TK Solver
Encyclopedia
TK Solver is a mathematical modeling and problem solving software system based on a declarative, rule-based language, commercialized by Universal Technical Systems, Inc.
in the late 1970s and initially developed in 1982 by Software Arts
, the company behind VisiCalc
, TK Solver was acquired by Universal Technical Systems in 1984 after Software Arts fell into financial difficulty and was sold to Lotus Software
. Konopasek's goal in inventing the TK Solver concept was to create a problem solving environment in which a given mathematical model built to solve a specific problem could be used to solve related problems (with a redistribution of input and output variables) with minimal or no additional programming required: once a user enters an equation, TK Solver can evaluate that equation as is—without isolating unknown variables on one side of the equals sign.
language, algebraic equation solver, an iterative equation solver, and a structured, object-based interface. The interface comprises nine classes of objects that can be shared between and merged into other TK files:
Each class of object is listed and stored on its own worksheet -- the Rule Sheet, Variable Sheet, Unit Sheet, etc. Within each worksheet, each object has properties summarized on subsheets or viewed in a property window. The interface uses toolbars and a hierarchal navigation bar that resembles the directory tree seen on the left side of the Windows Explorer
.
The declarative programming structure is embodied in the rules, functions and variables that form the core of a mathematical model.
environment, the rules can be in any order or sequence and are not expressed as assignment statements. "A + B = C / D" is a valid rule in TK Solver and can be solved for any of its four variables. Rules can be added and removed as needed in the Rule Sheet without regard for their order and incorporated into other models. A TK Solver model can include up to 32,000 rules, and the library that ships with the current version includes utilities for higher mathematics, statistics, engineering and science, finances, and programming.
Variables in a rule are automatically posted to the Variable Sheet when the rule is entered and the rule is displayed in mathematical format in the MathLook View window at the bottom of the screen. Any variable can operate as an input or an output, and the model will be solved for the output variables depending on the choice of inputs.
A database of unit conversion factors also ships with TK Solver, and users can add, delete, or import unit conversions in a way similar to that for rules. Each variable is associated with a "calculation" unit, but variables can also be assigned "display" units and TK automatically converts the values. For example, rules may be based upon meters and kilograms, but units of inches and pounds can be used for input and output.
TK Solver includes roughly 150 built-in functions
: mathematical, trigonometric
, Boolean
, numerical calculus
, database
access, and programming functions, including string handling and calls to externally compiled routines. Users may also define three types of functions: declarative rule functions; list functions, for table lookups and other operations involving pairs of lists; and procedure functions, for loops and other procedural operations which may also process or result in arrays (lists of lists). The complete NIST
database of thermodynamic and transport properties is included, with built-in functions for accessing it. TK Solver is also the platform for engineering applications marketed by UTS, including Advanced Spring Design, Integrated Gear Software, Interactive Roark’s Formulas, Heat Transfer on TK, and Dynamics and Vibration Analysis.
and .NET
tools, or they can be web-enabled using the RuleMaster product or linked with Excel
spreadsheets using the Excel Toolkit product. There is also a DesignLink option linking TK Solver models with CAD drawings and solid models. In the premium version, standalone models can be shared with others who do not have a TK license, opening them in Excel or the free TK Player.
and Lotus 123 may suffice if just a single output variable is to be reversed to input status but those do not allow for arbitrary assignment of input and output status to any variable as is the case with a declarative language. Another alternative is Eureka, a free 16-bit DOS solver that was once sold by Borland
.
History
Invented by Milos KonopasekMilos Konopasek
Milos Konopasek was a mechanical engineer best known as the creator of TK!Solver, an iterative, constraint-based declarative environment for the numerical solution of systems of equations....
in the late 1970s and initially developed in 1982 by Software Arts
Software Arts
Software Arts was a software company founded by Dan Bricklin and Bob Frankston in 1979 to develop VisiCalc, which was published by a separate company, Personal Software Inc...
, the company behind VisiCalc
VisiCalc
VisiCalc was the first spreadsheet program available for personal computers. It is often considered the application that turned the microcomputer from a hobby for computer enthusiasts into a serious business tool...
, TK Solver was acquired by Universal Technical Systems in 1984 after Software Arts fell into financial difficulty and was sold to Lotus Software
Lotus Software
Lotus Software is a software company with headquarters in Westford, Massachusetts...
