TK!Solver(ID:1061/tks001)for Tool Kit Solver Milos Konopasek Software Arts 1983. Numerical constraint-oriented language. Related languages
References: TK Solver. In 1981 Software Arts, the purveyors of VisiCalc, the first popular spreadsheet, wrote TK Solver, making it one of the first mathematical packages for the PC. When that company fell on hard times, TK Solver was sold off to Universal Technical Systems Inc. (Rockford, Ill.), a company producing software for mechanical engineers. UTS rewrote the code. TK Solver Plus is billed as an equation-solving and knowledge-management package. The program lets the user'set up problems in the form of rules and relationships. It comes with a library of ready-to-use models for differentiation and integration, solving differential equations, evaluating complex numbers, and curve-fitting. (Despite its billing, Kahan considers it a "glorified calculator.") A spokesperson estimated that 80 to 85 percent of the installed base of 100,000 users are mechanical engineers. The program is used by MEs at several divisions of Boeing and General Electric and is provided on PCs for students at the Georgia Institute of Technology's Department of Mechanical Engineering. It is also part of the package provided to the freshmen engineering students - who must furnish their own PCs - at Virginia Polytechnic Institute. TK Solver Plus runs on the Macintosh and the IBM PC as well as under Unix on Apollo, Hewlett-Packard, IBM, and Sun workstations, and a VMS version is available for DEC Vax minicomputers. The Mac and PC version cost $395 (an extended-memory version for the PC is $595). The cost for the first copy for a workstation or minicomputer is $995. UTS now offers three add-on modules for mechanical engineers: Roark and Young On TK, Heat Transfer on TK, and the Mechanical Engineering TK solverpacks. Roark and Young On TK is a computerized version of Roark's Handbook on Formulas of Stress and Strain. The module contains 37 tables, more than 5000 formulas, and over 1200 cases' worth of data that can be accessed by pull-down menus and massaged in TK itself. The software provides backsolving capabilities and costs $595 (for personal computers) or $1495 (per user for workstations and minicomputers). Heat Transfer on TK also is based on a book, in this case Fundamentals of Heat and Mass Transfer written by Frank Incropera and David DeWitt and published by John Wiley and Sons. It includes over 100 models divided into menu-selectable sections like steady-state and transient conduction; internal, external, and free-flow convection; boiling and condensation; etc. Prices are the same as those for Roark and Young On TK. Extract: TK!Solver and QAS Nearly two decades ago, while some programmers and mathematicians were working on math software to run on minicomputers, a few visionaries realized that personal computers could bring the computer-aided solution of mathematical problems to a very large audience. One of them was Dr Milos Konopasek, now vice president of Universal Technical Systems Inc (UTS). After developing a mathematical problem-solving program called QAS (question-answering system) that ran in a time-sharing mode on a PDP-10 computer at the University of Manchester, England, in the early 1970s, he emigrated to the US. Konopasek was teaching at Georgia Tech in the mid '70s when he first encountered a personal computer. It came from the now-defunct Intelligent Systems. He rewrote QAS to run on the machine. Basic was the native language of those early PCs, and Konopasek wrote the first microcomputer version of QAS in Basic. The program's essential "backsolving" capability--its ability to accept constraints on previously unconstrained variables and thus produce new and possibly more practical solutions--took fewer than 120 lines of code. Shortly after he wrote the microcomputer version of QAS, Konopasek became aware of Viscalc, the first commercial spreadsheet program. At first, Visicalc ran only on the Apple II, and was a product of a Massachusetts company, Software Arts. Konopasek proposed a numerical solver for scientific and technical problems as an add-on to Visicalc. Software Arts wasn't interested in marketing a special version of Visicalc, though. So a separate product, TK!Solver, the first microcomputer-based numeric solver with backsolving capability, was born. (The "TK" in the name stands for tool kit.) Eventually, Lotus Development (Cambridge, MA) acquired Software Art and TK, but didn't want to market software for technical applications. Lotus sold TK to UTS, which has enhanced the product and now sells it as TK Solver Plus for both the IBM Pc family and the Macintosh. Unlike programs that began as workstation and minicomputer software and migrated downward to microcomputers, TK has migrated upward to such machines as DEC VAXes and Sun and Apollo workstations. TK uses constructs called "sheets." For example, there are rule and variable