Equations

1. Click in text where you want to insert the equation. If the text is in a rotated text frame, unrotate the frame first by selecting the rotated text frame and pressing Esc g 0 (zero).

2. Choose Insert > Equations.

3. On the Equations pod, choose one of the New Equation commands from the Equations pop‑up menu. Small, Medium, and Large specify the font sizes used in the new equation.

   A new equation object appears as a question mark in a frame anchored below the line with the insertion point. The first math element that you insert replaces the question mark prompt.

   New inline equation
   

   

   
   

4. Insert the math elements in the equation by typing the elements or by clicking items on the Equations pod.

   Inserted elements
   

   

   
   

5. Choose Shrink-Wrap Equation from the Equations pop‑up menu. This option shrinks the frame around the equation and places the equation in the line of text at the anchor symbol.

   Shrink-wrapped inline equation
   

   

   
   

6. If the equation seems too close to the text on either side, insert a space before or after the frame. FrameMaker treats the frame that contains an inline equation as a character and doesn’t provide extra space around it.

7. If the equation is too tall for the line, open up more space above or below the line. Use the Line Spacing pop‑up menu on the formatting bar to turn off fixed line spacing.

1. Click in an empty paragraph.

2. Apply a paragraph format from the Paragraph Catalog, or set up your own format. The paragraph format determines the alignment, vertical spacing, and any autonumber for the paragraph that contains the equation.

   Tip: If you created the document from a book or report template, use the Equation paragraph format. You can also copy this format to your document, but you’ll probably want to make some changes (for example, to the Default Font and Spacing properties).

3. Click the Equations button at the right side of the document window.

4. On the Equations pod, choose one of the New Equation commands from the Equations pop‑up menu. Small, Medium, and Large specify the font sizes used in the new equation.

   A new equation object appears as a question mark in a frame anchored below the empty paragraph. The first math element you insert replaces the question mark prompt.

   New equation in anchored frame
   

   

   
   

5. Insert the math elements in the equation by typing the elements or by clicking items on the Equations pod.

   Inserted elements
   

   

   
   

6. Choose Shrink-Wrap Equation from the Equations pop‑up menu. This option shrinks the frame around the equation and places the equation in the empty paragraph.

   Shrink-wrapped equation in its own paragraph
   

   

   
   

1. Click the Equations button at the right side of the document window.

2. Select a graphic frame or an object in a graphic frame.

3. On the Equations pod, choose one of the New Equation commands from the Equations pop‑up menu. Small, Medium, and Large specify the font sizes used in the new equation.

   A new equation object appears as a question mark inside the frame. The first math element you insert replaces the question mark prompt.

   New equation object
   

   

   
   

4. Insert the math elements in the equation by typing the elements or by clicking items on the Equations pod.

5. To place the equation exactly where you want it, first select it by control-clicking the equation.

6. Move the equation by doing one of the following:

   • Drag it with the mouse.

   • Move it with the arrow keys.

   • Position it precisely with the Graphics > Object Properties command.

1. Select an expression or place the insertion point in an equation.

2. Do any of the following:

   • To insert a math element by using the Equations pod, click the element.

   • To insert an alphanumeric character or a symbol that appears on the keyboard, type it. You can type parentheses, brackets, plus signs, equal signs, and so on. If you type an open parenthesis, FrameMaker inserts the closing parenthesis.

   • To insert an element by typing a backslash sequence, type a backslash ( \ ) and the string that identifies the element, and then press Return. For example, to insert the symbol for infinity , type\infty  and press Return.

   • Insert a custom math element.

   If an element needs one or more operands, a question mark prompt appears for each operand; otherwise, an insertion point appears. To move from one operand to another, press Tab.

A text string is a series of characters that is interpreted as a unit. Unlike characters that make up an expression, the characters in a text string don’t usually appear in italics and aren’t multiplied together.

A. Text strings

Text strings have no mathematical meaning in FrameMaker. For example, evaluation commands can evaluate the function tan but not the string “tan”.

1. On the Symbols page of the Equations pod, click Start String. Two double quotation marks ( " " ) appear. You can also type an apostrophe ( ' ) or a double quotation mark (") to start the string.

2. Type the text of the string. The quotation marks disappear, and the text appears as you type. To insert a straight apostrophe or straight double quotation mark as part of the string, hold down Control while pressing the key.

