Content MathML
Token Elements
ci
X
X
ci type='vector'
W
W
ci type='vector' with subscript
X y
X
y
Cn with subscript
1
0
1
0
Omega with Over
ω
c
˜
ω
c
˜
Function
x t
x
t
Fn deprecated
f + g z
f
g
z
Function of Power
f x 2 t
f
x
t
2
Function Diff
φ ′ t
φ
t
Function with Subscript
ℛ
s
t
ℛ
s
t
Function with Subsup and Power
x
0
n
z t
x
0
n
t
z
Function with Power and Two Variables
x α z + y w + q
x
z
y
w
q
α
Discrete Function
x t
x
t
Discrete Function with Subscript
x
c
t
x
c
t
Csymbol Tests
Adjoint
X H
X
Adjoint
x + y H
x
y
Directional diff
∇ y x
y x
Stochastic Process
0 Prob p 1 Prob 1 - p
0
p
1
1
p
Mutual Information
ℐ x ; y
x
y
Distance
x ∥ y
x
y
Normal Distribution
0 y
0
y
Distributed In
r ∼ 0 σ 2
r
0
σ
2
Estimate
x
̂
x
Estimate
x ̂ y
x y
Estimate with msub
x ̂ 2
x 2
Estimate with msub
x ̂ 2
x 2
Estimate with complex msub
x ̂ a b c
x a b c
Estimate
x ̂ y + X
x y + X
CDF
C r
C
r
CDF wit condition
C r | θ
C
θ
r
CDF with multiple conditions
C r | θ β
C
θ
β
r
CDF with multiple conditions and bvar
C x | θ β r
C
x
θ
β
r
PDF
P a
x r
P a
x
r
PDF with condition
P x | θ r
P
x
θ
r
PDF with multiple conditions
P x | θ β r
P
x
θ
β
r
PDF multiple arguments with condition
P x y | θ r s
P
x
y
θ
r
s
Estimate of Function
P x ̂
P
x
Estimate of Function
P
̂ x
P
x
Expected Value
E x
x
Expected Value w/bvar and condition
E x
θ
̂
MMSE
| θ
x
θ
θ
̂
MMSE
Expected Value w condition
E
θ
̂
MMSE
| θ
θ
θ
̂
MMSE
Expected Value multiple conditions
E
θ
̂
MMSE
| θ ω φ
θ
ω
φ
θ
̂
MMSE
Probability
Pr X
X
Probability with multiple arguments
Pr X Y
X
Y
Complement
x y ′
x
y
Probability with Condition
Pr X | X ∈ ℝ
X
X
argmin
argmin X
X
Argmin with Condition
argmin C X
C
X
Argmin with domainofapplication
argmin D X
D
X
argmax
argmax X
X
Argmax with condition
argmax C X
C
X
Argmax with domainofapplication
argmax C X
C
X
Convolution
X * Y
X
Y
Probability
Pr A B
A
B
Evaluateat with interval
F x | 1 2
1
2
F
x
Evaluate with bvar and interval
F x | t = 1 2
t
1
2
F
x
Evaluateat with condition
F x |
z
z
F
x
Evaluateat with multiple conditions
F x |
z
,
a
z
a
F
x
Evaluate with bvar and condition
F x | t , t = y
t
y
F
x
Evaluate with lowlimit/uplimit
F x | z x
z
x
F
x
Evaluate with bvar and lowlimit/uplimit
F x | t = y t
t
y
t
F
x
Surface Integral with bvar and domainofapplication
∮ S X d x
x
S
X
Surface Intgral with bvar and condition
∮ S X d x
x
S
X
Surface Integral with bvar and lowlimit/uplimit
∮ 1 3 X d x
x
1
3
X
Surface Integral with bvar
∮ X d x
x
X
Basic Content Elements
Mult. Complex Cartesians
2 + 3 ⅈ 2 - 3 ⅈ
2
2
Apply
A B
A
B
Composition
x ∘ y ( z )
x
y
z
Inverse of a Function
u -1 t
u
t
Apply/Apply/Plus
F + G x
F
G
x
Apply/Apply/Diff
u
′ t
u
t
Apply/Apply/Diff/Apply/Plus
F + G ′ x
1
F
G
x
Apply/Apply/Power
x 2 2
x
2
2
Apply/Apply/Inverse
u -1 t
u
t
Arithmatic Algebra and Logic
Max
max { a b }
a
b
Min
min { a b }
a
b
min
