[Indigo]<CaminoReal>CaminoRealUserManual.tioga!3

CAMINOREAL USER MANUAL VERSION 1.0

XEROX PARC, CSL-87-5 (Preliminary Version), JULY, 1987

CaminoReal User Manual Version 1.0

Dennis Arnon, Carl Waldspurger, and Kevin McIsaac

CSL-87-5 (Preliminary Version) July 1987 [P87-00017]

Abstract: Three broad categories of Mathematical Software are Computer Algebra (Symbolic Mathematics), Numerical Computation, and Mathematical Typesetting. In each of these categories one finds powerful and sophisticated systems. Nonetheless, what one really would like is simultaneous, integrated access to all three facilities.

CaminoReal is a user interface for integrated access to documents and computation. It lives in Cedar, the programming environment of Xerox PARC's Computer Science Laboratory, and is used in conjunction with Tioga, Cedar's multimedia document editor. Printing and management of other document components, such as text and graphics, is provided by Tioga. For computation, CaminoReal offers a small builtin algebra package based on the notions of Domains and Objects, plus access to "algebra servers" on a network. Mathematical expressions are exchanged in pure functional notation. Our current algebra servers are Reduce, SMP, and SAC-2.

Keywords: Computational Mathematics, Document Processing, Mathematical Typesetting, Technical Documents, Mathematics Editing, WYSIWYG, User Interfaces, Direct Manipulation, Computer Algebra, Symbolic Mathematical Computation, Object-Oriented Programming

XEROX Xerox Corporation
Palo Alto Research Center
3333 Coyote Hill Road
Palo Alto, California 94304

DRAFT — Preliminary Version — DRAFT

There is no 'royal road' to geometry.

Euclid, said to Ptolemy I

Preface

To see the mathematical expressions in this document (whether you are reading it online or printing it), you need to have a running CaminoReal.

1. Introduction

There are computer algebra systems, there are numerical systems, and there are high quality document formatting systems that support mathematical expressions. There is still no adequate support for the working scientist who needs "living" notebooks and technical papers. Such a worker wants a system that will support both the exploration of his technical ideas through computations, and the production of the evolving technical document that describes them.

CaminoReal is a prototype system for the integration of documents, editing, and algebra. CaminoReal currently lives in Cedar, the programming environment of Xerox PARC's Computer Science Laboratory, and is used in conjunction with Tioga, Cedar's multimedia document editor. Actual document production (e.g. printing, management of other document constituents such as text and graphics) is provided by Tioga. CaminoReal supports interactive, syntax-directed, two-dimensional, WYSIWYG editing of mathematical expressions, placing/fetching such expressions in/from Tioga documents, and algebraic manipulation of expressions. Algebraic computation can be performed using either a small builtin package, or using well-known algebra systems such as Reduce, SMP, and SAC-2 over a network. The internal algebra package is based on an object-oriented paradigm that supports polymorphic procedures. For example, one can easily create and do simple arithmetic on matrices of polynomials with complex number coefficients, or matrices of such matrices, etc.

A basic type of activity that CaminoReal supports is the creation of "interactive" technical documents. For example, the user can browse a (nicely typeset) draft of a technical document on the WorkStation screen, select, edit and compute with mathematical expressions in it (besides editing text and graphics, of course), and insert the resulting expressions back into the document. One can extend this to the notion of a "computed document", two flavors of which are "spreadsheets" and "mathematical form letters". These are all documents with imbedded computations; see Section 6 for more details.

2. Editing Expressions

2.1. The Basics of Editing Expressions

The editor is similar to other syntax-directed editors, such as the Cornell Program Synthesizer. A selected placeholder can be replaced by a template, which itself typically contains placeholders. Templates are chosen either from menus or the keyboard. Keyboard input in standard infix notation is also accepted.

2.2. Terminology for Editing Expressions

PlaceHolder:

A placeholder is an empty Expression which needs to be filled in, and looks like

in your CaminoReal viewer. It is intended to be similar in appearance and function to placeholders () in Tioga.

Replace:

"Replace old with new" means to delete old Expression and insert new Expression in its place.

Wrap:

"Wrap template foo around bar" means to insert bar to fill in one of the placeholders in template foo, and then replace bar by this newly created Expression. Thus after the wrap, bar is a subExpression of foo.

2.3. Selecting Expressions

What can you select?

