A <cn> element is created whenever a numeric character is typed into a placeholder element. So there are no templates, menu items, or palette entries for creating <cn> elements in isolation.

Special care must be taken in handling <cn> elements using the base or type attribute. The values of these attributes may be supplied using the general attribute entry support, however, many values for the type attribute depend on the <sep> element to divide the character data for the <cn> element into separate parts. To enter such an element, first enter the character data for each of the separated parts all run together into one <cn> element, then go back and insert the necessary <sep> elements using the # key, from back to front. The character data after the <sep> element will seem to disappear, but supply the desired value of the type attribute and the character data will reappear in its proper position.

A <ci> element is created whenever an alphabetic character is typed into a placeholder element. So there are no templates, menu items, or palette entries for creating <ci> elements in isolation.

The general attribute entry support may be used to supply the value for the type attribute. The default configuration provides a special layout transformation for <ci> elements with type="vector"; others may be supplied using the layout rules configuration dialog.

Zed does not support editing <csymbol> elements, although they may be entered as MathML source.

Most instances of the <apply> constructor element are constructed as needed upon the application of operators and other templates that use them. However, the apply template, palette, and menu items may be used to construct references to general functions, particularly those not predefined as being represented by other elements. In addition, after entering the name of a function, the [ key may be used as an accelerator for the apply template. The apply template encloses the current expression in a new instance of an <apply> element, placing the expression as the function being applied, and creates a new placeholder for entering a first argument to the new function. After entering the argument list for the new function, the ] key may be used to navigate out to the newly created function expression to continue input.

The <apply> element is treated as an nary operator requiring at least two arguments, the function and an argument. In the absence of other presentation rules associated with the function being applied, the function is presented as a prefix argument, and the arguments to the function are presented in parenthesis, separated by commas.

In a postfix input context, the [ key invokes the <apply> template. The ] key navigates out to the next enclosing instance of the <apply> element used to construct a reference to a general function.

The <reln> constructor element has been superceded by the <apply> element. Zed does not support editing <reln> elements.

The fn palette and menu items each enclose the current expression with a new instance of the <fn> constructor element.

The <fn> element has been deprecated as obsolete. Zed supports creating <fn> elements, which are presented by the presentation of their single child element. Files containing <fn> elements can be saved to a file or to the clipboard, but when these files are read in, the <fn> elements are removed on input.

The interval template, palette, and menu item each enclose the current expression with a new instance of the <interval> constructor element. The enclosed expression becomes the left endpoint of the interval, and a placeholder provides a place for entering the right endpoint.

Additional templates and menu items are provided for specifying the value of the closure attribute, or for removing the attribute altogether. The general attribute entry support may also be used to supply the value for the closure attribute.

The <interval> element may appear as a child element of the <int> element. In this case, the <interval> element should appear as the lower limit of integration of a three argument <int> element.

The <interval> element is a binary operator, and is presented as a comma separated list of its arguments, enclosed in parentheses or square brackets as required by the closure attribute.

Zed does not support editing <interval> elements involving <condition> elements.

The inverse template, palette, and menu item each enclose the current expression with a new application of the <inverse> operator. The enclosed expression becomes the function being inverted.

The <inverse> element is a unary operator, and is presented as a postfix application of a superscript of -1.

The <sep> element only appears as a child element of the <cn> element. There are no templates, menu items, or palette entries for creating <sep> elements in isolation; the keyboard accelerator # can be used to insert a <sep> element within a <cn> element.

The <condition> element is usually found as a qualifier element on other elements, providing a range for an associated bound variable.

Zed supports creating <condition> elements, which are presented by the presentation of their single child element. However, Zed does not support editing <condition> elements as qualifier elements on other elements.

Zed does not support editing <declare> elements, although they may be entered as MathML source. Zed does not present <declare> elements in a visible way.

The lambda template, palette, and menu item each enclose the current expression with a new application of the <lambda> constructor. The enclosed expression becomes the body of the expression.

An additional template is provided to create <lambda> elements with additional qualifiers. The bound variables can be created by starting with the lambda2 named template.

The <lambda> element accepts from one to two arguments. The one argument version is presented as a lambda expression with no bound variables. The two argument version presents the lambda expression with its second argument as a list of bound variables, enclosed in parentheses.

Special input conventions are needed to enter the bound variables to the lambda expression. These conventions are borrowed from those used to create and remove elements of other nary operators.

The usual operations on nary operators can be used to insert or remove arguments of the <lambda> element. Creating the first argument follows the usual conventions for nary operators, but the second argument, containing the list of bound variables, requires special treatment.

When entering the list of bound variables, the list of variables can be viewed as its own element containing a list of arguments. So at this level of the expression, the usual operations on nary operators can be used to insert and remove additional bound variables.

In the content MathML generated by the <lambda> element, the second argument produces <bvar> qualifier elements for each of bound variable. These elements are generated as needed by the means used to create the <lambda> element.

The compose template, palette, and menu items each enclose the current expression with a new application of the <compose> operator. The enclosed expression becomes the first argument of the operator, and a placeholder provides a place for entering a second argument.

The <compose> element is an nary operator and an associative operator requiring at least two arguments, and is presented as an infix operator. A small circle symbol is used to present the operator.

The template, palette, and menu item each insert the empty constant element at the current cursor position.

The element is presented by the number "1".

The domain template, palette, and menu item each enclose the current expression with a new application of the <domain> operator. The enclosed expression becomes the argument of the function.

The <domain> element is a unary operator, and is presented as a prefix application of the string "domain".

The codomain template, palette, and menu item each enclose the current expression with a new application of the <codomain> operator. The enclosed expression becomes the argument of the function.

The <codomain> element is a unary operator, and is presented as a prefix application of the string "codomain".

The image template, palette, and menu item each enclose the current expression with a new application of the <image> operator. The enclosed expression becomes the argument of the function.

The <image> element is a unary operator, and is presented as a prefix application of the string "image".

The <domainofapplication> element typically appears as a child element of the <int> element. The domainofapplication template and menu item each act to wrap the current expression with a new <domainofapplication> element, which should appear as the lower limit of integration of a three argument <int> element.