3. Click End String on the Symbols page or press Return.

An equation object usually contains one equation or expression. You can set up a horizontal or vertical list in which several expressions are contained in the same object. When you select a list, all the expressions in the list are selected as one object.

A. Horizontal list B. Vertical list aligned on equal signs

FrameMaker aligns the expressions in the list automatically. When you move the list, all the expressions maintain their relative positions.

1. Select the expression you want to be the first item in the list or to add to a list.

2. On the Operators page of the Equations pod, click the horizontal list element or vertical list element . To add a math element, type the elements or click items on the Equations pod. A horizontal or vertical list appears. The selected expression appears as the first item in the list. A second item appears in the list as a question mark prompt.

   Before clicking	After clicking

In the first example, a horizontal list is inserted. In the second example, a vertical list is inserted, and the selected expression becomes the first item in the list. In the last example, a vertical list is inserted as part of a larger expression.

The Symbols page on the Equations pod contains the Greek alphabet, other symbols, and diacritical marks.

The Symbols page doesn’t include Greek letters that have Roman-alphabet equivalents, such as the uppercase alpha (A). The following examples show the result of clicking on the Symbols page.

Diacritical marks appear on the element to the left of the insertion point or on the selected expression. Click the dot or prime button once for each dot or prime diacritical mark you want to insert.

The Operators page on the Equations pod contains commonly used operators, roots, powers, signs, subscripts, superscripts, and logic symbols.

If an expression is selected when you insert the operator, the expression becomes the first operand. The following examples show the result of clicking the plus sign or the division operator on the Operators page.

You can represent the division operator as a slash (/), a horizontal bar , or a division sign .

FrameMaker can evaluate exponents mathematically, but not superscripts.

A. Superscript B. Exponent

The Large page on the Equations pod contains sums, products, integrals, intersections, and unions.

If an expression is selected when you insert a large element, the expression becomes the first operand. The following examples show the result of clicking the summation symbol on the Large page.

You can add an operand after inserting a math element from the Large page.

The Delimiters page contains delimiters such as parentheses, brackets, and curly brackets.

If an expression is selected when you insert a pair of delimiters, the expression is placed inside the delimiters. The following examples show the result of clicking the parentheses on the Delimiters page.

You can also represent parentheses as brackets ([ ]) or curly brackets ({ }).

The Relations page contains relation symbols such as =, <, >, , , , , and .

All relation symbols—except the binary equal sign —apply to the character to the left or right of the insertion point or to the selection. When you insert a relation symbol between multiplied elements, it applies to the elements on either side of the insertion point.

Binary equal signs appear to the right of the current expression (as shown in the second example). When the insertion point or selection is in a subscript or superscript, the equal sign appears in the subscript or superscript.

The Calculus page contains integrals, derivatives, partial derivatives, gradients, and the limit function.

If an expression is selected when you insert the calculus element, the expression becomes the first operand. The following examples show the result of clicking the integral symbol on the Calculus page.

You can change the position of operands and add operands.

The Matrices page contains elements for matrices ranging in size from 1 by 1 to 3 by 3. After creating a matrix, you can add rows and columns.

If an expression is selected when you insert the matrix element, the expression becomes the first cell in the matrix.

The Functions page contains trigonometric, hyperbolic, and logarithmic functions, and also the sign, limit, and general functions.

FrameMaker places functions at the insertion point or at the selection. When an expression is selected, the expression becomes the argument of the function—except for the limit and general functions and . The following examples show the result of clicking the sin function on the Functions page.

In addition to inserting math elements that are built in FrameMaker, you can insert custom math elements that have been defined for a document.

Custom math elements have no mathematical meaning in FrameMaker. For example, a custom math element for an operator is treated as an operator in an equation. However, FrameMaker cannot evaluate it.

1. On the Equations pod, choose Insert Math Element from the Equations pop‑up menu.

2. Select the element name and click Insert.

• Press the spacebar. The selection expands to include the next higher expression. The following example shows the result of pressing the spacebar repeatedly.

  Original selection
  Pressed once
  Pressed twice

• Do one of the following:

  • To change the selection to the next subexpression on the right, press the Right Arrow key.

  • To change the selection to the next subexpression on the left, press the Left Arrow key.

  • To change the selection to the next question mark prompt, press Tab.