CaminoReal considers each class of Expression (e.g. summation, integral) to be composed of Arguments and Symbols. An Argument is a "subExpression", i.e. something which is recursively an Expression; a Symbol is a glyph (e.g. the sigma symbol, the integral sign) which is part of the rendering of that notation, but is not itself an Expression. The basic rule is that you can select Arguments, but not Symbols.

If for example you are editing a summation Expression, you can select any of the summation's subExpressions (lowerlimit, upperlimit, summand) or the entire summation Expression. You cannot, however, select the sigma symbol by itself in the summation (clicking on the sigma will actually select the entire summation Expression).

Expressions can be thought of as trees (with operators at nodes and atoms at leaves), CaminoReal provides ways to move through the Expression tree with a minimum of fuss. Operations are available which allow you to: extend a selection to include its parent Expression (moving up the tree), narrow a selection to a child Expression (moving down the tree), and change a selection to select a sibling Expression (same level in tree). Thus, both CaminoReal and Tioga have hierarchical tree-like structures and commands for selecting subtrees and leaves.

There are four selection types, similar in appearance and function to Tioga selections:

Primary selection:

Selected Expression is highlighted by rendering it white on black, which is inverted from the normal black on white (just like Tioga).

Copy selection:

Selected Expression is highlighted in dark gray.

Move selection:

Selected Expression is highlighted in light gray.

Keyboard (KB) selection:

This selection type cannot be applied by the user. The selected Expression is highlighted using horizontal gray lines. This selection type is automatically invoked when there is an active keyboard entry for an atom (e.g. a number or a variable). Its purpose is mostly as an indicator. However, when template wrapping is invoked from the keyboard, an active keyboard selection becomes the primary selection.

How can you select?

You can select Expressions using either the mouse or keyboard. To select with the mouse, simply point at the Expression you wish to select and click the appropriate button. The selected Expression will be the smallest Expression (greatest depth in tree) which contains the point specified by the mouse. If you think of each Expression as being enclosed by a bounding box, this is the Expression enclosed by the smallest box which contains the point specified by the mouse.

The following mappings are currently used:

Single Clicks:

Red => Primary Select

Shift Red => Copy Select

Ctrl Red => Move Select

Double Clicks:

Red => Extend Primary Selection to Parent

Shift Red => Extend Copy Selection to Parent

Ctrl Red => Extend Move Selection to Parent

Keyboard selection actions:

Ctrl-P, '), '], '} => Primary Select the Parent of the current Keyboard or Primary Selection.

Ctrl-I => Primary Select entire Current Expression (entire contents of the viewer in which mouse sits)

Ctrl-K => Primary Select the Hot Child (Kind) of current Primary Selection.

Ctrl-L, ', => Primary Select sibling (Lateral movement) of current Keyboard or Primary Selection.

Ctrl-H => undo previous keystroke; Primary Select entire Current Expression

Ctrl-X => swap Primary and Move selections (can't really use in keyboard input, since mouse required to make Move selection)

Ctrl-M => Convert the Keyboard Selection into the Primary Selection

2.4. Entering Expressions

Using Menus:

ReplaceWithObject:

Replaces the primary selection with a "mathematical object". The type of object is chosen from a pop-up menu. Depending on the type of object, the actual Expression is either given a default value (rational, complex), obtained from additional pop-up menus, or from a Tioga viewer selection (variable, bool, integer, real). For example, "ReplaceWithObject Integer" tries to get an integer from an active text selection, and "ReplaceWithObject GreekVariable" provides a pop-up menu of choices for the variable.

"ReplaceWithObject Variable" may allow you to get characters you want into an Expression when no other way seems available. Whatever is in the active text (Tioga) selection, i.e. any valid rope, will be picked up and stuffed when you bug the "Variable" entry of the pop-up menu.

The "parseRope" option will parse the (Tioga)-selected string as though its characters were typed individually at the keyboard.

For sets, sequences, vectors, matrices, and blocks (see below for defn of block), the dimensions are chosen from pop-up menus. (note: CaminoReal can support arbitrarily big matrices, but the current user interface restricts the maximum dimension to be 10 x 10.)

The matrix is initialized by setting all elements = 0. This is useful when entering sparse matrices, and isn't really a hindarance when you aren't.

ReplaceWithOperator:

Brings up a pop-up menu listing classes of operators. You select a class of operators from these menus, and then get another pop-up menu listing the actual templates. Then the primary selection is replaced by the template for the operator you have selected.

