Wolfram alpha syntax. Wolfram mathematica how to use, tungsten alpha graph online. Computing a definite integral

After the direct carrying out of the RC experiment, it is necessary to extract information from the obtained data not only qualitatively, but also quantitatively. For this, software packages such as PeakFit, Origin and others are usually used. One of them is Wolfram Mathematica.

The advantage of this software package is precisely batch processing data, that is, the ability to process sequentially, using one given initial condition, at once a large number of files with experimental data at different external parameters (temperature, pressure).

For convenience and accuracy of fitting, the obtained fitted data of one spectrum are simultaneously the initial data for the next one.

For convenience and to eliminate any ambiguities during batch processing of spectra, an external parameter (temperature, pressure) is read from the file name in the program. It should be specific - contain the temperature in Kelvin at which the experiment was carried out. The file name itself should be split into several parts, for example, using the "_" character.

An example of the text of a program written in Wolfram Mathematica for processing CD data:

When processing spectra, the choice of a model for fitting the contours plays an important role. Below is a program fragment that describes eleven fitting functions and two Bose - Einstein coefficients (nbes, nbeas - for the Stokes and anti-Stokes components):

* When using physical constants in calculations, there is no need to enter their numerical value. It is enough to connect the Physical Constants package at the beginning of the program using the following entry:

The most common and used in many works, due to its versatility, is the Lorentz model.

However, when describing the low frequency range of the spectrum, it is recommended to use the Harmonic trim function (damped harmonic oscillator function). In addition, when working with the Harmonic function, there is no need to separately take into account the Bose - Einstein temperature factor, since it is one of the components of this function. Below we describe two sample programs using the Harmonic and Lorentz fitting models:

1. An example of a program text using the Harmonic spectra fitting model:

Full text of the program:

Description of the program in steps:

Set (MyPath) and select (SetDirectory) the directory in which the folder with the files we need with the experimental data is stored

Select the type and extension of files (* .txt)

We form the output form to a file

Here we set the model to fit. The If condition is present due to the fact that there are two options for the Harmonic function (for the Stokes and anti-Stokes components)

Setting the initial data for fitting the first spectrum

i1, v1, w1 - intensity, frequency and width of the first line, respectively

i2, v2, w2 - intensity, frequency and width of the second line, respectively

c, b - baseline parameters (slope and level along the Oy axis).

The Sfrom, Sto, Szero values ​​determine

Sfrom and Sto - cut out the frequency interval for fitting (in this case, it is 0 - 130 cm -1)

Szero - the value on the ordinate, on which the abscissa is fixed.

…… - the beginning of the cycle

- end of cycle

In this case, files from 1 to 100 are involved in the cycle.

In this line, the file name is parsed into elements (using the two functions ToExpression and StringSplit) and the value of the variable T (temperature, pressure) is read from the file name (iName). It is worth noting that the file name must be specific - it must contain the temperature in Kelvin at which this experiment was carried out. The file name itself should be split into several parts, for example, using the "_" character.

Displaying the value of T.

Reading data from the selected file using the ReadList function and naming it FullData.

We select the data range we need using the Select function and name it Data.

FindFit is the basic fitting function in Wolfram Mathematica. The maximum number of iterations is 5000.

Output to the screen of the initial data (Epilog-> Point) by the Plot function, the obtained lines separately (If condition), the fitted spectrum (model / .fit)

AxesOrigin - the range of values ​​along the Ox axis

PlotRange - the range of values ​​along the Oy axis

PlotStyle - a set of plot parameters

Axes-> True - axis visibility

Thickness - line thickness

AxesLabel - axis labels.

Allocation of fitted values ​​by points (Evaluate function), according to data from the file (iName).

Calculate the difference between the fitted values ​​and the experimental data.

Displaying the Diff value - fitting errors (ListLinePlot function)

PlotRange - the range of values ​​along the Ox axis

AxesOrigin - the point of intersection of the axes

FillingAxis - filling the area under the chart with color.

