Richard Fateman | University of California, Berkeley (original) (raw)

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Papers by Richard Fateman

ACM Communications in Computer Algebra, 2015

Applications to Scientific Computing, 1989

Symbolic Computation: Applications to Scientific Computing, 1987

Chapter 1 Computer Algebra and Operators Richard Fateman and Robert Grossman 1 The Symbolic Compu... more Chapter 1 Computer Algebra and Operators Richard Fateman and Robert Grossman 1 The Symbolic Computation of Operators After defining the two expansions exp (^)=£>«/»! t= 0 mi+ a)= f;(-i)« + Mvt, a computer algebra system such as Macsyma or Maple will quickly compute log (exp (A) exp (5))= A+ B+ 0 (N+ 1). Here 0 (N+ 1) denotes terms containing a product of N+ 1 or more A's and/or l?'s. This computation depends crucially upon the fact that AB—BA\ for objects for which this not true, certain correction terms enter. For example, if A and B are matrices, ...

Lisp and Symbolic Computation, Mar 1, 1991

Acm Sigsam Bulletin, Dec 1, 1997

Studies in Applied Mathematics, 1974

Proceedings of the Fourth Acm Symposium on Symbolic and Algebraic Computation, Aug 5, 1981

1. Introduction Numerous papers have been written comparing vari-ous algebraic manipulation syste... more 1. Introduction Numerous papers have been written comparing vari-ous algebraic manipulation systems. Almost without exception, these papers praise the Lisp-based systems for their flexibility, and condemn them for their slow-ness. Even systems which have been written ...

Encoding a univariate polynomial as a long integer conceptually unifies some processing tasks on ... more Encoding a univariate polynomial as a long integer conceptually unifies some processing tasks on polynomials with those on integers, including multiplication. An evaluation of a polynomial at a single point is sufficient to encode and decode all its coefficients if the point is sufficiently larger than the coefficients. This is sometimes referred to as "Kronecker's trick". We show that this idea has practical implications for efficient programs.

Information Linkage Between Applied Mathematics and Industry, 1979

Storage and Retrieval for Image and Video Databases, 1999

We describe the design of document analysis proceduresto separate mathematics from ordinary text ... more We describe the design of document analysis proceduresto separate mathematics from ordinary text on a scannedpage of mixed material. It is easy to observe that the accuracyof commercial OCR programs is helped by separatingmixed material into two (or more) streams, with only conventionalnon-math text handled by the usual OCR textbasedheuristic analysis. The second stream, consisting ofmaterial judged to be mathematics,

Storage and Retrieval for Image and Video Databases, 1996

Printed mathematics has a number of features which distinguish it from conventional text. These i... more Printed mathematics has a number of features which distinguish it from conventional text. These include structure in two dimensions (fractions, exponents, limits), frequent font changes, symbols with variable shape (quotient bars), and substantially differing notational conventions from source to source. When compounded with more generic problems such as noise and merged or broken characters, printed mathematics offers a challenging arena

Notation is a powerful tool for leveraging our thinking. As an example, most people believe we ca... more Notation is a powerful tool for leveraging our thinking. As an example, most people believe we can conceive of and express algorithms more effectively when we use a suitable computer programming language. It is clear that we lose some capabilities when inappropriately constrained by a language. It possible to accomodate different "paradigms" of thinking by choosing alternative notations or programming languages: this is often the essence of specially designed computer application languages or so-called "methodologies".

Programs in symbolic algebraic manipulation systems can compute certain classes of symbolic indef... more Programs in symbolic algebraic manipulation systems can compute certain classes of symbolic indefinite integrals in closed form. Although these answers are ordinarily formally correct algebraic anti-derivatives, their form is often unsuitable for further numerical or even analytical processing. In particular, we address cases in which such "exact answers" when numerically evaluated may give less-accurate answers than numerical approximations from first principles! The symbolic formulas may also behave inappropriately near singularities. We discuss techniques, based in part on the calculus of divided differences, for improving the form of results of symbolic mathematics systems. In particular, computer algebra systems must take explicit account of the possibility that they are producing not "mathematics" but templates of programs consisting of sequences of arithmetic operations. In brief, mathematical correctness is not enough. Forms produced by rational integration programs are used for examples.

The entry of mathematics into a computer system is important in a variety of contexts: educationa... more The entry of mathematics into a computer system is important in a variety of contexts: educational training and testing, publishing and communication of mathematical results, use of conventional notation for scientific programming. Numerous keyboard and mouse-activated methods have been implemented and used in various systems; in their most ambitious form these have been in computer algebra systems. Handwriting has been repeatedly proposed and demo nstrated (since at least 1968). Yet the use of handwriting alone has never put into production because of very high error rates. We now believe that a better prospect may emerge from using a combination of handwriting and voice.

Acm Sigsam Bulletin, Feb 1, 1981

1. The Difference Between Numeric and Algebraic Computation To illustrate the difference between ... more 1. The Difference Between Numeric and Algebraic Computation To illustrate the difference between numeric and symbolic processing, con-sider a computer program (in FORTRAN, say) which given the quantities a,b, and c, can apply the quadratic formula to approximate the roots ...

Acm Sigsam Bulletin, Mar 1, 1973

Firstly, "the run-time statistics mi£ht be considered predictable," except that MACSY[~... more Firstly, "the run-time statistics mi£ht be considered predictable," except that MACSY[~A, a LISP-lapsed system, was about as fast as, or faster than the ~mchine-hmguage or FORTI{AN systems. Why is this? While MACSYEA's data structures are not as bit-packingly tight as ...

An Excel link to Lisp functionality can provide a window into broader applicability of the spread... more An Excel link to Lisp functionality can provide a window into broader applicability of the spreadsheet interface to the general development of a scientific computing environment. Given the attempt by Microsoft to integrate all its applications via OLE, the same kind of technique can add powerful computation capabilities to other commonly used applications such as word processing and database programs.