原创 The evolving face of Mathcad (Part 2)

[Continued from The evolving face of Mathcad (Part 1)]

Generating print for textbooks is one thing. For a single scientist or small group, generating it for published papers was quite another. I well remember serious technical papers written on a typewriter, with all the math equations written by hand. Or, not much better, generated by a typist skilled in typing subscripts, superscripts, and Greek letters. It was only natural that we average computer users would yearn to be able to generate book-quality print and equations, from a computer. In other words, let the text output of a general-purpose computer be the text input to a typesetting system. One of the early typesetting systems was the Unix program, troff. Another was Donald Knuth's justly famous T_EX, developed ca. 1980. To see the quadratic formula written in T_EX, go to http://en.wikipedia.org/wiki/TeX.

The problem with troff and T_EX was that you couldn't actually see their output until it went to the typesetter or a pixel-capable printer. The input itself was still a mere text string.

WYSIWYG changes everything
All that changed when Apple introduced its ground-breaking MacIntosh computer, with its high-resolution pixel graphics and a laser printer to match. Suddenly, an affordable personal computer could generate output rivaling the book publishers.

Seemingly the next day, Microsoft came out with Word for the Mac, and we learned that we no longer had to deal with Courier-in, Courier-out text. We could see on the screen the printed page exactly as it would appear. WYSIWYG was upon us with a vengeance, and we'd never be satisfied with pure text editing again.

If we could create text and graphics on a personal computer, it was only natural that we'd want to create math equations as well. Microsoft came through again, with its Microsoft Equation Editor, based on Design Sciences very excellent MathType. It's Word with MathType that I use for all my columns you've seen.

Tying things together
As nice as the output of WYSIWYG editors with equation editing was, it was still completely dumb. Mathtype, like troff and T_EX, has no smarts behind it. You have to put the symbols where you want them, one by one. Symbolic math processing remained a largely text-only operation. Math aids like MacSyma, Maple, and Mathematica (loosely derived from MacSyma) still used ordinary text strings for input and output. Mathematica at least made an attempt to pretty-print math equations, by simply printing their parts on separate lines. But the results were a far cry from book-publishable.

The next step is obvious: Give me a math analysis program that lets me input my equations in a form that looks just like a book publisher might typeset it, and give me the results the same way.

This is where Mathcad comes in. To my knowledge, it was the very first personal computer program capable of accepting symbolic inputs in natural mathematical form, performing operations on them symbolically, and showing the results in the same form. As far as I'm concern, they still remain alone.

In fairness, Maple too has evolved over the years, and later versions do indeed support mathematical forms for both inputs and outputs. But, for me at least, the text-oriented nature underpinning Maple still shows through. The math expressions are basically sleight-of-hand tricks to hide its inherent nature.

A lot of my work involves deriving the math equations associated with new problems and documenting the results. For me, it's important that I be able to intermix text with math equations, as well as the numerical and symbolic computations associated with them. Only Mathcad can do this seamlessly.

Which is why I use it.
How hard can it be?
While the ability to input equations in WYSIWYG form is Mathcad's strength, you should never get the idea that it's easy to do. It's not, and that's because the most convenient input device remains the keyboard. So how do you get the computer to accept text inputs and display the equivalent WYSIWYG form? Granted, I should be able to type a "Fortranish" character string like:

"x = a+b+2*y"

And get:

x=a+b+2 ? y

But try to get fancier, and things start to go south in a hurry. Type the harmonic series:

"x = 1+1/2+1/3+1/4+..."

And you might be surprised by the result. It'll be:

Mathcad understands operator precedence but can't possibly know your intentions unless you tell it. Think about it for awhile, and you'll realize that you can't possibly avoid the need to navigate around inside an equation, selecting the place where you want to put the next symbol. To do it, you're going to need to use the navigation keys, plus some special keys for things like superscripts, subscripts, square root symbols, matrix operations, and the like.

It's this navigation that's the hard part. It gets even harder when you're not just inputting an expression from scratch, but modifying an existing one. Or, worse yet, editing the output of the symbolic processor. Over the years, the Mathcad folks have tried several schemes, each with their pros and cons.

This is the big area of change in Mathcad Prime 1.0. They've completely replaced the user interface, including the rules for navigating inside expressions. It's the area of the program that elicited by far my most vociferous comments and under-the-breath curses. And the new interface is exactly what I had hoped for. It's a dramatic change, and it's the reason I'm so excited about Mathcad 1.0 Prime.

Still incomplete
Now for the bad news: Mathcad Prime 1.0 is still not complete. In developing it, PTC decided—wisely, in my opinion—not to put things in until they were robust and fully refactored. So key parts of earlier versions are still missing, notably the symbolic processing.

What's that you say? A symbolic processing program that can't do symbolic processing? Well, don't forget that symbolics is far from Mathcad's only function. It can also do ordinary numerical computations, vector/matrix operations, graphing, and much more, just as Mathematica, Maple, Matlab, and others do. Plus a bewildering array of special functions and numerical methods. It's only the connection with the symbolic engine that's missing.

To complete the picture, PTC has a plan. First, the purchase price of Prime 1.0 includes a maintenance contract, providing free upgrades for a year. They expect that, long before the year is out, the missing features will be included. To cover the missing features in the interim, they're bundling Prime 1.0 with a new version, Version 15, of the old Mathcad.

Can you tell that I'm excited? I think it's a great plan, and a great product. If you have a need for math processing, I think you should take a hard look at Mathcad Prime 1.0. If you've been avoiding Mathcad because of its steep learning curve or my dire warnings, it's time to take another look.