You should comment on what you had hoped to learn by performing these lab exercises. We have to sort the final key-value pairs because MapReduce doesn’t sort the output for you, for efficiency reasons. Wolfram Demonstrations Project » Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more. Getting Started with MATHEMATICA. Samuelsons Keynesian cross diagram is an attempt to capture the essence of Keynes theory of effective demand. Mathematica 6. How to work and convert in thousands of units. , you don't have to pay for it). Mathematica knows the basic mathematical functions like sine and cosine. Title Page See sample below 2. If the sampling time is unspecified, the output time scale will be in samples. Internally, the toolbox can use a few more digits than you specify. This 8-part screencast series gives an overview of how to get started with Mathematica 8 and the benefits for education. In the Wolfram Language, rules associate symbols with values. These additional digits are called guard digits. Or if you don't want low precision from definition, but instead prefer crop the precision when output, you can use a=0. (a)Write a parametric function and the Mathematica input needed to produce the following helix in Mathematica. Now we have a fun fact that every element of can be written as a product of disjoint cycles, so a typical element of might look like Like I said before, the automorphism group of the Petersen graph is a subgroup of. In such, the user can define rules as a way of doing algebraic replacements. Mathematica supports comments, even when you can "just write it into a plain text cell" because every programming language supports them. You can refer to these directly, as in Simplify[Out[32]]. To use the link from Mathematica, you load the ExcelLink package. Pretty-printing mathematics. It allows the input and output of Mathematica to be organized in a convenient way. The source code is copyrighted but freely distributed (i. Each cell can be evaluated (shift-enter) and it will yield an output cell underneath them, thus allowing for changes and re-evaluation of cells in any order. Yes, the more command can be helpful here, but what if you want to look at the output later, or send it to a tech support group, or use it in a spreadsheet, etc. Thus, Mathematica is an integrated computing environment, meaning it is what. There are many posts on how to "beautify" a single Mathematica equation into LaTeX. WRITING YOUR OWN MATHEMATICA MODULE -- ALTERNATE EXECUTABLE MODULES See the Module Writer's Guide for more information on writing an 'alternate executable' module. then think for a moment and write the answer below the expression. Thus, the equation for a circle is not a function and you cannot write it in function form. I'm new to Mathematica and I am starting to work on its notebooks. Ending with a semicolon tells Mathematica not to show the output. It encompases computer algebra , numerical computation, visualization and statistics capabilities. Check the necessary and sufficient conditions for a maximum. I have a question about Mathematica. Mathematica also has tools for procedural programming, which is the style of programming used in Fortran, Pascal, and C. In this unit, students will be asked to copy and evaluate Mathematica code and analyze the output. Mathematica has many built-in functions that are familiar from calculus: sinx, cosx, expx, logx, to name but a few. The main item of the domain www. Next, we investigate elaborately the way of linking of external programs with mathematica, so-called the mathlink operation. To maintain formatting for non-textual output, use -format when writing to a file. By default, BUGS writes all of the values of the monitored nodes into a long column of values 1. You can format the output display using several provided options. For(Int32, Int32, Action) overload, the two simplest overloads of the Parallel. This feature is for programmers who are creating Mathematica packages. 4 Appendix A. Neither is the Notebook Interface required to develop Mathematica solutions. Below are code snippets in Python, MATLAB, and Mathematica that you can modify to create your own CSV files. Now we're ready to go beyond these simple examples and. It is used in many scientific, engineering, mathematical and computing fields, and is based on symbolic mathematics. After all instructions are typed in, we press the "enter" key to execute the sequence. Mathematica is a computational software program developed by Wolfram Research. Internally, the toolbox can use a few more digits than you specify. Yes, Larry, quite right. Mathematica supports comments, even when you can "just write it into a plain text cell" because every programming language supports them. When Mathematica starts up, it gives you a blank Mathematica file. The disadvantage is that it will change the - system-wide audio settings. This page contains a number of scenes that accept CSV file inputs for visualization of robot trajectories. By itself it means nothing. In fact, D will allow you to differentiate whole list of equations at once. We translate big questions into deep insights that improve programs, refine strategies, and enhance understanding. I write Mathematica code in a rather plain style, using only [] for function application (not @ or //), avoid pattern processing, and avoid declaring functions with the #-and-& syntax. MyGraph = Plot[Sin[x], {x, 0, 2Pi}, DisplayFunction->Identity] The plot can then be manipulated through the variable. Draw the coordinate axes on this output by hand