1. Select the element you want to delete and press Delete. A question mark prompt replaces the element.

2. Do one of the following:

   • To replace the element, click the Equations pod or type to insert the replacement.

   • To delete the element, press Delete again. FrameMaker removes any elements that are no longer necessary—for example, a plus sign or parentheses.

   • Control-click the equation to select the equation, and press Delete.

After entering or editing an equation, you sometimes end up with extra delimiters—parentheses, curly brackets, and brackets. You can remove extra delimiters. If you later use evaluation commands, FrameMaker evaluates the equation as if the delimiters are still present.

• To remove all delimiters, select the expression. On the Delimiters page of the Equations pod, click Remove Parentheses.

  Before clicking	After clicking

• To remove one delimiter, place the insertion point to the right of the delimiter and press Delete. If the delimiter has a mate, such as the left parenthesis between a and b in the example, the mate is also removed.

  Before	After

You can represent some math elements in more than one way. For example, delimiters can appear as , , or . Division can appear as , , or .

1. Select the entire element.

2. On the Operators, Large, Delimiters, or Calculus page of the Equations pod, click Toggle Format. The command is the same on all four pages and operates on any element with multiple formats. Click more than once to get the format you want in some cases.

Radical symbols, gradient symbols, and logarithms can have one or two operands. Integrals and other symbols on the Large and Calculus pages can have one, two, or three operands.

Operands

You can add operands to these elements without starting over.

1. Click or select anywhere in the expression with the element.

2. Click Add Operand on the Large or Calculus page. A question mark prompt appears where you specify the new operand.

You can change the number of rows or columns in a matrix and add or remove brackets around the matrix. You can allow the column width to vary from column to column, depending on the contents, or specify that all columns are equal width. Similarly, you can allow the row height to vary from row to row.

You can also transpose a matrix and perform matrix algebra.

• To add a row or column to a matrix, place the insertion point in the matrix. On the Matrices page of the Equations pod, choose Add Row or Add Column from the Matrix Commands pop‑up menu.

  Before Add Column	After Add Column

  Add Row adds a row at the bottom.

  Add Column adds a column at the far right.

• To delete a row or column from a matrix, select the row or column and press Delete.

• To add or remove brackets around a matrix, select the entire matrix. On the Matrices page of the Equations pod, click Add/Remove Brackets.

• To change the row height or column width in a matrix, select the matrix. On the Matrices page of the Equations pod, choose All Equal or Proportional from the Matrix Row Height or Matrix Column Width pop‑up menu.

Equal row heights (left) and Proportional row heights (right)

If you choose Proportional, each row is tall enough to hold the tallest cell in the row. Each column is wide enough to hold the widest cell in the column.

If you choose All Equal, each row is tall enough to hold the tallest cell in the entire matrix. Each column is wide enough to hold the widest cell in the entire matrix.

A math element type indicates how the element behaves in relation to other elements around it. For example, a plus sign (+) has the type infix, which means that it has two operands, one to the left and one to the right.

You can define custom math elements of the following types.

You cannot define custom math elements of the following types.

1. Choose View > Reference Pages and display a FrameMath reference page.

   If the document doesn’t contain a FrameMath reference page, display a reference page and then choose Insert > Add Reference Page. Name the new page FrameMath1. Capitalize the letters F and M as shown.

2. Use the Graphic Frame tool to draw an unanchored graphic frame on the page.

3. In the Frame Name dialog box, enter a name for the math element. If you are redefining a built-in element, enter that element name.

4. Use the Text Line tool to add a text line in the graphic frame.

5. Create the math element in the text line using the following guidelines:

   • You can type any characters in the text line, and you can change the character format. You can also move the characters by using micropositioning shortcuts.

   • For all math elements except delimiters, the text line represents just the mathematical symbol, not the operands. When you later insert the element in an equation, FrameMaker places the operands in the appropriate places, based on the type of math element. For example, a large element, such as a summation or an integral sign, has up to three operands—one above, one below, and one to the right of the symbol.

   • A custom delimiter can contain only one operand, even though some built-in delimiters contain two or three. To indicate the location of the operand, insert a space in the text line. If you do not insert a space in the text line, FrameMaker places the operand between two copies of the delimiter.

