## Symbols

Here you'll find the standard mathematical symbols.

• These buttons are for the nice-looking versions of the symbols. Sometimes you can write directly with the keyboard; it won't be charming, but it will work. For example, you can use the keyboard slash / for fractions. You can use the keyboard parentheses (), but the parentheses from buttons are better because they expand with the content.

### Constants

Constants

Number pi

The ratio of a circumference to its diameter

$\mathrm{\pi }\approx 3.1416$

π 

Number e

$f={e}^{x}$ is the only function such that $f\text{'}=f$ and $f\left(0\right)=1$.

$e\approx 2.7183$

e 

Imaginary unit

A number defined to satisfy $i\cdot i=-1$

i 

Imaginary unit

A number defined to satisfy $j\cdot j=-1$

Infinity

Use it to calculate limits.

You must use the buttons for e and i. Keyboard e and i are just variables; they aren't the standard constants.

### The four basic operations

Basic operations

Subtraction

Subtraction

Multiplication

Multiplication

Division

Division

You can use multiple symbols for multiplication: * asterisk, · middle dot, the one in the menu, and also a space. That's it; a space between variables or numbers is an implicit multiplication. The * asterisk is automatically converted to a nicer middle dot ·.

About division, apart from the symbol in the menu, you can also use / slash and, of course, the fraction symbol.

### Brackets

Brackets

Parentheses

Use them to control the order of the operations.

Brackets

Vector

See Linear algebra section.

Vector

List

Some results or parameters are given or requested in this form.

Absolute value

Removes the sign from a number.

Absolute value

Norm

Length of a vector.

Norm

Do not use curly or square brackets as parentheses. Use only proper parentheses.

$2·\left\{3+4·\left[5+6·\left(7+x\right)\right]\right\}$ : error

$2·\left(3+4·\left(5+6·\left(7+x\right)\right)\right)$ : ok

### Bidimensional symbols

Bidimensional symbols

Fraction

Fraction

Square root

Square root

Root

Root

Power

Power

Element of list

Use it also for a vector, a matrix, an equation, etc.

Subscript

### Inequality symbols

Inequality symbols

Greater-than sign

Inequality

Less-than sign

Greater than or equal to

Less than or equal to

Not equal to

### Other symbols

#### Decimal separator

The dot (.) is for the decimal point, the comma (,) is for lists, and the apostrophe ('' ' '') is for derivation. The decimal point is the dot, but the others don't have that function.

There is no digit grouping symbol, nor are there spaces. Spaces mean implicit multiplication. The head decimal point is not allowed; use leading zero in those cases. The trailing decimal point is allowed.

• ''3.1416'': OK

• ''3,1416'': Error

• ''3'1416'': Error

• ''1 234 567'': Error

• ''.12'': Error

• ''0.12'': OK

• ''12.0'': OK

• ''12.'': OK

#### Plus Minus

Sometimes we are interested in the result of an expression when we add and subtract the same amount, as when we want to compute the roots of a degree two polynomial. The $±$ symbol allows us such and more things.

• If, for instance, we want to compute $3±2$, we expect $\left\{5,1\right\}$

• We can also use it as a unary operator: $±2=\left\{2,-2\right\}$

Every possible sign will be computed when we use the $±$ symbol. Therefore, if we write $n$$±$ symbols, we will get a list of ${2}^{n}$ elements. Some of them may be repeated since it is a list, not a set (for instance, $±0=\left\{0,0\right\}$).

We can use the $±$ symbol in all the basic operations (plus, minus, product, division, root, power) and some elementary functions (exponential, logarithm, trigonometric and hyperbolic functions and its inverse).

## Arithmetic

Here you'll find commands concerning integers and the rounding of decimals. You'll also find some divisibility commands, which are shared with Polynomials.

### Tip

You can find all the available commands related to arithmetics here.

### Integers and rounding

Also, see the Document settings section to see how many decimal places are shown.

