Basic guide to CalcMe

You can write mathematics, and CalcMe will perform the calculations for you.

The CalcMe sheet is divided into three main areas:

Calculate

1. Write what you would like to compute.

2. Click Calc or Enter.

The default action is Calc, but you can choose the most appropriate one at your convenience.

Graph

1. Write the equation or figure you would like to plot.

2. Click Plot action.

Nota

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

Define

1. Store a computation in a variable.

2. Use it later.

Atenció

There is a new procedure to define variables in CalcMe using the code editor. You can see the problems intended to be solved and the expected user interaction here.

Mathematical operations in CalcMe are represented by a symbol associated with a keyboard key.

Operation	Symbol	Keyboard
Sum		+
Subtraction		-
Multiplication		* or ·
Division		/
Square root		Ctrl+.
Root		Ctrl+,
Power		Ctrl+Up

Below you can see several examples regarding their use.

You can compute the quotient and remainder of a division or factorize a number into prime factors. You can also compute the greatest common divisor or the least common multiple of a set of numbers.

Polynomials are created with a number multiplied by a variable raised to a power.

You can sum, multiply, divide and, for instance, find the roots of polynomials.

You can also create more complex expressions and operate with them.

Differentiation

There are plenty of ways to compute the derivative of a function or expression.

Using a prime	'
Using the symbol
Using the action
Using the command	differentiate

You can see several examples below.

Integration

There are also plenty of ways to compute the integral of a function or expression.

Using the symbol
Using the action
Using the command	integrate

You can see several examples below.

Limit

It is possible to compute the limit of a function or expression. Moreover, you can also take one-sided limits.

Taylor expansion

You can compute the Taylor series of a real function at a given point. If you are interested in the terms up to some order, you can cut the series too.

Series

You can determine whether a series is convergent, as well as calculate the sum of a convergent series in most cases.

CalcMe allows us to deal with geometrical figures such as points, lines, planes and conic sections. You can also create polygons and polyhedra, both in 2D and 3D. It is also possible to compute the distance between figures, the angle they form or the symmetry concerning an object.

Points, lines and planes

It is possible to work in 2 or 3 dimensions. To create points you simply define its components.

 

Given two points or a point and a vector, you can construct a line.

 

In a similar way, you can, for instance, construct a plane given three points.

Figures

There are a lot of functions useful for statistical calculations such as mean, quantile, quartile, etc. You can see the complete list here.

The most common probability distributions are also available. Analytical expressions for density and distribution functions are also available if possible.

Combinations, permutations or variations of a set of numbers can be calculated. Be careful, though: results are very large.

Counting	Symbol
Variations or k-permutations of n
Permutations
Combinations
Variations with repetition or n-tuples of m-sets
Permutations with repetition
Combinations with repetition
Binomial coefficient
Factorial You can also write ! with the keyboard.

You can see several examples here:

You can work with units, convert one into another (if it makes sense) and do basic operations with them. Units need to be introduced via the symbols available under the Units of measure tab. Discover more about the units or prefixes you can use here.

Currencies are similar to units but you cannot convert one into another. Check all the available currencies here.

The random function in CalcMe is adaptable to many cases of use. For example, you will see how to remove the "0" from a random selection. The normal command would be like:

CalcMe sheet	CalcMe code editor

By default, this includes all of the numbers between -10 and 10. If given the requirements of the question, the number 0 needs to be excluded from the set, you can remove it with one simple instruction:

CalcMe sheet	CalcMe code editor

You have to add brackets around the first list for this to work. This can, of course, work equally for any other number you need to exclude other than zero:

CalcMe sheet	CalcMe code editor

The above would produce a random number between -10 and 10, except the number 8. You can even do this with more than one number:

CalcMe sheet	CalcMe code editor

This would remove 8,-8, and 0 from the selection. As you can see, there are many more options when creating a random variable. So far, you have retrieved integer numbers, but you can also work with real numbers.

CalcMe sheet	CalcMe code editor

As a general rule, these real numbers will have as many decimal or significant figures as defined in the Application settings. You can adjust it by defining the step between the possible random values.

CalcMe sheet	CalcMe code editor
CalcMe sheet	CalcMe code editor

This section is a short guide to creating lists in CalcMe using the commands with and where. This method of defining lists is based on the standard mathematical notation of "set comprehension" or "set-builder notation", for instance:

We will explain the commands through the following examples.

Example 1

At the most basic level, with simply provides a more compact form of writing long lists. You can write

CalcMe sheet	CalcMe code editor

 

or you could greatly simplify it to the following:

CalcMe sheet	CalcMe code editor

 

The command where comes in handy when you would like to have additional restrictions. For example, retrieve the even numbers only:

CalcMe sheet	CalcMe code editor

 

Alternatively, you could, of course, have done this:

CalcMe sheet	CalcMe code editor

Example 2

In the first example, the size of the list was fixed. However, comprehension is especially useful when defining lists of variable size. Here, for example, is a list with random elements, of random size

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As you may have noticed, the first expression does not explicitly depend on $i$. You can think of $i$ as just a counter within a specified range. Then, you may or may not use it to define the list elements. It can also be any variable name you choose, as in the following:

CalcMe sheet	CalcMe code editor

Example 3

The list comprehension notation can also be extended to more than one variable. In that case, you should specify the range for each variable used as a counter. For example, here is a list with all positive proper fractions in simplest terms, with a single-digit numerator and denominator:

CalcMe sheet	CalcMe code editor

Another recommendation illustrated in the above example is enclosing each condition after where in parentheses if you have more than one joined by $\wedge,\vee$.

Example 4

Finally, note that the range for the counter variable can itself be a list, defined previously.

CalcMe sheet	CalcMe code editor

Example 5

It is also possible to create matrices using this notation. For instance, creating a $4\times3$ matrix with random coefficients is as simple as this:

CalcMe sheet	CalcMe code editor

You can use some programming functions. You can see the basic ones here. For example, given a list created as described before, you can easily compute the square of the first primes.

CalcMe sheet	CalcMe code editor

You can create custom functions. The random command is very useful, but it could be a bit tedious to write every time random(-10,10). Instead, you can create a function that generates a random number when called:

CalcMe sheet	CalcMe code editor

This eases the creation of a matrix with random coefficients. Another more elaborated example is creating a function that constructs a tri-diagonal matrix given three numbers. Therefore, every time you would like to create a tri-diagonal matrix, you just need to call this function with the upper-diagonal, diagonal and lower-diagonal terms you would like the matrix to have.

CalcMe sheet	CalcMe code editor