     A. Characters in delimiter.  B. Space indicates the operand.
     

     

     
     

   • FrameMaker uses the first text line in the frame for the custom math element. Make sure that only one text line exists in the frame.

6. Select the graphic frame.

7. On the Equations pod, choose Add Definition To Catalog from the Equations pop‑up menu.

8. If you’re defining a custom math element, choose an element type from the pop‑up menu, and click Add.

1. Place the insertion point in an equation.

2. On the Equations pod, choose Insert Math Element from the Equations pop‑up menu.

3. Turn off Show Custom Only, and then scroll through the element names to find the one you want.

4. Click Cancel.

1. Display the FrameMath reference page that contains the math element by doing one of the following:

   • If the custom math element appears in an equation, select the element, and choose Update Definition from the Equations pop‑up menu on the Equations pod. Then click Go To Frame.

   • If you haven’t inserted the custom math element into an equation, choose View > Reference Pages. Then display the FrameMath reference page you want.

2. Do one of the following:

   • Edit the text line that defines the math element. When you display a body page again, FrameMaker uses the modified definition, and shrinkwraps the equations again.

   • Delete the graphic frame. If the element appears in an equation, FrameMaker displays the element name, surrounded by question marks, instead of the element.

FrameMaker positions math elements according to their mathematical meaning in an equation. Sometimes you want to microposition elements—reposition them so they’re closer to or farther from other elements in the equation.

Before and after micropositioning

You can also control the amount of white space on each side of an element.

A. Default spacing B. Space added to the left and right C. Space removed from the left and right

• On the Positioning page of the Equations pod, do one of the following:

  • To position a selected expression, click a Micropositioning arrow. Click as many times as necessary. (Each click moves an expression one pixel on the screen.) Zoom in for greater precision.

    Micropositioning arrows
    

    

    
    

  • To remove micropositioning, click the button at the center of the Microposition area .

  • To inspect the position offsets and adjust them numerically, click Position Settings. The exact offsets appear in the Microposition Offset area of the Math Element Position Settings dialog box. To adjust the position, enter values in the Microposition Offset area and click Set.

  • To adjust white space, click a plus sign (+) to add white space or a minus sign (–) to remove it. Click as many times as necessary. Each click adds or subtracts one pixel of space. Zoom in for greater precision.

  Note: To change the spacing around a math element of type infix, prefix, postfix, or delimiter, adjust the space around the adjacent math elements instead. For example, to add space on either side of the plus sign in the expression a+b, selecta. Add space to the right. Then selectb. Add space to the left.

  • To adjust spacing values, click Position Settings. The exact spacing appears in the Spacing area of the Math Element Position Settings dialog box. To adjust the spacing values, enter values in the Spacing area, and click Set. To restore the default spacing values, click the button at the center of the Spacing area .

You can update some math element definitions—infix, prefix, postfix, large, scripts, and the division bar—with new spacing. When you do, FrameMaker adjusts the spacing around the element wherever it appears in the document and rewraps the equations.

You can also change the spread—the space between characters—uniformly in all small, medium, and large equations.

1. After you adjust the spacing around the element in an equation, select the element.

2. On the Equations pod, choose Update Definition from the Equations pop‑up menu.

3. Do one of the following:

   • To update the spacing for the element throughout the document, click Update.

   • To reset the spacing to the default, click Get Default.

When an equation breaks across lines, the entire equation remains in a single anchored frame. You can set where an equation breaks across lines automatically. When you change the line-break width, the equation is reformatted to the new width.

Original equation

Equation set to break at specific location"

You can also force a line break at a specific location in the equation. However, don’t use manual line breaks to create separate equations. Instead, insert a vertical list of expressions.

You can change line breaking in these ways:

• To change the automatic line break width, click in the equation or select any part of it. Choose Graphics > Object Properties. Edit the value in the Automatic Line Break After box, and click Set. The value is preset to the width of the equation frame.

• To insert a manual line break, click where you want the equation to break into two lines. On the Positioning page of the Equations pod, choose Set Manual from the Line Breaking pop‑up menu. A line-break symbol appears at the insertion point when text symbols are visible.

  Manual line break
  

  

  
  

• To remove a manual line break, select the part of the equation that contains the line-break symbol. On the Positioning page of the Equations pod, choose Clear Manual from the Line Breaking pop-up menu.

