mi></mtd>
    <mtd><mi>y</mi></mtd>
   </mtr>
  </mtable>
  <mo>)</mo>
 </mrow>
</math>
the 2 by 2 matrix; row 1; eigh, b; row 2; x, y; end matrix
§
<math intent=':common' display='block'>
the 2 by 2 matrix; row 1; eigh, b; row 2; x, y; end matrix
§
<math intent=':literal' display='block'>
open paren; table with 2 rows and 2 columns; row 1;
column 1; eigh,
column 2; b; row 2;
column 1; x,
column 2; y; close paren
 
§
<math display='block'>
 <mrow intent='$m'>
  <mo>(</mo>
  <mtable arg='m' intent=':matrix'>
   <mtr>
    <mtd><mi>a</mi></mtd>
    <mtd><mi>b</mi></mtd>
   </mtr>
   <mtr>
    <mtd><mi>x</mi></mtd>
    <mtd><mi>y</mi></mtd>
   </mtr>
  </mtable>
  <mo>)</mo>
 </mrow>
</math>
the 2 by 2 matrix; row 1; eigh, b; row 2; x, y; end matrix
 \begin{pmatrix} a&b\\ x&y \end{pmatrix} pmatrix
{ x + y = 2 x − y = 0 
§
<math display='block'>
 <mrow>
  <mo>{</mo>
  <mtable>
   <mtr>
    <mtd>
     <mi>x</mi>
     <mo>+</mo>
     <mi>y</mi>
    </mtd>
    <mtd><mo>=</mo></mtd>
    <mtd><mn>2</mn></mtd>
   </mtr>
   <mtr>
    <mtd>
     <mi>x</mi>
     <mo>&#x2212;</mo>
     <mi>y</mi>
    </mtd>
    <mtd><mo>=</mo></mtd>
    <mtd><mn>0</mn></mtd>
   </mtr>
  </mtable>
 </mrow>
</math>
2 cases,
case 1; x plus y, is equal to, 2;
case 2; x minus y, is equal to, 0;
§
<math intent=':common' display='block'>
2 cases,
case 1; x plus y, is equal to, 2;
case 2; x minus y, is equal to, 0;
§
<math intent=':literal' display='block'>
open brace; table with 2 rows and 3 columns; row 1;
column 1; x plus y,
column 2; is equal to,
column 3; 2; row 2;
column 1; x minus y,
column 2; is equal to,
column 3; 0;
 
§
<math display='block'>
 <mrow intent='$m'>
  <mo>{</mo>
  <mtable arg='m' intent=':system-of-equations'>
   <mtr>
    <mtd>
     <mi>x</mi>
     <mo>+</mo>
     <mi>y</mi>
    </mtd>
    <mtd><mo>=</mo></mtd>
    <mtd><mn>2</mn></mtd>
   </mtr>
   <mtr>
    <mtd>
     <mi>x</mi>
     <mo>&#x2212;</mo>
     <mi>y</mi>
    </mtd>
    <mtd><mo>=</mo></mtd>
    <mtd><mn>0</mn></mtd>
   </mtr>
  </mtable>
 </mrow>
</math>
2 cases,
case 1; x plus y, is equal to, 2;
case 2; x minus y, is equal to, 0;
 \left\{\begin{aligned} x+y &= 2 \\ x-y &=0 \end{aligned}\right. braced system of equations
f(x) = { −x  if  x<0 x  if  x≥0 
§
<math display='block'>
 <mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo>
 <mo>=</mo>
 <mrow>
  <mo>{</mo>
  <mtable columnalign="right left" columnspacing="0" rowspacing=".2em">
   <mtr>
    <mtd><mo>&#x2212;</mo><mi>x</mi></mtd>
    <mtd><mtext>&#160;if&#160;</mtext></mtd>
    <mtd><mi>x</mi><mo>&lt;</mo><mn>0</mn></mtd>
   </mtr>
   <mtr>
    <mtd><mi>x</mi></mtd>
    <mtd><mtext>&#160;if&#160;</mtext></mtd>
    <mtd><mi>x</mi><mo>&#x2265;</mo><mn>0</mn></mtd>
   </mtr>
  </mtable>
 </mrow>
</math>
f of x is equal to; 2 cases,
case 1; negative x if x is less than 0;
case 2; x if x is greater than or equal to 0;
§
<math intent=':common' display='block'>
f of x is equal to; 2 cases,
case 1; negative x if x is less than 0;
case 2; x if x is greater than or equal to 0;
§
<math intent=':literal' display='block'>
f open paren x close paren; is equal to; open brace; table with 2 rows and 3 columns; row 1;
column 1; minus x,
column 2; if ,
column 3; x is less than 0; row 2;
column 1; x,
column 2; if ,
column 3; x is greater than or equal to 0;
 
§
<math display='block'>
 <mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo>
 <mo>=</mo>
 <mrow>
  <mo intent=":silent">{</mo>
  <mtable intent=":piecewise" columnalign="right left" columnspacing="0" rowspacing=".2em">
   <mtr>
    <mtd><mo>&#x2212;</mo><mi>x</mi></mtd>
    <mtd><mtext>&#160;if&#160;</mtext></mtd>
    <mtd><mi>x</mi><mo>&lt;</mo><mn>0</mn></mtd>
   </mtr>
   <mtr>
    <mtd><mi>x</mi></mtd>
    <mtd><mtext>&#160;if&#160;</mtext></mtd>
    <mtd><mi>x</mi><mo>&#x2265;</mo><mn>0</mn></mtd>
   </mtr>
  </mtable>
 </mrow>
</math>
f of x is equal to; 2 cases,
case 1; negative x if x is less than 0;
case 2; x if x is greater than or equal to 0;
 f(x)=\begin{cases}... piecewise function definition
2 ⁢ x = 1 y > x − 3 
§
<math display='block'>
 <mtable>
  <mtr>
   <mtd columnalign='right'>
    <mn>2</mn>
    <mo>&#x2062;<!--InvisibleTimes--></mo>
    <mi>x</mi>
   </mtd>
   <mtd columnalign='center'>
    <mo>=</mo>
   </mtd>
   <mtd columnalign='left'>
    <mn>1</mn>
   </mtd>
  </mtr>
  <mtr>
   <mtd columnalign='right'>
    <mi>y</mi>
   </mtd>
   <mtd columnalign='center'>
    <mo>></mo>
   </mtd>
   <mtd columnalign='left'>
    <mi>x</mi>
    <mo>&#x2212;</mo>
    <mn>3</mn>
   </mtd>
  </mtr>
 </mtable>
</math>
2 equations,
equation 1; 2 x, is equal to, 1;
equation 2; y, is greater than, x minus 3;
§
<math intent=':common' display='block'>
2 equations,
equation 1; 2 x, is equal to, 1;
equation 2; y, is greater than, x minus 3;
§
<math intent=':literal' display='block'>
table with 2 rows and 3 columns; row 1;
column 1; 2 x,
column 2; is equal to,
column 3; 1; row 2;
column 1; y,
column 2; is greater than,
column 3; x minus 3;
 
