Toolbox

The toolbox key gives you access to an organized library of advanced functions. Press the toolbox key at any time while editing a calculation or expression to view a menu of functions. The advanced functions available in the toolbox menu change according to the application you are using.

When viewing a graph, the toolbox key gives you access to settings and additional features.

When writing an expression, the first functions in the Toolbox menu include: Absolute value, n-th root and Logarithm base a. When inputting expressions for the Grapher, the menu will also include Inequalities. Within the Sequences applicaiton, the Toolbox menu will also include defined sequences.

The Toolbox menu is then divided into several thematic sub-sections:

• Calculus
• Complex numbers
• Probability
• Units and constants
• Matrices and vectors
• Lists
• Arithmetic
• Trigonometry
• Decimal numbers
• Logic

abs(x)

Calculates the absolute value of the argument you enter in parentheses. abs(-4.5) gives the value of $\mid -4.5\mid$, that is $4.5$.

root(x,n)

Calculates the $n$-th root of a number. You must enter $n$ and $x$ in parentheses. root(x,n) gives the value of $\sqrt[n\,]{x}$. The value of $n$ doesn’t have to be an integer.

log(x,a)

Calculates the logarithm with base $a$. You must enter $a$ and $x$ in parentheses. log(x,a) gives the value of $\log_{a}(x)$.

Calculus

diff(f(x),x,a)

Calculates the derivative of a function at a point. diff(f(x),x,a) gives the value of $f'(a)$. For example, to calculate the derivative of a square root at 5: diff(sqrt(x),x,5).

diff(f(x),x,a,n)

Calculates the nth derivative of a function at a point. diff(f(x),x,a,n) gives the value of $f^{n}(a)$. For example, to calculate the 3rd derivative of a square root at 5: diff(sqrt(x),x,5,3).

int(f(x),x,a,b)

Calculates the integral of a function between two bounds. int(f(x),x,a,b) gives the value of $\int_{a}^{b} f(x) \, \mathrm{d}x$. For example, to calculate the integral of the square root between $0$ and $5$: int(sqrt(x),x,0,5).

sum(f(n),n,nmin,nmax)

Calculates the sums of terms in $n$. sum(f(n),n,nmin,nmax) gives the value of $\sum_{n=n_{min}}^{n_{max}} f(n)$.

product(f(n),n,nmin,nmax)

Calculates the products of terms in $n$. product(f(n),n,nmin,nmax) gives the value of $\prod_{n=n_{min}}^{n_{max}} f(n)$.

Complex numbers

abs(x)

Modulus of a complex number. abs(2+3i) gives the value of $\mid 2+3i\mid$.

arg(z)

Argument of a complex number. arg(2+3i) gives the value of $arg(2+3i)$ in radians.

re(z)

Real part of a complex number. For example, re(2+3i) returns $2$.

im(z)

Imaginary part of a complex number. For example, im(2+3i) returns $3$.

conj(z)

Conjugate of a complex number. conj(2+3i) returns the conjugate of $2+3i$, that is $2-3i$.

Probability

Combinatorics

binomial(n,k)

Number of ways to choose a subset of size $k$ elements, disregarding their order, from a set of $n$ elements. For example, $\dbinom{n}{k}$ returns $\frac{n!}{k! (n-k)!}$.

permute(n,k)

Number of different ordered arrangements of a $k$-element subset of an $n$-set. permute(n,k) returns $A_{n}^k$, that is $\frac{n!}{(n-k)!}$.

n!

Returns the product of the entered integer and all integers below it. For example, $5!$ returns $120$.

Distributions

Normal

normcdf(a,µ,σ)

$P(X<a)$ where X follows the normal distribution $N(\mu,\sigma)$.

normcdfrange(a,b,µ,σ)

$P(a<X<b)$ where X follows the normal distribution $N(\mu,\sigma)$.

invnorm(a,µ,σ)

Returns $m$ where $P(X<m)=a$ and X follows the normal distribution $N(\mu,\sigma)$.

normpdf(x,µ,σ)

Probability density function of $N(\mu,\sigma)$.

Student’s t

tcdf(a,k)

$P(X<a)$ where X follows the t-distribution with k degress of freedom.

tcdfrange(a,b,k)

$P(a<X<b)$ where X follows the t-distribution with k degress of freedom.

invt(a,k)

Returns $m$ where $P(X<m)=a$ and X follows the t-distribution with k degress of freedom.

tpdf(x,k)

Probability density function of $t(k)$.

Binomial

binompdf(m,n,p)

$P(X=m)$ where X follows the binomial distribution $B(n,p)$.

binomcdf(m,n,p)

$P(X \leq m)$ where X follows the binomial distribution $B(n,p)$.

invbinom(a,n,p)

Returns $m$ where $P(X \leq m)=a$ and X follows the binomial distribution $B(n,p)$.

Poisson

poissonpdf(m,λ)

$P(X=m)$ where X follows the Poisson distribution with parameter λ.

poissoncdf(m,λ)

$P(X \leq m)$ where X follows the Poisson distribution with parameter λ.

Geometric

geompdf(m,p)

$P(X=m)$ where X follows the geometric distribution with probability p.

geomcdf(m,p)

$P(X \leq m)$ where X follows the geometric distribution with probability p.

geomcdfrange(m,n,p)

$P(m \leq X \leq n)$ where X follows the geometric distribution with probability p.

invgeom(a,p)

Returns $m$ where $P(X \leq m)=a$ and X follows the geometric distribution with probability p.