The format of the paragraph that contains the equation controls the alignment (left, center, or right) of a display equation.

Paragraph alignment set to Center

1. Click in the paragraph that contains the equation (not in the equation itself).

2. Choose the alignment from the Alignment pop‑up menu in the formatting bar or in the Paragraph Designer.

1. Click in the equation or list.

2. On the Positioning page of the Equations pod, choose an item from the Left/Right pop‑up menu. When you choose Left Of = or Right Of =, the lines are aligned along one side of an equal sign. A line with no equal sign is aligned along its left side.

1. Select the part of the equation that contains the manual alignment point.

2. On the Positioning page of Equations pod, choose Clear Manual from the Left/Right pop‑up menu. You can also clear a manual alignment point by setting another.

1. Click in the list.

2. On the Positioning page of the Equations pod, choose an item from the Up/Down pop‑up menu.

1. Click in the matrix.

2. On the Positioning page of the Equations pod, choose an item from the Up/Down pop‑up menu or from the Left/Right pop‑up menu. The Left/Right and Up/Down commands affect the whole matrix. To align individual cells, use micropositioning.

1. Do one of the following to select the entire list or matrix:

   • Drag through the list or matrix.

   • Place the insertion point in the matrix and press the spacebar repeatedly.

2. On the Positioning Page of the Equations pod, click Position Settings.

You can align several equation objects with one another in a graphic frame, just as you align other objects. You can also align several equation objects along a manual alignment point, even when they’re in separate graphic frames.

Equations aligned at manual alignment points

FrameMaker maintains the alignment of the equation objects as you edit the equations. For example, if two equations are left aligned, the left alignment is maintained as the equations expand or shrink.

1. Select the equations to align by Control-clicking the first equation; Control+Shift-click the other equations.

   Make sure that the last equation you select is the one you want to align with.

2. Choose Graphics > Arrange > Align.

   

3. Select the alignment you want, and click OK.

1. Set the manual alignment point in one of the equations to align.

   If you don’t set a manual alignment point, FrameMaker aligns an equation on the left.

2. Click in the equation and choose Graphics > Object Properties.

3. Choose Manual from the Alignment pop-up menu and specify the location of the alignment point within the frame in the Alignment Point Offset area. The left offset is the distance from the left edge of the frame to the manual alignment point.

   Specifying the top offset precisely is unnecessary. You can move the equation up or down later, just as you do any other object.

4. Click Set.

5. Repeat steps 1 through 4 for each equation you want to align. Use the same distance from the left edge for each equation, but change the top offset to position the equation vertically in the frame. If the equations you’re aligning are in different anchored frames, make sure that the left edges align with one another.

You can’t change the spread, stretch, superscript, subscript, underline, overline, strikethrough, change bar, or pair kerning properties for any element. You also can’t change the font family for individual Greek characters and symbols and for some operators.

• To change the preset size or color of an equation, click in the equation, choose Graphics > Object Properties, and do one of the following:

  • To change the equation size, choose a size from the Size pop-up menu, and click Set. If the equation is shrinkwrapped, FrameMaker rewraps it.

  • To change the equation color, choose a color from the Color pop-up menu, and click Set.

• To change character format, select the element or expression, and change as you do for text.

• To create a superscript or subscript, insert the appropriate operator.

• To change the spread of characters, microposition them by using the positioning page of the Equations pod.

• To place a line over or under an expression, use the diacritical marks on the Symbols page of the Equations pod.

You can change the font size and spacing for all small, medium, and large equations in a document. When you make global font changes, FrameMaker reformats and rewraps all shrinkwrapped equations in the document.

Greek characters and symbols in equations normally appear in the Symbol font. You can use fonts such as Mathematical Pi and Universal Greek if these fonts are installed on your system.

Functions, numbers, and strings normally appear in Times New Roman or Times. Variables normally appear in italic. You can change the character format of each of these kinds of elements. For example, you can display all elements in Helvetica, with functions in italic and variables in bold.

Use Equation Sizes from the Equations pop‑up menu on the Equations pod for the following change:

• To change equation fonts throughout the document, do one of the following:

  • Specify the font sizes and spread, and click Set. Spread is expressed as a percentage of the font size. Positive spread values cause wider spacing around elements; negative values cause narrower spacing.

  • Click Get Defaults.

