Many posts of this blog are about the native Office math facility introduced in Microsoft Word in 2007 and added to PowerPoint, OneNote, and in Excel Text Boxes in 2010. But the first native math-text facility in Microsoft Word was the EQ field, one of many fields, such as time and date. Design Science designed MathType, which first shipped on the Mac in 1987 and was released on Windows in 1990. A simplified version of MathType called the Equation Editor was introduced in 1992 and has shipped as part of Office on Windows and the Mac ever since. This post overviews these three facilities for representing math text in Microsoft Office along with what math formats they support. There are more math programs, such as Mathematica, that interoperate with Office apps typically via MathML.

## EQ Field

The EQ field was added in an early version of Word and still works, although the user is responsible for math spacing and inserting the desired math symbols. Any Unicode characters can be used including the complete Unicode math set of 2310 characters. To enter an equation, click on Insert/Quick Parts/Field… and select Eq from the list. Click on Field Codes and the Options… button to see the possible math constructs, such as \F(,) for fraction. With alt+x’ing in the Unicode math symbols, adding spaces around the operators and using the Cambria Math font, one can insert the solution to the quadratic equation as

The EQ field for this is {EQ 𝑥 = \F(−𝑏 ± \R(,𝑏\S(2) − 4𝑎𝑐),2𝑎)} formatted with Cambria Math and Unicode math italic alphabetics for a, b, c, and x. You can toggle the EQ field between the math display and the field codes by right-clicking on the field and choosing “Toggle Field Codes”. Note that the math axis doesn't line up between the equal sign and the fraction bar. The display isn’t as typographically pretty as that of the Office math facility (type alt+= \quadratic<space><space>)

and it’s appreciably harder to use. Also, the superscript size for the square must be formatted explicitly. If you change the size of the formula, you have to reformat the superscript with an appropriate smaller size. The Office math facility automatically chooses superscript and subscript sizes appropriate for the base text. The EQ field doesn't support important constructs such as matrices and *N*-ary expressions other than simple integrals. Word represents ruby objects using EQ fields, although it uses LineServices in rendering them.

## MathType

MathType and its limited edition, the Equation Editor, made math entry easier and considerably more general than the EQ field by adding intuitive tool bars giving access to mathematical symbols and function templates. All common math constructs are supported, and the typography includes niceties such as automatic math spacing around operators and trig functions. You can download the current version of MathType and use it for free for 30 days. After that it goes into a “lite” version unless you pay $99. The lite version has advantages over the Equation Editor not the least of which is that it’s currently maintained.

Both MathType and the Equation Editor display the solution to the quadratic equation as This is easy to enter using hot keys or the templates on the template tool bar. You can also enter it by hand writing using the Math Input Panel which communicates with client apps via MathML.

On Windows and the Mac, MathType and the Equation Editor use embedded OLE objects for displaying and editing math text. As such they can be used by any programs that support OLE such as WordPad. For WordPad, click on Insert Object and choose Microsoft Equation 3.0. But OLE is only available on Win32 Windows and the Mac. Also, a program’s search and formatting commands don’t work with embedded OLE objects, while they do work with native Office math zones.

MathType incorporates the Unicode 2.0 math characters and adds many others in the Unicode Private Use Area (see the MTCode Encoding Tables). 364 characters have the math property in Unicode 2.0. This is considerably less than the 2310 math characters in the current Unicode Standard. Most of the characters in the MTCode Encoding Tables are in the current Unicode Standard, but there might be backward compatibility issues if MathType were to upgrade to that version of the standard. There are many math characters in the Unicode Standard that are not in MathType. I haven’t been able to enter such characters into MathType or the Equation Editor. Since these characters are not common, it’s not a major limitation. Chapter 6 of Creating Research and Scientific Documents with Microsoft Word describes both the native Office math facility discussed in many of this blog’s posts as well as MathType.

## Math entities

Now let’s consider how various math entities are represented in these math facilities and the file formats they support. The formats are Presentation MathML, OMML (Office MathML), RTF, [La]TeX, UnicodeMath, braille, and MathType. Math entities such as fractions and integrals have arguments. The number of arguments and the order in which they occur may differ between the representations. The MathType equation format is a binary format and is documented in detail in the MathType SDK. The discussion here is limited to what the templates reveal when one runs MathType and/or the Equation Editor.

### Fractions

All math formats have a numerator and a denominator for fractions and they occur in that order. The EQ field and math braille only have stacked fractions (numerator above denominator), but the other formats also have slashed, linear, and small fractions.

### Math functions

Math functions, such as trigonometric and log, have an explicit two-argument entity in OMML and RTF, but are handled by character formatting alone in the other formats. Having an object with two explicit arguments reveals the content better in the user interface and facilitates typographic refinements, such as precise spacing.

### Integrals and summations

OMML, RTF and MathType have three arguments for *N*-ary entities such as integral and summation, namely the upper and lower limits and the integrand or summand, which can be called *N*-aryands. [La]TeX and braille only have the two limits. Presentation MathML doesn’t have an explicit *N*-ary entity; instead it overloads other entities (msub, msup, msubsup, mover, munder, munderover) which don't have an *N*-aryand. This is a shortcoming of Presentation MathML. The EQ field has integrals with all three arguments, but no summations or other *N*-ary entities. UnicodeMath defines the *N*-aryand to be the first operand following the *N*-ary operator and its limits (if present). MathType puts the *N*-aryand before the limits, while OMML and RTF put it afterward since it follows the limits visually. Having it afterward makes navigating with arrow keys more natural. MathType traverses integrals and summations with the Tab key in visual order, but the left/right arrow keys bypass the limit arguments.

### Subscripts and superscripts

Subscript and superscript bases are not arguments in MathType, [La]TeX, braille or the EQ field. They are arguments in MathML, OMML and RTF. In UnicodeMath, the base is the variable, function name, number, or object immediately preceding the sub/sup operators. Knowing the base allows proper kerning of the base onto the script (superscript or subscript) as well as providing more exact semantics in interoperating with mathematical calculation engines. While the base can be determined algorithmically as in MathType, [La]TeX and UnicodeMath, having an explicit argument for it automatically gives it helpful shading in Office math zones and lends precision to the fine-grained math speech needed for unambiguous editing of math using speech.

### Parentheses, brackets, braces

The EQ field has the \B() option which puts appropriately sized parentheses around its argument. It doesn’t allow for other kinds of delimiters, such as [] and {}. Also, it doesn’t have multiple argument expressions that size the argument dividers appropriately, such as in Dirac notation. The other formats have many delimiter options and can handle multiple arguments correctly.

Yeah, the EQ field is probably a very little-known feature in Microsoft Word. But of course, today there is essentially no reason at all to use it. The formula editor introduced in Microsoft Word 2007 is simply way too awesome, and superior in every way. But the EQ field certainly is a cool beast in its own, quirky way!

It might be worth mentioning out that in some languages, the argument separator in the EQ field is a semicolon, not a comma. This is because comma is used as the decimal point.

When I try to double-click an EQ field in Word 2010, it is replaced by an empty Equation Editor OLE object and an error message is shown. I suppose this is a remnant from some old “upgrade” feature from EQ fields to Equation Editor OLE objects that doesn’t work any more?