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Alternatives: | (mml file) (full) (simple) (plain) (form) (slideshow)
File: | TortureTests/Complexity/complex4
CVS-ID: |
Author: | Design Science, Inc. (D. Doyle, R. Miner)
Description: | Testing content tags.
Sample Rendering: N/A

Your browser's rendering:

a + b - c
a b c

x + yz + z
x y z z

x * (y + z) * z
x y z z

sin(a + b)
a b

sin(x(y + z)z)
x y z z

sin(xy)2b
x y 2 b

(x + y) ^ (n - 3)
x y n 3

limit as x goes to a of sin x using <reln>
x x a x

limit as x goes to a of sin x using <apply>
x x a x

limit as x goes to a of sin(x + y) using <reln>
x x a x y

limit as x goes to a of sin(x + y) using <apply>
x x a x y

limit as x goes to a of sin(x + y)2b using <reln>
x x a x y 2 b

limit as x goes to a of sin(x + y)2b using <apply>
x x a x y 2 b

quotient
a b

moment
3 X

selector
1 2 3 4 1

factorial
n

(a + b)!
n m x

inverse function
f

inverse matrix
a A

conjugate
x ⅈ y

a + b + c
a b c

integral (a + x)dx
x 0 a a x

-1 + 7
1 7

7 + (-1)
7 1

max
x x 0 x 1 x x

lambda sin(x + 1)
x x 1

lambda integral f(x)dx
b x a b f x

compose f and g
f g

compose f and g (x)
f g x

f(g(x))
f g x

composition of f and inverse of f eq identity using <reln>
f f

composition of f and inverse of f eq identity using <apply>
f f

e^x
x

min(x, x not in B, x^2) using <reln>
x x B x 2

min(x, x not in B, x^2) using <apply>
x x B x 2

a mod (b)
a b

ab
a b

gcd(a b, c)
a b c

integral
x 0 a f x

abs(x)
x

tall abs(x)
H K

abs(x + y + z)
x y z

x > 0 and z < 1 as <reln>
x 0 x 1

x > 0 and z < 1 as <apply>
x 0 x 1

a and b
a b

a or b
a b

a xor b
a b

a eq b with <reln> tag
a b

a eq b with <apply> tag
a b

a neq b with <reln> tag
a b

a neq b with <apply> tag
a b

a > b with <reln> tag
a b

a > b with <apply> tag
a b

a < b with <reln> tag
a b

a < b with <apply> tag
a b

a <= b with <reln> tag
a b

a >= b with <apply> tag
a b

a <= b with <reln> tag
a b

a <= b with <apply> tag
a b

set: {b, a, c}
b a c

set with condition
x x 5

list: {b, a, c}
b a c

list: {x|x < 5}
x x 5

A union B
A B

A intersect B
A B

A intersect (B union C)
A B C

integral x in R as <reln>
x R

x in R as <apply>
x R

a in A
a A

a not in A as <reln>
a A

a not in A as <apply>
a A

not a
a

not (a and b)
a b

A -> B (reln)
A B

A -> B (apply)
A B

forall
x x x 0

forall/and/lt/power
p q p Q q Q p q p q 2

forall/exists/and/plus
n n Z n 0 x y z x Z y Z z Z x n y n z n

exists
x f x 0

forall/exists/and/plus
n n Z n 0 x y z x Z y Z z Z x n y n z n

ln a
a

log base 3 of x
3 x

integer
x x D f x

diff
x f x

partialdiff
x 2 y f x y

integral
x a b f x

partialdiff
x n y m x y

divide
a b

divide/plus/minus
a b a b

divide/plus/divide
a b a b

A is subset of B as <reln>
A B

A is subset of B as <apply>
A B

A is proper subset of B as <reln>
A B

A is proper subset of B as <apply>
A B

A is not subset of B as <reln>
A B

A is not subset of B as <apply>
A B

A is not proper subset of B as <reln>
A B

A is not proper subset of B as <apply>
A B

Set difference
A B

Log base 3 of x + y
3 x y

Sum as x goes from a to b of f(x)
x a b f x

sum
x x B f x

product
x a b f x

product
x x B f x

tendsto with <reln>
x 2 a 2

tendsto with <apply>
x 2 a 2

tendsto with <reln>
x y f x y g x y

tendsto with <apply>
x y f x y g x y

mean(X)
X

root(a + b)
n a b

standard deviation
X

variance(X)
X

median(X)
X

mode(X)
X

degree
3 X

vector
1 2 3 x

matrix
0 1 0 0 0 0 1 0 1 0 0 0

determinant
A

transpose
A

semantics
x 5 \sin x + 5

limit
x 0 x

symbol check
4.56 4.56 4 5 4 5 4.56 4.56 π ⅇ ⅇ ⅈ ⅈ γ ∞ ∞

multiset
4.56 4.56 4 5 4 5 4.56 4.56 π ⅇ ⅇ ⅈ ⅈ γ ∞ ∞

tendsto type = "above" with <reln>
x 2 a 2

tendsto type = "above" with <apply>
x 2 a 2

tendsto type = "below" with <reln>
x 2 a 2

tendsto type = "below" with <apply>
x 2 a 2

tendsto type = "two-sided" with <reln>
x 2 a 2

tendsto type = "two-sided" with <apply>
x 2 a 2

type check
x x x y θ v π ⅇ ⅇ ⅈ ⅈ γ ∞ ∞

sin + cos
x x

f(x)
f x

Source Code:

