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10 Mathematical Notations and Special Characters

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This section of Introduction to Wolfram Notebooks is about notations like special characters and notations used in mathematics. Much of this topic can be illustrated by considering various ways of entering this mathematical expression, which is a definite integral. One way of entering this expression is with palettes. Start by opening the Basic Math Assistant palette by choosing Basic Math Assistant under the Palettes menu. Each section of this palette shows a grid of buttons for pasting things into the notebook. There are keyboard commands for entering all of these things as well, which will be described in a moment, but we will start with the palette. All of the buttons that are needed for this input are in the section labeled Typesetting. Within this section, under the first tab are buttons for mathematical notations like fractions and exponents, and under the second tab are buttons for entering special symbols and Greek letters. Returning to the first tab, we can start by clicking the button that shows the definite integral, which enters into the notebook a template with empty boxes, called placeholders, for entering parts of the integral. The lower limit of integration is highlighted with a colored background, to indicate where input will appear. In this example, the lower limit of integration is 0, so enter 0, then press the TAB key to move to the next placeholder, which is the upper limit of integration. The upper limit of integration in this example is a special character, which is the mathematical symbol for infinity. To enter that symbol, click the second tab to open the grid of buttons for symbols and Greek letters, and enter the upper limit of integration, by clicking the infinity button in the palette. Then press the TAB key to move to the next placeholder in the template, which is the integrand. The first part of the integrand is an exponential, which is under the first tab. Pressing the button for an exponential enters that template. Then return to the second tab to enter the exponential <i>e</i> and press the TAB key to move to the next placeholder, which is the exponent. Now enter the exponent, which is –2<i>x</i>. Continuing to type at this point would enter more input into the exponent, but to continue with this example, it is necessary to get out of the exponent. The keyboard command to end the exponent and move to the enclosing expression is CONTROL+SPACE. So with the insertion point in the exponent, press CONTROL+SPACE and then finish entering the integrand. You could also move the insertion point out of the exponent by clicking the mouse outside of the exponent. Now press the TAB key to move to the next placeholder and enter <i>x</i> to complete the input. This is a live input and can be evaluated just like any other input to do that calculation and get a result. The input is still not formatted quite like the initial example. There are several differences in alignment and in the shapes of characters. Those differences are there because the example is shown in a format called TraditionalForm and the input that we just entered is shown in StandardForm. StandardForm can be converted to TraditionalForm by selecting the input and choosing Convert To ► TraditionalForm under the Cell menu. TraditionalForm looks more like traditional mathematics, which is frequently desirable, and the only reason that TraditionalForm isn't the default is that translating traditional mathematics into computer input requires a somewhat elaborate and nonuniform set of translation rules. For example, in StandardForm functions are shown with square brackets around the arguments, but in TraditionalForm function arguments are enclosed in parentheses. This use of parentheses is a potential ambiguity, however, because parentheses can also indicate arithmetic grouping and the computer cannot always guess correctly what the parentheses should mean in every situation. As a practical matter though, the rules for translating TraditionalForm input work pretty well. So if you prefer TraditionalForm, it is entirely reasonable to use it, and if it is only being used for display and not for input, than there is no real problem with it at all. This input and all of these notations can also be entered using keyboard commands. One way to learn about keyboard commands is by hovering the mouse over a corresponding button in the palette. For example, hovering the mouse pointer over the exponential <i>e</i> button in this palette gives a display called a tooltip that shows the name of the character, which is exponential <i>e</i>, and the keyboard command, which is ESCAPE+ee+ESCAPE. Typing ESCAPE+ee+ESCAPE on the keyboard enters the exponential constant <i>e</i> that came up in the example. There are also keyboard commands for mathematical templates. For example, under the tab for typesetting forms, hovering the mouse over the button for entering a definite integral shows the command ESCAPE+dintt+ESCAPE, which can be typed from the keyboard to get the definite integral template. The names of keyboard commands are chosen to have some logical way of remembering them. For example, the keyboard command for the integral character is ESCAPE+int+ESCAPE and the keyboard command for the definite integral template is ESCAPE+dintt+ESCAPE, where "d-i-n-t-t" is short for definite integral template. To continue with the input, enter the lower limit of integration, then press the TAB key to move to the upper limit of integration. The keyboard command for the infinity character is ESCAPE+inf+ESCAPE. Then press the TAB key to move to the integrand. ESCAPE+ee+ESCAPE enters the exponential <i>e</i> and CONTROL+6 gives a template for the exponent. On common keyboards the caret character, which is used in computer code for exponents, is on the key for the number 6, so a good way to remember CONTROL+6 for an exponent is that it is the CONTROL key and the key with the caret character on it. Then enter the exponent and press the TAB key to move to the last placeholder and complete the input. This