§
<math display='block'>
 <mtable intent=':system-of-equations'>
  <mtr>
   <mtd columnalign='right'>
    <mn>2</mn>
    <mo>&#x2062;<!--InvisibleTimes--></mo>
    <mi>x</mi>
   </mtd>
   <mtd columnalign='center'>
    <mo>=</mo>
   </mtd>
   <mtd columnalign='left'>
    <mn>1</mn>
   </mtd>
  </mtr>
  <mtr>
   <mtd columnalign='right'>
    <mi>y</mi>
   </mtd>
   <mtd columnalign='center'>
    <mo>></mo>
   </mtd>
   <mtd columnalign='left'>
    <mi>x</mi>
    <mo>&#x2212;</mo>
    <mn>3</mn>
   </mtd>
  </mtr>
 </mtable>
</math>
2 equations,
equation 1; 2 x, is equal to, 1;
equation 2; y, is greater than, x minus 3;
 \begin{align}... align 1
a = b + c − d + e − f 
§
<math display='block'>
 <mtable>
  <mtr>
   <mtd columnalign='right'>
    <mi>a</mi>
   </mtd>
   <mtd columnalign='center'>
    <mo>=</mo>
   </mtd>
   <mtd columnalign='left'>
    <mi>b</mi>
    <mo>+</mo>
    <mi>c</mi>
    <mo>&#x2212;</mo>
    <mi>d</mi>
   </mtd>
  </mtr>
  <mtr>
   <mtd columnalign='right'></mtd>
   <mtd columnalign='center'></mtd>
   <mtd columnalign='left'>
    <mo form='infix'>+</mo>
    <mi>e</mi>
    <mo>&#x2212;</mo>
    <mi>f</mi>
   </mtd>
  </mtr>
 </mtable>
</math>
2 equations,
equation 1; eigh, is equal to, b plus c minus d;
equation 2; plus e minus f;
§
<math intent=':common' display='block'>
2 equations,
equation 1; eigh, is equal to, b plus c minus d;
equation 2; plus e minus f;
§
<math intent=':literal' display='block'>
table with 2 rows and 3 columns; row 1;
column 1; eigh,
column 2; is equal to,
column 3; b plus c minus d; row 2;
column 1; empty,
column 2; empty,
column 3; plus e minus f;
 
§
<math display='block'>
 <mtable intent='equation:prefix($e1,$e1x)'>
  <mtr arg='e1'>
   <mtd columnalign='right'>
    <mi>a</mi>
   </mtd>
   <mtd columnalign='center'>
    <mo>=</mo>
   </mtd>
   <mtd intent='_($lhs)' columnalign='left'>
    <mrow arg='lhs'>
    <mi>b</mi>
    <mo>+</mo>
    <mi>c</mi>
    <mo>&#x2212;</mo>
    <mi>d</mi>
   </mrow>
   </mtd>
  </mtr>
  <mtr arg='e1x'>
   <mtd intent='_' columnalign='right'></mtd>
   <mtd intent='_' columnalign='center'></mtd>
   <mtd arg='rhs' columnalign='left'>
    <mo form='infix'>+</mo>
    <mi>e</mi>
    <mo>&#x2212;</mo>
    <mi>f</mi>
   </mtd>
  </mtr>
 </mtable>
</math>
equation row 1;
column 1; eigh,
column 2; is equal to, b plus c minus d row 2;
column 3; plus e minus f;
§
<math display='block'>
 <mtable intent=':system-of-equations'>
  <mtr>
   <mtd columnalign='right'>
    <mi>a</mi>
   </mtd>
   <mtd columnalign='center'>
    <mo>=</mo>
   </mtd>
   <mtd columnalign='left'>
    <mi>b</mi>
    <mo>+</mo>
    <mi>c</mi>
    <mo>&#x2212;</mo>
    <mi>d</mi>
   </mtd>
  </mtr>
  <mtr intent=':continued-equation'>
   <mtd columnalign='right'></mtd>
   <mtd columnalign='center'></mtd>
   <mtd columnalign='left'>
    <mo form='infix'>+</mo>
    <mi>e</mi>
    <mo>&#x2212;</mo>
    <mi>f</mi>
   </mtd>
  </mtr>
 </mtable>
</math>
2 equations,
equation 1; eigh, is equal to, b plus c minus d;
equation 2; plus e minus f;
 \begin{aligned}... wrapped alignment with wrapped line
(a+b) 2 = a2 + 2 ⁢ a ⁢ b + b2 ⩽ 2 ⁢ a ⁢ b + b2 = b ⁢ ( 2 ⁢ a + b ) 
§
<math display='block'>
 <mrow>
  <mtable>
   <mtr>
    <mtd>
     <msup>
      <mrow>
       <mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>)</mo>
      </mrow>
      <mn>2</mn>
     </msup>
    </mtd>
    <mtd>
     <mo>=</mo>
    </mtd>
    <mtd>
     <msup><mi>a</mi><mn>2</mn></msup>
     <mo>+</mo>
     <mrow>
      <mn>2</mn>
      <mo>&#x2062;<!--InvisibleTimes--></mo>
      <mi>a</mi>
      <mo>&#x2062;<!--InvisibleTimes--></mo>
      <mi>b</mi>
     </mrow>
     <mo>+</mo>
     <msup><mi>b</mi><mn>2</mn></msup>
    </mtd>
   </mtr>
   <mtr>
    <mtd></mtd>
    <mtd>
     <mo>&#x2a7d;</mo>
    </mtd>
    <mtd>
     <mrow>
      <mn>2</mn>
      <mo>&#x2062;<!--InvisibleTimes--></mo>
      <mi>a</mi>
      <mo>&#x2062;<!--InvisibleTimes--></mo>
      <mi>b</mi>
     </mrow>
     <mo>+</mo>
     <msup><mi>b</mi><mn>2</mn></msup>
    </mtd>
   </mtr>
   <mtr>
    <mtd></mtd>
    <mtd>
     <mo>=</mo>
    </mtd>
    <mtd>
     <mi>b</mi>
     <mo>&#x2062;<!--InvisibleTimes--></mo>
     <mrow>
      <mo>(</mo>
      <mn>2</mn>
      <mo>&#x2062;<!--InvisibleTimes--></mo>
      <mi>a</mi>
      <mo>+</mo>
      <mi>b</mi>
      <mo>)</mo>
     </mrow>
    </mtd>
   </mtr>
  </mtable>
 </mrow>
</math>
3 equations,
equation 1; open paren eigh plus b, close paren squared, is equal to, eigh squared plus 2 eigh b, plus b squared;
equation 2; less than or slanted equal to, 2 eigh b, plus b squared;
equation 3; is equal to, b times, open paren, 2 eigh plus b, close paren;
§
<math intent=':common' display='block'>
3 equations,
equation 1; open paren eigh plus b, close paren squared, is equal to, eigh squared plus 2 eigh b, plus b squared;
equation 2; less than or slanted equal to, 2 eigh b, plus b squared;
equation 3; is equal to, b times, open paren, 2 eigh plus b, close paren;
§
<math intent=':literal' display='block'>
table with 3 rows and 3 columns; row 1;
column 1; open paren eigh plus b, close paren super 2 end super,
column 2; is equal to,
column 3; eigh super 2 end super, plus 2 eigh b, plus b super 2 end super; row 2;
column 1; empty,
column 2; less than or slanted equal to,
column 3; 2 eigh b, plus b super 2 end super; row 3;
column 1; empty,
column 2; is equal to,
column 3; b, open paren, 2 eigh plus b, close paren;
 