Integers and rounding

Absolute value

You can write | (pipe) with the keyboard, too.

Absolute value

Floor

Round down to the next smaller integer.

Rounding

Ceiling

Round up to the next greater integer.

Round to nearest integer, and for tie-breaking round half up.

The sign for a number. It can be -1, 0 or 1.

Sign

The greater of two numbers, or a list.

The smaller of two numbers, or a list.

Generate a pseudo-random number between the two given ones (including both). Also, choose randomly from a list.

Pseudorandomness

### Divisibility

Divisibility

The numerator of a fraction.

Fraction

The denominator of a fraction.

The quotient of the integer division of the first number (dividend) by the second (divisor).

Quotient

The remainder of the integer division of the first number (dividend) by the second (divisor); also called modulus in many textbooks.

Remainder

Greatest common divisor.

gcd

Least common multiple.

lcm

Prime factorization of an integer.

Factorization

Tests to determine whether a number is prime. This is a predicate: a command that returns only true or false.

Prime number

## Polynomials

Polynomials are simpler types of functions. However, they're so important that they have their own naming system. Because you can divide polynomials, they share divisibility commands with the Arithmetic section.

Here you'll also find commands for complex numbers. Complex numbers were invented as a way to solve all the polynomials.

### Tip

You can find all the available commands related to polynomials here.

### Polynomials

Polynomials

The degree of a polynomial

Polynomial

How many terms does a polynomial has.

This is one term from a polynomial. The term number is the second parameter. The terms are ordered by descending grades. Therefore, term number 1 is always the leading term.

The content of a polynomial. That is, gcd of their coefficients.

Rearrange a polynomial with multiple variables arranged around the variable in the second parameter.

Finds the roots of a polynomial or, in other words, the values of x that make it 0.

• The command roots(p) does the same as solve(p=0) or apply the Calc action to p=0, but the results are shown in different forms. See the example.

• You can also find roots in the Complex field if you use as a second parameter the C from the Logic and sets section. See the example.

### Divisibility

Divisibility

The numerator of a rational fraction

Rational fraction

The denominator of a rational fraction

The quotient of the division of the first polynomial (dividend) by the second (divisor)

Polynomial

The remainder of the division of the first polynomial (dividend) by the second (divisor)

The greatest common divisor

The least common multiple

Factorization in irreducible polynomials

This tests whether a polynomial is irreducible. This is a predicate: a command that returns only true or false.

### Complex numbers

Complex numbers

Imaginary unit

i

The real part of a complex number.

Complex number

The imaginary part of a complex number, which is a real number.

The modulus of a complex number.

The argument of a complex number, in the range (-π,+π].

This converts a complex number from binomial form to polar form and the other way around(!). The polar form is a list formatted as {norm, argument}.

This is the conjugate of a complex number. Shift the sign of the imaginary part.

Complex numbers

## Statistics

### Tip

You can find all the available commands related to statistics here.

### Sets of data

Data sets must be entered as a comma-separated list, being enclosed by curly brackets {}.

Sets of data

List

### Single set

These commands summarize a set of data. Somehow, they're able to measure its centre or its variability. Because there are multiple definitions for that, there are also multiple measures.

Description of a single sample

Mean, arithmetic mean, average.

Mean

This is used to summarize measures with different units (length, cost, weight,...) of the same object. It has no sense alone, but it is helpful for comparisons among multiple objects.

This is used for ratios and rates, as in the context of speed.

A measure of variability that is convenient for calculations

Variance

A measure of variability that has the same physical units of the data

Standard deviation

A central measure, alternative to mean, is more robust, meaning it isn't affected by extreme data, generally known as outliers.

Median

These values divide the data once ordered into four groups of the same size. They're used to measure variability. See the formula reference section for details.

Quartile

Most frequent value in data. It can be a set if there are ties.

Mode

### Two sets

These commands measure the relationship between data pairs.