To create an integral having only the integrand and the domain of integration as arguments, use the int3 template to create a three argument <int> element, create the lower limit of integration, and use the domainofapplication template to enclose the lower limit with a <domainofapplication> element. The presentation of the domain of integration will change to reflect the fact that the integration variable is left unspecified.

The piecewise template, palette, and menu item each enclose the current expression with a new <piecewise> constructor element. The enclosed expression becomes the first piece.

The <piecewise> element is an nary operator, and is presented as a vertical list of its pieces, preceded by a curly brace. The various child elements of each piece of the <piecewise> element are left aligned using <maligngroup> elements in the presentation MathML.

The piece template, palette, and menu item each enclose the current expression with a new <piece> constructor element. The enclosed expression becomes the value conditionally supplied by the piece, and a new placeholder is created to hold the condition.

The <piece> element takes two child elements, and is presented as an infix application of the string "if".

The otherwise template, palette, and menu item each enclose the current expression with a new <otherwise> constructor element. The enclosed expression becomes the value used when no other piece applies.

The <otherwise> element takes one child element, and is presented as a postfix application of the string "otherwise".

The plus templates, palette, and menu items each enclose the current expression with a new application of the <plus> operator. The enclosed expression becomes the first argument of the operator. The palette and menu items for binary plus create an additional placeholder for entering a second argument.

The <plus> element is an nary operator and an associative operator, and is presented as an infix application of the "+" operator.

On input, the <plus> template is treated as a binary operator. Using the Ctrl key allows the user to create the <plus> element as a unary operator.

The minus templates, palette, and menu items each enclose the current expression with a new application of the <minus> operator. The enclosed expression becomes the first argument of the operator. The palette and menu items for binary minus create an additional placeholder for entering a second argument.

The <minus> element is overloaded: as a unary operator it is presented in prefix form, and with two or more arguments it is presented in infix form as an nary operator.

The <minus> element is also overloaded on input: in a prefix input context, it is treated as a unary operator, while in a postfix input context, it is treated as a binary operator. Using the Ctrl key reverses the assignment so that one can obtain either template in any input context.

The times template, palette, and menu items each enclose the current expression with a new application of the <times> operator. The enclosed expression becomes the first argument of the operator, and a placeholder provides a place for entering a second argument.

The <times> element is an nary operator and an associative operator requiring at least two arguments, and is presented as an infix operator. An invisible times symbol is used to present the operator.

The divide template, palette, and menu items each enclose the current expression with a new application of the <divide> operator. The enclosed expression becomes the numerator of the fraction, and a placeholder provides a place for entering the denominator.

The <divide> element is presented as an upright fraction.

The power template, palette, and menu items each enclose the current expression with a new application of the <power> operator. The enclosed expression becomes the base of the expression, and a placeholder provides a place for entering the exponent.

The <power> element is presented by placing the exponent as a superscript of the base.

The sqrt template, palette, and menu items each enclose the current expression with a new application of the <root> operator. The enclosed expression becomes the argument of the expression.

The <root> template, palette, and menu items each enclose the current expression with a new application of the <root> operator. The enclosed expression becomes the argument of the expression, and and a placeholder provides a place for entering the degree of the root.

The <root> element accepts one or two arguments. The usual operations on nary operators can be used to insert or remove arguments of the <root> element. The one argument version is presented with the radical sign enclosing the argument. The two argument version is presented as the one argument version, but with the second argument presented as the degree of the root as a preceding superscript of the operator.

In the content MathML generated by the <root> element, the second argument produces a <degree> qualifier element, generated as needed by the means used to create the <root> element.

The factorial template, palette, and menu item each enclose the current expression with a new application of the <factorial> operator. The enclosed expression becomes the argument of the function.

The <factorial> element is a unary operator, and is presented as a postfix application of the "!" operator.

The quotient template, palette, and menu item each enclose the current expression with a new application of the <quotient> operator. The enclosed expression becomes the first argument of the operator, and a placeholder provides a place for entering a second argument.

The <quotient> element is a binary operator, and is presented as a comma separated list of its arguments, enclosed in parentheses, preceded by the string "quo" as a prefix operator.

The rem template, palette, and menu item each enclose the current expression with a new application of the <rem> operator. The enclosed expression becomes the first argument of the operator, and a placeholder provides a place for entering a second argument.

The <rem> element is a binary operator, and is presented as a comma separated list of its arguments, enclosed in parentheses, preceded by the string "rem" as a prefix operator.

The gcd template, palette, and menu item each enclose the current expression with a new application of the <gcd> element. The enclosed expression becomes the first element of the set.

The <gcd> element is an nary operator, and is presented as a comma separated list of its child elements, enclosed in parentheses, preceded by the string "gcd" as a prefix operator.

The lcm template, palette, and menu item each enclose the current expression with a new application of the <lcm> element. The enclosed expression becomes the first element of the set.

The <lcm> element is an nary operator, and is presented as a comma separated list of its child elements, enclosed in parentheses, preceded by the string "lcm" as a prefix operator.

The max template, palette, and menu item each enclose the current expression with a new application of the <max> element. The enclosed expression becomes the first element of the set.

The <max> element is an nary operator, and is presented as a comma separated list of its child elements, enclosed in curly braces, preceded by the string "max" as a prefix operator.

Zed does not support editing <max> elements involving <condition> elements.

The min template, palette, and menu item each enclose the current expression with a new application of the <min> element. The enclosed expression becomes the first element of the set.

The <min> element is an nary operator, and is presented as a comma separated list of its child elements, enclosed in curly braces, preceded by the string "min" as a prefix operator.

Zed does not support editing <min> elements involving <condition> elements.

The floor template, palette, and menu item each enclose the current expression with a new application of the <floor> operator. The enclosed expression becomes the argument of the function.

The <floor> element is a unary operator, and is presented by enclosing its argument in floor fences.

The ceiling template, palette, and menu item each enclose the current expression with a new application of the <ceiling> operator. The enclosed expression becomes the argument of the function.