§
<math display='block'>
 <mrow intent='derivation($m)'>
  <mtable arg='m' intent=':lines'>
   <mtr>
    <mtd>
     <msup>
      <mrow>
       <mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>)</mo>
      </mrow>
      <mn>2</mn>
     </msup>
    </mtd>
    <mtd>
     <mo>=</mo>
    </mtd>
    <mtd>
     <msup><mi>a</mi><mn>2</mn></msup>
     <mo>+</mo>
     <mrow>
      <mn>2</mn>
      <mo>&#x2062;<!--InvisibleTimes--></mo>
      <mi>a</mi>
      <mo>&#x2062;<!--InvisibleTimes--></mo>
      <mi>b</mi>
     </mrow>
     <mo>+</mo>
     <msup><mi>b</mi><mn>2</mn></msup>
    </mtd>
   </mtr>
   <mtr>
    <mtd></mtd>
    <mtd>
     <mo>&#x2a7d;</mo>
    </mtd>
    <mtd>
     <mrow>
      <mn>2</mn>
      <mo>&#x2062;<!--InvisibleTimes--></mo>
      <mi>a</mi>
      <mo>&#x2062;<!--InvisibleTimes--></mo>
      <mi>b</mi>
     </mrow>
     <mo>+</mo>
     <msup><mi>b</mi><mn>2</mn></msup>
    </mtd>
   </mtr>
   <mtr>
    <mtd></mtd>
    <mtd>
     <mo>=</mo>
    </mtd>
    <mtd>
     <mi>b</mi>
     <mo>&#x2062;<!--InvisibleTimes--></mo>
     <mrow>
      <mo>(</mo>
      <mn>2</mn>
      <mo>&#x2062;<!--InvisibleTimes--></mo>
      <mi>a</mi>
      <mo>+</mo>
      <mi>b</mi>
      <mo>)</mo>
     </mrow>
    </mtd>
   </mtr>
  </mtable>
 </mrow>
</math>
derivation of, 3 lines,
line 1; open paren eigh plus b, close paren squared, is equal to, eigh squared plus 2 eigh b, plus b squared;
line 2; less than or slanted equal to, 2 eigh b, plus b squared;
line 3; is equal to, b times, open paren, 2 eigh plus b, close paren;
 \begin{align}... aligned derivation
Calculus
x ˙ 
§
<math display='block'>
 <mover>
  <mi>x</mi>
  <mo>&#x02D9;</mo>
 </mover>
</math>
x dot,
§
<math intent=':common' display='block'>
x dot,
§
<math intent=':literal' display='block'>
x dot
 
§
<math display='block'>
 <mover intent='derivative($x,1)'>
  <mi arg='x'>x</mi>
  <mo>&#x02D9;</mo>
 </mover>
</math>
derivative of, x comma 1
§
<math display='block'>
 <mover intent='derivative:function($x)'>
  <mi arg='x'>x</mi>
  <mo intent='derivative'>&#x02D9;</mo>
 </mover>
</math>
derivative of, x
§
<math display='block'>
 <mover intent='dot:postfix($x)'>
  <mi arg='x'>x</mi>
  <mo intent='derivative'>&#x02D9;</mo>
 </mover>
</math>
, x dot
 \dot{x} dot x
x ¨ 
§
<math display='block'>
 <mover>
  <mi>x</mi>
  <mo>&#x00A8;</mo>
 </mover>
</math>
x double dot,
§
<math intent=':common' display='block'>
x double dot,
§
<math intent=':literal' display='block'>
x double dot
 
§
<math display='block'>
 <mover intent='derivative($x,2)'>
  <mi arg='x'>x</mi>
  <mo>&#x00A8;</mo>
 </mover>
</math>
derivative of, x comma 2
§
<math display='block'>
 <mover intent='second-derivative:function($x)'>
  <mi arg='x'>x</mi>
  <mo intent='second-derivative'>&#x00A8;</mo>
 </mover>
</math>
second derivative of, x
§
<math display='block'>
 <mover intent='dot-dot:postfix($x)'>
  <mi arg='x'>x</mi>
  <mo intent='second-derivative'>&#x00A8;</mo>
 </mover>
</math>
, x dot dot
 \ddot{x} ddot x
dx dt 
§
<math display='block'>
 <mfrac>
  <mrow><mi>d</mi><mi>x</mi></mrow>
  <mrow><mi>d</mi><mi>t</mi></mrow>
 </mfrac>
</math>
fraction, d x, over, d t, end fraction;
§
<math intent=':common' display='block'>
fraction, d x, over, d t, end fraction;
§
<math intent=':literal' display='block'>
start, d x, over, d t, end over;
 