• The data set must be entered as a list of pairs. The list must be enclosed by curly brackets {}. The couples must be surrounded by regular parentheses (). Additionally, you can plot these paired data sets.

Relationship between two sets of paired data

This is the base for the correlation coefficient. It has the same sign.

Pearson correlation coefficient. It determines whether there is a linear relationship between the paired data.

Correlation

It gives the line equation that better fits the cloud of data.

Finds the best $y=a+bx$.

Regression line

It fits the data to a power function.

It finds the best $y=a{x}^{b}$.

Nonlinear regression

It fits the data to an exponential function.

It finds the best $y=a{\mathrm{e}}^{bx}$.

It fits the data to a logarithmic function.

It finds the best $y=a+\mathrm{ln}\left(bx\right)$.

### Formula reference

Formula reference

$\frac{1}{n}\sum _{i}{X}_{i}$

$\sqrt[n]{\prod _{i}{X}_{i}}$

$\frac{n}{\sum _{i}\frac{1}{{X}_{i}}}$

$\frac{1}{n-1}\sum _{i}\left({X}_{i}-\text{mean}\left(X\right){\right)}^{2}$

$\sqrt{\text{variance}\left(X\right)}$

$\left\{\begin{array}{lc}{X}_{k}& n=2k-1\\ \frac{{X}_{k}+{X}_{k+1}}{2}& n=2k\end{array}\right\$

$\begin{array}{l}\text{quartile}\left(0,X\right)={X}_{1}\\ \text{quartile}\left(1,X\right)=\left\{\begin{array}{lc}\text{median}\left(\left\{{X}_{1},\dots ,{X}_{k}\right\}\right)& n=2k-1\\ \text{median}\left(\left\{{X}_{1},\dots ,{X}_{k}\right\}\right)& n=2k\end{array}\right\\\ \text{quartile}\left(2,X\right)=\text{median}\left(X\right)\\ \text{quartile}\left(3,X\right)=\left\{\begin{array}{lc}\text{median}\left(\left\{{X}_{k},\dots ,{X}_{n}\right\}\right)& n=2k-1\\ \text{median}\left(\left\{{X}_{k+1},\dots ,{X}_{n}\right\}\right)& n=2k\end{array}\right\\\ \text{quartile}\left(4,X\right)={X}_{n}\end{array}$

$\frac{1}{n-1}\sum _{i}\left({X}_{i}-\text{mean}\left(X\right)\right)\left({Y}_{i}-\text{mean}\left(Y\right)\right)$

$\frac{covariance\left(X,Y\right)}{standard_deviation\left(X\right)·standard_deviation\left(Y\right)}$

$\frac{y-mean\left(Y\right)}{standard_deviation\left(Y\right)}=correlation\left(XY\right)\frac{x-mean\left(X\right)}{standard_deviation\left(X\right)}$

### Probability distributions

It is also possible to use the most common probability distributions. Currently, the following ones are available.

Probability distributions

All intervals of the same length on the distribution's support are equally probable in the uniform distribution.

Uniform variable

The normal distribution is determined by its mean $\mu$ and standard deviation $\sigma$. It is widely used in natural science, among other fields.

Normal variable

The exponential distribution is the probability distribution that describes the time between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate.

Exponential variable

The ${\chi }^{2}$ distribution with $k$ degrees of freedom is the distribution of a sum of the squares of $k$ independent standard normal random variables.

Chi-squared variable

Student's $t$-distribution arises when estimating the mean of a normally distributed population in situations where the sample size is small, and population standard deviation is unknown.

Student t-variable

The Bernoulli distribution is the probability distribution of a random variable which takes the value $1$ with probability $p$ and the value 0 with probability $q=1-p$.

Bernoulli variable

The binomial distribution with parameters $n$ and $p$ is the discrete probability distribution of the number of successes in a sequence of $n$ independent experiments, each asking a yes-no question, i.e. each ruled by the same Bernoulli distribution.