WrapWithOperator:

Similar to ReplaceWithOperator, but wraps a template around the primary selection instead of replacing it. In other words, the primary selection is used to fill in a placeholder in the template. This placeholder is usually the first (e.g. "a" in "a + b") or most important (e.g. integrand in integration) argument to the template.

Using the keyboard:

CaminoReal allows keyboard input for some of the most common expression types.

Integer, Real, and Variable atoms can be typed directly into a (Primary- or Keyboard-)selected Expression. As mentioned in the section on selections, the active Keyboard selection will be selected and highlighted using horizontal gray lines. This selection is terminated as soon as a Primary selection is made or any editing function is invoked (you can always select outside of an Expression to get rid of the Keyboard selection). A Real number must begin with a digit (e.g. 0), and not just a decimal point.

Typing operator characters into a selected Expression performs a template wrap around the currently active Keyboard or Primary selection. Currently supported keys, with their semantics, are:

'+ => binary sum

'— => unary difference

'- => binary negation

'* => binary product

'/ => binary fraction

'^ => binary pow

'← => binary subscript

'? => binary function of one argument

'( => unary parentheses

'{ => unary curlyBrackets

'! => unary factorial

'$ => unary exists

'@ => unary forAll

'& => binary and

'| => binary or

'~ => unary not

'= => binary eqFormula

'> => binary gtFormula

'< => binary ltFormula

'# => binary notEqFormula

For the binary operators, this gives "pseudo-infix" input. For example, to enter "a + b", simply select a placeholder, then type "a", "+", "b". What is really going on is that the operation "+" is wrapped around the Expression "a", and the placeholder for the augend is auto-selected. Typing the "b" fills in the augend placeholder. The ctrl-P "select parent" operation is very useful for keyboard input to avoid switching beteen the keyboard and the mouse. For example, to enter

use the keystrokes "x", "^", "2", ctrl—P, "+", "1", ctrl-P, "=", "0".

For the unary operators, the input paradigm is "prefix" or "postfix", depending on the operator. E.g. to enter

type the keystrokes "(", "$", "x".

2.5. Editing Expressions

Copy

Make a Primary selection, hold down the Shift key, make a Copy selection, release Shift, and the Primary selection will be replaced by the Copy selection. The Copy selection is unchanged.

Move

Make a Primary selection, hold down the Control key, make a Move selection, release Control, and the Primary selection will be replaced by the Move selection. The Move selection is replaced by a Placeholder.

Swap

Intended to mimic Tioga's swap. Make a Primary selection, hold down Control, hit and release the "X" key (continue holding down Control) make a Move selection, release the Control key, and the Primary and Move selections will be interchanged.

The selections (i.e. operands) for Copy, Move, and Swap can either lie within a single Camino viewer, or in two different Camino viewers. Note that Copy, Move, and Swap in CaminoReal are performed very much as in Tioga.

2.6. Other Menu Buttons

Scale

Scales the contents of the viewer:

red => scale by factor of 1.5 (zoom)

yellow => remove all scaling and return to default size (normal)

blue => scale by factor of 1/1.5 (shrink)

Home

Moves the Expression to its default location at the lower left-hand corner of the viewer. This is useful if you used the bi-scrollers and "lost" the Expression somewhereon the infinite plane.

SelectPrimary

Sets the primary selection to be the entire Current Expression. Note that SelectPrimary can also be done from the keyboard with Control-I.

SelectCopy

Sets the copy selection to be the entire Current Expression.

Undo

Undoes the last operation which changed the contents of the viewer. Undo in CaminoReal, unlike Tioga, undoes the last change to an individual viewer, not to the global collection of active viewers (There are pros and cons to this approach). Undo sets the primary selection to the entire Current Expression. Note that Undo can also be done from the keyboard with either Control-H or Backspace.

SetName

Sets the name of this Item to the contents of the ScratchPad.

NewItem

Get a new CaminoReal viewer.

3. Expressions and Documents

3.1. ToTioga button

To put an expression into a Tioga doc, make a primary selection in the Camino viewer, make a selection in the Tioga doc, and bug "ToTioga". The expression will be placed in the document immediately preceding the Tioga selection. The value in the ScratchPad will become its PointSize in the document.

The ScratchPad must either contain a REAL constant, or be empty, when you do this. If nonempty, the value it contains will become the PointSize of the expression in the document. 20.0 is the default if the ScratchPad is empty, and in general is a good initial choice.