§
<math display='block'>
 <mfrac intent='derivative($x,1,$t)'>
  <mrow><mi>d</mi><mi arg='x'>x</mi></mrow>
  <mrow><mi>d</mi><mi arg='t'>t</mi></mrow>
 </mfrac>
</math>
derivative of, x comma 1 comma t
§
<math display='block'>
 <mfrac intent='derivative:prefix(
                _of,$x,_with_respect_to,$t)'>
  <mrow><mi>d</mi><mi arg='x'>x</mi></mrow>
  <mrow><mi>d</mi><mi arg='t'>t</mi></mrow>
 </mfrac>
</math>
derivative of x with respect to t,
§
<math display='block'>
 <mfrac intent='derivative:silent(
                _d,$x,_by,_d,$t)'>
  <mrow><mi>d</mi><mi arg='x'>x</mi></mrow>
  <mrow><mi>d</mi><mi arg='t'>t</mi></mrow>
 </mfrac>
</math>
d x by d t
 \frac{dx}{dt} dx by dt
d dt f ⁡ ( t ) 
§
<math display='block'>
 <mrow>
  <mfrac>
   <mrow><mi>d</mi></mrow>
   <mrow><mi>d</mi><mi>t</mi></mrow>
  </mfrac>
  <mrow>
   <mi>f</mi>
   <mo>&#x2061;</mo>
   <mo>(</mo>
   <mi>t</mi>
   <mo>)</mo>
  </mrow>
 </mrow>
</math>
fraction, d over, d t, end fraction; f of t
§
<math intent=':common' display='block'>
fraction, d over, d t, end fraction; f of t
§
<math intent=':literal' display='block'>
start, d over, d t, end over; f of open paren t close paren
 
§
<math display='block'>
 <mrow intent='derivative($ft,1,$t)'>
  <mfrac>
   <mrow><mi>d</mi></mrow>
   <mrow><mi>d</mi><mi arg='t'>t</mi></mrow>
  </mfrac>
  <mrow arg='ft'>
   <mi>f</mi>
   <mo>&#x2061;</mo>
   <mo>(</mo>
   <mi>t</mi>
   <mo>)</mo>
  </mrow>
 </mrow>
</math>
derivative of, f of t comma 1 comma t
§
<math display='block'>
 <mrow intent='derivative:prefix(
               _of,$ft,_with_respect_to,$t)'>
  <mfrac>
   <mrow><mi>d</mi></mrow>
   <mrow><mi>d</mi><mi arg='t'>t</mi></mrow>
  </mfrac>
  <mrow arg='ft'>
   <mi>f</mi>
   <mo>&#x2061;</mo>
   <mo>(</mo>
   <mi>t</mi>
   <mo>)</mo>
  </mrow>
 </mrow>
</math>
derivative of f of t with respect to t,
 \frac{d}{dt}f(t) d by dt f of t
d2 x d t 2 
§
<math display='block'>
 <mfrac>
  <mrow>
   <msup>
    <mi>d</mi><mn>2</mn>
   </msup>
   <mi>x</mi>
  </mrow>
  <mrow>
   <mi>d</mi>
   <msup>
    <mi>t</mi>
    <mn>2</mn>
   </msup>
  </mrow>
 </mfrac>
</math>
fraction, d squared x, over, d t squared, end fraction;
§
<math intent=':common' display='block'>
fraction, d squared x, over, d t squared, end fraction;
§
<math intent=':literal' display='block'>
start, d super 2 end super x, over, d t super 2 end super, end over;
 
§
<math display='block'>
 <mfrac intent='derivative($x,2,$t)'>
  <mrow>
   <msup>
    <mi>d</mi><mn>2</mn>
   </msup>
   <mi arg='x'>x</mi>
  </mrow>
  <mrow>
   <mi>d</mi>
   <msup>
    <mi arg='t'>t</mi>
    <mn>2</mn>
   </msup>
  </mrow>
 </mfrac>
</math>
derivative of, x comma 2 comma t
§
<math display='block'>
 <mfrac intent='second-derivative:prefix(
                _of,$x,_with_respect_to,$t)'>
  <mrow>
   <msup>
    <mi>d</mi><mn>2</mn>
   </msup>
   <mi arg='x'>x</mi>
  </mrow>
  <mrow>
   <mi>d</mi>
   <msup>
    <mi arg='t'>t</mi>
    <mn>2</mn>
   </msup>
  </mrow>
 </mfrac>
</math>
second derivative of x with respect to t,
§
<math display='block'>
 <mfrac intent='derivative:silent(
                _d,_2,$x,_by,_d,$t,_squared)'>
  <mrow>
   <msup>
    <mi>d</mi><mn>2</mn>
   </msup>
   <mi arg='x'>x</mi>
  </mrow>
  <mrow>
   <mi>d</mi>
   <msup>
    <mi arg='t'>t</mi>
    <mn>2</mn>
   </msup>
  </mrow>
 </mfrac>
</math>
d 2 x by d t squared
 \frac{d^2x}{dt^2} dx2 by dt2
∂2 f ∂ x ∂ y 
§
<math display='block'>
 <mfrac>
  <mrow>
   <msup>
    <mo>&#x2202;</mo><mn>2</mn>
   </msup>
   <mi>f</mi>
  </mrow>
  <mrow>
   <mrow>
    <mo>&#x2202;</mo>
    <mi>x</mi>
   </mrow>
   <mrow>
    <mo>&#x2202;</mo>
    <mi>y</mi>
   </mrow>
  </mrow>
 </mfrac>
</math>
fraction, partial derivative squared f, over, partial derivative x, partial derivative y, end fraction;
§
<math intent=':common' display='block'>
fraction, partial derivative squared f, over, partial derivative x, partial derivative y, end fraction;
§
<math intent=':literal' display='block'>
start, partial derivative super 2 end super f, over, partial derivative x, partial derivative y, end over;
 
§
<math display='block'>
 <mfrac intent='partial-second-derivative(
                $f,$x,$y)'>
  <mrow>
   <msup>
    <mo>&#x2202;</mo><mn>2</mn>
   </msup>
   <mi arg='f'>f</mi>
  </mrow>
  <mrow>
   <mrow>
    <mo>&#x2202;</mo>
    <mi arg='x'>x</mi>
   </mrow>
   <mrow>
    <mo>&#x2202;</mo>
    <mi arg='y'>y</mi>
   </mrow>
  </mrow>
 </mfrac>
</math>
partial second derivative of, f comma x comma y
§
<math display='block'>
 <mfrac intent='partial-second-derivative:prefix(
                _of,$f,_with_respect_to,$x,_and,$y)'>
  <mrow>
   <msup>
    <mo>&#x2202;</mo><mn>2</mn>
   </msup>
   <mi arg='f'>f</mi>
  </mrow>
  <mrow>
   <mrow>
    <mo>&#x2202;</mo>
    <mi arg='x'>x</mi>
   </mrow>
   <mrow>
    <mo>&#x2202;</mo>
    <mi arg='y'>y</mi>
   </mrow>
  </mrow>
 </mfrac>
</math>
partial second derivative of f with respect to x and y,
 \frac{\partial^2 f}{\partial x \partial y} partial df by dx dy
∫ f ⁡ ( x ) d x 
§
<math display='block'>
 <mo>&#x222B;</mo>
 <mrow>
  <mi>f</mi>
  <mo>&#x2061;</mo>
  <mo>(</mo>
  <mi>x</mi>
  <mo>)</mo>
 </mrow>
 <mrow>
  <mi>d</mi>
  <mi>x</mi>
 </mrow>
</math>
the integral of f of x d x
§
<math intent=':common' display='block'>
the integral of f of x d x
§
<math intent=':literal' display='block'>
the integral of f of open paren x close paren; d x
 