• To change the font for Greek characters and symbols, choose one of the available fonts from the Math Symbols pop‑up menu, and click Set.

• To change the character format for functions, numbers, strings, and variables, first create the character format you want. Then choose the character format from the Functions, Numbers, Strings, or Variables pop‑up menu, and click Set. FrameMaker displays the format you created in the pop-up menus.

1. Select the expression, or part of it.

2. Choose a command on the Matrices or Functions page of the Equations pod. For example, select an expression and then choose Multiply Out from the Multiplication pop-up menu on the Functions page.

3. To transform or evaluate an expression, use the commands on the Matrix Commands pop-up menu of the Matrices page and the commands on the six pop-up menus of the Functions page.

Matrix Transpose

Transposes the rows and columns of a selected matrix.

Selected matrix	After transposing

Matrix Algebra

Performs matrix multiplication and addition, and evaluates dot and cross products in a selected matrix.

Selected matrix (or matrices)	After matrix algebra

After performing matrix algebra, you can use the Simplify command to combine like terms.

Add Fractions

Adds selected fractions, expressing the result as a single fraction. This command also combines like terms.

Selected fraction	After adding

If the selected expression contains the sum of more than two fractions, Add Fractions adds only the first two. Use this command repeatedly to combine all the fractions.

Selected expression
Added once
Added twice

Order Sum

Arranges polynomials in decreasing powers of a selected variable.

Before ordering	After ordering

Order Sum Reverse

Arranges polynomials in increasing powers of a selected variable. In the following example, you select an x—any x—before choosing Order Sum Reverse.

Before ordering	After ordering

Use the Multiplication pop‑up menu on the Functions page to factor terms, multiply out expressions, and distribute multiplication and division over addition.

Factor

Factors a selected term out of a product.

Before factoring	After factoring

Factor Some

Factors a selected term from only those terms that contain it.

Before factoring	After factoring

Multiply Out

Simplifies the selected expression, distributes multiplication over addition, and expands a selected term raised to a positive integral power.

Selected expression	After multiplying

The Simplify command also simplifies the selected expression.

Multiply Out Once

Multiplies the first pair of factors on the left side of a selected expression.

Selected expression	After multiplying

If you use this command several times, the results appear in a different form.

Distribute

Performs a variety of operations depending on the expression you select, as shown in the following examples:

• Distributes division over addition.

  Selected expression	After distributing

  Use the Add Fractions command to perform the reverse operation.

• Distributes multiplication over addition.

  Selected expression	After distributing

  Use the Factor command to perform the reverse operation.

• Transforms products and quotients involving radicals and exponents into a single expression raised to a power.

  Selected expression	After distributing

  Use the Simplify command to perform the reverse operation.

Distribute Over Equality

Performs the same operation on both sides of an equal sign.

Selected expression	After distributing

Long Division

Performs long division in a fraction that contains a polynomial numerator and denominator.

In the following example, you select an x—any x—before choosing Long Division. You select an x in the fraction of the first result and choose Long Division again to obtain the second result.

Before dividing
Divided once
Divided twice

Remove Division

Converts division to multiplication in a selected expression by changing positive exponents in a denominator to negative and negative exponents in a denominator to positive.

Selected expression	After removing division

To convert negative exponents to division operators, use the Remove Negative Powers command.

Remove Division 1 Level

Converts division to multiplication, as Remove Division does, but applies only to the first level of operators.

Selected expression	After removing division

To convert the first level of negative exponents into division operators, use the Remove Negative Powers 1 Level command.

Remove Negative Powers

Converts negative exponents to positive in a selected expression by replacing multiplication with division and division with multiplication.

Selected expression	After removing negative powers

Remove Negative Powers 1 Level

Converts negative exponents to positive, as Remove Negative Powers does, but applies only to the first level. If the selected expression has no negative exponents at the first level, this command has no effect.

Selected expression	After removing negative powers
	(no effect)

Number Crunch

Changes integers to floating-point numbers in a selected expression and then evaluates the expression.

Selected expression	After number crunch

Use the Show All Digits command to show up to 15 decimal places in a floating-point number.

Number Crunch displays NaN (Not a Number) for operations that result in undefined values. It displays Infinity for operations that result in a value too large to calculate. Small numbers can sometimes be evaluated to zero.

Selected expression	After number crunch

Show All Digits

Shows the full internal accuracy of a floating-point number.