The <ceiling> element is a unary operator, and is presented by enclosing its argument in ceiling fences.

The abs template, palette, and menu item each enclose the current expression with a new application of the <abs> operator. The enclosed expression becomes the argument of the function.

The <abs> element is a unary operator, and is presented by enclosing its argument in vertical bars.

The arg template, palette, and menu item each enclose the current expression with a new application of the <arg> operator. The enclosed expression becomes the argument of the function.

The <arg> element is a unary operator, and is presented as a prefix application of the string "arg".

The real template, palette, and menu item each enclose the current expression with a new application of the <real> operator. The enclosed expression becomes the argument of the function.

The <real> element is a unary operator, and is presented as a prefix application of the Fraktur capital "R".

The imaginary template, palette, and menu item each enclose the current expression with a new application of the <imaginary> operator. The enclosed expression becomes the argument of the function.

The <imaginary> element is a unary operator, and is presented as a prefix application of the Fraktur capital "I".

The conjugate template, palette, and menu item each enclose the current expression with a new application of the <conjugate> operator. The enclosed expression becomes the argument of the function.

The <conjugate> element is a unary operator, and is presented by a horizontal bar over the argument.

The and template, palette, and menu item each enclose the current expression with a new application of the <and> operator. The enclosed expression becomes the first argument of the operator, and a placeholder provides a place for entering a second argument.

The <and> element is an nary operator and an associative operator requiring at least two arguments, and is presented as an infix operator. The upwards "V" symbol is used to present the operator.

The or template, palette, and menu item each enclose the current expression with a new application of the <or> operator. The enclosed expression becomes the first argument of the operator, and a placeholder provides a place for entering a second argument.

The <or> element is an nary operator and an associative operator requiring at least two arguments, and is presented as an infix operator. The downwards "V" symbol is used to present the operator.

The xor template, palette, and menu item each enclose the current expression with a new application of the <xor> operator. The enclosed expression becomes the first argument of the operator, and a placeholder provides a place for entering a second argument.

The <xor> element is an nary operator and an associative operator requiring at least two arguments, and is presented as an infix operator. The circled plus symbol is used to present the operator.

The not template, palette, and menu item each enclose the current expression with a new application of the <xor> operator. The enclosed expression becomes the argument of the operator.

The <not> element is a unary operator, and is presented as an prefix operator. The negation symbol is used to present the operator.

The implies template, palette, and menu item each enclose the current expression with a new application of the <implies> operator. The enclosed expression becomes the first argument of the operator, and a placeholder provides a place for entering a second argument.

The <implies> element is a binary operator, and is presented as an infix operator. The double right arrow symbol is used to present the operator.

The forall template, palette, and menu item each enclose the current expression with a new application of the <forall> operator. The enclosed expression becomes the body of the expression.

An additional template is provided to create <forall> elements with additional qualifiers. The bound variables can be created by starting with the forall2 named template.

The <forall> element accepts from one to two arguments. The one argument version is presented as a quantified expression with no bound variables. The two argument version presents the quantified expression with its second argument as a list of bound variables, enclosed in parentheses.

Special input conventions are needed to enter the bound variables to the quantified expression. These conventions are borrowed from those used to create and remove elements of other nary operators.

The usual operations on nary operators can be used to insert or remove arguments of the <forall> element. Creating the first argument follows the usual conventions for nary operators, but the second argument, containing the list of bound variables, requires special treatment.

When entering the list of bound variables, the list of variables can be viewed as its own element containing a list of arguments. So at this level of the expression, the usual operations on nary operators can be used to insert and remove additional bound variables.

In the content MathML generated by the <forall> element, the second argument produces <bvar> qualifier elements for each of bound variable. These elements are generated as needed by the means used to create the <forall> element.

Zed does not support editing <forall> elements involving <condition> elements.

The exists template, palette, and menu item each enclose the current expression with a new application of the <exists> operator. The enclosed expression becomes the body of the expression.

An additional template is provided to create <exists> elements with additional qualifiers. The bound variables can be created by starting with the exists2 named template.

The <exists> element accepts from one to two arguments. The one argument version is presented as a quantified expression with no bound variables. The two argument version presents the quantified expression with its second argument as a list of bound variables, enclosed in parentheses.

Special input conventions are needed to enter the bound variables to the quantified expression. These conventions are borrowed from those used to create and remove elements of other nary operators.

The usual operations on nary operators can be used to insert or remove arguments of the <exists> element. Creating the first argument follows the usual conventions for nary operators, but the second argument, containing the list of bound variables, requires special treatment.

When entering the list of bound variables, the list of variables can be viewed as its own element containing a list of arguments. So at this level of the expression, the usual operations on nary operators can be used to insert and remove additional bound variables.

In the content MathML generated by the <exists> element, the second argument produces <bvar> qualifier elements for each of bound variable. These elements are generated as needed by the means used to create the <exists> element.

Zed does not support editing <exists> elements involving <condition> elements.

The eq template, palette, and menu item each enclose the current expression with a new application of the <eq> operator. The enclosed expression becomes the first argument of the function, and a placeholder provides a place for entering a second argument.

The <eq> element is an nary operator and an infix operator that takes two or more arguments. The equal sign is used to present the operator.

The neq template, palette, and menu item each enclose the current expression with a new application of the <neq> operator. The enclosed expression becomes the first argument of the function, and a placeholder provides a place for entering a second argument.

The <neq> element is presented as an infix operator. It is also a binary operator. The negated equal sign is used to present the operator.

The gt template, palette, and menu item each enclose the current expression with a new application of the <gt> operator. The enclosed expression becomes the first argument of the function, and a placeholder provides a place for entering a second argument.

The <gt> element is an nary operator and an infix operator that takes two or more arguments. The greater than sign is used to present the operator.

The lt template, palette, and menu item each enclose the current expression with a new application of the <lt> operator. The enclosed expression becomes the first argument of the function, and a placeholder provides a place for entering a second argument.

The <lt> element is an nary operator and an infix operator that takes two or more arguments. The less than sign is used to present the operator.