using the axes detailed in the Guidelines. Graphics are one of the most memory intensive aspects of Mathematica. If need be, write and debug a special function to export or format the output of your program. This includes the components written in Mathemat-. Here, I input a file call FS_data. Mathematica is a great computer algebra system to use, especially if you are in applied areas where it is necessary to solve differential equations and other complicated problems. Fitting data with Mathematica 1. Abs[ z ] (128 formulas) Introduction to the complex components : Plotting : Evaluation. DisplayFunction->Identity. Get corrections from Grammarly while you write on Gmail, Twitter, LinkedIn, and all your other favorite sites. • Although the documentation center doesn’t always explain beginning princples, it has very thorough. Also I define function list2 s. output of this function is a 2-rank list. When Mathematica's output is published using the code style (either by wrapping with ` or by adding four spaces on the start of the line, or by wrapping with /), we publish explicit form of the output (approximately equivalent to InputForm): strings are always wrapped by quotes, numbers usually have ` at the end, etc. Mathematica 5. Mathematica notebooks are a convenient document format for storing code, text, graphics, and human readable computation results. But, this procedure can not be manually implemented for a notebook containing over 100 in/out. One can set the maximum number of T E X windows to be N which appear using SeeTeX [N]. Since our primary goal is to use Mathematica. The N function can be used to compute approximate (decimal) values instead. This page contains information on getting started quickly with V-REP. You can select one of two numeric display options in MATLAB. The Mathematica commands in this tutorial are all written in bold black font, while Mathematica output is in normal font. Mathematica, we input each instruction and press the “return” key. » m - print Mathematica output. For example, N[E]returns 2. example, Mathematica is very good at typical calculus problems. 341) define without the leading factor of. This is the usual way we write some XPath. The variable y is not independent since it depends on the number chosen for x. Writing Graphical Output to Files. The ";" is suppressing the output. Linear Algebra in Mathematica Craig Beasley Department of Electrical and Systems Engineering Washington University in St. You can plot the output response using plot(t,y) and the state response using plot(t,x). Features The ExcelLink package provides: A set of Mathematica functions that allow you to: @Read and write data to Excel ranges. By default, MATLAB displays blanks lines in command window output. Once we have this we can start a subprocess kernel which will open a Mathematica front-end to interact with. Basic Vector Operations : We write vectors in Mathematica as a list of components. I will give the example below. Various manipulations of the data are also discussed. add-ons to Mathematica. If you use a 32-bit version of Mathematica 10. See Plotting Data , also. For example, compare the outcome of 1/2 * 2 with 1/ (2 * 2). This tutorial incorporates my personal preferences, which include the following: We’ll use Mathematica as a tool for graphics and numerical calculations, not (to any signi cant degree) for algebraic manipulations. But I was concentrating on the string, not considering it as part of a csv (which, as I went on to post, I don't think it should be). You may see a long string of output from your C compiler as the setup. through your code like Print statements, and the enclosing Reap will cause each one to output the net memory consumed in bytes between the previous use and the current one. SeeTeX[] is the same as. Objectives This section should consist of a few sentences written in your own words. WRITING YOUR OWN MATHEMATICA MODULE -- ALTERNATE EXECUTABLE MODULES See the Module Writer's Guide for more information on writing an 'alternate executable' module. It is used in many scientific, engineering, mathematical and computing fields, and is based on symbolic mathematics. 2: February2,2000) Contents 1 FirstThingsFirst 1. For now I always need to use Python to process a datafile created in Mathematica that format, because Mathematica always adds quotes " or multiple blank spaces or tabs. Mathematica identi es ALL built-in functions and commands by capitalizing the rst letter. If you type in the word qdot and it gets replaced with the symbol, you can typically use Command + z on a Mac, or ctrl-z on a PC product, and the symbol will revert to the characters. The blue line represents aggregate expenditure on domestically produced goods and services. }$ The equation and align environment The most useful math envorinments are the equation environment for typesetting single equationsand the align environment for multiple equations and automatic alignment:. Only use the special function to export or format your output. Features The ExcelLink package provides: A set of Mathematica functions that allow you to: Read and write data to Excel ranges. If you use a 32-bit version of Mathematica 10. 