B. W. Char, K. O. Geddes, G. H. Gonnet, B. Leong, M. B. Monagan, and S. M. Watt. Maple V: Language Reference Manual. Springer, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the generation of test cases for the Function Composition Tool. Expressions in the TTS are represented as tree structures rather than strings of text. A text string, however, is frequently a convenient means of representing mathematical expressions. Symbolic mathematics packages, such as the Maple [17] [18] system, generally accept lines of text as input, since it is a conventional way for the user to enter data. The purpose of the MapToTts Translator is to convert a text string having a simplified Maple syntax, into a TTS expression. Details concerning the MapToTts Translator comprise Appendix ....

....developments suggested. Some conclusions are drawn from the overall effort. 7.1 Results The Function Composition Tool is a significant contribution to the TTS. Initial considerations suggested that composition could best be accomplished with the use of a commercial symbolic engine. The Maple [18] [17] system was a clear option, which explains the use of Maple syntax in the MapToTts Translator. The later publication of the technical report [8] provided a way for composition to be performed within the tool. The restriction on tabular expressions to normal function tables was extended by ....

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B. W. Char, K. O. Geddes, G. H. Gonnet, B. L. Leong, M. B. Monagan, and S. M. Watt, Maple V Language Reference Manual. New York: Springer-Verlag, first ed., 1991.

....not divide q. Explicit results have been obtained in a number of cases; see [30, 32, 33, 18] for types A; B and [7, 23, 21, 47, 48] for exceptional types (see also [14] for a survey) In the latter cases, these computations use in an essential way the computer algebra systems GAP [49] and MAPLE [10]. But they have also been a stimulus for theoretical research and a source of evidence producing examples. 1. HECKE ALGEBRAS AND q SCHUR ALGEBRAS In this section, we describe the construction of Hecke algebras and q Schur algebras, and explain how they appear in the representation theory of ....

B.W. CHAR et. al. - Maple V, Language Reference Manual, Springer (1991); see also http://daisy.uwaterloo.ca

....groups. The matrix entries of our representations are rational functions in the variables p and q. These rational functions are quotients of polynomials in Z[p; q; p ] and the denominators contain only the polynomials [2] p ; 2] q ; 2] pq ; 2] pq Gamma1 ; 2] p q ; 2] p Gamma1 ; [3] p ; and [3] q ; 1.1) where [2] x = x x and [3] x = x . This means that our representations are well defined over any field F such that p; q 2 F and none of the polynomials in (1.1) are equal to 0. The research in this paper was begun while the first author was visiting Sydney University ....

....matrix entries of our representations are rational functions in the variables p and q. These rational functions are quotients of polynomials in Z[p; q; p ] and the denominators contain only the polynomials [2] p ; 2] q ; 2] pq ; 2] pq Gamma1 ; 2] p q ; 2] p Gamma1 ; 3] p ; and [3] q ; 1.1) where [2] x = x x and [3] x = x . This means that our representations are well defined over any field F such that p; q 2 F and none of the polynomials in (1.1) are equal to 0. The research in this paper was begun while the first author was visiting Sydney University on an ....

[Article contains additional citation context not shown here]

Bruce W. Char, Keith O. Geddes, Gaston H. Gonnet, Benton L. Leong, Michael B. Monagan, and Stephen M. Watt. Maple V Language Reference Manual. Springer-Verlag, New York, Berlin, Heidelberg, 1991.

....algorithms exhibit the behavior that the model possesses. Example 1.2 below presents a simple algorithmic theory that represents the standard model of the natural numbers. The computer algebra framework is mechanized by computer algebra systems. Examples include Axiom [39] Macsyma [41] Maple [10], and Mathematica [52] Most computer algebra systems are designed primarily for performing computations. Computations are performed at great speed, but the results are not always reliable. The algorithmic theories in which computation is performed are usually not represented as explicit, ....

Char, B. W., K. O. Geddes, G. H. Gonnet, B. L. Leong, M. B. Monagan, and S. M. Watt: 1991, Maple V Language Reference Manual. Springer-Verlag.

....minimizes the delay D is an , where a 0 and b 0 are constants. In this chapter, we show that the optimal wire sizing function, taking fringing capacitance into consideration, is f(x) 1) where W(x) is the Lambert s W function, a 0 and b 0 are constants. The Lambert s W function [37, 38] was first introduced by Euler in 1779 [39] when he studied Lambert s transcendental equation in [40] W(x) function is defined as the value of w that satisfies we = x. Like the exponential function, the W function is differentiable and integrable. For jxj , the W function has the following ....