Note that scaling an expression in a Camino viewer (with the Scale button) has no bearing on the PointSize an expression gets when put into a Tioga document; only the value in the ScratchPad controls that.

3.2. FromTioga button

To fetch an expression from a Tioga doc, make a primary selection in the Camino viewer, (character) select the expression in the Tioga doc, and bug "FromTioga". The ScratchPad will get set to the PointSize.

3.3. SetPtSize button

To adjust the PointSize of an expression in a document, put the value you want in the ScratchPad, (character) select the expr in the doc, and bug "SetPtSize".

3.4. Examples

Here are some sample paragraphs containing Expressions. This is a plain line of text which happens to include an expression X , and is above some Expressions:

Note that Expressions can easily be moved or copied around in text with Tioga character copy.

Let's place this expression here:

3.5. Printing the document

Create an interpress file with the command "TiogaToInterpress <doc>.tioga" and print it in any of the standard ways.

4. Computation with the Resident Algebra Facilities

4.1 Domains

1. What they are

The Ground Domains are:

Expressions (i.e. general expressions)

Variables

Bools

Integers (Mesa INTs)

Rationals (BigRats)

Reals (Mesa REALs)

Complexes (built from Mesa REALs)

The Domain Structuring Operations are:

SingleSet

FamilyOfSets

Sequences

Vectors

Matrices

Polynomials

2. Creating Domains

Bug the

Working Domain

button in the control panel. You'll get a pop-up menu of choices, including all the Ground Domains and Domain Structuring Operations. You must initially select a Ground Domain; a short name for it (e.g. Z for Integers) will appear in the text viewer next to the Working Domain button.

Matrices

These are rectangular matrices of specified size, whose entries are elements of the current Working Domain. When you select Matrices, you get a pop-up menu to select the size. Similarly for Vectors, Sequences, and Sets.

Polynomials

For any polynomial, we need to keep track of 'what variables it's a polynomial in'. This is accomplished by associating a variable sequence with the polynomial. This is a sequence of Ropes (the variables). In order for scanning to work, variables should be Cedar identifiers. A variable sequence should be written as comma-separated variables enclosed in parentheses (whitespace ok anywhere except within a variable). For example, "(x,y,z)".

What you do is enter the variable sequence into the ScratchPad, then bug WorkingDomain, and bug Polynomials in the menu. The coefficient domain is what was previously in the "WorkingDomain".

4.2 Evaluation

This is the most basic way to do algebra with the built in package. Any Expression can be evaluated; if CaminoReal doesn't know enough algebra to do something interesting with it, it just returns it unevaluated.

The result of an evaluation always belongs to some Domain. General Expressions (denoted MExprs) is the catchall if nothing narrower can be determined.

The semantics of Eval are: To evaluate a function of args (which every non-atomic Expression can be viewed as), we first (recursively) evaluate the arguments, then look for the function as a Method in some Domain (typically the Domain to which the first (evaluated) argument belongs), and if we find it, apply it to the evaluated arguments. If not found, then look for it as a Method in some other Domain (e.g. the Domain to which the next evaluated arg), etc. As a catchall we look for the desired Method in all the Domains that the system currently knows about.

Miscellaneous note: polynomial gcd's are currently done by the SAC-2 package on the Vax (via the Bridge). For uninteresting reasons, you'll get an error if the variables of polynomials whose gcd's you try to compute do not consist entirely of upper case letters.

EvalPrimaryInPlace button

Evaluate the Primary selection and replace it by the result. Domain of the result is shown in the "Result Domain" viewer.

EvalTiogaInPlace button

Evaluate the current CaminoReal Expression selected in a Tioga document, and replace it by the result. Domain of the result is shown in the "Result Domain" viewer.

Evaluation from the keyboard (Control-V)

Control-V evaluates the current Primary selection in place. Same as EvalPrimaryInPlace button, except that the Domain of the result is NOT shown in the "Result Domain" viewer.

4.3 Operations

OpPrimaryInPlace button

Evaluate the Primary selection, put up a pop-up menu of operations appropriate for that Domain, get the appropriate number of arguments for the selected operation from CaminoReal selections (e.g. for sum, the second arg is the CaminoReal Copy selection), and replace the Primary selection by the result of the operation.

OpWDinPlace button

Put up a pop-up menu of operations appropriate for the current Working Domain, get the appropriate number of arguments for the selected operation from CaminoReal selections, and replace the Primary selection by the result of the operation.