. Konopasek's goal in inventing the TK Solver concept was to create a problem solving environment in which a given mathematical model built to solve a specific problem could be used to solve related problems (with a redistribution of input and output variables) with minimal or no additional programming required: once a user enters an equation, TK Solver can evaluate that equation as is—without isolating unknown variables on one side of the equals sign.
Core technology
TK Solver's core technologies are a declarative programmingDeclarative programming
In computer science, declarative programming is a programming paradigm that expresses the logic of a computation without describing its control flow. Many languages applying this style attempt to minimize or eliminate side effects by describing what the program should accomplish, rather than...
language, algebraic equation solver, an iterative equation solver, and a structured, object-based interface. The interface comprises nine classes of objects that can be shared between and merged into other TK files:
- Rules: equations, formulas, function calls which may include logical conditions
- Variables: a listing of the variables that are used in the rules, along with values (numeric or non-numeric) that have been entered by the user or calculated by the software
- Units: all units conversion factors, in a single location, to allow automatic update of values when units are changed
- Lists: ranges of numeric and non-numeric values which can be associated with a variable or processed directly by procedure functions
- Tables: collections of lists displayed together
- Plots: line charts, scatterplots, bar charts, and pie chartPie chartA pie chart is a circular chart divided into sectors, illustrating proportion. In a pie chart, the arc length of each sector , is proportional to the quantity it represents. When angles are measured with 1 turn as unit then a number of percent is identified with the same number of centiturns...
s - Functions: rule-based, table look-up, and procedural programming components
- Formats: settings for displaying numeric and string values
- Comments: for explanation and documentation
Each class of object is listed and stored on its own worksheet -- the Rule Sheet, Variable Sheet, Unit Sheet, etc. Within each worksheet, each object has properties summarized on subsheets or viewed in a property window. The interface uses toolbars and a hierarchal navigation bar that resembles the directory tree seen on the left side of the Windows Explorer
Windows Explorer
This article is about the Windows file system browser. For the similarly named web browser, see Internet ExplorerWindows Explorer is a file manager application that is included with releases of the Microsoft Windows operating system from Windows 95 onwards. It provides a graphical user interface...
.
The declarative programming structure is embodied in the rules, functions and variables that form the core of a mathematical model.
Rules, variables and units
All rules are entered in the Rule Sheet or in user-defined functions. Unlike a spreadsheet or imperative programmingImperative programming
In computer science, imperative programming is a programming paradigm that describes computation in terms of statements that change a program state...
environment, the rules can be in any order or sequence and are not expressed as assignment statements. "A + B = C / D" is a valid rule in TK Solver and can be solved for any of its four variables. Rules can be added and removed as needed in the Rule Sheet without regard for their order and incorporated into other models. A TK Solver model can include up to 32,000 rules, and the library that ships with the current version includes utilities for higher mathematics, statistics, engineering and science, finances, and programming.
Variables in a rule are automatically posted to the Variable Sheet when the rule is entered and the rule is displayed in mathematical format in the MathLook View window at the bottom of the screen. Any variable can operate as an input or an output, and the model will be solved for the output variables depending on the choice of inputs.
A database of unit conversion factors also ships with TK Solver, and users can add, delete, or import unit conversions in a way similar to that for rules. Each variable is associated with a "calculation" unit, but variables can also be assigned "display" units and TK automatically converts the values. For example, rules may be based upon meters and kilograms, but units of inches and pounds can be used for input and output.
Problem-solving
TK Solver has three ways of solving systems of equations. The "direct solver" solves a system algebraically by the principle of consecutive substitution. When multiple rules contain multiple unknowns, the program can trigger an iterative solver which uses the Newton-Raphson algorithm to successively approximate based on initial guesses for one or more of the output variables. Procedure functions can also be used to solve systems of equations. Libraries of such procedures are included with the program and can be merged into files as needed. A list solver feature allows variables to be associated with ranges of data or probability distributions, solving for multiple values, which is useful for generating tables and plots and for running Monte Carlo simulations. The premium version now also includes a "Solution Optimizer" for direct setting of bounds and constraints in solving models for minimum, maximum, or specific conditions.TK Solver includes roughly 150 built-in functions
Subroutine
In computer science, a subroutine is a portion of code within a larger program that performs a specific task and is relatively independent of the remaining code....