Binomial variable

The geometric distribution with parameter $p$ is the discrete probability distribution of the number of failures before the first success. A Bernoulli variable rules each try with the parameter $p$.

Geometric variable

The Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant rate and independently of the time since the last event.

Poisson variable

The $F$-distribution is a continuous probability distribution that frequently arises as to the null distribution of a test statistic, most notably in the analysis of variance (ANOVA), e.g., $F$-test.

F variable

Moreover, we can get a random number following such distributions, obtain its distribution and density function and find the quantile of given probability.

Probability functions

It retrieves a random number following a given distribution.

Distribution function of a random variable at a given point. In some cases, the analytical expression is given. $distribution\left(X,x\right)={F}_{X}\left(x\right)=P\left(X\le x\right)={\int }_{-\infty }^{x}{f}_{X}\left(t\right)dt$, cumulative distribution function (CDF)

Density function of a random variable at a given point. In some cases, the analytical expression is given. $density\left(X,x\right)={f}_{X}\left(x\right)=\frac{d}{dx}{F}_{X}\left(x\right)$, probability density function (PDF).

Quantile function of a random variable for a given probability. $quantile\left(X,p\right)=x⟺distribution\left(X,x\right)=p$, inverse function of CDF.

### Statistical data representation

 Histograms are often used to represent continuous data visually. As opposed to histograms, bar charts are helpful for displaying discrete data, as well as categorical data. Pie charts are another standard tool for categorical data when we want to show the proportion that each category occupies out of the whole. Boxplots are very useful for a concise representation of a data set. In one boxplot, we see the median, the interquartile range (IQR), as well, as outliers.

## Functions

The most common functions are the polynomial and rational ones, both of which are called algebraic functions. They're covered in the Polynomials section. This section is about other groups of so-called transcendental functions. Their exact values can't be calculated with basic arithmetic alone. You can calculate approximations, but it's impractical to do so by hand. It's better to use an electronic calculator or a table or book of values as was done in the old days.

### Tip

You can find all the available commands related to the available functions here.

### Trigonometric functions

Trigonometric functions started in the basic geometry of triangles, but now they comprise a complex field that's a central subject of calculus.

Trigonometric functions have two modes of work: in degrees and in radians. See the Document settings section.

Trigonometric functions

Number pi This is useful when working with radians. $\mathrm{\pi }\approx 3.1416$

π

Angle degree

Degree

Direct

Sine, related to the side opposite the angle

Trigonometric function

Cosine, related to the side adjacent to the angle

Tangent, sin/cos

Reciprocal

Cosecant, 1/sin

Trigonometric function

Secant, 1/cos

Cotangent, 1/tan

Inverse

This is one of the many angles whose sine is the given number. It's the one in [-π/2,π/2].

Trigonometric function

This is one of the many angles whose cosine is the given number. It's the one in [0,π].

This is one of the many angles whose tangent is the given number. It's the one in (-π/2,π/2).

You can use the Simplify action to force non-trivial simplifications over trigonometric expressions. Moreover, the Verify action can test for trigonometric identities.

### Logarithms and exponentials

Exponential and logarithmic functions are essential in calculus. The logarithm is used for physical measures, such as the units pH in chemistry and dB in acoustic physics.

Logarithms and exponential

Number e This is the basis of the Napierian logarithm. $e\approx 2.7183$

e

Logarithm with base

Logarithm

Exponential, e powered to the given number.

Exponentiation

Natural or Napierian logarithm

Logarithm

Logarithm

You must enter e with the button. You can't simply type e with the keyboard because then it's just a variable called e but not the number.

The logarithm base can be set as a subindex of the function log().

If no base is set, just log() means the decimal logarithm or, in other words, the base 10 logarithm.

Also, ln() means the natural logarithm, which is the base e logarithm.

You can use the Simplify action to force non-trivial simplifications over logarithmic and exponential expressions. Also, the Verify action can test for identities.