OpPrimary, OpWD buttons

Put the result in a new CaminoReal viewer instead of replacing Primary Selection.

4.4 The Environment

Currently there is just one environment in place across all documents and all CaminoReal viewers. Running CaminoReal resets it.

A variable is placed into the environment by evaluating an assignment statement. For example, the evaluation of

will place a variable X into the environment with value X .

Evaluation of the functions

and

will respectively remove the values of all variables, and of the variable X, from the environment. Note the quoting of X in the second example to avoid evaluation.

Do not evaluate self-referential expressions such as X; this will loop.

5. Computation with Algebra Servers

The general loop is: you make an appropriate Primary selection, left (for SMP) or middle click (for Reduce) the "Algebra" button, and the result of passing the Primary selection as a command line to SMP or Reduce will replace the Primary selection.

CaminoReal Expressions are passed to an algebra system by first converting them to an appropriate linear representation; similarly, the output from an algebra system is received in linear notation and parsed into CaminoReal internal notation.

Left clicking the "ToASRope" button will show you the SMP linear representation that CaminoReal will create for a given expression, and Right clicking it will show you the Reduce string that CaminoReal will create for it. For example, if the current Primary selection is:

then left-clicking ToASRope will give:

Int[Div[Minus[1, Mult[2, Pow[x, 3]]], Pow[( Plus[1, Pow[x, 3]] ), 2]], x]

and middle clicking it will give:

int(quotient(difference(1, times(2, expt(x, 3))), expt(( plus(1, expt(x, 3)) ), 2)), x)

If we middle click the Algebra button to send this off to Reduce, after about ten seconds we get back

in our CaminoReal viewer.

6. Computed Documents

6.1 Introduction

CaminoReal's expression language supports an assignment statement. Also, expressions assigned to variables are maintained in a symbol table (the Environment). If desired, the math expressions imbedded in a Tioga document can be evaluated prior to being painted, whenever the document is displayed, and so can be defined as functions of other expressions. This makes possible Tioga documents that are "spreadsheets" or "mathematical form letters", or simply "computed documents". Having the math in a technical paper computed on the fly minimizes the introduction of typographical errors, and so reduces the burden of proofreading.

6.2. MathEval on/off

When the EvalBeforePaint flag is off (the default), CaminoReal Expressions in a Tioga document are painted just as they are stored. When the EvalBeforePaint flag is on, they are evaluated before being painted. This enables Computed Documents. The Cedar CommandTool commands "MathEval on" and "MathEval off" do the toggling.

6.3. Blocks

A block is an expression which is simply a sequence of other expressions, and whose value is the value of the last expression. You enter a block into the editor via the ReplaceWithObject button.

6.4. Some useful Expression constructors

sequenceFromIteration[function, variable, start, finish]; Result is a sequence of general expressions. prior value of variable is destroyed; at exit has value finish

matrixFromRowSequence[rowSequence]; rowSequence is a Sequence of Vectors over any Domain(s), all of same dimension; Result is a nRows x nCols matrix of general expressions, where nRows is length of rowSequence, and nCols is dimension of each row. The elements of the output matrix are obtained by evaluation of (the Exprs obtained) from the appropriate vector elements.

iteration[function, variable, start, finish]; Result is value of last iteration. prior value of variable is destroyed; at exit has value finish

squareMatrixFromFunction[function, rowIndex, colIndex, size]; Result is a size x size matrix of general expressions. prior values of rowIndex and colIndex are destroyed; at exit they have value size

7. Acknowledgements

Thanks to Rick Beach and Michael Plass for enlightenment on Tioga and other aspects of Cedar. Thanks to Ken Pier for the "point and stuff" part of the CaminoReal-Tioga interface. Thanks to Christian LeCocq for the BridgeSubmit package. Thanks to those in the Computer Science Lab at PARC who have used CaminoReal for their documents and computations, and suggested improvements. Thanks to Rick Beach, Alan Perlis, and Alan Demers for inspiration.

References

Selected References on Mathematical Typesetting

Bell Telephone Laboratories, "The Preparation and Typing of Mathematical Manuscripts", Third Revised Edition, 1979.

Knuth, Donald, "Mathematical Typography", Bull. AMS (New Series), March 1979, V. 1, No. 2, 337-372.

Palais, Richard, Column on Technical Wordprocessing, Notices of the AMS, ongoing.