1 Characterization of Local and Global Variables The local and global variables in mathematica play an important role, and therefore care should be taken about these two types of variables when we write a program in mathematica. and put that a variable on a line by itself to signal explicit output. But it's much more—it's the only development platform fully integrating computation into complete workflows, moving you seamlessly from initial ideas all the way to deployed individual or enterprise solutions. First, you call OpenWrite or OpenAppend to "open the stream", telling Mathematica that you want to write output to a particular file or external program, and in what form the output should be written. FormCalc is a Mathematica package for the calculation of tree-level and one-loop Feynman diagrams. For Mathematica, I agree with the pros and cons listed by Yura Koroliov. In the Wolfram System's standard notebook interface, you are directly giving input and getting output every time you press Null. Serial monitor is used to see receive data, send data,print data and so on. MATLAB ® displays output in both the Command Window and the Live Editor. Note: this is NOT a forum for technical questions about non-FreeBSD operating systems!. Because of this interface, we have chosen Mathematica to assist students in learning linear systems theory. some_command | tee command. Draw the coordinate axes on this output by hand using the axes detailed in the Guidelines. Arduino Function Serial. Writing a CSV File. Mathematica is a powerful technical programming language developed by Wolfram Research. This is the only output (aside from exported files) that this notebook generates. You are trying to find the value of b. So let me see if I can write this in a little bit of a clearer way. Various manipulations of the data are also discussed. Mathematica, however, uses some non-standard notation which requires the user to translate back and forth between standard mathematics and Mathematica syntax. You can refer to these directly, as in Simplify[Out[32]]. Online Help. Also, Mathematica 6. Audio data to write, specified as an m-by-n real matrix, where m is the number of audio samples to write and n is the number of audio channels to write. 4: February 2, 2000) Applying computer technology is just a matter offinding. You can select one of two numeric display options in MATLAB. This page contains a number of scenes that accept CSV file inputs for visualization of robot trajectories. Together with the advancement of science and technology, technological innovations grew along with it, resulting to the emergence of new equipment and gadgets. Mathematica – Science topic. The following will take a fundamental frequency, generate a bell sound using harmonics, export it to a temporary file and play it in your system’s default audio player. In standard format, we would write this gradient as:. Each output node computes a sort of score for the associated category. The % symbol tells Mathematica to insert the output of the previous calculation. For more than 25 years, Mathematica has been the principal computation environment for millions of innovators, educators, students, and others around the world. The core functionality of a CAS is manipulation of mathematical expressions in symbolic form. In the Wolfram Language, exact input (like fractions) will provide exact output: (Use CTRL + / to enter fractions. GNU TeXmacs is a free scientific editing platform designed to create beautiful technical documents. If need be, write and debug a special function to export or format the output of your program. However, the reader is strongly encouraged to refer to the documentation center that is part of Mathematica. Suppose you, or someone else created a useful method or routine, that was producing some computation that you'd like to benefit from, but the routine was writing output to process principal device. The result will appear in an output cell. If you encounter any issues with a relatively modern operating system or a supported Mathematica /MATLAB version, please open a new issue at GitHub. Hopefully I’ve given you a good starting point for writing MapReduce algorithms using Mathematica and HadoopLink. The first machine learning algorithm is an autoencoder, w. A two-argument form giving is also implemented as Erf[z0, z1]. Sometimes I want to ask mathematica to plot or calculate something without given a certain value for it. OpenWrite["file"] opens a file to write output to it, and returns an OutputStream object. Writing a Mathematica command The input line above is an example of writing the definition of y as a cubic polynomial in x. Next, do the exercises on the handout. It performs symbolic manipulation of equations, integrals, differential equations, and most other mathematical expressions. output, to yield the states x1 and x2, as shown next: The first derivative of each state is the signal just back on the upstream side of each integrator. Each file contains 200 pairs of coordinates [x,y]. This is the way to go. The writing of the article was meant to show the sieves to get the primes, and also give you a quick overview of some of the properties of primes and the problems that are still unresolved. have moved to new projects under the name Jupyter. The Leontief model is a model for the economics of a whole country or region. By pre-conditioning the iterate a first order correction can be obtained which recovers the bulk of quantal oscillations missing in the zeroth order approximation. In math, a function is an equation with only one output for each input. Technology-enabling science of the computational universe. You can get MATHEMATICA to enlarge the picture by first clicking on the graphic output and then dragging one of the little black rectangles while holding down the left mouse button. You can export plots to files with the Export[] function:. With a text ‐ based interface, Print