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Review of Theorist: a Symbolic mathematics and graphics application
Review of Theorist: a Symbolic Mathematics and Graphics Application Andy R. Bobyarchick Department of Geography and Earth Sciences University of North Carolina at Charlotte, Charlotte NC 28223, U.S.A. [email protected] http://anb-mac.uncc.edu
A b s t r a c t - This note presents a critical review of Theorist TM, a symbolic mathemathics and graphing application of potential interest to the field of structural geology.
Introduction Theorist is a symbolic mathematics and graphing application for microcomputers. The software is available for the MacOS TM, Windows TM, and Windows NT T M operating systems. Minimum requirements on the Macintosh are a Mac Plus or above (including Quadras and PowerPCs), 2 MB of RAM, 2 MB hard disk space, and System 6, 7, or A / UX. Suitable performance on PowerMacs and for graphics intensive applications benefit from additional RAM. On the Windows side, you need a minimum 386 processor, 4 MB RAM, 2 MB hard disk space, and Windows 3.1, NT, or95. The version reviewed here is 2.01 running on a Macintosh 900 with a PowerPC upgrade card installed under System 7.5.1. Earlier versions of Theorist were marketed by Prescience Inc., but the program is now distributed by Waterloo Maple Software Inc., makers of the popular Maple TM mathematical system for microcomputers and workstations. Evidently, much of the core code in Theorist resembles Maple anyway. Theorist supports all basic mathematical procedures you would expect in such software including: roots, factorials, and powers; integer and floating point numbers; mathematical constants and trigonometric functions; polynomial simplification and expansion; simultaneous solutions for systems of equations; vector and matrix algebra; and differentiation and integration. The maximum numerical precision is 15 digits. In addition, Theorist comes with reasonable graphing abilities in two and three dimensions. Graphics can be animated in real time, and the program supports several projection systems (Cartesian, polar, cylindrical, and spherical). Options for coloring and shading plots allow creation of presentation-quality 299
Structural Geology and Personal Computers graphics t h a t can also be exported in MetaFile format (Windows), or PICT format (Macintosh). Files copied onto the Macintosh clipboard within Theorist can be pasted into other Macintosh applications t h a t accept the PICT format. EPS (Encapsulated Postscript) files can also be generated. These resolution-independent files can then be placed in page processors for publication. It is also possible to create a text version of the EPS file on the Macintosh; this file, with some editing, may then be opened in an modifiable form in a program such as Adobe Illustrator TM. The basic user environment in Theorist is the notebook. You can create notebooks optimized for your work t h a t will open automatically every time the program is started. A notebook' s format is independent of the operating system, so it can be readily transferred between platforms with e-mail or over a network. Notebooks contain hot graphics windows t h a t update automatically when an expression is changed within the notebook. A "statement" is the f u n d a m e n t a l expression in a notebook. S t a t e m e n t s are either "assumptions" or "conclusions" S t a t e m e n t s entered by the user are assumptions; results from the p r o g r a m are conclusions. S t a t e m e n t s may be equations or expressions composed of numbers, names, or wildcard variables. You can also define functions to be used within the notebook.
Theorist uses, in part, an iconic interface. You can create expressions and equations by clicking on a palette t h a t contains either variable n a m e s or functions and m a t h e m a t i c a l operators. The program automatically positions an entry point in an expression where you may enter information from the keyboard. Expressions may also be created from the keyboard directly. With the appropriate typed operators (especially the placement of parentheses), Theorist will i n t e r p r e t keyboard entry in a syntax similar to the point-and-click entry technique. A F o r t r a n i s h keyboard entry option lets you enter data in a way t h a t you might use in p r o g r a m m i n g or in a spreadsheet application. For example, ifyou type x^2 +2 with the F o r t r a n i s h option on, the result in the notebook will be x: + 2. With the F o r t r a n i s h option off, the result is x ~§ These different formats give the interface some flexibility, but they may also be confusing to the first-time user. A simple notebook might show the somewhat busy icon palette, an equation in the notebook, and a graph of the function defined in the notebook. Details of the graph can be displayed at the bottom of the notebook by clicking on the "graph details" button at the bottom of a small palette within the graph window. Pop-up menus in the graph details area allow you to adjust some of the display attributes such as line width, style, and color. Other options accessible through icons in the graph window let you change the n u m b e r of data points used in creating the curve, zoom in or out of the current view, or isolate certain parts of the plot. The graph is dynamically linked to the notebook s t a t e m e n t t h a t created it; the graph will update as you type changes in the s t a t e m e n t definition. You can also click and drag within the graph window to see different parts of a graph in real time.
Theorist also handles the creation and import of t a b u l a r data. Import may be as simple as generating a table in a spreadsheet or word processing program, 300
Theorist: Symbolic Math and Graphics copying the text, and using a paste command in the table details window to automatically make a new table. You can also load tables saved in text format into Theorist. Theorist defines a table as a "... model of a smooth, continuous function defined by function values at regular intervals." Both real and complex data tables can be created or imported. Arrays of data can also be imported or exported within Theorist, but you should note t h a t large tables or matrices of d a t a use RAM space rapidly.
Conclusion Theorist is a fine program for learning to apply m a t h e m a t i c s to problems in structural geology because of the program's ability to dynamically link notebook expressions and graphs. The real-time manipulation of graphs (including such things as rotation of three dimensional spaces) is not currently implemented in high-end symbolic m a t h programs like Mathematica. The notebook metaphor, with embedded graphics, is also available in some versions of Mathematica, however. Theorist does have its limitations, however. It does not have the extensive resources of freely available notebooks and libraries that Maple and MathematicaTM have. The application is also limited in precision if you work with high numerical precision or very large or with very small numbers. If you are at an institution t h a t has a site license for Maple, you should check with your computing services department; it may be t h a t a site license for Theorist has already been purchased.