        <p>a + b - c
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <plus/>
              <ci>a</ci>
              <apply>
                <minus/>
                <ci>b</ci>
                <ci>c</ci>
              </apply>
            </apply>
          </math>
        </p>
        <p>
    x + yz + z
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <plus/>
              <ci>x</ci>
              <apply>
                <times/>
                <ci>y</ci>
                <ci>z</ci>
              </apply>
              <ci>z</ci>
            </apply>
          </math>
        </p>
        <p>
    x * (y + z) * z
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <times/>
              <ci>x</ci>
              <apply>
                <plus/>
                <ci>y</ci>
                <ci>z</ci>
              </apply>
              <ci>z</ci>
            </apply>
          </math>
        </p>
        <p>
    sin(a + b)
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <sin/>
              <apply>
                <plus/>
                <ci>a</ci>
                <ci>b</ci>
              </apply>
            </apply>
          </math>
        </p>
        <p>
    sin(x(y + z)z)
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <sin/>
              <apply>
                <times/>
                <ci>x</ci>
                <apply>
                  <plus/>
                  <ci>y</ci>
                  <ci>z</ci>
                </apply>
                <ci>z</ci>
              </apply>
            </apply>
          </math>
        </p>
        <p>
    sin(xy)2b
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <times/>
              <apply>
                <sin/>
                <apply>
                  <times/>
                  <ci>x</ci>
                  <ci>y</ci>
                </apply>
              </apply>
              <apply>
                <times/>
                <cn>2</cn>
                <ci>b</ci>
              </apply>
            </apply>
          </math>
        </p>
        <p>
    (x + y) ^ (n - 3)
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <power/>
              <apply>
                <plus/>
                <ci>x</ci>
                <ci>y</ci>
              </apply>
              <apply>
                <minus/>
                <cn>n</cn>
                <cn>3</cn>
              </apply>
            </apply>
          </math>
        </p>
        <p>
    limit as x goes to a of sin x using &lt;reln&gt;
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <limit/>
              <bvar>
                <ci>x</ci>
              </bvar>
              <condition>
                <reln>
                  <tendsto type='above'/>
                  <ci>x</ci>
                  <ci>a</ci>
                </reln>
              </condition>
              <apply>
                <sin/>
                <ci>x</ci>
              </apply>
            </apply>
          </math>
        </p>
        <p>
    limit as x goes to a of sin x using &lt;apply&gt;
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <limit/>
              <bvar>
                <ci>x</ci>
              </bvar>
              <condition>
                <apply>
                  <tendsto type='above'/>
                  <ci>x</ci>
                  <ci>a</ci>
                </apply>
              </condition>
              <apply>
                <sin/>
                <ci>x</ci>
              </apply>
            </apply>
          </math>
        </p>
        <p>
    limit as x goes to a of sin(x + y) using &lt;reln&gt;
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <limit/>
              <bvar>
                <ci>x</ci>
              </bvar>
              <condition>
                <reln>
                  <tendsto type='above'/>
                  <ci>x</ci>
                  <ci>a</ci>
                </reln>
              </condition>
              <apply>
                <sin/>
                <apply>
                  <plus/>
                  <ci>x</ci>
                  <ci>y</ci>
                </apply>
              </apply>
            </apply>
          </math>
        </p>
        <p>
    limit as x goes to a of sin(x + y) using &lt;apply&gt;
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <limit/>
              <bvar>
                <ci>x</ci>
              </bvar>
              <condition>
                <apply>
                  <tendsto type='above'/>
                  <ci>x</ci>
                  <ci>a</ci>
                </apply>
              </condition>
              <apply>
                <sin/>
                <apply>
                  <plus/>
                  <ci>x</ci>
                  <ci>y</ci>
                </apply>
              </apply>
            </apply>
          </math>
        </p>
        <p>
    limit as x goes to a of sin(x + y)2b using &lt;reln&gt;
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <limit/>
              <bvar>
                <ci>x</ci>
              </bvar>
              <condition>
                <reln>
                  <tendsto type='above'/>
                  <ci>x</ci>
                  <ci>a</ci>
                </reln>
              </condition>
              <apply>
                <times/>
                <apply>
                  <sin/>
                  <apply>
                    <times/>
                    <ci>x</ci>
                    <ci>y</ci>
                  </apply>
                </apply>
                <apply>
                  <times/>
                  <cn>2</cn>
                  <ci>b</ci>
                </apply>
              </apply>
            </apply>
          </math>
        </p>
        <p>
    limit as x goes to a of sin(x + y)2b using &lt;apply&gt;
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <limit/>
              <bvar>
                <ci>x</ci>
              </bvar>
              <condition>
                <apply>
                  <tendsto type='above'/>
                  <ci>x</ci>
                  <ci>a</ci>
                </apply>
              </condition>
              <apply>
                <times/>
                <apply>
                  <sin/>
                  <apply>
                    <times/>
                    <ci>x</ci>
                    <ci>y</ci>
                  </apply>
                </apply>
                <apply>
                  <times/>
                  <cn>2</cn>
                  <ci>b</ci>
                </apply>
              </apply>
            </apply>
          </math>
        </p>
        <p>
    quotient
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <quotient/>
              <ci>a</ci>
              <ci>b</ci>
            </apply>
          </math>
        </p>
        <p>
    moment
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <moment/>
              <degree>
                <cn>3</cn>
              </degree>
              <ci>X</ci>
            </apply>
          </math>
        </p>
        <p>
    selector
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <selector/>
              <matrix>
                <matrixrow>
                  <cn>1</cn>
                  <cn>2</cn>
                </matrixrow>
                <matrixrow>