§
<math display='block'>
 <mo>&#x222B;</mo>
 <mrow>
  <mi>f</mi>
  <mo>&#x2061;</mo>
  <mo>(</mo>
  <mi>x</mi>
  <mo>)</mo>
 </mrow>
 <mrow>
  <mi>d</mi>
  <mi>x</mi>
 </mrow>
</math>
the integral of f of x d x
 \int f(x) dx int f(x) dx
∫ 0 1 x2 d x 
§
<math display='block'>
 <mrow>
  <msubsup>
   <mo>∫</mo>
   <mn>0</mn>
   <mn>1</mn>
  </msubsup>
  <msup><mi>x</mi><mn>2</mn></msup>
  <mi>d</mi>
  <mi>x</mi>
 </mrow>
</math>
the integral from 0 to 1 of, x squared d x
§
<math intent=':common' display='block'>
the integral from 0 to 1 of, x squared d x
§
<math intent=':literal' display='block'>
integral sub 0 super 1 end super; x super 2 end super d x
 
§
<math display='block'>
 <mrow>
  <msubsup>
   <mo>∫</mo>
   <mn>0</mn>
   <mn>1</mn>
  </msubsup>
  <msup><mi>x</mi><mn>2</mn></msup>
  <mi>d</mi>
  <mi>x</mi>
 </mrow>
</math>
the integral from 0 to 1 of, x squared d x
 \int_0^1 x^2 dx defint 0 to 1 x squared
[ 2 ⁢ x ] 0 1 
§
<math display='block' mathbackground='yellow'>
 <mrow>
  <mo>[</mo>
  <mn>2</mn>
  <mo>&#x2062;</mo>
  <mi>x</mi>
  <msubsup>
   <mo>]</mo>
   <mn>0</mn>
   <mn>1</mn>
  </msubsup>
 </mrow>
</math>
open bracket evaluated at 1 minus the same expression evaluated at 0
§
<math intent=':common' display='block' mathbackground='yellow'>
open bracket evaluated at 1 minus the same expression evaluated at 0
§
<math intent=':literal' display='block' mathbackground='yellow'>
open bracket 2 x close bracket sub 0 super 1 end super
 
§
<math display='block'>
 <mrow>
  <mo>[</mo>
  <mn>2</mn>
  <mo>&#x2062;</mo>
  <mi>x</mi>
  <msubsup>
   <mo>]</mo>
   <mn>0</mn>
   <mn>1</mn>
  </msubsup>
 </mrow>
</math>
open bracket evaluated at 1 minus the same expression evaluated at 0
 [2x]_0^1 evaluate 2x at 1 and 0 bracket
[ 2 ⁢ x ] 0 1 
§
<math display='block' mathbackground='yellow'>
 <msubsup>
  <mrow>
   <mo>[</mo>
   <mn>2</mn>
   <mo>&#x2062;</mo>
   <mi>x</mi>
   <mo>]</mo>
  </mrow>
  <mn>0</mn>
  <mn>1</mn>
 </msubsup>
</math>
open bracket evaluated at 1 minus the same expression evaluated at 0
§
<math intent=':common' display='block' mathbackground='yellow'>
open bracket evaluated at 1 minus the same expression evaluated at 0
§
<math intent=':literal' display='block' mathbackground='yellow'>
open bracket 2 x close bracket sub 0 super 1 end super
 
§
<math display='block'>
 <msubsup>
  <mrow>
   <mo>[</mo>
   <mn>2</mn>
   <mo>&#x2062;</mo>
   <mi>x</mi>
   <mo>]</mo>
  </mrow>
  <mn>0</mn>
  <mn>1</mn>
 </msubsup>
</math>
open bracket evaluated at 1 minus the same expression evaluated at 0
 [2x]_0^1 evaluate 2x at 1 and 0 bracket expression in base
2 ⁢ x | 0 1 
§
<math display='block' mathbackground='yellow'>
 <mrow>
  <mn>2</mn>
  <mo>&#x2062;</mo>
  <mi>x</mi>
  <msubsup>
   <mo>|</mo>
   <mn>0</mn>
   <mn>1</mn>
  </msubsup>
 </mrow>
</math>
2 x evaluated at 1 minus the same expression evaluated at 0
§
<math intent=':common' display='block' mathbackground='yellow'>
2 x evaluated at 1 minus the same expression evaluated at 0
§
<math intent=':literal' display='block' mathbackground='yellow'>
2 x, vertical line sub 0 super 1 end super
 
§
<math display='block'>
 <mrow>
  <mn>2</mn>
  <mo>&#x2062;</mo>
  <mi>x</mi>
  <msubsup>
   <mo>|</mo>
   <mn>0</mn>
   <mn>1</mn>
  </msubsup>
 </mrow>
</math>
2 x evaluated at 1 minus the same expression evaluated at 0
 2x|_0^1 evaluate 2x at 1 and 0 vertical bar
2 ⁢ x | 0 1 
§
<math display='block' mathbackground='yellow'>
 <msubsup>
  <mrow>
   <mn>2</mn>
   <mo>&#x2062;</mo>
   <mi>x</mi>
   <mo>|</mo>
  </mrow>
  <mn>0</mn>
  <mn>1</mn>
 </msubsup>
</math>
2 x vertical line sub 0, to the first
§
<math intent=':common' display='block' mathbackground='yellow'>
2 x vertical line sub 0, to the first
§
<math intent=':literal' display='block' mathbackground='yellow'>
2 x vertical line sub 0 super 1 end super
 
§
<math display='block'>
 <msubsup>
  <mrow>
   <mn>2</mn>
   <mo>&#x2062;</mo>
   <mi>x</mi>
   <mo>|</mo>
  </mrow>
  <mn>0</mn>
  <mn>1</mn>
 </msubsup>
</math>
2 x vertical line sub 0, to the first
 2x|_0^1 evaluate 2x at 1 and 0 vertical bar expression in base
∮ C 1 z d z 
§
<math display='block'>
 <msub>
  <mo>&#x222E;</mo>
  <mi>C</mi>
 </msub>
 <mfrac>
  <mn>1</mn>
  <mi>z</mi>
 </mfrac>
 <mrow>
  <mi>d</mi>
  <mi>z</mi>
 </mrow>
</math>
the contour integral over c of; 1 over z, d z
§
<math intent=':common' display='block'>
the contour integral over c of; 1 over z, d z
§
<math intent=':literal' display='block'>
contour integral sub c, 1 over z, d z
 