ends its output with a single newline (line feed). When Mathematica's output is published using the code style (either by wrapping with ` or by adding four spaces on the start of the line, or by wrapping with /), we publish explicit form of the output (approximately equivalent to InputForm): strings are always wrapped by quotes, numbers usually have ` at the end, etc. Features The ExcelLink package provides: A set of Mathematica functions that allow you to: Read and write data to Excel ranges. The basic command for sketching the graph of a real-valued function of one variable in MATHEMATICA is Plot[ f, {x,xmin,xmax} ] which will draw the graph of y=f(x) over the closed interval [xmin,xmax] on the x-axis. For example, if the input number is 12,. They will typically have their own style file which must be used, and often other requirements which Mathematica's output may or may not satisfy. Write a table to a file. m) file and load that into an interactive notebook with Get. GNU TeXmacs is a free scientific editing platform designed to create beautiful technical documents. In the Wolfram Language, rules associate symbols with values. In more advanced classes you'll learn about far more complex functions! However, a simple function might return the input plus one. We can begin learning about this. Mathematica¶ Description and Overview¶. where is the vector of state variables (nx1), is the time derivative of the state vector (nx1), is the input or control vector (px1), is the output vector (qx1), is the system matrix (nxn), is the input matrix (nxp), is the output matrix (qxn), and is the feedforward matrix (qxp). Samuelsons Keynesian cross diagram is an attempt to capture the essence of Keynes theory of effective demand. Wolfram Natural Language Understanding System. They can be used to give approximate solutions to hard problems such as Steiner tree and traveling salesman. Note that this time the variable type is a graph, rather than a number or array. results in the following output from Maple: 1 2 3 but it is easy to write a function that will 3 Mathematica This is a Mathematica translation of the code. would write it down, and it appears in Maple as it would when written in your textbook. This page is still under construction until everything is migrated from the old site. I am trying to include a Mathematica code in LaTeX. It will be helpful to write a statement that models the conjecture, and a module that uses the conjecture to do the various calculations. Linear Algebra in Mathematica Craig Beasley Department of Electrical and Systems Engineering Washington University in St. have moved to new projects under the name Jupyter. The IGraph/M package provides a Mathematica interface to the popular igraph network analysis and graph theory package, as well as many other functions for working with graphs in Mathematica. e an m- le) that asks the user for the mean and standard deviation of the Gaussian, and the number of points to generate. Tutorial for Mathematica & Wolfram Language. Mathematica sometimes produces output that is long and unnecessary. , using a trigonometric function-like convention), it is also common to write. Do not use Mathematica comments in interactive sessions; instead, alternate explanatory text using complete sentences with input/output pairs. I can't seem to get the output from this mess into a list, I know the code is poor, but it works. How to Write a Program in Mathematica: Basic Programming Principles If you look at the code of the creators of Mathematica's programming language, Stephen Wolfram (e. Editing, copying and pasting Mathematica equations via LaTeX Here is some information on how to convert formulas from Mathematica to LaTeX and vice versa (see also this post ). I can do it manually but its a pain with 1000+ values Thanks in advance for any help. Many Mathematica functions such as Solve or FindRoot return "rules" as their output. I searched Stack Overflow and googled for a way to do it, found a lot of ways to do it, but non of it worked. When you begin typing commands, you'll notice that brackets appear on the right side of the notebook. Mathematica applies expertise at the intersection of data, methods, policy, and practice to improve well-being around the world. There are two solutions to this problem. However, the reader is strongly encouraged to refer to the documentation center that is part of Mathematica. This exercise is to produce a histogram of a set of random numbers, distributed according to a gaussian. Now, in my defense, I have to explain that I had used the Mathematica REPL (read, evaluate, print loop) on code and never had any reason to write paragraphs of typeset text as notes to myself. To run these programs, first download them into a file with the. I have a question about Mathematica. Graphics are one of the most memory intensive aspects of Mathematica. But if I do so, I am not able to see the output of that command on terminal. I'm new to Mathematica and I am starting to work on its notebooks. 