The geq template, palette, and menu item each enclose the current expression with a new application of the <geq> operator. The enclosed expression becomes the first argument of the function, and a placeholder provides a place for entering a second argument.

The <geq> element is an nary operator and an infix operator that takes two or more arguments. The greater than or equal sign is used to present the operator.

The leq template, palette, and menu item each enclose the current expression with a new application of the <leq> operator. The enclosed expression becomes the first argument of the function, and a placeholder provides a place for entering a second argument.

The <leq> element is an nary operator and an infix operator that takes two or more arguments. The less than or equal sign is used to present the operator.

The equivalent template, palette, and menu item each enclose the current expression with a new application of the <equivalent> operator. The enclosed expression becomes the first argument of the function, and a placeholder provides a place for entering a second argument.

The <equivalent> element is an nary operator and an infix operator that takes two or more arguments. The equivalent sign is used to present the operator.

The approx template, palette, and menu item each enclose the current expression with a new application of the <approx> operator. The enclosed expression becomes the first argument of the function, and a placeholder provides a place for entering a second argument.

The <approx> element is presented as an infix operator. It is also a binary operator. The approximately equal sign is used to present the operator.

The factorof template, palette, and menu item each enclose the current expression with a new application of the <factorof> operator. The enclosed expression becomes the first argument of the function, and a placeholder provides a place for entering a second argument.

The <factorof> element is presented as an infix operator. It is also a binary operator. A vertical bar is used to present the operator.

The int template, palette, and menu item each enclose the current expression with a new application of the <int> operator. The enclosed expression becomes the first element of the operator.

Additional templates, palette, and menu items are provided to create <int> elements with additional qualifiers. Indefinite integrals are created with the int2 named template. The lower limit of integration is given as the third argument, and the upper limit of integration is given with the fourth. The templates int3 and int4 act as shortcuts for creating these forms. Each of the four integration creating templates have a corresponding entry on the Calculus palette.

The <int> element accepts from one to four arguments. The usual operations on nary operators can be used to insert or remove arguments of the <int> element. The one argument version is presented using the integral sign as a prefix operator, where the argument is presented as the integrand. The two argument version presents the second argument as the integration variable, separated from the integrand by a differential "d" operator. The three and four argument versions present the third and fourth arguments as lower and upper integration limits presented above and below the integral sign, respectively.

In the content MathML generated by the <int> element, the second argument produces a <bvar> qualifier element, and the third and fourth arguments produce <lowlimit> and <uplimit> qualifier elements. These elements are generated as needed by the means used to create the <int> element.

Zed does not support editing <int> elements involving <condition> elements. Other qualifier elements are supported, see the description of these qualifiers for information on how to create integrals using these forms.

The diff template, palette, and menu item each enclose the current expression with a new application of the <diff> operator. The enclosed expression becomes the first element of the operator.

Additional templates, palette, and menu items are provided to create <diff> elements with additional qualifiers. The differentiation variable can be created with the diff2 named template, and repeated derivatives can be created with the diff3 named template. Each of the three derivative creating templates have a corresponding entry on the Calculus palette.

The <diff> element accepts from one to three arguments. The usual operations on nary operators can be used to insert or remove arguments of the <diff> element. The one argument version is presented using the differential "d" as a prefix operator, where the argument is the expression being differentiated. The two argument version is presented using the fraction form of the differential operator as a prefix operator, with the second argument in the denominator as the differentiation variable. The three argument version presents the third argument as the degree of differentiation, as a superscript of the differential "d" operator in the numerator, and as a superscript of the differentiation variable in the denominator.

In the content MathML generated by the <diff> element, the second argument produces a <bvar> qualifier element, and the third argument produces a <degree> qualifier within the <bvar> element. These elements are generated as needed by the means used to create the <diff> element.

The partialdiff template, palette, and menu item each enclose the current expression with a new application of the <partialdiff> operator. The enclosed expression becomes the first element of the operator.

Additional templates, palette, and menu items are provided to create <partialdiff> elements with additional qualifiers. The differentiation variables can be created by starting with the partialdiff2 named template, and the total degree of differentiation can be supplied with the partialdiff3 named template. Each of the three partial derivative creating templates have a corresponding entry on the Calculus palette.

The <partialdiff> element accepts from one to three arguments. The one argument version is presented using the partial differential "d" as a prefix operator, where the argument is the expression being differentiated. The two argument version presents the derivative in the fraction form, by presenting the differentiation variables found within the second argument in the denominator of the fraction. The three argument version presents the third argument as the total degree of differentiation, as a superscript of the partial differential "d" operator in the numerator. Each of the differentiation variables in the denominator is expected to have its own degree of differentiation, displayed as a superscript of the variable.

The <partialdiff> element is the only element that accepts a list of <bvar> elements, each of which is allowed to have its own separate <degree> element. As such, special input conventions are needed to enter the differentiation variables and their degrees. These conventions are borrowed from those used to create and remove elements of other nary operators.

The usual operations on nary operators can be used to insert or remove arguments of the <partialdiff> element. Creating the first and third arguments follow the usual conventions for nary operators, but the second argument, containing the list of differentiation variables, requires special treatment.

When entering the list of differentiation variables, the denominator of the partial derivative operator can be viewed as its own element containing a list of arguments. So at this level of the expression, the usual operations on nary operators can be used to insert and remove additional differentiation variables.

Each differentiation variable may itself be viewed as its own element, similar in form to the <bvar> element it will ultimately generate. Each variable may have one or two arguments, the first argument being the differentiation variable, and the second the differentiation degree. So within this third level of the <partialdiff> expression, templates for nary operators allow for the insertion or removal of the degree of differentiation for this particular variable.

In the content MathML generated by the <partialdiff> element, the second argument produces <bvar> qualifier elements, with <degree> elements included as needed to supply the degree of differentiation for each differentiation variable. The third argument produces a total <degree> qualifier for the <partialdiff> element. These elements are generated as needed by the means used to create the <partialdiff> element.

Zed does not support editing <partialdiff> elements involving <list> elements as the indices of differentiation.