Hypergeometric

hgeompdf(m,N,K,n)

$P(X=m)$ where X follows the hypergeometric distribution with population size N, number of featured items K and sample size n.

hgeomcdf(m,N,K,n)

$P(X \leq m)$ where X follows the hypergeometric distribution with population size N, number of featured items K and sample size n.

hgeomcdfrange(m,q,N,K,n)

$P(m \leq X \leq n)$ where X follows the hypergeometric distribution with population size N, number of featured items K and sample size n.

invhgeom(a,N,K,n)

Returns $m$ where $P(X \leq m)=a$ and X follows the hypergeometric distribution with population size N, number of featured items K and sample size n.

Random

random()

Returns a floating point number in [0,1).

randint(a,b)

Returns a random integer in [a,b].

randintnorep(a,b,n)

Returns n unique random integers in [a,b].

Units and constants

This menu contains sub-menus for constants and each type of measurement listed below. Units and constants can be selected from the menu or typed manually.

a→b

This menu item is a template that allows you to perform a unit conversion.

Length and angle

Length

Imperial

Metric

Angle

Time and frequency

Time

Frequency

Volume and area

Volume

Imperial

Metric

Area

Imperial

Metric

Mass

Imperial

Metric

Electricity

Current

Voltage

Resistance

Capacitance

Others

Force and pressure

Force

Pressure

Energy and power

Joule

Power

Electronvolt

Temperature

Others

Amount of substance

Constants

Matrices and vectors

New matrix or vector

Create a new matrix or vector. This option creates a template. Enter your numbers using the directional keys.

transpose(M)

Transpose the matrix M. For instance, transpose([[1,2][3,4]]) returns $\left[\begin{array}{cc}1 & 3 \\ 2 & 4 \end{array}\right]$.

dim(M)

Size of the matrix M. For instance, dim([[1,2][3,4]]) returns [2,2].

Matrices

det(M)

Determinant of the matrix M. For instance, det([[1,2][3,4]]) returns $-2$.

inverse(M)

Inverse of the matrix M. For instance, inverse([[0.25,0][0,0.25]]) returns $\left[\begin{array}{cc}4 & 0 \\ 0 & 4 \end{array}\right]$.

identity(n)

Identity matrix of size n.

trace(M)

Trace of the matrix M. For instance, trace([[1,2][3,4]]) returns $5$.

ref(M)

Returns the scaled shape of matrix M.

rref(M)

Returns the scaled form of matrix M.

Vectors

Vectors can be row vectors or column vectors.

dot(U,V)

Calculates the dot product of two vectors.

cross(U,V)

Calculates the cross product of two vectors of size 3.

norm(U)

Calculates the magnitude of a vector.

Lists

New list

Create a new list. This option provides opening and closing curly braces. Enter your elements using the number keys with a comma to separate each element.

List of f(k) for k from 1 to n

Create a new list using a function. This option creates a template. Enter your function f(k) and your upper bound.

Statistics

mean(L)

Calculates the mean of L.

stddev(L)

Calculates the standard deviation of L.

samplestddev(L)

Calculates the sample standard deviation of L.

med(L)

Calculates the median of L.

var(L)

Calculates the variance of L.

Operations

dim(L)

Returns the length of L.

min(L)

Returns the minimum element of L.

max(L)

Returns the maximum element of L.

sort(L)

Sorts the elements of L in ascending order.

sum(L)

Calculates the sum of the elements of L.

prod(L)

Calculates the product of the elements of L.

Arithmetic

gcd(p,q)

Greatest Common Divisor of two integers. For instance, gcd(55,11) returns $11$. This function accepts more than two integers as arguments.

lcm(p,q)

Least Common Multiple of two integers. For instance, lcm(13,2) returns $26$. This function accepts more than two integers as arguments.

factor(n)

Integer factorization of $n$. For instance, factor(24) returns $2^3 \times 3$.

Mixed fraction

A template to input a mixed fraction.

rem(p,q)

Remainder of the Euclidian division of $p$ by $q$. For instance, rem(50,45) returns the remainder of the division of $50$ by $45$ that is $5$.

quo(p,q)

Quotient of the Euclidian division of $p$ by $q$. For instance, quo(80,39) returns the quotient of the division of $80$ by $39$ that is $2$.

Trigonometry

Hyperbolic

sinh(x)

Hyperbolic sine.

cosh(x)

Hyperbolic cosine.

tanh(x)

Hyperbolic tangent.

arsinh(x)

Inverse hyperbolic sine.

arcosh(x)

Inverse hyperbolic cosine.

artanh(x)

Inverse hyperbolic tangent.

Advanced

csc(x)

Cosecant

sec(x)

Secant

cot(x)

Cotangent

arccsc(x)

Arccosecant

arcsec(x)

Arcsecant

arccot(x)

Arccotangent

Decimal numbers

floor

Floor function. For instance, floor(5.8) returns $5$.

frac(x)

Fractional part. For instance, frac(5.8) returns $0.8$.

ceiling

Ceiling function. For instance, ceil(5.4) returns $6$.

round(x,n)

Rounds a number to $n$ digits after the decimal point. For instance round(8.6576,2) returns $8.66$.

Logic

piecewise(-x,x<0,x,x≥0

A piecewise template. Input an expression followed by its domain or conditions

≤

Less than or equal to

≥

Greater than or equal to

≠

Different

and

And

or

Or (inclusive)

not

Not

xor

Or (exclusive)

nor

Not or (inclusive)

nand

Not and