                  <cn>3</cn>
                  <cn>4</cn>
                </matrixrow>
              </matrix>
              <cn>1</cn>
            </apply>
          </math>
        </p>
        <p>
    factorial
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <factorial/>
              <ci>n</ci>
            </apply>
          </math>
        </p>
        <p>
    (a + b)!
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <factorial/>
              <apply>
                <plus/>
                <apply>
                  <plus/>
                  <ci>n</ci>
                  <ci>m</ci>
                </apply>
                <ci>x</ci>
              </apply>
            </apply>
          </math>
        </p>
        <p>
    inverse function
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <inverse/>
              <ci>f</ci>
            </apply>
          </math>
        </p>
        <p>
    inverse matrix
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <apply>
                <inverse/>
                <ci type='matrix'>a</ci>
              </apply>
              <ci>A</ci>
            </apply>
          </math>
        </p>
        <p>
    conjugate
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <mrow>
              <apply>
                <conjugate/>
                <apply>
                  <plus/>
                  <ci>x</ci>
                  <apply>
                    <times/>
                    <cn>&ImaginaryI;</cn>
                    <ci>y</ci>
                  </apply>
                </apply>
              </apply>
            </mrow>
          </math>
        </p>
        <p>
    a + b + c
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <plus/>
              <ci>a</ci>
              <ci>b</ci>
              <ci>c</ci>
            </apply>
          </math>
        </p>
        <p>
    integral (a + x)dx
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <int/>
              <bvar>
                <ci>x</ci>
              </bvar>
              <lowlimit>
                <cn>0</cn>
              </lowlimit>
              <uplimit>
                <ci>a</ci>
              </uplimit>
              <apply>
                <plus/>
                <ci>a</ci>
                <ci>x</ci>
              </apply>
            </apply>
          </math>
        </p>
        <p>
    -1 + 7
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <plus/>
              <apply>
                <minus/>
                <cn>1</cn>
              </apply>
              <cn>7</cn>
            </apply>
          </math>
        </p>
        <p>
    7 + (-1)
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <plus/>
              <cn>7</cn>
              <apply>
                <minus/>
                <cn>1</cn>
              </apply>
            </apply>
          </math>
        </p>
        <p>
    max
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <max/>
              <bvar>
                <ci>x</ci>
              </bvar>
              <condition>
                <apply>
                  <and/>
                  <reln>
                    <gt/>
                    <ci>x</ci>
                    <cn>0</cn>
                  </reln>
                  <reln>
                    <lt/>
                    <ci>x</ci>
                    <cn>1</cn>
                  </reln>
                </apply>
              </condition>
              <apply>
                <minus/>
                <ci>x</ci>
                <apply>
                  <sin/>
                  <ci>x</ci>
                </apply>
              </apply>
            </apply>
          </math>
        </p>
        <p>
    lambda sin(x + 1)
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <lambda>
              <bvar>
                <ci>x</ci>
              </bvar>
              <apply>
                <sin/>
                <apply>
                  <plus/>
                  <ci>x</ci>
                  <cn>1</cn>
                </apply>
              </apply>
            </lambda>
          </math>
        </p>
        <p>
    lambda integral f(x)dx
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <lambda>
              <bvar>
                <ci>b</ci>
              </bvar>
              <apply>
                <int/>
                <bvar>
                  <ci>x</ci>
                </bvar>
                <lowlimit>
                  <ci>a</ci>
                </lowlimit>
                <uplimit>
                  <ci>b</ci>
                </uplimit>
                <apply>
                  <fn>
                    <ci>f</ci>
                  </fn>
                  <ci>x</ci>
                </apply>
              </apply>
            </lambda>
          </math>
        </p>
        <p>
    compose f and g
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <compose/>
              <fn>
                <ci>f</ci>
              </fn>
              <fn>
                <ci>g</ci>
              </fn>
            </apply>
          </math>
        </p>
        <p>
    compose f and g (x)
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <apply>
                <compose/>
                <fn>
                  <ci>f</ci>
                </fn>
                <fn>
                  <ci>g</ci>
                </fn>
              </apply>
              <ci>x</ci>
            </apply>
          </math>
        </p>
        <p>
    f(g(x))
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <fn>
                <ci>f</ci>
              </fn>
              <apply>
                <fn>
                  <ci>g</ci>
                </fn>
                <ci>x</ci>
              </apply>
            </apply>
          </math>
        </p>
        <p>
    composition of f and inverse of f eq identity using &lt;reln&gt;
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <reln>
              <eq/>
              <apply>
                <compose/>
                <fn>
                  <ci>f</ci>
                </fn>
                <apply>
                  <inverse/>
                  <fn>
                    <ci>f</ci>
                  </fn>
                </apply>
              </apply>
              <ident/>
            </reln>
          </math>
        </p>
        <p>
    composition of f and inverse of f eq identity using &lt;apply&gt;
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <eq/>
              <apply>
                <compose/>
                <fn>
                  <ci>f</ci>
                </fn>
                <apply>
                  <inverse/>
                  <fn>
                    <ci>f</ci>
                  </fn>
                </apply>
              </apply>
              <ident/>
            </apply>
          </math>
        </p>
        <p>
    e^x
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <exp/>
              <ci>x</ci>
            </apply>
          </math>
        </p>
        <p>
    min(x, x not in B, x^2) using &lt;reln&gt;
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <min/>
              <bvar>
                <ci>x</ci>
              </bvar>
              <condition>
                <reln>
                  <notin/>
                  <ci>x</ci>
                  <ci type='set'>B</ci>