sheets. In today's software lexicon, TK's sheets hold different classes of objects. This object-oriented structure is well suited to the creation of sets of models that solve classes of problems. UTS sells these model sets as add-ons to TK and calls them TK Solver Packs. One Pack is for electrical engineering. In a recent effort aimed at structural engineers, UTS created a Pack of 800 models that solve the equations in Roark and Young's Formulas for Stress and Strain. TK's backsolving ability, a hallmark of the program from the beginning, is especially useful with structural problems. of purposes. It is a numerical package which has been in existence for something like 10 years, in one form or another. A number of significant improvements have been introduced in its latest version, TKSolver Release 2.0 ("Son of TKSolverPlus") or TK2 for short. Extract: TK Solver TK Solver is driven by the use of multiple sheets where you set up equations and manage variables, unit conversions, and plots. Every time I look closely at this product?about once in five years?its multiple-sheet interface has become more natural. In the initial DOS version that I looked at in 1987, I found the plethora of sheets and subsheets confusing (it turns out that it was merely ahead of its time). The first Windows version of TK that came out (about five years ago) let you put sheets in separate windows so multiple sheets could be viewed simultaneously. The newer interface uses an Explorer-like look with the sheets in a tree on the left and selected sheets viewable in work windows. It?s now downright comfortable. The interface designers are also to be complimented on providing multiple routes to many features: button bars, menus, drop-downs, and the Explorer interface. TK Solver 4.0 offers numerous enhancements of which the most notable are Excel interoperability and a feature called MathLook. MathLook provides a sheet that displays mathematics in ?blackboard format? with fractions shown in natural notation and which also allows display of TK tables and plots. MathLook presentations can be printed or cut and pasted into Word. The tables remain live, that is, linked to the sheets from which they were pasted. In terms of breadth and sophistication, at the top of the pyramid are the programs that have symbolic manipulation in their cores using the triad of exact rational arithmetic, arbitrary precision reals, and computer algebra. The leaders here are Mathematica 5.0 (just released, $1,880; see sidebar, "New Versions of Mathematica," p. 35) and Maple 9 ($1,795). An alternative to these hefty prices is MuPad 2.5 ($500), developed in Germany and sold in this country by Mackichan Software. MuPad offers only a fraction of the features of the powerhouses but with considerable symbolics and improving graphics it will suffice for many potential users. Derive 5 ($199) remains so underpowered that it isn?t a tool for professionals and is of interest for the education market and, of course, for its embedding in the higher-end TI calculators. Maple has licensed its engine to MATLAB and MathCAD while Scientific Workplace has moved from a Maple to a MuPad linked engine. While these borrowed symbolics can be useful, they are limited and if you need to make extensive use of the special features of computer algebra, you?ll want Mathematica, Maple, or MuPad. Extract: Matrix-Based Languages For many professionals, the biggest mathematical need is number crunching, the ability to perform complex calculations, typically on large data sets. While Maple and Mathematica have vastly improved their number-crunching speeds over the years, there is no question that for serious numerical calculations you want to use either custom C programming or else use programs written in one of the mathematical programming languages that are matrix based. The leading such language is MATLAB ($1,900 for the base product; toolboxes run from $500-$1000 or more each), which has oodles of functions and lots of toolboxes containing additional specialized routines and functions. With several toolboxes added, MATLAB can be quite pricey, which makes the $265 O-Matrix an attractive alternative to consider. In compatibility mode, O-Matrix will run Matlab mfiles that use functions in the extensive O-Matrix library, which includes Matrix and special functions, ODE solvers, and 2D and 3D plots. Another Matrix language is Octave. Extract: TK Solver TK Solver TK Solver has always been in a category of its own. Rather than a general mathematical tool, it?s a model builder that allows you to input sets of equations (both algebraic and differential) and then explore the solutions. For those interested in this niche, it?s an excellent choice. There is a wide array of math software products available to meet the wide set of user needs. And for us old-timers, it sure beats slide rules and punch cards. Resources
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