Selected number	After showing all digits

Evaluate

Evaluates the selected expression. The operations performed depend on the type of expression selected, as shown in the following examples:

• Rewrites an expression raised to a power less than 20 as a product.

  Selected expression	After evaluating

• Computes the factorial of an integer. If the result is too large to calculate, the result appears as Infinity.

  Selected expression	After evaluating

• Computes the determinant of a 1-by-1 or 2-by-2 matrix.

  Selected expression	After evaluating

• Extracts a term from a sum or product.

  Selected expression	After evaluating

• Evaluates a substitution just as the Evaluate Substitution command does.

• Rewrites an Evaluate Between operator as a difference.

  Selected expression	After evaluating

• Rewrites the logarithm of a product as a sum of logarithms and rewrites a logarithm of a power as a product.

  Selected expression	After evaluating

• Rewrites a logarithm to a base in terms of natural logarithms.

  Selected expression	After evaluating

• Rewrites a choice function in terms of factorials.

  Selected expression	After evaluating

Evaluate Substitution

Performs a specified substitution and then simplifies the expression. When an Evaluate Between operator is selected, this command rewrites the expression as a difference.

Selected expression	After evaluating

Evaluate Integrals

Rewrites a selected integral with a polynomial integrand. This command converts a definite integral into an indefinite integral evaluated between the upper and lower bounds. Use Evaluate Integrals several times to integrate a polynomial fully.

Selected expression
Evaluated once
Evaluated twice

Evaluate Derivatives

Evaluates a selected derivative, applying the chain rule to complex expressions when necessary. This command evaluates a partial derivative only when all dependencies are explicitly written.

This command treats elements in a total derivative as if they depended on the variable of differentiation. Use the Evaluate command to expand an nth derivative before using Evaluate Derivatives to evaluate it.

Before	After

Evaluate Derivatives 1 Level

Evaluates only the first level of a selected derivative.

Before	After

Use the Rules pop-up menu on the Functions page to store and apply rules that transform expressions.

For example, use Enter Rule to store a rule such as a = a + 3. Then use Apply Rule to substitute a + 3 for a in another expression.

Enter Rule

Stores a rule for substituting one expression for another. Select the expression you want to store as a rule before you choose Enter Rule. You can store only one rule at a time.

Designate Dummy

Designates a selected term to be a dummy variable. Use a dummy variable in a rule to substitute the expression on the right side of the rule for any variable, not just the variable explicitly named on the left. A dummy variable appears in boldface. For example, if you designate x in the rule x = a 2– as a dummy variable, you can substitute a 2– or x for any variable in an expression.

Select the term you want to be a dummy variable before you choose Designate Dummy. Then use the Apply Rule command to replace a selected expression with the expression assigned to the dummy variable.

Apply Rule

Substitutes one term or set of terms for another in a selected expression, using the rule stored with the Enter Rule command.

Rule entered
Selected expression
After rule is applied

Before you apply a rule that contains a dummy variable, select the term you want the variable to replace. In the following example, x is the dummy variable in the rule.

Rule entered
Before rule is applied
After rule is applied

Simplify

Simplifies the selected expression. To evaluate fractions that involve infinity or division by zero, use the Number Crunch command instead of Simplify.

The operations performed depend on the type of expression selected, as shown in the following examples:

• Performs integer arithmetic.

  Selected expression	After simplifying

  When the result is too large to calculate, it appears as Infinity.

• Groups terms in a sum or product.

  Selected expression	After simplifying

• Divides out common factors in a fraction.

  Selected expression	After simplifying

  Use the Remove Negative Powers command to remove negative powers from the result.

• Interprets the complex number i, represented by the Greek letter iota .

  Selected expression	After simplifying

• Distributes exponentiation across multiplication and division.

  Selected expression	After simplifying

  Simplifying x produces rather than .

Simplify Some

Simplifies the selected expression, as the Simplify command does, but does not multiply fractions.

Selected expression	After simplifying

Isolate Term

Isolates a selected expression on one side of the equal sign. This command does not combine terms or solve for the selected expression.

Selected expression	After isolating term

Expand First Term

Expands the first term of a selected summation or product.

Selected expression	After expanding

Expand All Terms

Expands all terms of a selected summation or product.

Selected expression	After expanding