                </reln>
              </condition>
              <apply>
                <power/>
                <ci>x</ci>
                <cn>2</cn>
              </apply>
            </apply>
          </math>
        </p>
        <p>
    min(x, x not in B, x^2) using &lt;apply&gt;
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <min/>
              <bvar>
                <ci>x</ci>
              </bvar>
              <condition>
                <apply>
                  <notin/>
                  <ci>x</ci>
                  <ci type='set'>B</ci>
                </apply>
              </condition>
              <apply>
                <power/>
                <ci>x</ci>
                <cn>2</cn>
              </apply>
            </apply>
          </math>
        </p>
        <p>
    a mod (b)
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <rem/>
              <ci>a</ci>
              <ci>b</ci>
            </apply>
          </math>
        </p>
        <p>
    ab
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <times/>
              <ci>a</ci>
              <ci>b</ci>
            </apply>
          </math>
        </p>
        <p>
    gcd(a b, c)
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <gcd/>
              <ci>a</ci>
              <ci>b</ci>
              <ci>c</ci>
            </apply>
          </math>
        </p>
        <p>
    integral
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <int/>
              <bvar>
                <ci>x</ci>
              </bvar>
              <lowlimit>
                <cn>0</cn>
              </lowlimit>
              <uplimit>
                <ci>a</ci>
              </uplimit>
              <apply>
                <fn>
                  <ci>f</ci>
                </fn>
                <ci>x</ci>
              </apply>
            </apply>
          </math>
        </p>
        <p>
    abs(x)
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <abs/>
              <ci>x</ci>
            </apply>
          </math>
        </p>
        <p> tall abs(x)
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <abs/>
              <apply>
                <divide/>
                <ci>H</ci>
                <ci>K</ci>
              </apply>
            </apply>
          </math>
        </p>
        <p>
    abs(x + y + z)
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <abs/>
              <apply>
                <plus/>
                <ci>x</ci>
                <ci>y</ci>
                <ci>z</ci>
              </apply>
            </apply>
          </math>
        </p>
        <p>
    x &gt; 0 and z &lt; 1 as &lt;reln&gt;
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <and/>
              <reln>
                <gt/>
                <ci>x</ci>
                <cn>0</cn>
              </reln>
              <reln>
                <lt/>
                <ci>x</ci>
                <cn>1</cn>
              </reln>
            </apply>
          </math>
        </p>
        <p>
    x &gt; 0 and z &lt; 1 as &lt;apply&gt;
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <and/>
              <apply>
                <gt/>
                <ci>x</ci>
                <cn>0</cn>
              </apply>
              <apply>
                <lt/>
                <ci>x</ci>
                <cn>1</cn>
              </apply>
            </apply>
          </math>
        </p>
        <p>
    a and b
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <and/>
              <ci>a</ci>
              <ci>b</ci>
            </apply>
          </math>
        </p>
        <p>
    a or b
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <or/>
              <ci>a</ci>
              <ci>b</ci>
            </apply>
          </math>
        </p>
        <p>
    a xor b
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <xor/>
              <ci>a</ci>
              <ci>b</ci>
            </apply>
          </math>
        </p>
        <p>
    a eq b with &lt;reln&gt; tag
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <reln>
              <eq/>
              <ci>a</ci>
              <ci>b</ci>
            </reln>
          </math>
        </p>
        <p>
    a eq b with &lt;apply&gt; tag
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <eq/>
              <ci>a</ci>
              <ci>b</ci>
            </apply>
          </math>
        </p>
        <p>
    a neq b with &lt;reln&gt; tag
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <reln>
              <neq/>
              <ci>a</ci>
              <ci>b</ci>
            </reln>
          </math>
        </p>
        <p>
    a neq b with &lt;apply&gt; tag
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <neq/>
              <ci>a</ci>
              <ci>b</ci>
            </apply>
          </math>
        </p>
        <p>
    a &gt; b with &lt;reln&gt; tag
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <reln>
              <gt/>
              <ci>a</ci>
              <ci>b</ci>
            </reln>
          </math>
        </p>
        <p>
    a &gt; b with &lt;apply&gt; tag
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <gt/>
              <ci>a</ci>
              <ci>b</ci>
            </apply>
          </math>
        </p>
        <p>
    a &lt; b with &lt;reln&gt; tag
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <reln>
              <lt/>
              <ci>a</ci>
              <ci>b</ci>
            </reln>
          </math>
        </p>
        <p>
    a &lt; b with &lt;apply&gt; tag
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <lt/>
              <ci>a</ci>
              <ci>b</ci>
            </apply>
          </math>
        </p>
        <p>
    a &lt;= b with &lt;reln&gt; tag
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <reln>
              <geq/>
              <ci>a</ci>
              <ci>b</ci>
            </reln>
          </math>
        </p>
        <p>
    a &gt;= b with &lt;apply&gt; tag
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <geq/>
              <ci>a</ci>
              <ci>b</ci>
            </apply>
          </math>
        </p>
        <p>
    a &lt;= b with &lt;reln&gt; tag
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <reln>
              <leq/>
              <ci>a</ci>
              <ci>b</ci>
            </reln>
          </math>
        </p>
        <p>
    a &lt;= b with &lt;apply&gt; tag
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <leq/>
              <ci>a</ci>
              <ci>b</ci>
            </apply>
          </math>
        </p>
        <p>
    set: {b, a, c}
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <set>
              <ci>b</ci>
              <ci>a</ci>
              <ci>c</ci>
            </set>
          </math>
        </p>
        <p>
    set with condition
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <set>
              <bvar>
                <ci>x</ci>
              </bvar>
              <condition>
                <reln>
                  <lt/>
                  <ci>x</ci>
                  <cn>5</cn>
                </reln>
              </condition>
            </set>
          </math>
        </p>
        <p>
    list: {b, a, c}
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <list>