2: February2,2000) Contents 1 FirstThingsFirst 1. In such, the user can define rules as a way of doing algebraic replacements. For example, N[E]returns 2. Thus, the equation for a circle is not a function and you cannot write it in function form. This tutorial incorporates my personal preferences, which include the following: We'll use Mathematica as a tool for graphics and numerical calculations, not (to any signi cant degree) for algebraic manipulations. Introduction to Mathematica Commands Numerical approximation Mathematica returns exact answers whenever possible. m file when saved. In the output file, I want 27 = 3x3x3 rows. In Mathematica 10 at least, if you paste LaTeX code into the front end, Mathematica detects that it's LaTeX and offers to interpret it. Including favorites such as vi, Emacs, or, for Windows users, Notepad. For equations such as y = 3x – 2, the independent variable is x. New in Wolfram Mathematica 8: Free-Form Linguistic Input Basic Examples. Only use the special function to export or format your output. To write a paper in a Mathematica notebook is to reveal your results and methods at the same time; the published paper and the work that begot it. When I want to discuss my matrix output on StackExchange, I can use TeXForm: you can write it in. If you save it to a file, you can load it into a MATHEMATICA session. $\begingroup$ @yulinlinyu Perhaps, I interpreted the OPs use of "column" to mean that the output file should contain 2 columns. MATLAB ® displays output in both the Command Window and the Live Editor. Mathematica. Someone emailed me recently complaining that the ParallelTable function in Mathematica didn't work. To obtain the Mathematica code I just exported notebook as PDF. Mathematica is a fully integrated environment for technical computing. Written by Stephen Wolfram. Two other arch-typical data structure functions are constants, that always return the same thing either with no input or no matter what the input, and predicates, that take an input and. The default tab delimiter in. (a) Calculate and write out a table of function values for the function f(x) as xapproaches 0 (use Mathematica to calculate the function values but you can write out the table by hand on a separate piece of paper if it is easier). It’s le name should be something like getwfm. Individual instructions in the code can be assignment statements, iteration statements (loops), conditional (if), input or output statements, functions, or other programming constructs. It's often easy and natural to write mathematics using TeX, whereas it can otherwise be quite difficult to express clearly in plaintext notation. Write is a low-level Wolfram Language output function. Adjacency List; read_adjlist; write_adjlist; parse_adjlist; generate_adjlist. PLOTTING AND GRAPHICS OPTIONS IN MATHEMATICA In addition to being a powerful programming tool, Mathematica allows a wide array of plotting and graphing options. Grammarly allows me to get those communications out and. option to the command generating the graphics. How do I use the output of functions like Solve? Solve and other functions such as FindInstance , NSolve , and NDSolve return a list of rules. A rule is a mapping that defines a replacement operation. Now it is quite desirable to run jobs in background which take much time to finish and to do other works in. 4 Appendix A. Do not use Mathematica comments in interactive sessions; instead, alternate explanatory text using complete sentences with input/output pairs. Mathematica is renowned as the world's ultimate application for computations. Serial monitor is connected to the Arduino through serial communication. My mathematica output was originally a DiLog which I've interpreted in terms of the usual mathematica function PolyLog using the mathematica help notes online. It provides a unified and user friendly framework for editing structured documents with different types of content: text, mathematics, graphics, interactive content, slides, etc. Cool Way to Show Matrix Output in Mathematica Stack Exchange. I have three lists x, y, z and the output include all possible combinations of sums. The default tab delimiter in. To run these programs, first download them into a file with the. Mathematica also has tools for procedural programming, which is the style of programming used in Fortran, Pascal, and C. Each output in your session causes a seperate window to open on the screen and this window displays the T E X version of the output. When I want to discuss my matrix output on StackExchange, I can use TeXForm: you can write it in. Mathematica sometimes produces output that is long and unnecessary. GitHub is home to over 40 million developers working together to host and review code, manage projects, and build software together. It is also called the gate function, pulse function, or window function, and is defined by It is also called the gate function, pulse function, or window function, and is defined by. 0_01/jre\ gtint :tL;tH=f %Jn! [email protected]@ Wrote%dof%d if($compAFM){ -ktkeyboardtype =zL" filesystem-list \renewcommand{\theequation}{\#} L;==_1 =JU* L9cHf lp. It is standardized as ISO 14230-3. These are complex examples, I just need the syntax of writting a function. However, it does not address the other question: "which attributes of self does the function read". Chapter 08. The reader is encouraged to have a look at them as well. Someone emailed me recently complaining that the ParallelTable function in Mathematica didn't work. where is the vector of state variables (nx1), is the time derivative of the state vector (nx1), is the input or control vector (px1), is the output vector (qx1), is the system matrix (nxn), is the input matrix (nxp), is the output matrix (qxn), and is the feedforward matrix (qxp). Get the free "Definite Integral Calculator" widget for your website, blog, Wordpress, Blogger, or iGoogle. , Cellular Automata, of A New Kind of Science ) and Roman Maeder (see his superb books), you will see simplicity and organization. The output of the mediation package (single mediator) has given me an