Name the array of fitted values ​​tmp.

Supplementing the ResultData array with the tmp array at each step of the loop (Append function).

Display an array of tmp values.

End of the cycle.

Displaying the obtained values ​​in tabular form using the TableForm function.

2. An example of a program text using the Lorentz spectra fitting model:

The program described in this paragraph, in its structure, almost completely corresponds to the program described earlier, with the exception of the fitting model.

Due to the fact that when using the Lorentz fitting model, the Bose - Einstein temperature factor must be taken into account separately, a new fragment appeared in the program text.

An array of numbers named BoseFactor is specified. It is filled with zeros, has two columns and the number of rows is the same as the FullData array.

An array of elements Eva1 is set, which is the Bose - Einstein factor for the Stokes component of the spectrum (calculated for each point of the FullData array (experimental data array)). X-> FullData [] means that in the expression Eva1 the variable x takes all the values ​​of the first column of the FullData element array.

An array named Diff1 is calculated using the Eva1 array (Bose - Einstein factor). This entry means that the second column of the FullData array is elementwise divisible by an array of Bose - Einstein factors.

- assigning values ​​to each column of the BoseFactor array. the first column is equal to the first column of the Fulldata experimental dataset. The second column is assigned the Diff1 value. Diff1 has the meaning of the intensity at each point in the experimental spectrum multiplied by the inverse Bose - Einstein temperature factor.

- selection of the spectral range of interest to us using the Select function. A similar line is also present in the text of the program presented in A.1, but the original array is the experimental data array FullData.

The program described in this section

Wolfram alpha

Wolfram Alpha is a system designed to store, process and serve structured data to users on demand in natural English language... Wolfram Alpha is not a search engine. This is due to the fact that it is not intended for automatic processing of unstructured texts. For its operation, you must first manually enter factual information into the database, as well as develop and implement algorithms for its processing. These procedures are performed manually by the Wolfram Alpha community of developers and experts.

From the analysis of the description of the system, the Wolfram Alpha system, it follows that the receipt of answers by the Wolfram Alpha system should:

- be able to correctly parse the user's request in natural language;

- have appropriate structured factual information;

- have algorithms for processing factual information, ensuring the formation of a response to a user's request.

Thus, the Wolfram Alpha system is automatically capable of processing only the manually structured factual information stored in the DBMS. Deterministic sampling algorithms can be used to synthesize responses additional information and calculations based on factual data. According to these formal characteristics, the Wolfram Alpha system can be attributed to the well-known class of Business Intelligence systems. Systems of this class are highly specialized, which leads to a small range of questions that can be answered by the Wolfram Alpha system. This limitation is systemic, since it is incorporated into the concept of its functioning.

Thus, the Wolfram Alpha system fundamentally does not allow users to search for answers to any questions they are interested in. For this, question-answer search engines are intended. Unlike the Wolfram Alpha system, question-and-answer search engines automatically identify factual information in processed texts and index it without human intervention. Due to this, a significant increase in the completeness of the search is achieved. For generalization, inference and synthesis of answers, question-answer search engines also use the rules for processing factual information. However, unlike the Wolfram Alpha system, logical processing rules are not separate algorithms aimed at solving predetermined relatively simple tasks, but logical rules that can be automatically applied in a dynamically generated sequence that determines the order of processing primary factual information and forming an answer to a user's question. To verify these provisions, we will conduct a comparative testing of the Wolfram Alpha and AskNet.ru systems.

