Symposium on Symbolic and Algebraic Manipulation最新文献_第2页

Code generation for hybrid mixed mode formulation in finite element analysis 有限元分析中混合模态公式的代码生成

Symposium on Symbolic and Algebraic Manipulation Pub Date : 1986-10-01 DOI: 10.1145/32439.32448

Paul S. Wang, H. Tan, A. Saleeb, Tse-Yung P. Chang

引用次数: 12

Edusym—educational symbolic manipulator on a microcomputer 微机上的教育符号操纵器

Symposium on Symbolic and Algebraic Manipulation Pub Date : 1986-10-01 DOI: 10.1145/32439.32470

Neven Jurkovic

引用次数: 3

New results for random determination of equivalence of expressions 表达式等价性随机确定的新结果

Symposium on Symbolic and Algebraic Manipulation Pub Date : 1986-10-01 DOI: 10.1145/32439.32465

G. Gonnet

{"title":"New results for random determination of equivalence of expressions","authors":"G. Gonnet","doi":"10.1145/32439.32465","DOIUrl":"https://doi.org/10.1145/32439.32465","url":null,"abstract":"We devise several procedures based on signatures (or hashing functions) to determine equivalence of expressions in Random Polynomial Time (also called Probabilistic Polynomial Time) (RPT). We extend the previous results known to include various new functions that can be tested. These procedures return as result: <italic>“equivalent”</italic> or <italic>“not-equivalent”</italic>. The result “not-equivalent” is always correct, while the result “equivalent” is correct with probability at least 1 — ε. This probability depends on a random number generator and is <italic>independent</italic> of the problem being solved. In all our procedures, the value ε can be made arbitrarily small. This method works for determining equivalence over an important class of functions as well as answering other questions like linearity, polynomial dependence, squareness, independence, etc.\u0000The general scheme for all these algorithms is to use a basic heuristic <italic>“test”</italic> several times. I.e. solve( problem, epsilon ) repeat select suitable characteristic p randomly; assign random values to all variables; t := test( problem, p ); if t = “not-equivalent” then return( t ) until Prob of cumulative failures >= epsilon; return( “equivalent” );\u0000It is assumed that <italic>“test”</italic> gives a wrong answer with probability δ, where δ remains bounded below 1. For all our <italic>“test”</italic> procedures, δ ≤ 1/2.\u0000In what follows we will describe the <italic>“test”</italic> part of the different procedures, it is always assumed that these are used in the above context.\u0000Without loss of generality we will assume that equivalence of expressions (<italic>A ≡ B</italic>) can be transformed into testing for 0 (<italic>A — B ≡ 0</italic>).\u0000This test can be performed “quickly” in the sense that it can run in polynomial time on the size of the <italic>dag</italic> (directed acyclic graph) representation of the expression, also known as “linear program representation” of an expression.","PeriodicalId":314618,"journal":{"name":"Symposium on Symbolic and Algebraic Manipulation","volume":"110 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128163982","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 18

Applications of a software interconnection system in mathematical problem solving environments 软件互连系统在数学解题环境中的应用

Symposium on Symbolic and Algebraic Manipulation Pub Date : 1986-10-01 DOI: 10.1145/32439.32443

James M. Purtilo

引用次数: 13

Formal solutions of linear difference equations: method of Pincherle-Ramis 线性差分方程的形式解:Pincherle-Ramis方法

Symposium on Symbolic and Algebraic Manipulation Pub Date : 1986-10-01 DOI: 10.1145/32439.32477

J. Dora, E. Tournier

引用次数: 5

The design of Macaulay: a system for computing in algebraic geometry and commutative algebra 麦考利的设计:代数几何和交换代数的计算系统

Symposium on Symbolic and Algebraic Manipulation Pub Date : 1986-10-01 DOI: 10.1145/32439.32471