min { X }
X
Min with Condition
min { X | C }
C
X
Min with domainofapplication
min D { X }
D
X
Min with domainofapplication and condition and
multiple bvars
min D V , T { X | a ∈ b }
D
V
T
a
b
X
Max with domainofapplication and condition and
multiple bvars
max D V , T { X | a ∈ b }
D
V
T
a
b
X
Max with Condition
max { X | C }
C
X
Max with domainofapplication
max D { X }
D
X
Infimum with bvar and condition
inf x { x 2 | x ∉ B }
x
x
B
x
2
Minus
a - b
a
b
Quotient
integer part of a / b
a
b
Times
x y
x
y
Power Test
- 1 b n
1
b
n
Power of a Function
S 0 2 n
S 0 n
2
Power of a Discrete Function
x 2 t
x
t
2
And
a ∧ c
a
c
Or
a ∨ c
a
c
Not Test
W
W
XOR test
a ⊕ b
a
b
XOR test 2
H a ⊕ b
H
a
b
Forall test
∀ x , x ∈ 0 1 2 x ∈ ℤ : y = 2 x + 3
x
x
0
1
2
x
ℤ
y
2
x
3
This is a test of the above as inline math:
∀ x , x ∈ 0 1 2 x ∈ ℤ : y = 2 x + 3
x
x
0
1
2
x
ℤ
y
2
x
3
Forall x, x
∀ x : x
x
x
Forall x,(x) and y
∀ x : x ∧ y
x
x
y
Forall x,(x and y)
∀ x : x ∧ y
x
x
y
x and y or z : or(and(x,y),z)
x ∧ y ∨ z
x
y
z
x and (y or z): and(x,or(y,z))
x ∧ y ∨ z
x
y
z
Conjugate Test
x ¯
x
Remainder
a mod b
a
b
Relations
Equals
a = b
a
b
Equals with Line Breaking
a = b = c = d
a
b
c
d
Real
ℜ x
x
Calculus and Vector Calculus
Int
∫ y d x
x
y
Int
∫ a - b d x
x
a
b
Int with domain of application and nothing else
∫ ℝ d x
x
Diff
f
′
f
Diff of Sum
f + g ′
f
g
Diff with degree
u 5
5
u
Diff with bvar
d d x f x
x
f
x
diff with bvar and bvar/degree
d 2 d x 2 f x
x
2
f
x
Diff of a Function
u ′ t
u
t
Partial Diff
∂ 4 ∂ x f
x
4
f
Partial Diff with multiple bvar
∂ 2 ∂ x ∂ y f x y
x y
f
x
y
Partial Diff with Degree
∂ 2 f
2
f
Partial Diff with Degree
∂ 2 f x
2
f
x
Grad Test
grad T
T
Curl Test
curl R
R
Norm Test
∥ x ∥
x
Norm Test with Domain of Application
∥ x ∥ ℤ
x
Theory of Sets
Set
0 1 2
0
1
2
Proper Subset
X ⊂ Y
X
Y
Sequences and Series
Sum with nothing
∑ x
x
Sum with Bvar
∑ x
x x
Sum with Mulitple Bvar
∑ x
x y x
Sum with Limits and Condition
∑ x = 0 x ∈ ℝ ∞ x 3
x
0
x
x
3
Sum with Domainofapplication and Condition
∑ n …
n
m
x ∈ ℝ x 3
x
x
n
…
n
m
x
3
Product with Limits and Condition
∏ x = 0 x ∈ ℝ ∞ x 3
x
0
x
x
3
Product with Domainofapplication and Condition
∏ n …
n
m
x ∈ ℝ x 3
x
x
n
…
n
m
x
3
Product Times Test
∑ w ∏ i = 1 2 x
j
w
i
1
2
x
Elementary Classical Functions
Sin
sin x
x
Statistics
Mean Test
〈 m , n , o 〉
m
n
o
Mean Times Test
X ¯ Y ¯
X
Y
Moment
〈 x 3 〉
3
p
x
Linear Algera
Selector
x -1 i
x
i
Vector Entity Test
π
π
Vector Product Test
C × D
C
D
Scalar Product Test
< A , B >
A
B
Outer Product Test
V . X
V
X
Semantic Mapping Elements
Annotation
Constant and Symbol Elements
Integers
ℤ
Other MathML Tests
Applying an m:ci to a single m:ci
∠ x t
∠
x
t
Applying a ci with an mo in it
x ≫ y
≫ x
y
Applying a ci with an mo in it
x ≫ y ≫ z
≫ x
y
z
Laplace in ci
ℒ x
ℒ x
Fourier Transform in ci
ℱ x
ℱ x
Apply ci to apply
∠ a + b
∠
a
b