§
<math display='block'>
 <msub>
  <mo>&#x222E;</mo>
  <mi>C</mi>
 </msub>
 <mfrac>
  <mn>1</mn>
  <mi>z</mi>
 </mfrac>
 <mrow>
  <mi>d</mi>
  <mi>z</mi>
 </mrow>
</math>
the contour integral over c of; 1 over z, d z
 \oint \frac{1}{z} dz oint 1 over z dz
Names
v ˙ ** 2 + w ˙ ** 2 
§
<math display='block'>
 <mrow>
  <mrow>
   <mover>
    <mi>v</mi>
    <mo>&#x02d9;</mo>
   </mover>
   <mo>**</mo>
   <mn>2</mn>
  </mrow>
  <mo>+</mo>
  <mrow>
   <mover>
    <mi>w</mi>
    <mo>&#x02d9;</mo>
   </mover>
   <mo>**</mo>
   <mn>2</mn>
  </mrow>
 </mrow>
</math>
v dot, ** 2, plus w dot, ** 2
§
<math intent=':common' display='block'>
v dot, ** 2, plus w dot, ** 2
§
<math intent=':literal' display='block'>
v dot ** 2 plus w dot ** 2
 
§
<math display='block'>
 <mrow>
  <mrow intent='power($v̇, $n)'>
   <mover arg='v̇' intent='first-deriv(v)'>
    <mi>v</mi>
    <mo>&#x02d9;</mo>
   </mover>
   <mo>**</mo>
   <mn arg='n'>2</mn>
  </mrow>
  <mo>+</mo>
  <mrow intent='power($ẇ, $n)'>
   <mover arg='ẇ' intent='first-deriv(w)'>
    <mi>w</mi>
    <mo>&#x02d9;</mo>
   </mover>
   <mo>**</mo>
   <mn arg='n'>2</mn>
  </mrow>
 </mrow>
</math>
first deriv of, v squared, plus first deriv of, w squared
 \dot{v}**2+\dot{w}**2 NFC v dot and w dot
Templates
x 
§
<math display='block'>
 <mi>x</mi>
</math>
x
§
<math intent=':common' display='block'>
x
§
<math intent=':literal' display='block'>
x
 
§
<math display='block'>
 <mi intent='the_variable_x'>x</mi>
</math>
the variable x
 x x with string
a + b ! 
§
<math display='block'>
 <mrow>
  <mi>a</mi>
  <mo>+</mo>
  <mi>b</mi>
  <mo>!</mo>
 </mrow>
</math>
eigh plus b factorial
§
<math intent=':common' display='block'>
eigh plus b factorial
§
<math intent=':literal' display='block'>
eigh plus b exclamation point
 
§
<math display='block'>
 <mrow intent='$p(_($a, $f($b)))'>
  <mi arg='a'>a</mi>
  <mo arg='p' intent='plus'>+</mo>
  <mi arg='b'>b</mi>
  <mo arg='f' intent='factorial'>!</mo>
 </mrow>
</math>
plus eigh factorial of, b
 a+b! a plus b factorial unary plus intent
a + b 
§
<math display='block'>
 <mrow>
  <mi>a</mi>
  <mo>+</mo>
  <mi>b</mi>
 </mrow>
</math>
eigh plus b
§
<math intent=':common' display='block'>
eigh plus b
§
<math intent=':literal' display='block'>
eigh plus b
 
§
<math display='block'>
 <mrow intent='foo:int:silent(bar:positive-int-int, $a:foo-bar-foo-bar, $b:number)'>
  <mi arg='a'>a</mi>
  <mo arg='p' intent='plus'>+</mo>
  <mi arg='b' intent='b:negative-int-int'>b</mi>
 </mrow>
</math>
bar eigh b
 a+b Properties on argref
R ⟨ X ⟩ 
§
<math display='block'>
 <mrow>
  <mi>R</mi>
  <mo>&#x27e8;</mo>
  <mi>X</mi>
  <mo>&#x27e9;</mo>
 </mrow>
</math>
r, left angle bracket x right angle bracket
§
<math intent=':common' display='block'>
r, left angle bracket x right angle bracket
§
<math intent=':literal' display='block'>
r, left angle bracket x right angle bracket
 
§
<math display='block'>
 <mrow intent='_(free, $r, _algebra_on, $x)'>
  <mi arg='r'>R</mi>
  <mo>&#x27e8;</mo>
  <mi arg='x'>X</mi>
  <mo>&#x27e9;</mo>
 </mrow>
</math>
free r algebra on x
§
<math display='block'>
 <mrow intent='_:silent(free, $r, _algebra_on, $x)'>
  <mi arg='r'>R</mi>
  <mo>&#x27e8;</mo>
  <mi arg='x'>X</mi>
  <mo>&#x27e9;</mo>
 </mrow>
</math>
free r algebra on x
§
<math display='block'>
 <mrow intent='free-algebra:silent(_free, $r, _algebra_on, $x)'>
  <mi arg='r'>R</mi>
  <mo>&#x27e8;</mo>
  <mi arg='x'>X</mi>
  <mo>&#x27e9;</mo>
 </mrow>
</math>
free r algebra on x
 R\langle X\rangle free r-algebra on x
x + 2 | y - z | 
§
<math display='block'>
 <mrow>
  <mi>x</mi>
  <mo>+</mo>
  <mn>2</mn>
  <mo>|</mo>
  <mi>y</mi>
  <mo>-</mo>
  <mi>z</mi>
  <mo>|</mo>
 </mrow>
</math>
x plus; 2, the absolute value of y minus z, end absolute value,
§
<math intent=':common' display='block'>
x plus; 2, the absolute value of y minus z, end absolute value,
§
<math intent=':literal' display='block'>
x plus, 2, vertical line y minus z, vertical line
 