D. Bayer, M. Stillman

{"title":"The design of Macaulay: a system for computing in algebraic geometry and commutative algebra","authors":"D. Bayer, M. Stillman","doi":"10.1145/32439.32471","DOIUrl":"https://doi.org/10.1145/32439.32471","url":null,"abstract":"Macaulay is a system for computing in algebraic geometry and cummutative algebra; it is capable of a variety of computations which are tedious or impossible to perform by hand. The primitive types in the system are polynomials, matrices, ideals, polynomial rings, modules, maps between rings, and complexes of modules. The system performs algebraic manipulation on objects of these types. The possible manipulations include the computation of standard (Gröbner) bases, modules of syzygies, finite free resolutions, Hilbert polynomials and functions. Using these basic operations, a variety of derived operations are possible, such as projections, ideal intersections, and the computation of coherent sheaf cohomology groups. The algorithm used for constructing standard (Gröbner) bases and syzygies is described in ([Buc76], [Zac78], [Sch80], [Bay82], [BaSt86a]).\u0000Macaulay is intended to provide a computational research tool for working mathematicians. Macaulay is designed primarily to aid in generating non-trivial examples in algebraic geometry and commutative algebra. Such examples help mathematicians to gain intuition, and formulate or gather evidence for conjectures. In certain cases, an example can provide a step in the proof of a theorem.\u0000This system has been continuously evolving since 1977 where it was first developed at the University of Illinois by the second author. The algorithms have become substantially more sophisticated and efficient and the scope and power of the system has increased dramatically since its inception.\u0000Macaulay differs in a number of significant ways from other computer algebra systems. The computation of standard bases is its fundamental operation, rather than simplification and factoring. Unlike other systems which provide for the computation of standard bases, submodules of free modules can uniformly be used wherever ideals can be used. Macaulay is written in the language C and its design has been optimized for execution on small systems; Macaulay is available, and reasonably powerful, on a Macintosh microcomputer. Macaulay uses a novel encoding scheme for monomials which considerably reduces the storage requirements for polynomials, further enhancing its viability on small systems. Computations in Macaulay are interruptible, with the full power of the system available to study and use partial results. Macaulay is command-driven, and is quickly learned by mathematicians having no experience with computers.\u0000The basic data types of Macaulay are highly structured, reflecting its focus on the construction of standard bases and syzygies, not the simplification of general expressions. This design allows Macaulay to outperform more general systems, within its problem domain. Macaulay is capable of many computations that are not available in more general systems. These include the computation of syzygies, finite free resolutions of modules and ideals, and coherent sheaf cohomology groups. The set of commands provided allow the user ","PeriodicalId":314618,"journal":{"name":"Symposium on Symbolic and Algebraic Manipulation","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122186111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 34

Conform: a conformal mapping system 一致性:一种共形映射系统

Symposium on Symbolic and Algebraic Manipulation Pub Date : 1986-10-01 DOI: 10.1145/32439.32472

H. R. Seymour

引用次数: 6

An operator algebra for Macsyma Macsyma的算子代数

Symposium on Symbolic and Algebraic Manipulation Pub Date : 1986-10-01 DOI: 10.1145/32439.32488

J. Golden

引用次数: 4

Critical-pair criteria for the Knuth-Bendix completion procedure Knuth-Bendix完井程序的关键对标准

Symposium on Symbolic and Algebraic Manipulation Pub Date : 1986-10-01 DOI: 10.1145/32439.32481

L. Bachmair, N. Dershowitz

引用次数: 8

A fast carry-free algorithm and hardware design for extended integer GCD computation 扩展整数GCD计算的快速无携带算法及硬件设计

Symposium on Symbolic and Algebraic Manipulation Pub Date : 1986-10-01 DOI: 10.1145/32439.32455

D. Yun, Chang Nian Zhang

{"title":"A fast carry-free algorithm and hardware design for extended integer GCD computation","authors":"D. Yun, Chang Nian Zhang","doi":"10.1145/32439.32455","DOIUrl":"https://doi.org/10.1145/32439.32455","url":null,"abstract":"I$ is well known that finding the greatest common divisor (GCD) of two integers is one of the fundamental computations in exact rational arithmetic, factorization and cryptography. Euclid3 algorithm and its variants are the widely used for GCD computations [Knu 811. However they are not suitable in the parallel computation. Since the whole-word comparisons is required. G.B. Purdy /Pur 831 proposed a different way to compute GCD which requires no comparison. The advantage of the Purdy’s algorithm is provided a possible way to speed up the period of each iteration time by using carry save technique. However, it requires 0( n2) iterations in its worst case where n denotes the number of bits of two inputs. In addition, it requires the additional hardware support to handle the overflow problem. R. P. Brent and H. T. Kung [B&K 85) have developed a plus-minus (PM) algorithm that test only the two least significant bits of two integers. The advantage of the PM algorithm is that the number of the iteration is at most 3.012*n units. In particular, this gives a linear time implementation on a systolic array [B&K 851. Although reaaonabl efficient in its use of silicon area, the delay between first input and first output of a computation for the serial-in-serial-out GCD is great than 3 n time units which may be undesirable long depending on the application. The basic idea in our algorithm is to combine two sequence operations of PM algorithm of BrenbKung into one basic operation, and also to avoid swap operations during the iterations to achieve higher parallelism. It has been proved that for any two n bit integers, the number of iterations of the new algorithm is less than 1.51*n+ 1 time units. A preliminary hardware design shows that the algorithm can be implemented in a simple way which consists of several conventional computer components such ss shift registers, borrow save adder, counter and a small PLA as controller. The algorithm can be extended to find not only the greatest common divisor of two numbers A and B, but also to find a pair of integers (2, y) such that AZ + By =GCD(A,B) with the same time complexity. A scheme to cascade a number of such GCD chips to compute very large GCD’s is also at hand, which alleviates a critical difficulty in such fields as cryptography.","PeriodicalId":314618,"journal":{"name":"Symposium on Symbolic and Algebraic Manipulation","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134576225","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 14