### Hyperbolic functions

Hyperbolic functions

$\mathrm{sinh}\left(x\right)=\frac{{e}^{x}-{e}^{-x}}{2}$

Hyperbolic function

$\mathrm{cosh}\left(x\right)=\frac{{e}^{x}+{e}^{-x}}{2}$

$\mathrm{tanh}\left(x\right)=\frac{\mathrm{sinh}\left(x\right)}{\mathrm{cosh}\left(x\right)}$

### Examples

Trigonometric functions

Trigonometric reciprocal functions

Trigonometric inverse functions

Logarithmic and exponential functions

Hyperbolic functions

## Calculus

### Tip

You can find all the available commands related to calculus here.

Here you'll find lots of buttons and commands that are relevant to calculus, functions and successions.

Calculus actions

Derive

Derivative

Integrate

Integral

A derivation or integration will use the first alphabetical variable by default. You can change that by configuring these actions, clicking on the action icon in the line.

Calculus buttons

Derivative You can also use the apostrophe (') from the keyboard.

Derivative

An integral with differential.

Integral

A definite integral with differential. Be aware that the sign of the function matters. The definite integral isn't always the area.

Limit You can use infinity here.

Limit

Limit right.

Limit of a function

Limit left.

To infinity . . . and beyond!.

Piece-wise function.

Piecewise function

Function application.

Expression with a restricted domain.

Restriction

Summation with under-and-over scripts.

Sum

Summation with under scripts.

The product with under-and-over scripts.

Product

The product with under scripts.

Function application must be used only when the function is not yet defined (such as in ODEs). Do not use it to define or to use a function. Instead, use simple parentheses. See the example below.

Calculus commands

Domain of a function.

Function

Taylor's polynomial.

Taylor's polynomial

Ordinary Differential Equations

This fills the plane with vectors defined by a function. Use it to visualize gradients, forces, derivatives in a phase plane, etc.

Vector field

This fills the plane with curves that follow the given vector field, i.e., curves as the solution to the ODE associated with a vector field. Use it to get an overview of the stability of the field.

Integral curve

This draws a particular integral curve, which begins at a given point.

## Linear algebra

### Tip

You can find all the available commands related to linear algebra here.

Find here operations of vectors and matrices. Vectors, which use brackets, are written horizontally. You can write them with the button of the men, or directly with the keyboard.

Matrices are best written with the button of the menu. However, they can also be written with the keyboard as a vector of multiple same-dimension vectors, as in many programming languages. Once a matrix is created, you can still modify its layout. You can, for example, insert or remove columns and rows. There are buttons for that in the menu. Usually, they're disabled, but they become enabled when the cursor enters a matrix.

Vectors are automatically seen as matrices by some commands. You needn't be concerned about the conversion. The usual operations are aware of vectors and matrices. For example, the common product symbol means different things when used between a scalar and a vector, two vectors, a vector and a matrix, or two matrices.

Linear algebra

Makers

Vector

Vector

Matrix

Matrix

Determinant

Determinant

 Buttons for vectors Scalar product, dot product Dot product Vector product, cross product Cross product Norm Norm Element of vector
 Buttons about matrices Determinant Determinant Inverse Matrix Transpose Transpose Identity matrix Matrix Element of matrix
 Commands Dimension of a vector Vector Dimensions of a matrix; first files, then rows Matrix Rank of a matrix; max number of linearly independent rows or columns Rank A matrix whose rows are a base of the kernel Kernel A matrix whose rows are a base of the image Image A list of eigenvalues, repeated as many times as their multiplicity Eigenvalues A matrix whose rows are eigenvectors, ordered matching the eigenvalues result list Eigenvectors The Jordan normal form of the matrix, if it exists. It gives the lower triangular form but not the upper. Jordan normal form Angle between two vectors.
• For the kernel(), image() and eigenvectors() commands, the result is a matrix whose columns are the vectors that form a base. Note that, because there are always many bases, there are many other correct results. You can get a particular vector from the result R using RT1, RT2, RT3,...