35 Commands That Showcase Where Wolfram Alpha Is Better Than Google

Methodology for comparative testing of Wolfram Alpha and AskNet.ru systems

For objective testing of the Wolfram Alpha system, a collection of questions from the TREC 2003 Q&A track was taken (http://trec.nist.gov/data/qa/2003_qadata/03QA.tasks/test.set.t12.txt). This is due to the fact that these test questions are quite general in nature and can be used to test question-answer search systems operating on the Internet. Unlike other test tracks of the TREC conference question-answer search, the used test cases of the TREC 2003 conference are not tied to test collections of documents and are not grouped into thematically related sequences of questions. Test collections of the ROMIP seminar were not used due to the fact that they are intended to assess the quality of search in Russian, and the Wolfram Alpha system does not work with Russian-language user requests - “Wolfram Alpha does not understand Russian at the moment”. Testing was carried out by sequential entry of queries from the test collection of the TREC 2003 conference. The systems were tested on the first 71 test cases out of 500 available in the collection of the TREC 2003 conference. This was due to the receipt of test results that clearly reflect the characteristics of the systems and allow you to formulate reliable conclusions.

Results of comparative testing of systems Wolfram Alpha and AskNet.ru

Generalized results comparative testing systems Wolfram Alpha and AskNet.ru are presented in the table.

Detailed information on test cases is given in the appendix. In total, 71 test cases were performed.

When analyzing the issue of question-and-answer search engine AskNet.ru kept track of the presence and position number of the correct answer. The average value of the position of the correct answer on the page, if the answer was found, is 1.63. This means that, on average, the correct answer was in the first or second place in the question-answer search engine AskNet.ru.

The Wolfram Alpha system in 57 cases could not determine the meaning of the user's request and issued the message “Wolfram Alpha isn’t sure what to do with your input”. In three test cases, the Wolfram Alpha system brought up a dialog for clarifying the semantic content of the query entered by the user.

Online charting service

This service was created to help schoolchildren and students in the study of mathematics (algebra and geometry) and physics and is intended for online graphing of functions (conventional and parametric) and graphs by points (graphs by values), as well as graphs of functions in polar system coordinates.

Just enter the function formula in the "Graphs:" field and click the "Build" button.

WolframAlpha

Read the Help for how to enter function formulas correctly.

Take a look in the examples section, for sure, there are function graphs that are similar to what you need, you just need to slightly correct the ready-made function formulas.

Additionally, on our website, you can use the matrix calculator, with which you can perform various transformations and operations with matrices online.

Feature List

Name	Description
log base 2 of x
log base 10 of x
logarithm base b log (x; 3)
natural logarithm (log base e (2.71828 ...)) of x
exponent of x (e to the power of x)
square root of x
sign function: -1 if x<0, 1 если x>0 and 0 if x = 0
Trigonometric functions
sine x
cosine x
or	tangent x
or	cotangent x
or	arcsine x
or	inverse cosine x
or	arctangent x
or	arc cotangent x
or	hyperbolic sine x
or	hyperbolic cosine x
or	hyperbolic tangent x
or	hyperbolic cotangent x
hyperbolic arcsine x
hyperbolic inverse cosine x
arctangent hyperbolic x
hyperbolic arc cotangent x

Built-in constants

Download free Wolfram Mathematica 10.0.2 for MS Windows 2000 / XP / Vista / 7/8

A reasonable question is why this particular system?

Because principles are important! More than 25 years of development based on bold, innovative design principles, and as the apotheosis - Wolfram Mathematica, the most powerful computing platform.

Automation... The key to all productive computing. The fundamental difference Wolfram Mathematica- the use of intelligent automation in all parts, without exception, from the choice of algorithms to the derivation of graphs and construction user interfaces... As a result - obtaining high-quality final results without the need for algorithmic knowledge, plus performance even with expert use.

Integrated universal platform. Special programs and additional toolboxes hinder the creative development of new ideas and directions, and their cost is even higher than their face value. For the Wolfram Mathematica system to work, no additional packages are needed, which means no unnecessary costs. The program contains specialized functions of many technical areas, such as computational biology, wavelet analysis, etc.

Hybrid symbolic-numeric methodology.