: mathematical, trigonometric
Trigonometry
Trigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves...
, Boolean
Boolean logic
Boolean algebra is a logical calculus of truth values, developed by George Boole in the 1840s. It resembles the algebra of real numbers, but with the numeric operations of multiplication xy, addition x + y, and negation −x replaced by the respective logical operations of...
, numerical calculus
Calculus
Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem...
, database
Database
A database is an organized collection of data for one or more purposes, usually in digital form. The data are typically organized to model relevant aspects of reality , in a way that supports processes requiring this information...
access, and programming functions, including string handling and calls to externally compiled routines. Users may also define three types of functions: declarative rule functions; list functions, for table lookups and other operations involving pairs of lists; and procedure functions, for loops and other procedural operations which may also process or result in arrays (lists of lists). The complete NIST
National Institute of Standards and Technology
The National Institute of Standards and Technology , known between 1901 and 1988 as the National Bureau of Standards , is a measurement standards laboratory, otherwise known as a National Metrological Institute , which is a non-regulatory agency of the United States Department of Commerce...
database of thermodynamic and transport properties is included, with built-in functions for accessing it. TK Solver is also the platform for engineering applications marketed by UTS, including Advanced Spring Design, Integrated Gear Software, Interactive Roark’s Formulas, Heat Transfer on TK, and Dynamics and Vibration Analysis.
Data display and sharing
Tables, plots, comments, and the MathLook notation display tool can be used to enrich TK Solver models. Models can be linked to other components with Microsoft Visual BasicVisual Basic
Visual Basic is the third-generation event-driven programming language and integrated development environment from Microsoft for its COM programming model...
and .NET
.NET Framework
The .NET Framework is a software framework that runs primarily on Microsoft Windows. It includes a large library and supports several programming languages which allows language interoperability...
tools, or they can be web-enabled using the RuleMaster product or linked with Excel
Microsoft Excel
Microsoft Excel is a proprietary commercial spreadsheet application written and distributed by Microsoft for Microsoft Windows and Mac OS X. It features calculation, graphing tools, pivot tables, and a macro programming language called Visual Basic for Applications...
spreadsheets using the Excel Toolkit product. There is also a DesignLink option linking TK Solver models with CAD drawings and solid models. In the premium version, standalone models can be shared with others who do not have a TK license, opening them in Excel or the free TK Player.
Alternatives
If one particular solution to a set of equations is required, mathematical models can be constructed in virtually any programming language and in many calculators. If declarative programmability is required, the goal-seeking and solver facilities in spreadsheets such as Microsoft ExcelMicrosoft Excel
Microsoft Excel is a proprietary commercial spreadsheet application written and distributed by Microsoft for Microsoft Windows and Mac OS X. It features calculation, graphing tools, pivot tables, and a macro programming language called Visual Basic for Applications...
and Lotus 123 may suffice if just a single output variable is to be reversed to input status but those do not allow for arbitrary assignment of input and output status to any variable as is the case with a declarative language. Another alternative is Eureka, a free 16-bit DOS solver that was once sold by Borland
Borland
Borland Software Corporation is a software company first headquartered in Scotts Valley, California, Cupertino, California and finally Austin, Texas. It is now a Micro Focus subsidiary. It was founded in 1983 by Niels Jensen, Ole Henriksen, Mogens Glad and Philippe Kahn.-The 1980s:...
.
See also
- The mathematics of optimizationOptimization (mathematics)In mathematics, computational science, or management science, mathematical optimization refers to the selection of a best element from some set of available alternatives....
- Multidisciplinary design optimizationMultidisciplinary design optimizationMulti-disciplinary design optimization is a field of engineering that uses optimization methods to solve design problems incorporating a number of disciplines. As defined by Prof. Carlo Poloni, MDO is "the art of finding the best compromise"...
External links
- TK Solver product listing on the UTS website
- Short introduction to using TK Solver
- Tips for new users of TK Solver
- CadDigest reviews of various versions of TK Solver
- Computers in Higher Education Economics Review discusses version 4
- Design News review of version 3.0
- IEEE Spectrum review of version 3.0
- Review of TK Solver 5.0