Matrix layout modifiers

Insert column at left

Insert column at right

Remove column

Insert row above

Insert row below

Remove row

## Combinatorics

### Tip

You can find all the available commands related to combinatorics here.

Here you'll find the elementary combinatorial functions. You can calculate their values. You can also apply these functions to a list and see the entire collection. Please be careful, though. The results can easily be too big.

Combinatorics

Variations or k-permutations of n

Variations

Permutations

Permutation

Combinations

Combination

Variations with repetition or n-tuples of m-sets

Variations with repetition

Permutations with repetition

Permutation

Combinations with repetition

Combination

Binomial coefficient

Binomial coefficient

Factorial You can also write ! with the keyboard.

Factorial

## Logic and sets

You can verify whether a statement is true or false. Use it to test identities, for example. There are logical (Boolean) operators, which you can use to combine statements. There are logical (Boolean) operators, which you can use to combine statements.

You can make statements about sets. There are two types of them:

• finite sets: a list of elements inside curly brackets, such as {1,2,3}.

• standard number sets: represented by standard symbols, for example, R.

You can make operations with the finite sets, but not with the others. You can also work with intervals and do operations with them

Intervals

The interval $\left(a,b\right)$, that is all the numbers $x$ between $a$ and $b$: $a

The interval $\left(a,b\right]$, that is all the numbers $x$ between $a$ and $b$ including $b$: $a

The interval $\left[a,b\right)$, that is all the numbers $x$ between $a$ and $b$ including $a$: $a\le x

The interval $\left[a,b\right]$, that is all the numbers $x$ between $a$ and $b$ including both $a$ and $b$: $a\le x\le b$

Logic and sets

Actions

Verify

Proposition

Equal to

Inequality

Not equal to

Less-than sign

Greater-than sign

Less than or equal to

Greater than or equal to

Logical and

and

Logical or

or

List

Element of

Set

Contains as member

Union

Intersection

Set minus

Natural numbers

Number

Integer numbers

Rational numbers

Real numbers

Complex numbers

## Solve

### Tip

You can find all the available commands related to equations, inequations and systems of equations and inequations here.

This section contains commands to find solutions to equations, inequalities and their corresponding systems. You can perform the Calc action over equations, inequalities and systems of them, and they'll be solved by default. Alternatively, you can use the solve command. The results are the same, but they have different forms.

There isn't a solution for every equation in the real numbers. You can also use solve complex numbers. Not all equations have algorithms to find the answers. If the system can't see all the exact solutions, you can try numerical_solve to find one approximate solution. The command numerical_solve doesn't find all solutions. Instead, it finds one each time.

The Calc action first tries the complete solve internally, and if it fails, it uses numerical_solve. We can also store the equation's solutions in a set and then access each answer using the commands you can see in the last example below.

### Note

Writing a system of equations is simple: separate each equation by commas; write them inside braces and separate them by commas; or put all of them inside braces, each one in a new line (Shift+Enter).

Solve

Find all solutions: all values that satisfy the equation.

Equation

Find one approximate value that satisfies the equation. An iterative method is used, and you can set the initial value.

Newton's method

Solve inequalities and their corresponding systems.

Inequality

Evaluate the first parameter (expression) by replacing the second (variable) with the third (value) and performing the operations.

## Greek

It's common to use Greek letters in formulas, and this section contains them all. See Greek alphabet for background information.

You can use Greek letters for the names of the variables. You could even use Chinese, Japanese or Russian letters, for example. You'd need an appropriate keyboard for that, or you could copy and paste the symbols from a web page, for example. See Unicode for background information.

• Do not use this π for 3.1416, use the one in the Symbols section. The π here is only text, so it has no value.