Wolfram alpha

Usually symbolic and numerical computation is considered separate, and this is detrimental to users. In Mathematica, they are both tightly integrated, which makes it possible to build hybrid methods for quickly solving various types of problems and at the same time guarantees results with combinations of values ​​of arbitrary accuracy.

Multiparadigm language.

There are many languages ​​and programming styles, but none of them is ideal for all tasks. Mathematica differs from standard programming languages ​​by supporting a large number of programming paradigms at the same time: procedural, functional, rule-based or pattern-based, and many others.

Embedded information... Searching for various data in standard databases, as well as their constant updates, take a lot of time and distract from the main work. Mathematica compares favorably with other programs with a huge collection of carefully selected data of various types, which are periodically expanded and updated.

Workflow with documentation... During extensive work with electronic documentation, it becomes necessary to use several programs: for processing, for visualization, for interactive presentation ... Mathematica includes all the elements of this working project, plus interactive applications - together in uniquely flexible documents.

An online mathematical processor, a knowledge processor that, at your request, provides data about the world around you in numbers.

It all looks very simple - you enter your query in the search field, press the "=" button, you get the result:

In fact, WolframAlpha provides free and unlimited access to its knowledge base, which includes a huge amount of information about our world in numerical terms. Demography, economics, history, linguistics, physics, biology, chemistry ..., and of course MATHEMATICS - mathematical rules, formulas, algorithms - there is all this, and much, much more.

For math students, WolframAlpha is a godsend. This web service easily solves equations and systems, plots functions, calculates limits, finds derivatives, takes integrals ...

It looks like it's hard to find a problem that WolframAlpha can't handle. You just need to correctly formulate your request. By the way, although WolframAlpha uses a special syntax, as in other systems of computer mathematics, however, it understands quite well the usual questions asked in ordinary English. For example, you might ask WolframAlpha: “How many students are in Russia now?” Are you wondering what WolframAlpha will answer?

How do I use WolframAlpha? Short description service capabilities in Russian is possible.

To get to know WolframAlpha in detail, and to learn more about how to use this service for mathematical calculations, you should look at the only web resource where the mathematical capabilities of WolframAlpha are detailed, accessible and systematically described in Russian - this is the Wolfram | Alpha blog in Russian.

This blog, while the only one of this kind, is probably also because competent and Full description mathematical capabilities of WolframAlpha is a rather difficult task for students (enthusiasts or moneymakers) (even very good ones!), who usually take the trouble to place and maintain mathematical resources on the Runet. What's more, WolframAlpha's math skills, which start at the most rudimentary, extend too far beyond the standard university math course. I think they can be compared without a stretch to the mathematical abilities of Stephen Wolfram himself, the developer of the Mathematica system and the mastermind of WolframAlpha.

These abilities are partly illustrated by examples of solving problems from different areas of mathematics posted on the service support site.

Take a look at how WolframAlpha solves a system of two nonlinear algebraic equations of equations x ^ 2-2y + 1 = 0, x ^ 3 + y ^ 2 = 6:

Since the WolframAlpha math engine works on the basis of algorithms from the well-known computer mathematics system Mathametica, these results can be completely trusted.

The knowledge base from which WolframAlpha draws its abilities is constantly updated with relevant materials, factual and numerical data, algorithms - every day WolframAlpha is becoming "smarter"! The capabilities of this system best allow you to evaluate numerous examples of its use from different fields of knowledge.

Among other things, WolframAlpha offers a variety of math products: free website widgets, inexpensive mobile math apps for installing on students' smartphones, add-ons and plugins for major browsers, developer tools, and more.

For example, for ease of use, you can embed a Wolfram Alpha query box on your site. But if you have already appreciated the capabilities of Wolfram Alpha, then for sure you want to have this tool always at hand. It is enough to install in your browser suitable extension, toolbar or plugin from among those offered by the official Wolfram Alpha website. With them, you can turn to Wolfram Alpha at any time. More on this.