The <lowlimit> element only appears as a child element of the other elements listed above. The facilities for inserting and deleting child elements of these other elements are used to create the <lowlimit> qualifiers as they are needed. So there are no templates, menu items, or palette entries for creating <lowlimit> elements in isolation.

The <uplimit> element only appears as a child element of the other elements listed above. The facilities for inserting and deleting child elements of these other elements are used to create the <uplimit> qualifiers as they are needed. So there are no templates, menu items, or palette entries for creating <uplimit> elements in isolation.

The <bvar> element only appears as a child element of the other elements listed above. The facilities for inserting and deleting child elements of these other elements are used to create the <bvar> qualifiers as they are needed. So there are no templates, menu items, or palette entries for creating <bvar> elements in isolation.

The <bvar> element is the only qualifier element that itself accepts another element (<degree>) as a qualifier element. When <bvar> elements are generated as a result of structure needed for other elements, <degree> elements are also generated as needed.

The <degree> element only appears as a child element of the other elements listed above. The facilities for inserting and deleting child elements of these elements are used to create the <degree> qualifier if one is required. So there are no templates, menu items, or palette entries for creating <degree> elements in isolation.

The divergence template, palette, and menu item each enclose the current expression with a new application of the <divergence> operator. The enclosed expression becomes the argument of the function.

The <divergence> element is a unary operator, and is presented as a prefix application of the string "div".

The grad template, palette, and menu item each enclose the current expression with a new application of the <grad> operator. The enclosed expression becomes the argument of the function.

The <grad> element is a unary operator, and is presented as a prefix application of the string "grad".

The curl template, palette, and menu item each enclose the current expression with a new application of the <curl> operator. The enclosed expression becomes the argument of the function.

The <curl> element is a unary operator, and is presented as a prefix application of the string "curl".

The laplacian template, palette, and menu item each enclose the current expression with a new application of the <laplacian> operator. The enclosed expression becomes the argument of the function.

The <laplacian> element is a unary operator, and is presented as a prefix application of the nabla symbol with exponent "2".

The set template, palette, and menu item each enclose the current expression with a new <set> constructor element. The enclosed expression becomes the first element of the set.

The <set> element is an nary constructor, and is presented as a comma separated list of its child elements, enclosed in curly braces.

Zed does not support editing <set> elements involving <condition> elements.

The list template, palette, and menu item each enclose the current expression with a new <list> constructor element. The enclosed expression becomes the first element of the list.

The <list> element is an nary constructor, and is presented as a comma separated list of its child elements, enclosed in square brackets.

Zed does not support editing <list> elements involving <condition> elements.

The union template, palette, and menu item each enclose the current expression with a new application of the <union> operator. The enclosed expression becomes the first argument of the operator, and a placeholder provides a place for entering a second argument.

The <union> element is an nary operator requiring at least two arguments, and is presented as an infix operator. The upwards "U" union symbol is used to present the operator.

The intersect template, palette, and menu item each enclose the current expression with a new application of the <intersect> operator. The enclosed expression becomes the first argument of the operator, and a placeholder provides a place for entering a second argument.

The <intersect> element is an nary operator requiring at least two arguments, and is presented as an infix operator. The downwards "U" intersection symbol is used to present the operator.

The in template, palette, and menu item each enclose the current expression with a new <in> element. The enclosed expression becomes the first argument of the operator, and a placeholder provides a place for entering the second argument.

The <in> element is presented as an infix operator. It is also a binary operator. The mathematical "element of" symbol is used to present the operator.

The notin template, palette, and menu item each enclose the current expression with a new <notin> element. The enclosed expression becomes the first argument of the operator, and a placeholder provides a place for entering the second argument.

The <notin> element is presented as an infix operator. It is also a binary operator. The negated "element of" symbol is used to present the operator.

The subset template, palette, and menu item each enclose the current expression with a new application of the <subset> operator. The enclosed expression becomes the first argument of the operator, and a placeholder provides a place for entering a second argument.

The <subset> element is an nary operator requiring at least two arguments, and is presented as an infix operator. The underlined rightwards "U" subset symbol is used to present the operator.

The prsubset template, palette, and menu item each enclose the current expression with a new application of the <prsubset> operator. The enclosed expression becomes the first argument of the operator, and a placeholder provides a place for entering a second argument.

The <prsubset> element is an nary operator requiring at least two arguments, and is presented as an infix operator. The rightwards "U" subset symbol is used to present the operator.

The notsubset template, palette, and menu item each enclose the current expression with a new application of the <notsubset> operator. The enclosed expression becomes the first argument of the operator, and a placeholder provides a place for entering the second argument.

The <notsubset> element is a binary operator, and is presented as an infix operator. The negated underlined rightwards "U" subset symbol is used to present the operator.

The notprsubset template, palette, and menu item each enclose the current expression with a new application of the <notprsubset> operator. The enclosed expression becomes the first argument of the operator, and a placeholder provides a place for entering the second argument.

The <notprsubset> element is a binary operator, and is presented as an infix operator. The negated rightwards "U" subset symbol is used to present the operator.

The setdiff template, palette, and menu item each enclose the current expression with a new application of the <setdiff> operator. The enclosed expression becomes the first argument of the operator, and a placeholder provides a place for entering the second argument.

The <setdiff> element is a binary operator, and is presented as an infix operator. The backwards slash set difference symbol is used to present the operator.

The card template, palette, and menu item each enclose the current expression with a new application of the <card> operator. The enclosed expression becomes the argument of the operator.

The <card> element is a unary operator, and is presented by enclosing its argument in vertical bars.

The cartesianproduct template, palette, and menu item each enclose the current expression with a new <cartesianproduct> element. The enclosed expression becomes the first argument of the product, and a placeholder provides a place for entering a second argument.

The <cartesianproduct> element is an nary operator requiring at least two arguments, and is presented as an infix operator. The times symbol is used to present the operator.

The sum template, palette, and menu item each enclose the current expression with a new application of the <sum> operator. The enclosed expression becomes the first element of the operator.

