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 File: /TortureTests/Complexity/complex4.xml Author: Design Science, Inc. (D. Doyle, R. Miner) Description: Test of most content elements in a single page. Sample Rendering: N/A

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a + b - c:

$a+b-c$

x + yz + z:

$x+yz+z$

x * (y + z) * z:

$x(y+z)z$

sin(a + b):

$\sin (a+b)$

sin(x(y + z)z):

$\sin (x(y+z)z)$

sin(xy)2b:

$\sin (xy)2b$

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

$(x+y)^{(n-3)}$

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

$\lim_{(x, a)}\sin x$

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

$\lim_{x\to a}\sin x$

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

$\lim_{(x, a)}\sin (x+y)$

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

$\lim_{x\to a}\sin (x+y)$

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

$\lim_{(x, a)}\sin (xy)2b$

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

$\lim_{x\to a}\sin (xy)2b$

quotient:

$\left\lfloor\frac{a}{b}\right\rfloor$

moment:

$\langle X^{3}\rangle$

selector:

$\begin{pmatrix}1 & 2\\ 3 & 4\end{pmatrix}_{1}$

factorial:

$n!$

(a + b)!:

$(n+m+x)!$

inverse function:

$f^{(-1)}$

inverse matrix:

$a^{(-1)}(A)$

conjugate:

$\overline{x+iy}$

a + b + c:

$a+b+c$

integral (a + x)dx:

$\int_{0}^{a} a+x\,d x$

-1 + 7:

$-1+7$

7 + (-1):

$7+-1$

max:

$\max\{x-\sin x, (x, 0)\land (x, 1)\}$

lambda sin(x + 1):

$\mathrm{lambda}\: x.\: \sin (x+1)$

lambda integral f(x)dx:

$\mathrm{lambda}\: b.\: \int_{a}^{b} f(x)\,d x$

compose f and g:

$f\circ g$

compose f and g (x):

$(f\circ g)(x)$

f(g(x)):

$f(g(x))$

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

$(f\circ f^{(-1)}, \mathrm{id})$

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

$f\circ f^{(-1)}=\mathrm{id}$

e^x:

$e^{x}$

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

$\min\{x^{2}, (x, B)\}$

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

$\min\{x^{2}, x\notin B\}$

a mod (b):

$a\mod b$

ab:

$ab$

gcd(a b, c):

$\gcd (a, b, c)$

integral:

$\int_{0}^{a} f(x)\,d x$

abs(x):

$\left|x\right|$

tall abs(x):

$\left|\frac{H}{K}\right|$

abs(x + y + z):

$\left|x+y+z\right|$

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

$(x, 0)\land (x, 1)$

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

$(x> 0)\land (x< 1)$

a and b:

$a\land b$

a or b:

$a\lor b$

a xor b:

$a\mathop{\mathrm{xor}}b$

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:

$a\neq b$

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:

$a\ge b$

a <= b with <reln> tag:

$(a, b)$

a <= b with <apply> tag:

$a\le b$

set: {b, a, c}:

$\{b, a, c\}$

set with condition:

$\{x\colon (x, 5)\}$

list: {b, a, c}:

$\left[b, a, c\right]$

list: {x|x < 5}:

$\left[x\colon (x, 5)\right]$

A union B:

$A\cup B$

A intersect B:

$A\cap B$

A intersect (B union C):

$A\cap (B\cup C)$

integral x in R as <reln>:

$(x, R)$

x in R as <apply>:

$x\in R$

a in A:

$(a, A)$

a not in A as <reln>:

$(a, A)$

a not in A as <apply>:

$a\notin A$

not a:

$\neg a$

not (a and b):

$\neg (a\land b)$

A -> B (reln):

$(A, B)$

A -> B (apply):

$A\implies B$

forall:

$\forall x\colon (x-x, 0)$

forall/and/lt/power:

$\forall p, q, (p, Q)\land (q, Q)\land (p, q)\colon (p, q^{2})$

forall/exists/and/plus:

$\forall n, (n, Z)\land (n, 0)\colon \exists x, y, z, (x, Z)\land (y, Z)\land (z, Z)\colon (x^{n}+y^{n}, z^{n})$

exists:

$\exists x\colon (f(x), 0)$

forall/exists/and/plus:

$\forall n, (n, Z)\land (n, 0)\colon \exists x, y, z, (x, Z)\land (y, Z)\land (z, Z)\colon (x^{n}+y^{n}, z^{n})$

ln a:

$\ln a$

log base 3 of x:

$\log_{3}x$

integer:

$\int_{(x, D)} f(x)\,d x$

diff:

$\frac{d f(x)}{d x}}$

partialdiff:

$\frac{\partial^{3}f(x, y)}{\partial x^{2}\partial y}$

integral:

$\int_{a}^{b} f(x)\,d x$

partialdiff:

$\frac{\partial^{n+m}\sin (xy)}{\partial x^{n}\partial y^{m}}$

divide:

$\frac{a}{b}$

divide/plus/minus:

$\frac{a+b}{a-b}$

divide/plus/divide:

$\frac{a+b}{\frac{a}{b}}$

A is subset of B as <reln>:

$(A, B)$

A is subset of B as <apply>:

$A\subseteq B$

A is proper subset of B as <reln>:

$(A, B)$

A is proper subset of B as <apply>:

$A\subset B$

A is not subset of B as <reln>:

$(A, B)$

A is not subset of B as <apply>:

$A\nsubseteq B$

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

$(A, B)$

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

$A\not\subset B$

Set difference:

$A\setminus B$

Log base 3 of x + y:

$\log_{3}(x+y)$

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

$\sum_{x=a}^{b} f(x)$

sum:

$\sum_{(x, B)} f(x)$

product:

$\prod_{x=a}^{b} f(x)$

product:

$\prod_{(x, B)} f(x)$

tendsto with <reln>:

$(x^{2}, a^{2})$

tendsto with <apply>:

$x^{2}\to a^{2}$

tendsto with <reln>:

$(\left(\begin{array}{c}x\\ y\end{array}\right), \left(\begin{array}{c}f(x, y)\\ g(x, y)\end{array}\right))$

tendsto with <apply>:

$\left(\begin{array}{c}x\\ y\end{array}\right)\to \left(\begin{array}{c}f(x, y)\\ g(x, y)\end{array}\right)$

mean(X):

$\langle X\rangle$

root(a + b):

$\sqrt[n]{a+b}$

standard deviation:

$\sigma (X)$

variance(X):

$\sigma(X)^2$

median(X):

$\mathop{\mathrm{median}}(X)$

mode(X):

$\mathop{\mathrm{mode}}(X)$

degree:

$\langle X^{3}\rangle$

vector:

$\left(\begin{array}{c}1\\ 2\\ 3\\ x\end{array}\right)$

matrix:

$\begin{pmatrix}0 & 1 & 0 & 0\\ 0 & 0 & 1 & 0\\ 1 & 0 & 0 & 0\end{pmatrix}$

determinant:

$\det A$

transpose:

$A^T$

semantics:

$\sin x + 5$

limit:

$\lim_{x\to 0}\sin x$

symbol check:

$4.56+4.56+4/5+4+5i+4.56e^{i 4.56}+\pi +e+e+i+i+\gamma +\infty$

multiset:

$\{4.56, 4.56, 4/5, 4+5i, 4.56e^{i 4.56}, \pi , e, e, i, i, \gamma , \infty \}$

tendsto type = "above" with <reln>:

$(x^{2}, a^{2})$

tendsto type = "above" with <apply>:

$x^{2}\to a^{2}$

tendsto type = "below" with <reln>:

$(x^{2}, a^{2})$

tendsto type = "below" with <apply>:

$x^{2}\to a^{2}$

tendsto type = "two-sided" with <reln>:

$(x^{2}, a^{2})$

tendsto type = "two-sided" with <apply>:

$x^{2}\to a^{2}$

type check:

$x+x+x+y+\theta +v+\pi +e+e+i+i+\gamma +\infty$

sin + cos:

$\sin x+\cos x$

f(x):

$f(x)$

Source Code: Omitted