input could have been entered in many different ways. For example, to enter the exponential rather than starting with the template, we can start with the exponential <i>e</i> character, select that character and then click the button for the template. This had the effect of inserting the exponential <i>e</i> character in place of the filled black square that is shown on the button. Several of the buttons in this palette have placeholders that are filled black squares rather than empty black squares. The filled black squares are selection placeholders, which work just like the empty square placeholders except that if something in the notebook is selected when one of those buttons with a filled black square selection placeholder is clicked, then the selected expression gets inserted in place of the selection placeholder. For example, the definite integral example could have been entered by starting with the inner expression. The button that was used earlier for entering the definite integral template does not have a filled black square selection placeholder, but there is a similar button in the Basic Commands section of the palette that does have a selection placeholder. To enter the input, select the expression and click the button, which inserts the selected expression in place of the selection placeholder. This template is also different in that it has descriptive placeholders that display as shaded boxes with reminders about the purpose of each part of the input. These descriptive placeholders work just like the empty box placeholders and can be filled in just as before to complete the input. All of these notations and special characters can be used in Text cells and in graphics and almost anywhere else in the notebook. For example, here is a Text cell with some mathematical notations within the text. This Text cell can be entered using much the same process as was used for entering input. Start with a Text cell and use either the palette or keyboard commands to enter mathematical notations. An important aspect of this Text cell is that the formatted mathematics is actually in a separate cell called an Inline cell. Clicking within the formatted mathematics changes the background color to highlight the Inline cell. To leave the Inline cell and continue entering text, you can either click beyond the Inline cell or press CONTROL+0, which is the keyboard command to end the Inline cell. In that example, the Inline cell was created automatically as soon as some notation other than text was entered, but in general it is necessary to first create a new Inline cell, which you can do by choosing Start Inline Cell from the Typesetting menu under the Insert menu, and right below that is End Inline Cell, which is the command that was used to end an Inline cell. The keyboard command for Start Inline Cell is CONTROL+9 and the keyboard command for End Inline Cell is CONTROL+0. So to enter another Inline cell, press CONTORL+9 to create the cell, then enter the fraction, press CONTROL+0 to end the inline cell and return to the enclosing text cell and complete the input. These notations can also be used in graphics. For example, this input uses the Epilog option to add a formatted label to a plot. The label is entered here just as it would be in any other input. Keyboard commands for special characters are referred to as aliases. Many common characters have aliases and often several aliases. For example, the tooltip for the Greek letter alpha shows that the long name of the character is the capitalized word Alpha, which can be entered by typing backslash, square bracket, followed by the long name, and as soon as the closing square bracket is entered, the display turns into the character. Characters can also be entered using tech or SGML names. For example, typing ESCAPE+BACKSLASH+alpha, which is the tech name for this character, and pressing the ESCAPE key a second time gives the same alpha character. The SGML name, which comes up in HTML documents, can be entered as ESCAPE, ampersand, then the SGML name of the character, which is also Alpha, followed by a semicolon and then pressing the ESCAPE key a second time to get the character. So if you already know character names from tech or from SGML, you can use those names to enter characters in Wolfram Notebooks. There are many thousands of special characters. At the bottom of each grid of characters in the basic math assistant palette is a button that opens the Special Characters palette, which is the same palette that is opened by choosing Special Character under the Insert menu. If you see a character like this one and would like to know how to enter it, you can select the character and choose Find Selected Function from the Help menu to bring up the documentation page for that character, which for this character shows the long name of the character, which is DoubleLongRightArrow and the Unicode number and the alias and some other information. Not all characters have aliases and some less common characters do not even have long names, but it is essentially always possible to enter a character as Unicode. For example, backslash, colon, followed by the Unicode number gives the double long right arrow character. That's the end of the examples for this section. You can find more information in the Wolfram documentation in this tutorial on two-dimensional expression input. This section covered the basic process for entering mathematics and special characters, but there are many details that can also be controlled involving things like the size and alignment of characters and ways to customize the formatting and customize the handling of various inputs. If your application requires that sort of control, you can find more information in the section on math typesetting options and tweaking and in links from this guide page on defining custom notation.

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Duration: 10 minutes and 46 seconds
Language: English
License: Dotsub - Standard License
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Posted by: wolfram on Feb 6, 2020

10 Mathematical Notations and Special Characters

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