Additional templates, palette, and menu items are provided to create <sum> elements with additional qualifiers. Summations with an unbounded index variable are created with the sum2 named template. The lower bound of the summation is given as the third argument, and the upper bound of the summation is given with the fourth. The templates sum3 and sum4 act as shortcuts for creating these forms. Each of the four summation creating templates have a corresponding entry on the Sequences palette.

The <sum> element accepts from one to four arguments. The usual operations on nary operators can be used to insert or remove arguments of the <sum> element. The one argument version is presented using the Greek capital letter sigma as a prefix operator, where the argument is the expression being collected in the sum. The two argument version presents the second argument, the index over which the expression is being collected, as an underscript of the operator. The three and four argument versions present the third and fourth arguments as lower and upper limits of the summation index, presented above and below the operator, respectively.

In the content MathML generated by the <sum> element, the second argument produces a <bvar> qualifier element, and the third and fourth arguments produce <lowlimit> and <uplimit> qualifier elements. These elements are generated as needed by the means used to create the <sum> element.

Zed does not support editing <sum> elements involving <condition> elements.

The product template, palette, and menu item each enclose the current expression with a new application of the <product> operator. The enclosed expression becomes the first element of the operator.

Additional templates, palette, and menu items are provided to create <product> elements with additional qualifiers. Products with an unbounded index variable are created with the product2 named template. The lower bound of the product is given as the third argument, and the upper bound of the product is given with the fourth. The templates product3 and product4 act as shortcuts for creating these forms. Each of the four product creating templates have a corresponding entry on the Sequences palette.

The <product> element accepts from one to four arguments. The usual operations on nary operators can be used to insert or remove arguments of the <product> element. The one argument version is presented using the Greek capital letter pi as a prefix operator, where the argument is the expression being collected in the product. The two argument version presents the second argument, the index over which the expression is being collected, as an underscript of the operator. The three and four argument versions present the third and fourth arguments as lower and upper limits of the product index, presented above and below the operator, respectively.

In the content MathML generated by the <product> element, the second argument produces a <bvar> qualifier element, and the third and fourth arguments produce <lowlimit> and <uplimit> qualifier elements. These elements are generated as needed by the means used to create the <product> element.

Zed does not support editing <product> elements involving <condition> elements.

The limit template, palette, and menu item each enclose the current expression with a new application of the <limit> operator. The enclosed expression then becomes the limit expression, and placeholders are created for creating the bound variable and the limit point.

The <limit> element accepts three arguments: the expression being evaluated, the bound variable over which the limit is being considered, and the limit point for the bound variable. The <limit> operator is presented as a prefix application of the string "lim" in an upright font, with an underscript displaying the bound variable and the limit point with an infix right arrow operator.

In the content MathML generated by the <limit> element, the second argument produces a <bvar> qualifier element, and the third argument produces a <lowlimit> qualifier element. These elements are generated as needed by the means used to create the <limit> element.

Zed does not support editing <limit> elements involving <condition> elements.

The tendsto template, palette, and menu item each enclose the current expression with a new application of the <tendsto> operator. The enclosed expression then becomes the first argument of the <tendsto> operator, representing the subject of the relation, and a placeholder is supplied for creating the destination of the relation.

The <tendsto> element may accept the type attribute to specify the direction from which the subject approaches its destination. Valid values for the attribute include type="two-sided", type="above", and type="below". These values may be supplied using the corresponding named templates and menu items, and they may be removed using the none template and menu item. The general attribute entry support may also be used to supply the value for the type attribute.

The <tendsto> element is presented using an infix right arrow operator separating the subject from its destination. The directionality specified by the type attribute is displayed as a superscript on the destination, either as a plus sign (above) or a minus sign (below).

The exp template, palette, and menu item each enclose the current expression with a new application of the <exp> operator. The enclosed expression becomes the argument of the function.

The <exp> element is a unary operator, and is presented as an italic lowercase "e" with the argument as an exponent.

The ln template, palette, and menu item each enclose the current expression with a new application of the <ln> operator. The enclosed expression becomes the argument of the function.

The <ln> element is a unary operator, and is presented as a prefix application of the string "ln".

The log template and palette item, and the log 10 menu item each enclose the current expression with a new application of the <log> operator. The enclosed expression becomes the argument of the function.

Additionally, the log2 template and palette item, and the log n menu item each enclose the current expression with a new application of the <log> operator, and provide an extra placeholder for the input of the base of the logarithm.

The <log> element accepts one or two arguments. The usual operations on nary operators can be used to insert or remove arguments of the <log> element. The one argument version is presented as a prefix application of the string "log". The two argument version is presented as the one argument version, but with the second argument presented as the base of the logarithm as a subscript of the operator.

In the content MathML generated by the <log> element, the second argument produces a <logbase> qualifier element, generated as needed by the means used to create the <log> element.

The <logbase> element only appears as a child element of the <log> element. The facilities for inserting and deleting child elements of the <log> element are used to create the <logbase> qualifier if one is required. So there are no templates, menu items, or palette entries for creating <logbase> elements in isolation.

The sin template, palette, and menu item each enclose the current expression with a new application of the <sin> operator. The enclosed expression becomes the argument of the function.

The <sin> element is a unary operator, and is presented as a prefix application of the string "sin".

The cos template, palette, and menu item each enclose the current expression with a new application of the <cos> operator. The enclosed expression becomes the argument of the function.

The <cos> element is a unary operator, and is presented as a prefix application of the string "cos".

The tan template, palette, and menu item each enclose the current expression with a new application of the <tan> operator. The enclosed expression becomes the argument of the function.

The <tan> element is a unary operator, and is presented as a prefix application of the string "tan".

The sec template, palette, and menu item each enclose the current expression with a new application of the <sec> operator. The enclosed expression becomes the argument of the function.

The <sec> element is a unary operator, and is presented as a prefix application of the string "sec".

The csc template, palette, and menu item each enclose the current expression with a new application of the <csc> operator. The enclosed expression becomes the argument of the function.

The <csc> element is a unary operator, and is presented as a prefix application of the string "csc".

The cot template, palette, and menu item each enclose the current expression with a new application of the <cot> operator. The enclosed expression becomes the argument of the function.