              <ci>b</ci>
              <ci>a</ci>
              <ci>c</ci>
            </list>
          </math>
        </p>
        <p>
    list: {x|x &lt; 5}
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <list order='numeric'>
              <bvar>
                <ci>x</ci>
              </bvar>
              <condition>
                <reln>
                  <lt/>
                  <ci>x</ci>
                  <cn>5</cn>
                </reln>
              </condition>
            </list>
          </math>
        </p>
        <p>
    A union B
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <union/>
              <ci>A</ci>
              <ci>B</ci>
            </apply>
          </math>
        </p>
        <p>
    A intersect B
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <intersect/>
              <ci type='set'>A</ci>
              <ci type='set'>B</ci>
            </apply>
          </math>
        </p>
        <p>
    A intersect (B union C)
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <intersect/>
              <ci type='set'>A</ci>
              <apply>
                <union/>
                <ci type='set'>B</ci>
                <ci type='set'>C</ci>
              </apply>
            </apply>
          </math>
        </p>
        <p>integral
    x in R as &lt;reln&gt;
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <reln>
              <in/>
              <ci>x</ci>
              <ci type='set'>R</ci>
            </reln>
          </math>
        </p>
        <p>
    x in R as &lt;apply&gt;
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <in/>
              <ci>x</ci>
              <ci type='set'>R</ci>
            </apply>
          </math>
        </p>
        <p>
    a in A
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <reln>
              <in/>
              <ci>a</ci>
              <ci type='set'>A</ci>
            </reln>
          </math>
        </p>
        <p>
    a not in A as &lt;reln&gt;
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <reln>
              <notin/>
              <ci>a</ci>
              <ci>A</ci>
            </reln>
          </math>
        </p>
        <p>
    a not in A as &lt;apply&gt;
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <notin/>
              <ci>a</ci>
              <ci>A</ci>
            </apply>
          </math>
        </p>
        <p>
    not a
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <not/>
              <ci>a</ci>
            </apply>
          </math>
        </p>
        <p>
    not (a and b)
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <not/>
              <apply>
                <and/>
                <ci>a</ci>
                <ci>b</ci>
              </apply>
            </apply>
          </math>
        </p>
        <p>
    A -&gt; B (reln)
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <reln>
              <implies/>
              <ci>A</ci>
              <ci>B</ci>
            </reln>
          </math>
        </p>
        <p>
    A -&gt; B (apply)
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <implies/>
              <ci>A</ci>
              <ci>B</ci>
            </apply>
          </math>
        </p>
        <p>
    forall
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <forall/>
              <bvar>
                <ci>x</ci>
              </bvar>
              <reln>
                <eq/>
                <apply>
                  <minus/>
                  <ci>x</ci>
                  <ci>x</ci>
                </apply>
                <cn>0</cn>
              </reln>
            </apply>
          </math>
        </p>
        <p>
    forall/and/lt/power
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <forall/>
              <bvar>
                <ci>p</ci>
              </bvar>
              <bvar>
                <ci>q</ci>
              </bvar>
              <condition>
                <apply>
                  <and/>
                  <reln>
                    <in/>
                    <ci>p</ci>
                    <ci type='set'>Q</ci>
                  </reln>
                  <reln>
                    <in/>
                    <ci>q</ci>
                    <ci type='set'>Q</ci>
                  </reln>
                  <reln>
                    <lt/>
                    <ci>p</ci>
                    <ci>q</ci>
                  </reln>
                </apply>
              </condition>
              <reln>
                <lt/>
                <ci>p</ci>
                <apply>
                  <power/>
                  <ci>q</ci>
                  <cn>2</cn>
                </apply>
              </reln>
            </apply>
          </math>
        </p>
        <p>
    forall/exists/and/plus
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <forall/>
              <bvar>
                <ci>n</ci>
              </bvar>
              <condition>
                <apply>
                  <and/>
                  <reln>
                    <in/>
                    <ci>n</ci>
                    <ci type='set'>Z</ci>
                  </reln>
                  <reln>
                    <gt/>
                    <ci>n</ci>
                    <cn>0</cn>
                  </reln>
                </apply>
              </condition>
              <apply>
                <exists/>
                <bvar>
                  <ci>x</ci>
                </bvar>
                <bvar>
                  <ci>y</ci>
                </bvar>
                <bvar>
                  <ci>z</ci>
                </bvar>
                <condition>
                  <apply>
                    <and/>
                    <reln>
                      <in/>
                      <ci>x</ci>
                      <ci type='set'>Z</ci>
                    </reln>
                    <reln>
                      <in/>
                      <ci>y</ci>
                      <ci type='set'>Z</ci>
                    </reln>
                    <reln>
                      <in/>
                      <ci>z</ci>
                      <ci type='set'>Z</ci>
                    </reln>
                  </apply>
                </condition>
                <reln>
                  <eq/>
                  <apply>
                    <plus/>
                    <apply>
                      <power/>
                      <ci>x</ci>
                      <ci>n</ci>
                    </apply>
                    <apply>
                      <power/>
                      <ci>y</ci>
                      <ci>n</ci>
                    </apply>
                  </apply>
                  <apply>
                    <power/>
                    <ci>z</ci>
                    <ci>n</ci>
                  </apply>
                </reln>
              </apply>
            </apply>
          </math>
        </p>
        <p>
    exists
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <exists/>
              <bvar>
                <ci>x</ci>
              </bvar>
              <reln>
                <eq/>
                <apply>
                  <fn>
                    <ci>f</ci>
                  </fn>
                  <ci>x</ci>
                </apply>