Bruce W. Char, Keith O. Geddes, Gaston H. Gonnet, Benton L. Leong, Michael B. Monagan, and Stephen M. Watt, The Maple V Language Reference Manual, Springer-Verlag, 1991.

....possible values of # and A and also for l 0 # r 0 . All points with an initial opening angle of # 2 lie on the lower half circle. 0.5 0 Y 0.5 0.5 X Figure 8: The curves fulfilling condition (4) for all values of # and A. Thisfigurewascreated by using the computer algebra system Maple [5] which was also very helpful in checking the transformations of the formulae in Sections 3.3 and 3.4. Two cases can be distinguished. For A # 1 the curves can be continuously completed to an endpoint on the line v l v r with X(#) A 2 and Y (#) 0 where also (4) is fulfilled. For A 1 the ....

B. W. Char, K. O. Geddes, G. H. Gonnet, B. L. Leong, M. B. Monagan, and S. M. Watt. Maple V Language Reference Manual. Springer-Verlag, New York, 1991.

.... 4 (X 3 p 3 ) 4 (X 1 q 1 ) 4 (X 2 q 2 ) 4 (X 3 q 3 ) 4 , and p 1 ,p 2 ,p 3 ,q 1 , s 3 denote the concrete coordinates of the four points p, q, r, s given above (note that these polynomials are of degree 3 since the forth powers cancel out) 9 Using the MAPLE [3] implementation of Buchberger s algorithm [2] we find that the ideal generated by the polynomials in (2)hasaGrobner basis aX 1 g 1 (X 3 ) bX 2 g 2 (X 3 ) g 3 (X 3 ) 3) where ab #=0,g 1 and g 2 are polynomials in X 3 of degree 26, and g 3 is a polynomial in X 3 of degree 27. The ....

B. W. Char, K. O. Geddes, G. H. Gonnet, B. L. Leong, M. B. Monagan, and S. M. Watt. Maple V Language Reference Manual. Springer-Verlag, New York, 1991.

....algorithms exhibit the behavior that the model possesses. Example 1.2 below presents a simple algorithmic theory that represents the standard model of the natural numbers. The computer algebra framework is mechanized by computer algebra systems. Examples include Axiom [36] Macsyma [35] Maple [10], and Mathematica [49] Most computer algebra systems are designed primarily for performing computations. Computations are performed at great speed, but the results are not always reliable. The algorithmic theories in which computation is performed are usually not represented as explicit, ....

B. W. Char, K. O. Geddes, G. H. Gonnet, B. L. Leong, M. B. Monagan, and S. M. Watt. Maple V Language Reference Manual. Springer-Verlag, 1991.

....1 c 0 d 4 T 4 P (r) n d 3 T 3 P (r) n d 2 T 2 P (r) n d 1 T P (r) n d 0 P (r) n d 1 d 0 fi fi fi fi fi fi fi = 0 ; 3.27) which can be written in the form 4 X j=0 I j (r; n; x) T j P (r) n (x) 0: 3.28) remark 3.2. We have used Maple V Release 4 (see Char et al. 1991)) to compute and factorize the coefficients I j (r; n; x) for the Charlier, Krawtchouk and Meixner cases. The Hahn and Hahn Eberlein cases need heavy computation to receive readable results, and we had to use both Maple V release 4 and Reduce 3.6 (see Hearn (1995) to compute and factorize the ....

Char, B., W. et al. (1991).: Maple V Language Reference Manual. Springer, New York.

....where different theoretic descriptions are available which should be tested against the available empiric data, such that the best model for a given experiment can be picked without much effort. The symbolic part of our system is currently implemented on top of the computer algebra system Maple [1], the numeric part on top of a library based on algorithms described in [4] 2 Building Blocks of the System All steps of the data analysis are done within the Maple graphical user interface environment. A Maple worksheet has been designed for the visualization and manipulation of data. Typing ....

CHAR, B. W., GEDDES, K. O., GONNET, G. H., BENTON, L. L., MONAGAN, M. B., AND WATT, S. M. Maple V Language Reference Manual. Springer-Verlag, New York, 1991.

....which allow additional decreases in the computational complexity with the help of CR technique. All the algorithms proposed are effective, unconditional (w.r.t. relative speed of different arithmetic operations) and easy to implement. They are implemented in Maple V Computer Algebra system [8]. In addition, we have implemented a CR code generator. From the theory of compiling point of view, problems in the implementation of the CR interpreter and the CR code generator are very similar. The code which is generated by a given CR expression looks like a CR interpreting scheme from the ....

Char B.W., Geddes K.O. (and others) Maple-V. Language Reference Manual. Springer-Verlag, 1991.