Lowercase

Alpha

Beta

Gamma

Delta

Epsilon

Zeta

Eta

Theta

Iota

Kappa

Lambda

Mu

Nu

Xi

Omicron

Pi

Rho

Final sigma

Sigma

Tau

Upsilon

Phi

Chi

Psi

Omega

Uppercase

Capital alpha

Capital beta

Capital gamma

Capital delta

Capital epsilon

Capital zeta

Capital eta

Capital theta

Capital iota

Capital kappa

Capital lambda

Capital mu

Capital nu

Capital xi

Capital omicron

Capital pi

Capital rho

Capital sigma

Capital tau

Capital upsilon

Capital phi

Capital chi

Capital psi

Capital omega

Greek

## Units of measure

### Tip

You can find all the available commands related to units of measurement here.

You can do calculations using units. We follow the metric system, also called the International System of Units or SI for short. Find out all the units and metric prefixes supported. See Metric system for background information.

• You must write the units with the buttons of this section. You can't write them with the keyboard. An m from here is a meter, but an m from the keyboard is just a variable.

• Usually, a space between symbols means product, but it implies sum between quantities. If you want to multiply quantities, you must write the product symbol in between.

At the top of the section, there is a selector of the SI prefixes for the units below. The result of an operation between quantities has its unit selected automatically. You can force the unit of a quantity by using the Convert command.

You can obtain a quantity by multiplying a number and a unit. Using those commands can split a quantity into its coefficient and unit.

Commands

Convert the quantity in the first parameter to the unit of the second parameter. If there is no second parameter, it will be converted to the SI default unit.

Coefficient of a quantity.

Unit of a quantity.

SI Prefixes

n

nano

0.000 000 001

µ

micro

0.000 001

m

mili

0.001

c

centi

0.01

d

deci

0.1

da

deca

10

h

hecto

100

k

kilo

1000

M

mega

1 000 000

G

giga

1 000 000 000

Units

Meter

Gram

Second

Ampere

Kelvin

Mol

Candela

Angle degree

Angle minute

Angle second

Hour

Minute

Second

Liter

Newton

Hertz

Pascal

Watt

Joule

Coulomb

Volt

Ohm

Siemens

Weber

Bar

Henry

Tesla

Lux

Lumen

Gray

Becquerel

Sievert

Katal

Atmosphere

Molar

Dalton

Electronvolt

Pond

Yard

Foot

Inch

Mile

Nautical mile

Gallon

Ounce

Pound

Fluid ounce

Pint

Percent

Permil

Units of measure

### Currencies

Besides units, we can use currencies and do basic arithmetic with them but it is not possible to convert one unit into another. We should use the currency symbol provided in the tab.

Currencies

Dollar

Euro

Pound

Franc

Krone

Bitcoin

Ruble

Rupee

Won

Yen

Currencies

## Graphs

### Tip

You can find all the available commands related to graphics here.

The Sheet can have an area for plotters on the right. Plotters are containers for graphs of functions. They can be heavily configured. You can see that plotters have background, axis and grid. They also have centre and scale concerning the view. Each plotter has a name on top and a button to configure its properties. You can change the point of view in real-time by dragging the mouse or rolling the mouse wheel over the plotter.

There are bigger versions of plotters, too. Click on the arrow at the bottom-left to see them. In the bigger version, there are sliders to change the point of view. Moreover, the bigger version of the 2-D plotter has a crosshair and shows, at the bottom-right, the coordinates of the selected point. This is useful for obtaining information about the drawn functions.

You can put things in the plotter by using the Plot action over a formula. If there is no plotter in the sheet, a new one will be created. Otherwise, the graph object will be placed in an existing plotter.

Graph objects can also be heavily configured. Each graph object has label, color and width, and maybe border, interior and transparency. These properties can be configured by clicking the Plot action icon located next to the formula. You can also move one graph object from one plotter to another through the configuration popup next to the Plot icon.

Furthermore, you can create several objects using top-bar actions or drawing by hand through handwritten geometry recognition. You can configure them like you had made it through the sheet. See Graph for background.

Graphs

Actions

Plot

Plot 3-D

Commands

Place the boundaries as parameters, and you'll get a region object that's ready to plot.