Swanson, E., "Mathematics into Type: Copying, Editing, and Proofreading of Mathematics for Editorial Assistants and Authors", American Mathematical Society, Revised Edition, 1979.

Markup Languages for Representation of Mathematics (Form-focused)

Association of American Publishers, Electronic Manuscript Series, "Markup of Mathematical Formulas", 1985.

Kernighan, B.L., Cherry, L, "A system for typesetting mathematics", CACM, 18 (March 1975), 151-157.

Knuth, D.E., "The TeXBook", Addison-Wesley, 1984.

Algebraic Languages for Representation of Mathematics (Content-focused)

Foderaro, J.K., "The Design of a Language for Algebraic Computation Systems", Report No. UCB/CSD 83/160, Computer Science Division (EECS), UC Berkeley, August 1983, 81pp. (Ph.D. Thesis)

Jenks, R., "A language for computational algebra", Proc. ACM 1981 Symposium on Symbolic and Algebraic Computation, Snowbird, Utah, Aug 5-7, 1981, pp. 6-13. Report RC8930, Math. Science Dept., IBM TJ Watson Research Center, July 14, 1981.

Martin, William, "Symbolic Mathematical Laboratory", Ph.D. thesis, MIT, Jan. 1967.

Old work on Computer Input and Output of Mathematics

Anderson, Richard, "Computer Recognition of Hand-Drawn Math" (not quite right), Harvard Ph.D. thesis, 1965?

Martin, William, "Symbolic Mathematical Laboratory", Ph.D. thesis, MIT, Jan. 1967.

Martin, William, "Computer input/output of mathematical expressions.", Proc. Second Symp. on Symbolic and Algebraic Manipulation (SIGSAM '71), ACM, pp. 78-89.

Selected References on Technical Document Production Systems

Knuth, D., "The TeXBook", Addison-Wesley, 1984.

M. Spivak, "The Joy of TeX", Addison-Wesley, 1986.

Selected References on Computer Algebra

Fenichel, An online system for mathematics (?), Harvard Ph.D., 60's.

Hearn, A., The Personal Algebra Machine, Proc. IFIP '80, North-Holland, Amsterdam, 1980, pp. 620-628.

R. Pavelle, M. Rothstein, and J. Fitch, "Computer Algebra", Scientific American, 245, 6 (December 1981), pp. 136-152.

S. Watt, Parallel algorithms for computer algebra, Ph.D., University of Waterloo, 1984

Selected References on Numerical Computation

Dongarra, J., and Grosse, E., "Distribution of Mathematical Software via Electronic Mail", Comm. ACM, 30,5 (May 1987), pp. 403-407.

Selected References on Mathematical Hardware

Hewlett-Packard HP-28C Reference Manual

Report on the Interset 2000 System, Seybold Report on Publishing Systems, February 2, 1987, pp. 1-18.

Selected References on Cedar

Swinehart, D.C., Zellweger, P.T., Beach, R.J., Hagmann, R.B., "A Structural View of the Cedar Programming Environment", Report CSL-86-1, Xerox Palo Alto Research Center, June 1986, 74pp., also ACM Trans. on Programming Lang. and Systems (TOPLAS), 1986.

Selected References on Object-Oriented programming

Bobrow D. et al, "CommonLoops: Merging Lisp and Object-Oriented Programming", OOPSLA Proceedings, 1986.

M. Stefik and D. Bobrow, "Object-oriented programming: themes and variations", AI Magazine, VI, 4, Winter 1986, pp. 40-62.

Selected References on User Interfaces

S. Card and T. Moran, "User technology: from pointing to pondering", ACM Conf. on Personal Workstations, 1986, pp. 183-197

Shneiderman, B., "The Future of Interactive Systems and the Emergence of Dirct Manipulation", Behav. Inf. Technol. 1, 2 (1982), 237-256.

Furnas, G., "Generalized Fisheye Views", "Human Factors in Computing Systems", CHI-86 Conference Proceedings, ACM, 1986, 16-23.

Selected References on Integrated Systems for Mathematical Work

Calmet, J. and Lugiez, D., "A Knowledge-Based System for Computer Algebra", ACM SIGSAM Bulletin, V. 21, No. 1, Issue #79, pp. 7-13.

Bloomberg, D. and Hogg, T., "Engineering/Scientific Workstation Project", Internal Report GSL-87-01, P87-00001, Xerox Palo Alto Research Center, January 1987.