The <cot> element is a unary operator, and is presented as a prefix application of the string "cot".

The arcsin template, palette, and menu item each enclose the current expression with a new application of the <arcsin> operator. The enclosed expression becomes the argument of the function.

The <arcsin> element is a unary operator, and is presented as a prefix application of the string "sin", with a superscript of -1.

The arccos template, palette, and menu item each enclose the current expression with a new application of the <arccos> operator. The enclosed expression becomes the argument of the function.

The <arccos> element is a unary operator, and is presented as a prefix application of the string "cos", with a superscript of -1.

The arctan template, palette, and menu item each enclose the current expression with a new application of the <arctan> operator. The enclosed expression becomes the argument of the function.

The <arctan> element is a unary operator, and is presented as a prefix application of the string "tan", with a superscript of -1.

The arcsec template, palette, and menu item each enclose the current expression with a new application of the <arcsec> operator. The enclosed expression becomes the argument of the function.

The <arcsec> element is a unary operator, and is presented as a prefix application of the string "sec", with a superscript of -1.

The arccsc template, palette, and menu item each enclose the current expression with a new application of the <arccsc> operator. The enclosed expression becomes the argument of the function.

The <arccsc> element is a unary operator, and is presented as a prefix application of the string "csc", with a superscript of -1.

The arccot template, palette, and menu item each enclose the current expression with a new application of the <arccot> operator. The enclosed expression becomes the argument of the function.

The <arccot> element is a unary operator, and is presented as a prefix application of the string "cot", with a superscript of -1.

The sinh template, palette, and menu item each enclose the current expression with a new application of the <sinh> operator. The enclosed expression becomes the argument of the function.

The <sinh> element is a unary operator, and is presented as a prefix application of the string "sinh".

The cosh template, palette, and menu item each enclose the current expression with a new application of the <cosh> operator. The enclosed expression becomes the argument of the function.

The <cosh> element is a unary operator, and is presented as a prefix application of the string "cosh".

The tanh template, palette, and menu item each enclose the current expression with a new application of the <tanh> operator. The enclosed expression becomes the argument of the function.

The <tanh> element is a unary operator, and is presented as a prefix application of the string "tanh".

The sech template, palette, and menu item each enclose the current expression with a new application of the <sech> operator. The enclosed expression becomes the argument of the function.

The <sech> element is a unary operator, and is presented as a prefix application of the string "sech".

The csch template, palette, and menu item each enclose the current expression with a new application of the <csch> operator. The enclosed expression becomes the argument of the function.

The <csch> element is a unary operator, and is presented as a prefix application of the string "csch".

The coth template, palette, and menu item each enclose the current expression with a new application of the <coth> operator. The enclosed expression becomes the argument of the function.

The <coth> element is a unary operator, and is presented as a prefix application of the string "coth".

The arcsinh template, palette, and menu item each enclose the current expression with a new application of the <arcsinh> operator. The enclosed expression becomes the argument of the function.

The <arcsinh> element is a unary operator, and is presented as a prefix application of the string "sinh", with a superscript of -1.

The arccosh template, palette, and menu item each enclose the current expression with a new application of the <arccosh> operator. The enclosed expression becomes the argument of the function.

The <arccosh> element is a unary operator, and is presented as a prefix application of the string "cosh", with a superscript of -1.

The arctanh template, palette, and menu item each enclose the current expression with a new application of the <arctanh> operator. The enclosed expression becomes the argument of the function.

The <arctanh> element is a unary operator, and is presented as a prefix application of the string "tanh", with a superscript of -1.

The arcsech template, palette, and menu item each enclose the current expression with a new application of the <arcsech> operator. The enclosed expression becomes the argument of the function.

The <arcsech> element is a unary operator, and is presented as a prefix application of the string "sech", with a superscript of -1.

The arccsch template, palette, and menu item each enclose the current expression with a new application of the <arccsch> operator. The enclosed expression becomes the argument of the function.

The <arccsch> element is a unary operator, and is presented as a prefix application of the string "csch", with a superscript of -1.

The arccoth template, palette, and menu item each enclose the current expression with a new application of the <arccoth> operator. The enclosed expression becomes the argument of the function.

The <arccoth> element is a unary operator, and is presented as a prefix application of the string "coth", with a superscript of -1.

The mean template, palette, and menu item each enclose the current expression with a new application of the <mean> operator. The enclosed expression becomes the first element of the operator.

The <mean> element is an nary operator, and is presented as a comma-separated list of its arguments, enclosed in angle brackets.

The sdev template, palette, and menu item each enclose the current expression with a new application of the <sdev> operator. The enclosed expression becomes the first element of the operator.

The <sdev> element is an nary operator, and is presented as a comma-separated list of its arguments, enclosed in a prefix application of the Greek lowercase letter sigma.

The <var> element is an nary operator, and is presented as a comma-separated list of its arguments, enclosed in a prefix application of the Greek lowercase letter sigma, with a postfix exponent of 2.

The <var> element has been superceded by the <variance> element.

The variance template, palette, and menu item each enclose the current expression with a new application of the <variance> operator. The enclosed expression becomes the first element of the operator.

The <variance> element is an nary operator, and is presented as a comma-separated list of its arguments, enclosed in a prefix application of the Greek lowercase letter sigma, with a postfix exponent of 2.

The median template, palette, and menu item each enclose the current expression with a new application of the <median> operator. The enclosed expression becomes the first element of the operator.

The <median> element is an nary operator, and is presented as a comma-separated list of its arguments, enclosed in a prefix application of the word "median" in an upright font.

The mode template, palette, and menu item each enclose the current expression with a new application of the <mode> operator. The enclosed expression becomes the first element of the operator.

The <mode> element is an nary operator, and is presented as a comma-separated list of its arguments, enclosed in a prefix application of the word "mode" in an upright font.

The moment template, palette, and menu item each enclose the current expression with a new application of the <moment> operator. The enclosed expression becomes the first element of the operator.