§
<math display='block'>
 <mrow intent='plus:infix($x,times:infix(2,absolute-value(minus:infix($y,$z))))'>
  <mi arg='x'>x</mi>
  <mo>+</mo>
  <mn>2</mn>
  <mo>|</mo>
  <mi arg='y'>y</mi>
  <mo>-</mo>
  <mi arg='z'>z</mi>
  <mo>|</mo>
 </mrow>
</math>
, x plus; 2 times, the absolute value of, y minus z; end absolute value;,
§
<math display='block'>
 <mrow intent='plus($x,times(2,absolute-value(infix($y,$z))))'>
  <mi arg='x'>x</mi>
  <mo>+</mo>
  <mn>2</mn>
  <mo>|</mo>
  <mi arg='y'>y</mi>
  <mo>-</mo>
  <mi arg='z'>z</mi>
  <mo>|</mo>
 </mrow>
</math>
plus of, x comma; times of, 2 comma, the absolute value of infix of, y comma z, end absolute value,
§
<math display='block'>
 <mrow>
  <mi>x</mi>
  <mo>+</mo>
  <mn>2</mn>
  <mo intent='absolute-value'>|</mo>
  <mi>y</mi>
  <mo>-</mo>
  <mi>z</mi>
  <mo intent='end-absolute-value'>|</mo>
 </mrow>
</math>
x plus; 2, the absolute value of y minus z, end absolute value,
 x+2\lvert y-z\rvert x plus 2 times the absolute-value of y minus z
XML Features
log X 
§
<math display='block'>
 <mrow>
  <mi>log</mi>
  <mi>X</mi>
 </mrow>
</math>
log x
§
<math intent=':common' display='block'>
log x
§
<math intent=':literal' display='block'>
log x
 
§
<math display='block'>
 <mrow intent='log(x)'/>
</math>
log of, x
§
<math display='block'>
 <mrow intent='log($x)'>
  <mi arg='x'>X</mi>
 </mrow>
</math>
log of, x,
§
<math display='block'>
 <mrow intent='log&#x28;&#x24;x)'>
  <mi>log</mi>
  <mi arg='x'>Y</mi>
 </mrow>
</math>
log of, y
 \log x NCR x28 and x24
HTML
x + a bold word 
§
<math display='block'>
 <mi>x</mi>
 <mo>+</mo>
 <mtext>a <b>bold</b> word</mtext>
</math>
x plus a bold word
§
<math intent=':common' display='block'>
x plus a bold word
§
<math intent=':literal' display='block'>
x plus a bold word
 
§
<math display='block'>
 <mi>x</mi>
 <mo>+</mo>
 <mtext>a <b>bold</b> word</mtext>
</math>
x plus a bold word
 x+\text{a \textbf{bold} word nested html b
Units
1.5km 
§
<math display='block'>
 <mn>1.5</mn><mi>km</mi>
</math>
1.5 km
§
<math intent=':common' display='block'>
1.5 km
§
<math intent=':literal' display='block'>
1.5 km
 
§
<math display='block'>
 <mn>1.5</mn><mi intent=':unit'>km</mi>
</math>
1.5 kilometres
 \qty{1.5}{\kilogram} Km units
2Ω 
§
<math display='block'>
 <mn>2</mn><mi mathvariant='normal'>Ω</mi>
</math>
2 omega
§
<math intent=':common' display='block'>
2 omega
§
<math intent=':literal' display='block'>
2 omega
 
§
<math display='block'>
 <mn>2</mn><mi intent=':unit' mathvariant='normal'>Ω</mi>
</math>
2 ohms
 \qty{2}{\ohm} Ohm units
Chemistry
H 2 O 
§
<math display='block'>
 <mrow>
     <mmultiscripts>
       <mi mathvariant='normal'>H</mi>
       <mn>2</mn>
       <mrow/>
     </mmultiscripts>
     <mi mathvariant='normal'>O</mi>
   </mrow>
</math>
h, subscript 2; o,
§
<math intent=':common' display='block'>
h, subscript 2; o,
§
<math intent=':literal' display='block'>
h subscript 2 o
 
§
<math display='block'>
 <mrow intent=':chemical-formula'>
     <mmultiscripts>
       <mi mathvariant='normal' intent=':chemical-element'>H</mi>
       <mn>2</mn>
       <mrow/>
     </mmultiscripts>
     <mi mathvariant='normal' intent=':chemical-element'>O</mi>
   </mrow>
</math>
h, subscript 2; o,
 \ce{H20} H20
2 ⁢ H 2 ⁣ O ⟶ 2 ⁢ H 2 + O 2 
§
<math display='block'>
 <mrow>
  <mrow>
   <mn>2</mn>
   <mo>&#x2062;</mo>
   <mrow>
    <mmultiscripts>
     <mi mathvariant='normal'>H</mi>
     <mn>2</mn>
     <mrow/>
    </mmultiscripts>
    <mo>&#x2063;</mo>
    <mi mathvariant='normal'>O</mi>
   </mrow>
  </mrow>
  <mo>⟶</mo>
  <mrow>
   <mrow>
    <mn>2</mn>
    <mo>&#x2062;</mo>
    <mmultiscripts>
     <mi mathvariant='normal'>H</mi>
     <mn>2</mn>
     <mrow/>
    </mmultiscripts>
   </mrow>
   <mo>+</mo>
   <mmultiscripts>
    <mi mathvariant='normal'>O</mi>
    <mn>2</mn>
    <mrow/>
   </mmultiscripts>
  </mrow>
 </mrow>
</math>
2, h, subscript 2; o; reacts to form; 2 h, subscript 2; plus o, subscript 2,
§
<math intent=':common' display='block'>
2, h, subscript 2; o; reacts to form; 2 h, subscript 2; plus o, subscript 2,
§
<math intent=':literal' display='block'>
2 h subscript 2 o; long rightwards arrow; 2 h subscript 2, plus o subscript 2
 
§
<math display='block'>
 <mrow intent=':chemical-equation'>
  <mrow intent=':chemical-equation'>
   <mn>2</mn>
   <mo>&#x2062;</mo>
   <mrow intent=':chemical-equation'>
    <mmultiscripts intent=':chemical-formula'>
     <mi mathvariant='normal' intent=':chemical-element'>H</mi>
     <mn>2</mn>
     <mrow/>
    </mmultiscripts>
    <mo>&#x2063;</mo>
    <mi mathvariant='normal' intent=':chemical-element'>O</mi>
   </mrow>
  </mrow>
  <mo>⟶</mo>
  <mrow intent=':chemical-equation'>
   <mrow intent=':chemical-equation'>
    <mn>2</mn>
    <mo>&#x2062;</mo>
    <mmultiscripts intent=':chemical-formula'>
     <mi mathvariant='normal' intent=':chemical-element'>H</mi>
     <mn>2</mn>
     <mrow/>
    </mmultiscripts>
   </mrow>
   <mo>+</mo>
   <mmultiscripts intent=':chemical-formula'>
    <mi mathvariant='normal' intent=':chemical-element'>O</mi>
    <mn>2</mn>
    <mrow/>
   </mmultiscripts>
  </mrow>
 </mrow>
</math>
2, h, subscript 2; o; reacts to form; 2 h, subscript 2; plus o, subscript 2,
 \ce{2 H2O → 2 H2 + O2} 2 H2O → 2 H2 + O
Unexpected arity
x y 
§
<math display='block'>
 <mfrac>
  <mi>x</mi>
  <mi>y</mi>
 </mfrac>
</math>
x over y,
§
<math intent=':common' display='block'>
x over y,
§
<math intent=':literal' display='block'>
x over y,
 