Klerer, M. and Reinfelds, J., "Interactive Systems for Experimental Applied Mathematics", Academic Press, New York, 1968, 472 pp

Martin, William, "Symbolic Mathematical Laboratory", Ph.D. thesis, MIT, Jan. 1967.

PC Magazine, The Scientific PC: Software for Problem Solving", April 14, 1987, pp. 155ff.

Wells, M. B. and Morris, J. B. (eds.), Proceedings of a Symposium on Two-Dimensional Man-Machine Communication, ACM SIGPLAN notices, Vol 7, No 10, October 1972.

Evaluation of Mathematical Expressions

MathLab Group, "Macsyma Reference Manual", Version 9, Laboratory for Computer Science, MIT, December 1977, Chapter 3.

Domain and/or Object-oriented Computer Algebra Systems

Abdali, S.K., Cherry, G.W., Soiffer, N., "An Object-Oriented Approach to Algebra System Design", Proc. 1986 Symp. Symbolic and Algebraic Computation (B. Char, ed.), ACM, pp. 24-30.

A. Fortenbacher et al, "An Overview of the Scratchpad Language and System", Document Number Pre-Release V0M11, Mathematical Sciences Department, Knowledge Systems, Computer Algebar group, IBM TJ Watson Research Center, April 1987, 116pp.

Soiffer, N., "A Perplexed User's Guide to Andante", MS, UC Berkeley, 12+1 pp, November, 1981.

User Interfaces for Computer Algebra Systems

Abdali, S.K., Cherry, G.W., Soiffer, N., "On the Road to Better Computer Algebra System Interfaces", TR #CR-87-26, Computer Research Laboratory, Tektronix Laboratories, Beaverton OR, March 1987, 10pp.

Foderaro, J.K., "Typesetting MACSYMA Equations", in Proc. of the 1979 MACSYMA Users Conf, V.E. Lewis (ed), Washington DC 345-361, also, UCB MS Project Rpt. EECS Dept. 1978.

Fateman, R., "TeX Output from Macsyma-like systems", MS, 5pp, University of California, Berkeley, May 1987.

Foster, G., "User interface considerations for algebraic manipulation systems", Report No. UCB/CSD 84/192, Computer Science Division (EECS), University of California, Berkeley, June 1984.

Foster, G., "DREAMS: Display REpresentation for Algebraic Manipulation Systems", Report No. UCB/CSD 84/193, Computer Science Division (EECS), University of California, Berkeley, April 1984.

Leong, B. "Iris: Design of a User Interface Program for Symbolic Algebra", Proc. 1986 Symp. Symbolic and Algebraic Computation (B. Char, ed.), ACM, pp. 1-6.

C.J. Smith and N. Soiffer, "MathScribe: A User Interface for Computer Algebra Systems", Proc. 1986 Symp. Symbolic and Algebraic Computation (B. Char, ed.), ACM, pp. 7-12.

User Interfaces for Technical Document Production; Mathematical Expression Editing

Kimball, R., "Formula User Interface Issues", Internal memo, Xerox PARC, March 8, 1978.

McGregor, S., "Desktop Formula Frames Implementation", Xerox Office Products Division Internal Memo, November 1978, 13pp.

McGregor, S., "Star Formula Implementation", Xerox Office Products Division Internal Memo, November 1978, 3pp.

McGregor, S., "Tasks for Implementing Formulae in Star", Xerox Office Products Division Internal Memo, August 1980, 4pp.

Quint, V., "An interactive system for Mathematical Text Processing", Technology and Science of Informatics, V. 2, #3, (1983), pp. 169-179.

Quint, V., "Interactive Editing of Mathematics", Proc. First International Conference on Text Processing Systems, 24-26 October 1984, Dublin, Ireland, Boole Press, Dublin, 1984, pp. 55-68.

Schelter, W.F., "Sample INFOR Display", MS, Department of Mathematics, University of Texas-Austin, August 1986, 11pp.

User Interfaces for Numerical Systems

G. Culler, "Mathematical laboratories: a new tool for the physical and social sciences", ACM Conf. on Personal Workstations, 1986, pp. 59-72, reprinted from Klerer and Reinfelds 1968 (op. cit.)

Rice, J. and Rosen, S., "NAPSS, Numerical Analysis and Problem Solving System", Proc. ACM 21st National Conference, Los Angeles, 1966, ACM Publication P-66, (1966), p. 51ff.