Recently, WolframAlpha has started using a new math document format - CDF. It is a format that allows you to create documents that contain interactive math objects. For example, as such, there can be graphs of functions, differential equations etc. The user can change the parameters of such objects using the controls built into the document, while simultaneously observing the changes taking place (similar to the GeoGebra Java applets). Based on this format, as well as the Wolfram Alpha widgets, you can, for example, create dynamic illustrations of mathematical rules and algorithms, conduct research, and laboratory classes in mathematics.

Get to know Wolfram Alpha immediately if you haven't already!

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If this post solved your problem or you just liked it, share the link to it with your friends on social networks.

One of these code variants must be copied and pasted into the code of your web page, preferably between the tags and or right after the tag ... According to the first option, MathJax loads faster and slows down the page less. But the second option automatically tracks and loads the latest versions of MathJax. If you insert the first code, then it will need to be updated periodically. If you insert the second code, the pages will load more slowly, but you will not need to constantly monitor MathJax updates.

The easiest way to connect MathJax is in Blogger or WordPress: in your site's dashboard, add a widget designed to insert third-party JavaScript code, copy the first or second version of the loading code presented above into it, and place the widget closer to the beginning of the template (by the way, this is not necessary at all because the MathJax script is loaded asynchronously). That's all. Now, learn the MathML, LaTeX, and ASCIIMathML markup syntax, and you're ready to embed math formulas into your website's web pages.

Another New Year's Eve ... frosty weather and snowflakes on the window pane ... All this prompted me to write again about ... fractals, and what Wolfram Alpha knows about it. On this occasion, there is interesting article, which contains examples of two-dimensional fractal structures. Here we will look at more complex examples of 3D fractals.

A fractal can be visualized (described) as a geometric figure or body (meaning that both are a set, in this case, a set of points), the details of which have the same shape as the original figure itself. That is, it is a self-similar structure, considering the details of which with magnification, we will see the same shape as without magnification. Whereas in the case of a regular geometric shape (not a fractal), when we zoom in, we will see details that have a simpler shape than the original shape itself. For example, at a high enough magnification, part of the ellipse looks like a line segment. This does not happen with fractals: at any increase, we will again see the same complex shape, which will repeat over and over again with each increase.

Benoit Mandelbrot, the founder of the science of fractals, wrote in his article Fractals and Art for Science: “Fractals are geometric shapes that are as complex in their details as in their general form. part of the fractal will be enlarged to the size of the whole, it will look like a whole, or exactly, or perhaps with a slight deformation. "

Intelligent "knowledge computation engine". Unlike traditional search engines, which provide links to various sites, Wolfram Alpha service independently analyzes the user's requests and provides him with relevant information.

Wolfram Alpha will answer all questions
For example, if you enter the name of a settlement as a search query, the user will be shown the number of its inhabitants, location on the map, weather, local time, names of nearby large cities, etc. All this data can be downloaded to a PC as a PDF document.

Also Wolfram alpha intended for scientific use. By entering the name of a species of animal or plant world, you can get a lot of different scientific data about it. In addition, the service can be used to analyze various trends and many other purposes.

Basically, Wolfram alpha can be called a search engine. After all, he really looks for information by processing a user request. However, the search results for Wolfram Alpha and, for example, Google, differ like heaven and earth, despite the Alpha version of the service and the relatively small base that has Wolfram alpha, the service may interest the user with some of the features that he provides as a result of a request to him.
So, an ordinary search engine searches the Web for an already existing answer to the question posed. And if no one has asked a similar question before and there is no answer to it on the Internet, then the user will be left with nothing - which, on the one hand, is a disadvantage of conventional search engines (they have a large search base and issue results simply by giving relevant information to the user), and Wolfram alpha draws conclusions based on complex mathematical analysis and has the functionality of practically “Mathlab”.