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A b s t r a c t - This note presents a critical review of Theorist TM, a symbolic mathemathics and graphing application of potential interest to the field of structural geology.
Introduction Theorist is a symbolic mathematics and graphing application for microcomputers. The software is available for the MacOS TM, Windows TM, and Windows NT T M operating systems. Minimum requirements on the Macintosh are a Mac Plus or above (including Quadras and PowerPCs), 2 MB of RAM, 2 MB hard disk space, and System 6, 7, or A / UX. Suitable performance on PowerMacs and for graphics intensive applications benefit from additional RAM. On the Windows side, you need a minimum 386 processor, 4 MB RAM, 2 MB hard disk space, and Windows 3.1, NT, or95. The version reviewed here is 2.01 running on a Macintosh 900 with a PowerPC upgrade card installed under System 7.5.1. Earlier versions of Theorist were marketed by Prescience Inc., but the program is now distributed by Waterloo Maple Software Inc., makers of the popular Maple TM mathematical system for microcomputers and workstations. Evidently, much of the core code in Theorist resembles Maple anyway. Theorist supports all basic mathematical procedures you would expect in such software including: roots, factorials, and powers; integer and floating point numbers; mathematical constants and trigonometric functions; polynomial simplification and expansion; simultaneous solutions for systems of equations; vector and matrix algebra; and differentiation and integration. The maximum numerical precision is 15 digits. In addition, Theorist comes with reasonable graphing abilities in two and three dimensions. Graphics can be animated in real time, and the program supports several projection systems (Cartesian, polar, cylindrical, and spherical). Options for coloring and shading plots allow creation of presentation-quality 299
Structural Geology and Personal Computers graphics t h a t can also be exported in MetaFile format (Windows), or PICT format (Macintosh). Files copied onto the Macintosh clipboard within Theorist can be pasted into other Macintosh applications t h a t accept the PICT format. EPS (Encapsulated Postscript) files can also be generated. These resolution-independent files can then be placed in page processors for publication. It is also possible to create a text version of the EPS file on the Macintosh; this file, with some editing, may then be opened in an modifiable form in a program such as Adobe Illustrator TM. The basic user environment in Theorist is the notebook. You can create notebooks optimized for your work t h a t will open automatically every time the program is started. A notebook' s format is independent of the operating system, so it can be readily transferred between platforms with e-mail or over a network. Notebooks contain hot graphics windows t h a t update automatically when an expression is changed within the notebook. A "statement" is the f u n d a m e n t a l expression in a notebook. S t a t e m e n t s are either "assumptions" or "conclusions" S t a t e m e n t s entered by the user are assumptions; results from the p r o g r a m are conclusions. S t a t e m e n t s may be equations or expressions composed of numbers, names, or wildcard variables. You can also define functions to be used within the notebook.
Theorist uses, in part, an iconic interface. You can create expressions and equations by clicking on a palette t h a t contains either variable n a m e s or functions and m a t h e m a t i c a l operators. The program automatically positions an entry point in an expression where you may enter information from the keyboard. Expressions may also be created from the keyboard directly. With the appropriate typed operators (especially the placement of parentheses), Theorist will i n t e r p r e t keyboard entry in a syntax similar to the point-and-click entry technique. A F o r t r a n i s h keyboard entry option lets you enter data in a way t h a t you might use in p r o g r a m m i n g or in a spreadsheet application. For example, ifyou type x^2 +2 with the F o r t r a n i s h option on, the result in the notebook will be x: + 2. With the F o r t r a n i s h option off, the result is x ~§ These different formats give the interface some flexibility, but they may also be confusing to the first-time user. A simple notebook might show the somewhat busy icon palette, an equation in the notebook, and a graph of the function defined in the notebook. Details of the graph can be displayed at the bottom of the notebook by clicking on the "graph details" button at the bottom of a small palette within the graph window. Pop-up menus in the graph details area allow you to adjust some of the display attributes such as line width, style, and color. Other options accessible through icons in the graph window let you change the n u m b e r of data points used in creating the curve, zoom in or out of the current view, or isolate certain parts of the plot. The graph is dynamically linked to the notebook s t a t e m e n t t h a t created it; the graph will update as you type changes in the s t a t e m e n t definition. You can also click and drag within the graph window to see different parts of a graph in real time.
Theorist also handles the creation and import of t a b u l a r data. Import may be as simple as generating a table in a spreadsheet or word processing program, 300
Theorist: Symbolic Math and Graphics copying the text, and using a paste command in the table details window to automatically make a new table. You can also load tables saved in text format into Theorist. Theorist defines a table as a "... model of a smooth, continuous function defined by function values at regular intervals." Both real and complex data tables can be created or imported. Arrays of data can also be imported or exported within Theorist, but you should note t h a t large tables or matrices of d a t a use RAM space rapidly.
Conclusion Theorist is a fine program for learning to apply m a t h e m a t i c s to problems in structural geology because of the program's ability to dynamically link notebook expressions and graphs. The real-time manipulation of graphs (including such things as rotation of three dimensional spaces) is not currently implemented in high-end symbolic m a t h programs like Mathematica. The notebook metaphor, with embedded graphics, is also available in some versions of Mathematica, however. Theorist does have its limitations, however. It does not have the extensive resources of freely available notebooks and libraries that Maple and MathematicaTM have. The application is also limited in precision if you work with high numerical precision or very large or with very small numbers. If you are at an institution t h a t has a site license for Maple, you should check with your computing services department; it may be t h a t a site license for Theorist has already been purchased.
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