Very very basic guide to CalcMe CalcMe is an online calculator based on Javascript, so it runs on any browser and operating system, including mobile and tablet devices. CalcMe is integrated within Wiris Quizzes, enhancing the power of your math questions. CalcMe offers a powerful calculation and graphics engine covering basic and advanced mathematical needs: random number generation, polynomials, general expressions, vectors, matrices, lists, geometry, statistics, user functions, programming and many more.Live demosThere are several live demos on this page. If you click into the area containing the CalcMe parameters, it will open in CalcMe. Try it out, change the parameters or options. You won't break anything. How does CalcMe work? You can write mathematics, and CalcMe will perform the calculations for you. The CalcMe sheet is divided into three main areas: Area for Calculating Area for Graphing Area for Defining Calculate Write what you would like to compute Click Calc or Enter The default action is Calc but you can choose the most appropriate one at your convenience LIVE DEMO Graph Write the equation or figure you would like to plot Click Plot action NewFrom 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. Define Store a computation in a variable Use it later NewThere is a new procedure to define variables in CalcMe using the code editor. You can see the problems intended to be solved with it and the expected user interaction here. Arithmetic Learn more Mathematical operations in CalcMe are represented by a symbol associated with a keyboard key. Operation Symbol Keyboard Sum + Substraction - Multiplication * or · Division / Square root Ctrl+. Root Ctrl+, Power Ctrl+↑ LIVE DEMO 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. LIVE DEMO Vector and Matrix constructor Learn more Vectors Vector are constructed with square brackets [], and the elements are separated by commas ,. You can sum vectors or compute their scalar product. LIVE DEMO Matrices Matrices are vectors of vectors, that is, vectors whose elements are vectors. You can create matrices with two different syntaxes As vectors, you can sum and multiply matrices (as long as their dimensions are compatible). LIVE DEMO Basic operations As you have previously seen, you can work with vectors and matrices and perform basic arithmetic with them. However, you can do many more things: you can compute the cross product between two vectors, check if they are linearly independent; a matrix can be inverted or raised to a whole power, you can also compute its rank or its determinant. LIVE DEMO Element access You can access a specific element of a vector using subindices, that start on 1. In the same way, you can retrieve an element of a matrix LIVE DEMO Polynomials and expressions Learn more Polynomials are created with a number multiplied by a variable raised to a power. LIVE DEMO You can sum, multiply, divide and, for instance, find roots of polynomials. LIVE DEMO You can also create more complex expressions and operate with them. LIVE DEMO 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 LIVE DEMO 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 LIVE DEMO Limit It is possible to compute the limit of a function or expression. Moreover, you can also take one-sided limits. LIVE DEMO 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. LIVE DEMO Series You can determine whether a series is convergent, as well as calculating the sum of a convergent series in most cases. LIVE DEMO Geometry Learn more CalcMe allows us to deal with geometrical figures such 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 with respect to an object. Points, lines and planes It is possible to work in 2 or 3 dimensions. To create points you simply define its components. LIVE DEMO Given two points or a point and a vector, you can construct a line. LIVE DEMO In a similar way, you can, for instance, construct a plane given three points. LIVE DEMO Figures LIVE DEMO Solving Learn more Equations It is possible to solve an equation or a system of equations exactly. LIVE DEMO You can also use a numerical method to solve more complicated equations. LIVE DEMO You can also use a numerical method to solve more complicated equations. LIVE DEMO Inequations It is also possible to find the solution to an inequation. LIVE DEMO Statistics Learn more There are a lot of functions useful for statistical calculations such as mean, quantile, quartile, etc. You can see the complete list here. LIVE DEMO Probability Learn more The most common probability distributions are also available. Analytical expressions for density and distribution functions are also available if possible. LIVE DEMO Combinatorics Learn more 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. LIVE DEMO Units and currencies Learn more 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. LIVE DEMO Currencies are similar to units but you cannot convert one into another. Check all the available currencies here. LIVE DEMO Randomness Learn more Algorithm lines optionAs you may use these commands to generate an algorithm for a Wiris Quizzes question, we show how to create them through the sheet and using the code editor. You can see more details about it 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: LIVE DEMO 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: LIVE DEMO 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: LIVE DEMO 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: LIVE DEMO 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. LIVE DEMO 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. LIVE DEMO CalcMe sheet CalcMe code editor Moreover, these random variables can also be selected from a concrete set of values or words. In the following section, you will see with more details on how to create this kind of sets. LIVE DEMO CalcMe sheet CalcMe code editor As you may have seen, we can use {} and [] to exclude several numbers for the set of possible values when generating random variables. We use each of them as follows: [] define arrays and matrices (arrays are supposed to contain the same data types). {} define lists (lists can have different data types). The random function can exclude values as long as the two parameters you pass are in the same format. In other words, if you include a list as a first parameter, you should pass a list as the second parameter as well. Creating lists via comprehension Learn more 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 common mathematical notation of "set comprehension" or "set-builder notation", for instance: We will explain the commands through the following examples. Algorithm lines optionAs you may use these commands to generate an algorithm for a Wiris Quizzes question, we show how to create them through the sheet and using the code editor. You can see more details about it here. Example 1 At the most basic level, with simply provides a more compact form of writing long lists. You can write LIVE DEMO CalcMe sheet CalcMe code editor or you could greatly simplify it to the following: LIVE DEMO 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: LIVE DEMO CalcMe sheet CalcMe code editor Alternatively, you could, of course, have done this: LIVE DEMO 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 LIVE DEMO CalcMe sheet CalcMe code editor As you may have noticed, the first expression does not explicitly depend on . You can think of 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: LIVE DEMO 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: LIVE DEMO 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 . Example 4 Finally, note that the range for the counter variable can itself be a list, defined previously. LIVE DEMO CalcMe sheet CalcMe code editor Example 5 It is also possible to create matrices using this notation. For instance, creating a matrix with random coefficients is as simple as this: LIVE DEMO CalcMe sheet CalcMe code editor Programming Learn more Algorithm lines optionAs you may use these commands to generate an algorithm for a Wiris Quizzes question, we show how to create them through the sheet and using the code editor. You can see more details about it here. 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. LIVE DEMO CalcMe sheet CalcMe code editor User functions Learn more Algorithm lines optionAs you may use these commands to generate an algorithm for a Wiris Quizzes question, we show how to create them through the sheet and using the code editor. You can see more details about it here. 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: LIVE DEMO 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. LIVE DEMO CalcMe sheet CalcMe code editor Table of Contents How does CalcMe work? Arithmetic Vector and Matrix constructor Polynomials and expressions Geometry Solving Statistics Probability Combinatorics Units and currencies Randomness Creating lists via comprehension Programming User functions