                <cn>0</cn>
              </reln>
            </apply>
          </math>
        </p>
        <p>
    forall/exists/and/plus
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <forall/>
              <bvar>
                <ci>n</ci>
              </bvar>
              <condition>
                <apply>
                  <and/>
                  <reln>
                    <in/>
                    <ci>n</ci>
                    <ci type='set'>Z</ci>
                  </reln>
                  <reln>
                    <gt/>
                    <ci>n</ci>
                    <cn>0</cn>
                  </reln>
                </apply>
              </condition>
              <apply>
                <exists/>
                <bvar>
                  <ci>x</ci>
                </bvar>
                <bvar>
                  <ci>y</ci>
                </bvar>
                <bvar>
                  <ci>z</ci>
                </bvar>
                <condition>
                  <apply>
                    <and/>
                    <reln>
                      <in/>
                      <ci>x</ci>
                      <ci type='set'>Z</ci>
                    </reln>
                    <reln>
                      <in/>
                      <ci>y</ci>
                      <ci type='set'>Z</ci>
                    </reln>
                    <reln>
                      <in/>
                      <ci>z</ci>
                      <ci type='set'>Z</ci>
                    </reln>
                  </apply>
                </condition>
                <reln>
                  <eq/>
                  <apply>
                    <plus/>
                    <apply>
                      <power/>
                      <ci>x</ci>
                      <ci>n</ci>
                    </apply>
                    <apply>
                      <power/>
                      <ci>y</ci>
                      <ci>n</ci>
                    </apply>
                  </apply>
                  <apply>
                    <power/>
                    <ci>z</ci>
                    <ci>n</ci>
                  </apply>
                </reln>
              </apply>
            </apply>
          </math>
        </p>
        <p>
    ln a
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <ln/>
              <ci>a</ci>
            </apply>
          </math>
        </p>
        <p>
    log base 3 of x
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <log/>
              <logbase>
                <cn>3</cn>
              </logbase>
              <ci>x</ci>
            </apply>
          </math>
        </p>
        <p>
    integer
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <int/>
              <bvar>
                <ci>x</ci>
              </bvar>
              <condition>
                <reln>
                  <in/>
                  <ci>x</ci>
                  <ci type='set'>D</ci>
                </reln>
              </condition>
              <apply>
                <fn>
                  <ci>f</ci>
                </fn>
                <ci>x</ci>
              </apply>
            </apply>
          </math>
        </p>
        <p>
    diff
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <diff/>
              <bvar>
                <ci>x</ci>
              </bvar>
              <apply>
                <fn>
                  <ci>f</ci>
                </fn>
                <ci>x</ci>
              </apply>
            </apply>
          </math>
        </p>
        <p>
    partialdiff
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <partialdiff/>
              <bvar>
                <ci>x</ci>
                <degree>
                  <cn>2</cn>
                </degree>
              </bvar>
              <bvar>
                <ci>y</ci>
              </bvar>
              <apply>
                <fn>
                  <ci>f</ci>
                </fn>
                <ci>x</ci>
                <ci>y</ci>
              </apply>
            </apply>
          </math>
        </p>
        <p>
    integral
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <int/>
              <bvar>
                <ci>x</ci>
              </bvar>
              <lowlimit>
                <ci>a</ci>
              </lowlimit>
              <uplimit>
                <ci>b</ci>
              </uplimit>
              <apply>
                <fn>
                  <ci>f</ci>
                </fn>
                <ci>x</ci>
              </apply>
            </apply>
          </math>
        </p>
        <p>
    partialdiff
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <partialdiff/>
              <bvar>
                <ci>x</ci>
                <degree>
                  <ci>n</ci>
                </degree>
              </bvar>
              <bvar>
                <ci>y</ci>
                <degree>
                  <ci>m</ci>
                </degree>
              </bvar>
              <apply>
                <sin/>
                <apply>
                  <times/>
                  <ci>x</ci>
                  <ci>y</ci>
                </apply>
              </apply>
            </apply>
          </math>
        </p>
        <p>
    divide
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <divide/>
              <ci>a</ci>
              <ci>b</ci>
            </apply>
          </math>
        </p>
        <p>
    divide/plus/minus
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <divide/>
              <apply>
                <plus/>
                <ci>a</ci>
                <ci>b</ci>
              </apply>
              <apply>
                <minus/>
                <ci>a</ci>
                <ci>b</ci>
              </apply>
            </apply>
          </math>
        </p>
        <p>
    divide/plus/divide
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <divide/>
              <apply>
                <plus/>
                <ci>a</ci>
                <ci>b</ci>
              </apply>
              <apply>
                <divide/>
                <ci>a</ci>
                <ci>b</ci>
              </apply>
            </apply>
          </math>
        </p>
        <p>
    A is subset of B as &lt;reln&gt;
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <reln>
              <subset/>
              <ci>A</ci>
              <ci>B</ci>
            </reln>
          </math>
        </p>
        <p>
    A is subset of B as &lt;apply&gt;
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <subset/>
              <ci>A</ci>
              <ci>B</ci>
            </apply>
          </math>
        </p>
        <p>
    A is proper subset of B as &lt;reln&gt;
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <reln>
              <prsubset/>
              <ci>A</ci>
              <ci>B</ci>
            </reln>
          </math>
        </p>
        <p>
    A is proper subset of B as &lt;apply&gt;
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <prsubset/>
              <ci>A</ci>
              <ci>B</ci>
            </apply>
          </math>
        </p>
        <p>
    A is not subset of B as &lt;reln&gt;
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <reln>
              <notsubset/>