§
<math display='block'>
 <mfrac intent='divides'>
  <mi>x</mi>
  <mi>y</mi>
 </mfrac>
</math>
divides
 - 0-ary divides
x y 
§
<math display='block'>
 <mfrac>
  <mi>x</mi>
  <mi>y</mi>
 </mfrac>
</math>
x over y,
§
<math intent=':common' display='block'>
x over y,
§
<math intent=':literal' display='block'>
x over y,
 
§
<math display='block'>
 <mfrac intent='divides(z)'>
  <mi>x</mi>
  <mi>y</mi>
 </mfrac>
</math>
divides of, z
 - 1-ary divides
x y 
§
<math display='block'>
 <mfrac>
  <mi>x</mi>
  <mi>y</mi>
 </mfrac>
</math>
x over y,
§
<math intent=':common' display='block'>
x over y,
§
<math intent=':literal' display='block'>
x over y,
 
§
<math display='block'>
 <mfrac intent='divides(w,x,y)'>
  <mi>x</mi>
  <mi>y</mi>
 </mfrac>
</math>
divides of, w comma x comma y
 - 3-ary divides
X → 
§
<math display='block'>
 <mover>
  <mi>X</mi>
  <mo>→</mo>
 </mover>
</math>
vector x
§
<math intent=':common' display='block'>
vector x
§
<math intent=':literal' display='block'>
x right arrow
 
§
<math display='block' mathbackground='yellow'>
 <mover intent='ray($X)'>
  <mi arg='X'>X</mi>
  <mo>→</mo>
 </mover>
</math>
ray of, x
 - 1-ary ray
Content MathML
x 
§
<math display='block'>
 <apply>
  <sin/>
  <ci>x</ci>
 </apply>
</math>
problem with SetMathML
§
<math intent=':common' display='block'>
problem with SetMathML
§
<math intent=':literal' display='block'>
problem with SetMathML
 
§
<math display='block'>
 <apply intent='sin(x)'>
  <sin/>
  <ci>x</ci>
 </apply>
</math>
problem with SetMathML
 \sin x content mathml sin x
Intent Grammar Errors
x y 
§
<math display='block'>
 <mfrac>
  <mi>x</mi>
  <mi>y</mi>
 </mfrac>
</math>
x over y,
§
<math intent=':common' display='block'>
x over y,
§
<math intent=':literal' display='block'>
x over y,
 
§
<math display='block'>
 <mfrac><mi intent='hmm)('>x</mi>
 <mi>y</mi>
 </mfrac>
</math>
x over y,
 - bad intent paren
1.234 + x 
§
<math display='block'>
 <mrow>
  <mn>1.234</mn>
  <mo>+</mo>
  <mi>x</mi>
 </mrow>
</math>
1.234 plus x
§
<math intent=':common' display='block'>
1.234 plus x
§
<math intent=':literal' display='block'>
1.234 plus x
 
§
<math display='block' mathbackground='yellow'>
 <mrow intent='sum($a,$b)'>
  <mn>1.234</mn>
  <mo>+</mo>
  <mi>x</mi>
 </mrow>
</math>
1.234 plus x
 - bad intent argref
1.234 + x 
§
<math display='block'>
 <mrow>
  <mn>1.234</mn>
  <mo>+</mo>
  <mi>x</mi>
 </mrow>
</math>
1.234 plus x
§
<math intent=':common' display='block'>
1.234 plus x
§
<math intent=':literal' display='block'>
1.234 plus x
 
§
<math display='block'>
 <mrow intent='sum($1.234,$:x:)'>
  <mn arg='1.234'>1.234</mn>
  <mo>+</mo>
  <mi arg=':x:'>x</mi>
 </mrow>
</math>
1.234 plus x
 - bad intent arg names
x 
§
<math display='block'>
 <mi>x</mi>
</math>
x
§
<math intent=':common' display='block'>
x
§
<math intent=':literal' display='block'>
x
 
§
<math display='block'>
 <mi intent='one two'>x</mi>
</math>
x
 - multiple identifiers
12 
§
<math display='block'>
 <mn>12</mn>
</math>
12
§
<math intent=':common' display='block'>
12
§
<math intent=':literal' display='block'>
12
 
§
<math display='block'>
 <mn intent='1.2e1'>12</mn>
</math>
12
 - bad number
X ‾ + Y ‾ 
§
<math display='block'>
 <mover>
  <mi>X</mi>
  <mo>&#x203e;</mo>
 </mover>
 <mo>+</mo>
 <mover>
  <mi>Y</mi>
  <mo>&#x203e;</mo>
 </mover>
</math>
x bar, plus y bar,
§
<math intent=':common' display='block'>
x bar, plus y bar,
§
<math intent=':literal' display='block'>
x line plus y line
 
§
<math display='block'>
 <mover intent='mean($x('>
  <mi arg='x'>X</mi>
  <mo>&#x203e;</mo>
 </mover>
 <mo>+</mo>
 <mover intent='mean($x)'>
  <mi arg='x'>Y</mi>
  <mo>&#x203e;</mo>
 </mover>
</math>
x bar, plus mean of, y
 - bad intent subexpression
x 
§
<math display='block'>
 <mi>x</mi>
</math>
x
§
<math intent=':common' display='block'>
x
§
<math intent=':literal' display='block'>
x
 
§
<math display='block'>
 <mi intent='just say this'>x</mi>
</math>
x
 x Free text just say this
x 
§
<math display='block'>
 <mrow>
  <mi>x</mi>
 </mrow>
</math>
x
§
<math intent=':common' display='block'>
x
§
<math intent=':literal' display='block'>
x
 
§
<math display='block'>
 <mrow intent='just say this about $x'>
  <mi arg='x'>x</mi>
 </mrow>
</math>
x
 x Free text with argref
🐇 X 
§
<math display='block'>
 <mrow>
  <mo>&#x1F407;</mo>
  <mi>X</mi>
 </mrow>
</math>
🐇 x
§
<math intent=':common' display='block'>
🐇 x
§
<math intent=':literal' display='block'>
🐇 x
 
§
<math display='block'>
 <mrow>
  <mo intent='&#x1F407;'>&#x1F407;</mo>
  <mi>X</mi>
 </mrow>
</math>
🐇 x
 🐇 X intent 🐇