ACME that is negative and statistically significant, an ADE that is positive but not significant and a total effect that is neg. This feature is for programmers who are creating Mathematica packages. I didn't like the way it was included in my TEX code so I just thought of adding. To use the link from Microsoft Excel, you load the MathematicaLink add-in. through your code like Print statements, and the enclosing Reap will cause each one to output the net memory consumed in bytes between the previous use and the current one. After writing 2+2, hold down the Shift key and press Enter (this is abbreviated as Shift+Enter). Finally, J/Link comes with full source code. Quite often people wish to transfer data between these two applications or write code so that these two applications can use the functions of the other application or can communicate with each other. The Output Nodes. This notebook shows the three resulting formulas, none of which worked when I plugged in test values. I have two machine learning algorithms that deal with time series data. , using a trigonometric function-like convention), it is also common to write. Mathematica includes a large list of features for finding a solution to almost any problem. Here is my code. Mathematica Tips, Tricks, and Techniques When Things Go Wrong (and they will) MichaelA. If the command is the last command in thepipeline, the objects are displayed in the console. 1 Characterization of Local and Global Variables The local and global variables in mathematica play an important role, and therefore care should be taken about these two types of variables when we write a program in mathematica. However, the reader is strongly encouraged to refer to the documentation center that is part of Mathematica. The square brackets on the right edge of the window delineate cells, and each cell has in input and an output portion, also delineated by brackets with di erent forms. Mathematica works in the interactive mode by taking input at the In[number]:= statement and then performing the requested operation and giving the result in an Out[number] statement. You can format the output display using several provided options. It is especially important to explain the commands in a long interactive session as you go along rather than all at once at the beginning or end of the session. But I get a case of (2. (a)Write a parametric function and the Mathematica input needed to produce the following helix in Mathematica. Variables storing solutions of differential equation, returned as a vector of symbolic variables. You can format the output display using several provided options. It's much more natural to structure your programs as successive replacements that transform symbolic expressions. In summary, M's flexibility is both a pro and a con, entirely dependent on the size and complexity of the program being written. Consult Mathematica documentation for more complex output handling using i/o streams and Write[]. The IGraph/M package provides a Mathematica interface to the popular igraph network analysis and graph theory package, as well as many other functions for working with graphs in Mathematica. By itself it means nothing. 0, a major upgrade, has over 2200 of them. As in natural language, there are always many ways one can in principle express something. Note: this is NOT a forum for technical questions about non-FreeBSD operating systems!. This tells Mathematica to process your input. Other than this, one product which is a good alternative to Mathematica is SageMath. Internally, the toolbox can use a few more digits than you specify. Mathematica supports comments, even when you can "just write it into a plain text cell" because every programming language supports them. This screencast covers writing for loops using Mathematica. And then here we have, when x is 3, y is equal to-- so 5 and 1/4-- if I would write it as an improper fraction-- 4 times 5 is 20, plus 1 is 21. New in Wolfram Mathematica 8: Free-Form Linguistic Input Basic Examples. Which shouldn’t just make it easier for readers. These additional digits are called guard digits. Wolfram Natural Language Understanding System. I suppose that this way is uncivilized, and Mathematica should have a regular way to hide inner outputs. Really, nothing! I can already enter and store data in that type and write functions that recognize that type because "type" is just an arbitrary symbol used as a wrapper for a collection of contents, and Mathematica eats symbolic data for breakfast! We can proceed directly to teaching Mathematica what is special about the. Mathematica is a great computational tool, and the Notebook interface makes it an almost self-contained system for doing calculations and documenting your work. So, in every stable version of the module I have to put comments (* *) and delete them for gebugging. But more importantly, I would not use Mathematica to write a math report unless I was giving a demonstration and needed to imbed Mathematica code for the demonstration. DisplayFunction->Identity. Note that this time the variable type is a graph, rather than a number or array. Saving Mathematica Definitions in Encoded Form When you create files for input to Mathematica, you usually want them to contain only "plain text", which can be read or modified directly. Many Mathematica functions such as Solve or FindRoot return "rules" as their output. The definition of a function is based on a set of ordered pairs, where the first element in each pair is from the domain and the second is from the codomain.