              <ci>A</ci>
              <ci>B</ci>
            </reln>
          </math>
        </p>
        <p>
    A is not subset of B as &lt;apply&gt;
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <notsubset/>
              <ci>A</ci>
              <ci>B</ci>
            </apply>
          </math>
        </p>
        <p>
    A is not proper subset of B as &lt;reln&gt;
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <reln>
              <notprsubset/>
              <ci>A</ci>
              <ci>B</ci>
            </reln>
          </math>
        </p>
        <p>
    A is not proper subset of B as &lt;apply&gt;
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <notprsubset/>
              <ci>A</ci>
              <ci>B</ci>
            </apply>
          </math>
        </p>
        <p>
    Set difference
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <setdiff/>
              <ci>A</ci>
              <ci>B</ci>
            </apply>
          </math>
        </p>
        <p>
    Log base 3 of x + y
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <log/>
              <logbase>
                <cn>3</cn>
              </logbase>
              <apply>
                <plus/>
                <ci>x</ci>
                <ci>y</ci>
              </apply>
            </apply>
          </math>
        </p>
        <p>
    Sum as x goes from a to b of f(x)
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <sum/>
              <bvar>
                <ci>x</ci>
              </bvar>
              <lowlimit>
                <ci>a</ci>
              </lowlimit>
              <uplimit>
                <ci>b</ci>
              </uplimit>
              <apply>
                <fn>
                  <ci>f</ci>
                </fn>
                <ci>x</ci>
              </apply>
            </apply>
          </math>
        </p>
        <p>
    sum
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <sum/>
              <bvar>
                <ci>x</ci>
              </bvar>
              <condition>
                <reln>
                  <in/>
                  <ci>x</ci>
                  <ci type='set'>B</ci>
                </reln>
              </condition>
              <apply>
                <fn>
                  <ci>f</ci>
                </fn>
                <ci>x</ci>
              </apply>
            </apply>
          </math>
        </p>
        <p>
    product
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <product/>
              <bvar>
                <ci>x</ci>
              </bvar>
              <lowlimit>
                <ci>a</ci>
              </lowlimit>
              <uplimit>
                <ci>b</ci>
              </uplimit>
              <apply>
                <fn>
                  <ci>f</ci>
                </fn>
                <ci>x</ci>
              </apply>
            </apply>
          </math>
        </p>
        <p>
    product
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <product/>
              <bvar>
                <ci>x</ci>
              </bvar>
              <condition>
                <reln>
                  <in/>
                  <ci>x</ci>
                  <ci type='set'>B</ci>
                </reln>
              </condition>
              <apply>
                <fn>
                  <ci>f</ci>
                </fn>
                <ci>x</ci>
              </apply>
            </apply>
          </math>
        </p>
        <p>
    tendsto with &lt;reln&gt;
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <reln>
              <tendsto type='above'/>
              <apply>
                <power/>
                <ci>x</ci>
                <cn>2</cn>
              </apply>
              <apply>
                <power/>
                <ci>a</ci>
                <cn>2</cn>
              </apply>
            </reln>
          </math>
        </p>
        <p>
    tendsto with &lt;apply&gt;
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <tendsto type='above'/>
              <apply>
                <power/>
                <ci>x</ci>
                <cn>2</cn>
              </apply>
              <apply>
                <power/>
                <ci>a</ci>
                <cn>2</cn>
              </apply>
            </apply>
          </math>
        </p>
        <p>
    tendsto with &lt;reln&gt;
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <reln>
              <tendsto/>
              <vector>
                <ci>x</ci>
                <ci>y</ci>
              </vector>
              <vector>
                <apply>
                  <fn>
                    <ci>f</ci>
                  </fn>
                  <ci>x</ci>
                  <ci>y</ci>
                </apply>
                <apply>
                  <fn>
                    <ci>g</ci>
                  </fn>
                  <ci>x</ci>
                  <ci>y</ci>
                </apply>
              </vector>
            </reln>
          </math>
        </p>
        <p>
    tendsto with &lt;apply&gt;
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <tendsto/>
              <vector>
                <ci>x</ci>
                <ci>y</ci>
              </vector>
              <vector>
                <apply>
                  <fn>
                    <ci>f</ci>
                  </fn>
                  <ci>x</ci>
                  <ci>y</ci>
                </apply>
                <apply>
                  <fn>
                    <ci>g</ci>
                  </fn>
                  <ci>x</ci>
                  <ci>y</ci>
                </apply>
              </vector>
            </apply>
          </math>
        </p>
        <p>
    mean(X)
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <mean/>
              <ci>X</ci>
            </apply>
          </math>
        </p>
        <p>
    root(a + b)
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <root/>
              <degree>
                <ci>n</ci>
              </degree>
              <apply>
                <plus/>
                <ci>a</ci>
                <ci>b</ci>
              </apply>
            </apply>
          </math>
        </p>
        <p>
    standard deviation
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <sdev/>
              <ci>X</ci>
            </apply>
          </math>
        </p>
        <p>
    variance(X)
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <variance/>
              <ci>X</ci>
            </apply>
          </math>
        </p>
        <p>
    median(X)
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <median/>
              <ci>X</ci>
            </apply>
          </math>
        </p>
        <p>
    mode(X)
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <mode/>
              <ci>X</ci>
            </apply>
          </math>
        </p>
        <p>
    degree
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <moment/>
              <degree>
                <cn>3</cn>
              </degree>
              <ci>X</ci>
            </apply>
          </math>
        </p>
        <p>
    vector
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <vector>
              <cn>1</cn>
              <cn>2</cn>
              <cn>3</cn>