### 2-D

You can plot in the Cartesian plane:

• functions, of one variable

• equations, of two variables, that are implicit functions

• inequations, of two variables, that are regions

• lists of them

• regions, defined by command region()

You can also plot elements of ODEs, as explained in the Calculus section.

### 3-D

In the Cartesian space, you can plot:

• functions, of two variables

• linear equations, of three variables, which are planes

• lists of them

### Plotter settings

You can change some plotter settings by clicking on the settings button at the right corner of the plotter top bar. The options you can modify are the following.

Dimensions

Color

Horizontal

Vertical

All these settings can also be changed through the sheet. The attributes() command will allow you to see them and the notation you have to use to modify the default values.

Attributes

Thus, you will be able to create plotters as the following defining its attributes by hand.

Example

### Plot settings

It's also possible to change the settings of a particular plot by clicking on the object's graph. You will see a bar below it as the following.

Plot settings

The options you can modify (from left to right) are the following:

• Fix label: choose whether or not the function's label is fixed.

• Line width: define the line width.

• Line style: define the line style (solid, dashes, dots or dots and dashes).

• Line colour: define the line colour.

• Delete: erase the plotted object.

Finally, you can also change the location of a particular plot by clicking on the graph icon next to the function which is being represented. A pop-up window as the following will appear on your screen.

Plot location

### Note

From this moment on, it's possible to download the graphic plotter as a square image in PNG format of the size you desire. Take advantage of this new CalcMe feature to save the generated images directly to your device.

### Graph

An object in CalcMe is plotted in Graph; but Graph is much more than a simpler viewer, we can build segments, vectors, lines, and conic sections. Moreover, handwritten geometry recognition allows us to draw by hand, as we do on paper, and it will translate our drawings to mathematical objects.

To see more details, take a look at its dedicated page.

## Programming

### Tip

You can find all the available commands related to programming methods here.

Here you'll find the usual commands for programming. These include conditional statements, loops, begin-end block, local variables and return.

### Note

As you may use these commands to generate an algorithm for a WirisQuizzes question, we show how to create them through the sheet and using the code editor. You can see more details about it here.

### Range notation

We can create a range of numbers using the syntax: start..end or start..end..step. It is also possible to couple ranges.

CalcMe sheet

CalcMe code editor

### Concatenation

We can concatenate two strings, lists, or vectors. Moreover, we can add a column or a row to a matrix easily.

CalcMe sheet

CalcMe code editor

### Conditional statements

Conditional statements

if statement. If the condition is held, then performs the action inside the block.

else statement. It should be preceded by an if. If the condition specified in the if statement is not held, then runs the commands inside the else's block.

It should be preceded by an if. If the condition specified in the previous if statement is not held and the current condition is satisfied, then performs the action inside the block.

### Loop statements

Loop statements

for statement. Write quickly a loop that needs to be run a specific number of times.

while statement repeats the code block until the condition is not satisfied. Be sure that the condition does not hold in some cases. Otherwise, the code will run infinitely.

repeat statement. While the condition does not hold, duplicate the code block. Again, be sure that the condition is satisfied sometimes.

### Begin, local and return

Begin, local and return

This block is extremely useful when one defines its own functions. It allows performing different actions inside one block and defining local variables.

return statement. Returns a value in a user function.

Allows defining local variables: variables defined just in one code block.

### Examples

CalcMe sheet

CalcMe code editor

CalcMe sheet

CalcMe code editor

CalcMe sheet

CalcMe code editor

CalcMe sheet

CalcMe code editor

CalcMe sheet

CalcMe code editor

CalcMe sheet

CalcMe code editor

CalcMe sheet

CalcMe code editor

CalcMe sheet

CalcMe code editor

CalcMe sheet

CalcMe code editor

## Format

You can apply some formatting options but only to texts in text lines (created by that Text action).

Options

apply to characters

Bold

Italics

Colour

apply to the whole line

Font family

Font size

Format