Additional templates, palette, and menu items are provided to create <moment> elements with additional qualifiers. Nth moments are created with the nth moment menu item and the moment2 named template. Nth moments around a particular point are created with the moment about menu item and the moment3 named template. Each of the three moment creating templates have a corresponding entry on the Statistics palette.

The <moment> element accepts one, two, or three arguments. The usual operations on nary operators can be used to insert or remove arguments of the <moment> element. The one argument version is presented with its argument in angle brackets, and the first argument is assumed to be a set. The two argument version is presented much as the one argument version, but with the second argument presented as an exponent of the first argument to denote the nth moment. The three argument version is presented much as the two argument version, but with the third argument presented as the point around which the moment is being computed.

In the content MathML generated by the <moment> element, the second argument produces a <degree> qualifier element, and the third argument produces a <momentabout> qualifier element. These elements are generated as needed by the means used to create the <moment> element.

The <momentabout> element only appears as a child element of the <moment> element. The facilities for inserting and deleting child elements of the <moment> element are used to create the <momentabout> qualifier if one is required. So there are no templates, menu items, or palette entries for creating <momentabout> elements in isolation.

The vector template, palette, and menu item each enclose the current expression with a new <vector> constructor element. The enclosed expression becomes the first element of the vector.

The <vector> element is an nary operator, and is presented as a column vector of its child elements, enclosed in square brackets.

The matrix template, palette, and menu item each enclose the current expression with a new <matrix> constructor element. The enclosed expression becomes the first element of the first row of the new matrix.

The <matrix> element is an array operator that is presented as a two-dimensional table of its child elements, enclosed in parentheses.

The <matrixrow> constructor element only appears as a child element of the <matrix> element. The facilities for inserting and deleting child elements of a matrix are used to create the matrix rows and elements, without manipulating the <matrixrow> elements directly. So there are no templates, menu items, or palette entries for creating <matrixrow> elements in isolation.

The <matrixrow> element is an nary operator, and is presented as a row vector of its child elements, without any enclosing fences.

The determinant template, palette, and menu item each enclose the current expression with a new application of the <determinant> operator. The enclosed expression becomes the argument of the determinant.

The <determinant> element is a unary operator, and is presented as a prefix application of the string "det".

The transpose template, palette, and menu item each enclose the current expression with a new application of the <transpose> operator. The enclosed expression becomes the argument of the transpose operator.

The <transpose> element is a unary operator, and is presented as a postfix application of a superscript "T".

The <select> element is an nary operator that takes two or more arguments. It is presented by placing a comma separated list of the indices as a subscript of the first argument.

The <select> element has been superceded by the <selector> element.

The selector template, palette, and menu item each enclose the current expression with a new application of the <selector> operator. The enclosed expression becomes the first argument of the selector operator, and a new placeholder is created that allows for the creation of the indices of the selection.

The <selector> element is an nary operator that takes two or more arguments. It is presented by placing a comma separated list of the indices as a subscript of the first argument.

The vectorproduct template, palette, and menu item each enclose the current expression with a new <vectorproduct> element. The enclosed expression becomes the first argument of the product, and a placeholder provides a place for entering the second argument.

The <vectorproduct> element is presented as an infix operator. It is also a binary operator. The times symbol is used to present the operator.

The scalarproduct template, palette, and menu item each enclose the current expression with a new <scalarproduct> element. The enclosed expression becomes the first argument of the product, and a placeholder provides a place for entering the second argument.

The <scalarproduct> element is presented as an infix operator. It is also a binary operator. A centered dot is used to present the operator.

The outerproduct template, palette, and menu item each enclose the current expression with a new <outerproduct> element. The enclosed expression becomes the first argument of the product, and a placeholder provides a place for entering the second argument.

The <outerproduct> element is presented as an infix operator. It is also a binary operator. A circled times symbol is used to present the operator.

The semantics template, palette, and menu item each enclose the current expression with a new <semantics> element. The enclosed expression becomes the first argument of the new element that will be annotated by <annotation> and/or <annotation-xml> elements. The comma key creates additional child expressions where the annotations can be created.

The <semantics> element in Zed uses the other attribute to provide two ways of presenting the element. If the attribute other="edit" is specified, each child element of the <semantics> element is presented, separated by commas, and enclosed in parentheses. This mode allows you to view and edit the content and each of the annotations of the element. If the other attribute is absent and one of the annotations is an <annotation-xml> element with encoding="MathML-Presentation", then the MathML presentation annotation is used to present the element, hiding the other annotations.

The edit template and menu item add the attribute other="edit" to a <semantics> element, while the show template and menu item remove it. These two templates allow you to toggle between the two presentation modes for a <semantics> element. The general attribute entry support may also be used to supply the value for the other attribute.

The <semantics> element is an nary operator.

The annotation template, palette, and menu item each enclose the current expression with a new <annotation> element. The enclosed expression becomes the content of the annotation.

In principle, this element may be used to hold annotations in any general input format. In practice, Zed allows any MathML expression to be entered as the annotation, which will appear in its usual XML encoding.

The <annotation> element may accept the encoding attribute to specify the encoding for the element. The general attribute entry support may also be used to supply the value for the encoding attribute.

The <annotation> element is presented by enclosing its annotation in curly braces. If an encoding attribute is present, it is displayed as a subscript of the annotation.

The annotation-xml template, palette, and menu item each enclose the current expression with a new <annotation-xml> element. The enclosed expression becomes the content of the annotation.

In principle, this element may be used to hold annotations containing any XML elements from any vocabulary. In practice, Zed allows any MathML expression to be entered as the annotation.

The <annotation-xml> element may accept the encoding attribute to specify the encoding for the element. Conventional values for the attribute include encoding="MathML-Presentation" and encoding="MathML-Content". The value of the encoding attribute can be set by the content and present templates and menu items, and can be removed by the other menu item and the remove template. The general attribute entry support may also be used to supply the value for the encoding attribute.

The <annotation-xml> element is presented by enclosing its annotation in square brackets. If an encoding attribute is present, it is displayed as a subscript of the annotation.

The template, palette, and menu item each insert the empty constant element at the current cursor position.

The element is presented as a double-struck capital "Z".