              <ci>x</ci>
            </vector>
          </math>
        </p>
        <p>
    matrix
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <matrix>
              <matrixrow>
                <cn>0</cn>
                <cn>1</cn>
                <cn>0</cn>
                <cn>0</cn>
              </matrixrow>
              <matrixrow>
                <cn>0</cn>
                <cn>0</cn>
                <cn>1</cn>
                <cn>0</cn>
              </matrixrow>
              <matrixrow>
                <cn>1</cn>
                <cn>0</cn>
                <cn>0</cn>
                <cn>0</cn>
              </matrixrow>
            </matrix>
          </math>
        </p>
        <p>
    determinant
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <determinant/>
              <ci type='matrix'>A</ci>
            </apply>
          </math>
        </p>
        <p>
    transpose
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <transpose/>
              <ci type='matrix'>A</ci>
            </apply>
          </math>
        </p>
        <p>
    semantics
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <semantics>
              <apply>
                <plus/>
                <apply>
                  <sin/>
                  <ci>x</ci>
                </apply>
                <cn>5</cn>
              </apply>
              <annotation encoding='TeX'>\sin x + 5
              </annotation>
            </semantics>
          </math>
        </p>
        <p>
    limit
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <limit/>
              <bvar>
                <ci>x</ci>
              </bvar>
              <lowlimit>
                <cn>0</cn>
              </lowlimit>
              <apply>
                <sin/>
                <ci>x</ci>
              </apply>
            </apply>
          </math>
        </p>
        <p>
    symbol check
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <plus/>
              <cn type='real'>4.56</cn>
              <cn type='integer'>4.56</cn>
              <cn type='rational'>4
                <sep/>5
              </cn>
              <cn type='complex-cartesian'>4
                <sep/>5
              </cn>
              <cn type='complex-polar'>4.56
                <sep/>4.56
              </cn>
              <cn type='constant'>&pi;</cn>
              <cn>&ExponentialE;</cn>
              <cn>&ee;</cn>
              <cn>&ImaginaryI;</cn>
              <cn>&ii;</cn>
              <cn>&gamma;</cn>
              <cn>&infin;</cn>
              <cn>&infin;</cn>
            </apply>
          </math>
        </p>
        <p>
    multiset
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <set type='multiset'>
              <cn type='real'>4.56</cn>
              <cn type='integer'>4.56</cn>
              <cn type='rational'>4
                <sep/>5
              </cn>
              <cn type='complex-cartesian'>4
                <sep/>5
              </cn>
              <cn type='complex-polar'>4.56
                <sep/>4.56
              </cn>
              <cn type='constant'>&pi;</cn>
              <cn>&ExponentialE;</cn>
              <cn>&ee;</cn>
              <cn>&ImaginaryI;</cn>
              <cn>&ii;</cn>
              <cn>&gamma;</cn>
              <cn>&infin;</cn>
              <cn>&infin;</cn>
            </set>
          </math>
        </p>
        <p>
    tendsto type = "above" with &lt;reln&gt;
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <reln>
              <tendsto type='above'/>
              <apply>
                <power/>
                <ci>x</ci>
                <cn>2</cn>
              </apply>
              <apply>
                <power/>
                <ci>a</ci>
                <cn>2</cn>
              </apply>
            </reln>
          </math>
        </p>
        <p>
    tendsto type = "above" with &lt;apply&gt;
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <tendsto type='above'/>
              <apply>
                <power/>
                <ci>x</ci>
                <cn>2</cn>
              </apply>
              <apply>
                <power/>
                <ci>a</ci>
                <cn>2</cn>
              </apply>
            </apply>
          </math>
        </p>
        <p>
    tendsto type = "below" with &lt;reln&gt;
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <reln>
              <tendsto type='below'/>
              <apply>
                <power/>
                <ci>x</ci>
                <cn>2</cn>
              </apply>
              <apply>
                <power/>
                <ci>a</ci>
                <cn>2</cn>
              </apply>
            </reln>
          </math>
        </p>
        <p>
    tendsto type = "below" with &lt;apply&gt;
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <tendsto type='below'/>
              <apply>
                <power/>
                <ci>x</ci>
                <cn>2</cn>
              </apply>
              <apply>
                <power/>
                <ci>a</ci>
                <cn>2</cn>
              </apply>
            </apply>
          </math>
        </p>
        <p>
    tendsto type = "two-sided" with &lt;reln&gt;
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <reln>
              <tendsto type='two-sided'/>
              <apply>
                <power/>
                <ci>x</ci>
                <cn>2</cn>
              </apply>
              <apply>
                <power/>
                <ci>a</ci>
                <cn>2</cn>
              </apply>
            </reln>
          </math>
        </p>
        <p>
    tendsto type = "two-sided" with &lt;apply&gt;
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <tendsto type='two-sided'/>
              <apply>
                <power/>
                <ci>x</ci>
                <cn>2</cn>
              </apply>
              <apply>
                <power/>
                <ci>a</ci>
                <cn>2</cn>
              </apply>
            </apply>
          </math>
        </p>
        <p>
    type check
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <plus/>
              <ci type='real'>x</ci>
              <ci type='integer'>x</ci>
              <ci type='rational'>x</ci>
              <ci type='complex-cartesian'>y</ci>
              <ci type='complex-polar'>&theta;</ci>
              <ci type='vector'>v</ci>
              <ci type='constant'>&pi;</ci>
              <ci>&ExponentialE;</ci>
              <ci>&ee;</ci>
              <ci>&ImaginaryI;</ci>
              <ci>&ii;</ci>
              <ci>&gamma;</ci>
              <ci>&infin;</ci>
              <ci>&infin;</ci>
            </apply>
          </math>
        </p>
        <p>
    sin + cos
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <plus/>
              <apply>
                <sin/>
                <ci>x</ci>
              </apply>
              <apply>
                <cos/>
                <ci>x</ci>
              </apply>
            </apply>
          </math>
        </p>
        <p>
    f(x)
          <br />
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <fn>
                <ci>f</ci>
              </fn>
              <ci>x</ci>
            </apply>
          </math>
        </p>