....systems and numerous specialized packages. Advanced algorithms to perform basic operations on arbitrary precision integers are very well known. Many books [1, 4, 7] give overviews of those algorithms together with detailed implementation remarks. Most computer algebra systems (such as Maple [3]) and specialized number theory packages (such as NTL [8] contain implementations of these algorithms. For example for multiplication they typically use the Karatsuba [7] algorithm. Even some general purpose programming languages have arbitrary precision arithmetic. As examples, Java has ....

Char B.W., Geddes K.O., Gonnet G.H., Leong B.L., Monagan M.B., Watt S.M. Maple-V. Language Reference Manual. Springer-Verlag, 1991.

....cooperation can be achieved by adding links to interactive tools. The interfaces between HOL and Maple [13] and Isabelle and Maple [4] introduce the powerful arithmetics of a computer algebra system into a tactical theorem prover to reason about numbers or polynomials much more efficient. Maple [6] acts as a slave to the prover which controls external calls by evaluation tactics. 15] presents an interaction to provide expressive algebra of constructive type theory in computer algebra. The theorem prover Nuprl is an algebraic oracle to the CAS Weyl. Analytica [7] is an example for ....

B.W. Char, K.O. Geddes, G.H. Gonnet, B.L. Leong, M.B. Monagan, S.M. Watt Maple V Language Reference Manual, Springer-Verlag, 1992.

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Char, B. W. Maple V language Reference Manual. Springer-Verlag, 1991.

....All computer algebra systems can differentiate functions represented by formulae. But not all functions can be described by formulae. And formulae are not always the most effective means for representing functions and derivatives. In this paper we describe the algorithms used by the Maple [2] routine GRADIENT that accepts as input a Maple procedure for the computation of f and outputs a new Maple procedure that computes the gradient of f . The design of the GRADIENT routine is such that it is also trivial to generate Maple procedures for the computation Jacobians and Hessians. ....

....f shall return a onedimensional array with m entries. By using GRADIENT we get a new procedure for rf that returns the Jacobian matrix of f with m Delta n entries. Lets look at two simple examples to illustrate the use of arrays: f : proc(x,y) local a; a : array(1 . 2) a[1] x2 y2; a[2] : x2 y2; a end: eval(f(x,y) 2 2 2 2 [ x y , x y ] df : GRADIENT(f) df : proc(x,y) local da; da : array(1 . 2,1 . 2) da[1,1] 2 x y2; da[1,2] 2 x2 y; da[2,1] 2 x; da[2,2] 2 y; da end eval(df(x,y) 2 2 ] 2 x y 2 x y ] 2 x 2 y ] 5 f : ....

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B. Char, K. Geddes, G. Gonnet, B. Leong, M. Monagan, S. Watt, Maple V Language Reference Manual, Springer, 1991

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B. W. Char, K. O. Geddes, G. H. Gonnet, B. Leong, M. B. Monagan, and S. M. Watt. Maple V: Language Reference Manual. Springer, 1991.

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B. W. Char, K. O. Geddes, G. H. Gonnet, B. L. Leong, M. B. Monagan, and S. M. Watt. Maple V Language Reference Manual. Springer-Verlag, New York, 1991.

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B. W. Char, K. O. Geddes, G. H. Gonnet, B. L. Leong, M. B. Monagan, and S. M. Watt. Maple V Language Reference Manual. Springer-Verlag, 1991.

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B. W. Char et al. Maple V Language Reference Manual. Springer-Verlag, 1991.

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B. W. Char, K. O. Geddes, G. H. Gonnet, B. L. Leong, M. B. Monagan, and S. M. Watt. Maple V Language Reference Manual. Springer-Verlag, 1991.

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B.W. Char, K.O. Geddes, G.H. Gonnet, B.L. Leong, M.B. Monagan, S.M. Watt, Maple V, Language Reference Manual, Springer, 1991.

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B. W. Char, K. O. Geddes, G. H. Gonnet, B. L. Leong, M. B. Monagan, and S. M. Watt. Maple V Language Reference Manual. Springer-Verlag, New York, 1991.

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B.W. Char, K.O. Geddes, G.H. Gonnet, B.L. Leong, M.B. Monagan, and S.M. Watt. Maple V Language Reference Manual. Springer Verlag, 1991.

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B. W. Char, K. O. Geddes, G. H. Gonnet, B. L. Leong, M. B. Monagan, and S. M. Watt. Maple V Language Reference Manual. Springer-Verlag, 1992.

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Char, B.W. et al. Maple V Language Reference Manual. SpringerVerlag, 1991.

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