And of course the search results Wolfram alpha is very different from the search engines we are used to (Google, Yandex, etc.), it does not have the usual links for everyone. The system processes the received data and, using millions of algorithms, formulates its own answer to the question posed. As a result, the user sees this very answer, which, perhaps, consists of only a couple of words or numbers - just what we sometimes need.

For example, you can ask: "How old is the singer Madonna?" I wrote simply

In response, the system will report the age to the exact day.

Alas, Wolfram Alpha doesn't know all the big names, but I hope it does.

The functionality of Wolfram Alpha is not limited to finding answers to the questions posed. Using this system, you can, for example, build graphs and compare various data, which is much clearer and better perceived than just text. In addition, with the help of Wolfram Alpha, you can perform mathematical operations, both elementary (which Google does without problems), and solve equations of varying complexity. Wolfram Alpha also knows how to graph functions, calculate sine or cosine values, and so on.

For example, you can solve the following equation:

but for example, you can find out what is the distance between Moscow and Tel Aviv, I entered into the field

Moscow to Tel Aviv

And here's the result:

One of the downsides of the Wolfram Alpha service is its English language ... so if you want to ask a question, the system will have to write it in English. It is not even known if Russian version this search and computing system.

With Wolfram Alpha, you can compare almost anything, you just need to enter a question into the search bar: books, comics, TV shows, films, and even fictional characters - any pop culture product. This is done by a standard request of the form x vs y... For example, the query result AC / DC vs ABBA can be seen in the screenshot above.

Calculating parameters for camera setup

Those who use cameras with a sufficient number of settings (including smartphones) often need to calculate the values ​​of certain parameters: ISO, contrast, brightness, focal length, and others. Wolfram Alpha can help with this difficult endeavor.

Clarification of the terms of family relationship

Unfortunately, it only works for English. But how simple: you do not need to invent anything, you just need to enter the necessary sequence of terms: the sister of the uncle's father's cousin. And the system will not only tell who such a distant relative is, but will also present the information in the form of a simple diagram.

Calculating your blood alcohol level

Of course, approximately, but how else can you calculate this without instruments? The search query in this case will look ridiculously simple: "weight growth quantity in time". Weight is in pounds and height is in inches. Under the amount drunk, you need to indicate the amount of alcohol in the form of drinks, shots, pints - Wolfram Alpha will itself estimate what you drank and what degree it was. And then he will tell you after what time the alcohol will be completely removed from the body.

Converting shoe sizes

Wolfram Alpha is capable of instantly transferring data from one system to another. This function works not only with engineering and physical units of measurement, but also with the dimensional grid of clothing or shoes. And there is no need to remember where the corresponding plate is saved if you have a smartphone and access to the Internet. Example request: US men's size 8.5 shoe in france size.

Calorie counting

The system copes with this task outrageously simply. Enter the quantity and name of the product and get a detailed report on the content of calories, proteins, fats, carbohydrates and even vitamins. Unfortunately, the names of the products must be in English - the phrase "15 plates of buckwheat with meat" is not recognized by Wolfram Alpha.

Popularity of names

Choosing a nickname for your dog? You can use search query of the form "name name". The system will issue detailed information about how popular this name is, where it is most common and in what years it was most often used.

Exchange rates

Of course, every search engine knows this. But not everyone immediately gives out the result, what is the current value of a certain amount of the currency of a particular country. And Wolfram Alpha can do this for the query "country, amount, year" (by country, we mean the country whose currency you are interested in). The best way calculate real inflation.

Tuning a musical instrument

You no longer need tuners and separate apps to tune your instruments. Wolfram Alpha makes it easy to enter the desired note, for example, and listen to the sound. At the same time, the capabilities of the mathematical search engine approach the functions professional programs for customization (like Guitar Pro). A very handy feature that works on any platform, as long as there is a browser.

As you can see, mathematical calculations can simplify our life a little. Maybe you know some other handy tricks for working with Wolfram Alpha? Let us know in the comments.