PowerMath is a symbolic algebra system for the MacIntosh computer. This paper outlines the design decisions that were made during its development, and explains how the novel MacIntosh environment helped and hindered the development of the system. While the interior of PowerMath is fairly conventional, the user interface has many novel features. It is these that make PowerMath not just another micro-computer algebra system.
{"title":"PowerMath: a system for the Macintosh","authors":"J. Davenport, C. E. Roth","doi":"10.1145/32439.32442","DOIUrl":"https://doi.org/10.1145/32439.32442","url":null,"abstract":"PowerMath is a symbolic algebra system for the MacIntosh computer. This paper outlines the design decisions that were made during its development, and explains how the novel MacIntosh environment helped and hindered the development of the system. While the interior of PowerMath is fairly conventional, the user interface has many novel features. It is these that make PowerMath not just another micro-computer algebra system.","PeriodicalId":314618,"journal":{"name":"Symposium on Symbolic and Algebraic Manipulation","volume":"43 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":"133094321","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}
CM1 consists of the following aodulee: (1) Input of one-dimenelonel and output of two-demtneioael notations for methemetical expressions; (2) Evaluetion of numerical expressions with indefinite precision, floating number, fraction, nth root of integer; (3) Algebraic simplification; (4) Polynomial and rationel function manipulation including GCD, square-fret decomposition, partial fraction decomposition; (5) Symbolic derivative; (6) Indefinite integration; (7) Switches controlling the diraction of manipulation or output, and systematic vaziablre; (8) Evaluation statamtnt, assignment stataaent.
{"title":"The computer algebra system CAS1 for the IBM-PC","authors":"Z. Renbao, X. Ling, R. Zhaoyang","doi":"10.1145/32439.32474","DOIUrl":"https://doi.org/10.1145/32439.32474","url":null,"abstract":"CM1 consists of the following aodulee: (1) Input of one-dimenelonel and output of two-demtneioael notations for methemetical expressions; (2) Evaluetion of numerical expressions with indefinite precision, floating number, fraction, nth root of integer; (3) Algebraic simplification; (4) Polynomial and rationel function manipulation including GCD, square-fret decomposition, partial fraction decomposition; (5) Symbolic derivative; (6) Indefinite integration; (7) Switches controlling the diraction of manipulation or output, and systematic vaziablre; (8) Evaluation statamtnt, assignment stataaent.","PeriodicalId":314618,"journal":{"name":"Symposium on Symbolic and Algebraic Manipulation","volume":"83 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":"124686966","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}
{"title":"Fast parallel algorithms for similarity of matrices","authors":"E. Kaltofen, M. Krishnamoorthy, B. D. Saunders","doi":"10.1145/32439.32452","DOIUrl":"https://doi.org/10.1145/32439.32452","url":null,"abstract":"","PeriodicalId":314618,"journal":{"name":"Symposium on Symbolic and Algebraic Manipulation","volume":"1 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":"129011228","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}
Intr oduction Among modern physical theories, non-Abel i-an gauge fiel d theories are most important, The development of these theories and the explanation of experimental data necessitated the higher-or der pertur bation cal culations of Feynman diagrams. As opposed to the us-al quantum electr odynamics, in non-Abelian gauge theories it is necessary to calculate the factor associated with the gauge gr oup. In what foll ows this factor will be r effered to as a group-theoretic weight. Knowledge of this factor is essential for solving the problem of summation of some classes of Feynman diagrams. In some cases the group-theoretic weight allows one to estimate the asymptotic behaviour of Feynman diagrams in the l/N expansion The pr esent paper describes the pr og-ram COLOR which realizes the Cvitanovic al gor ithm /2/ of computation of the gr oup-theoretic weight for the gauge groups SU(n) and SO(n). The pr ogram is written in a symbolic mode of the REDUCE 1 an-sage Ill. 2. Cvitanovic algor ithm. The problem of the group-theor etic weight for Feynman diagrams arises when treating non-Abelian gauge theories. Q CD describing n quarks and N gl uons is an exampl e of such theories. This theor y Lagr angian is Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specfic permission. q ar e the quark fiel ds transformed as a fundamental repr esentation of a Lie group, Aip are gluon fiel ds transformed as its adjoint representation, Ti are generator s of a Lie group.
{"title":"Usage of REDUCE for computations of group-theoretical weight of Feynman diagrams in non-Abelian gauge theories","authors":"A. Kryukov, A. Rodionov","doi":"10.1145/32439.32458","DOIUrl":"https://doi.org/10.1145/32439.32458","url":null,"abstract":"Intr oduction Among modern physical theories, non-Abel i-an gauge fiel d theories are most important, The development of these theories and the explanation of experimental data necessitated the higher-or der pertur bation cal culations of Feynman diagrams. As opposed to the us-al quantum electr odynamics, in non-Abelian gauge theories it is necessary to calculate the factor associated with the gauge gr oup. In what foll ows this factor will be r effered to as a group-theoretic weight. Knowledge of this factor is essential for solving the problem of summation of some classes of Feynman diagrams. In some cases the group-theoretic weight allows one to estimate the asymptotic behaviour of Feynman diagrams in the l/N expansion The pr esent paper describes the pr og-ram COLOR which realizes the Cvitanovic al gor ithm /2/ of computation of the gr oup-theoretic weight for the gauge groups SU(n) and SO(n). The pr ogram is written in a symbolic mode of the REDUCE 1 an-sage Ill. 2. Cvitanovic algor ithm. The problem of the group-theor etic weight for Feynman diagrams arises when treating non-Abelian gauge theories. Q CD describing n quarks and N gl uons is an exampl e of such theories. This theor y Lagr angian is Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specfic permission. q ar e the quark fiel ds transformed as a fundamental repr esentation of a Lie group, Aip are gluon fiel ds transformed as its adjoint representation, Ti are generator s of a Lie group.","PeriodicalId":314618,"journal":{"name":"Symposium on Symbolic and Algebraic Manipulation","volume":"37 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":"132550639","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}
B. Char, K. Geddes, G. Gonnet, B. J. Marshman, P. Ponzo
Unrestricted usage of the computer algebra system Maple was made available to many sections of undergraduate mathematics classes in 1985 as part of an on-going investigation into the uses of computers in mathematics education. The paper discusses some of the results of the experiment as it has proceeded so far, as well as directions for future work.
{"title":"Computer algebra in the undergraduate mathematics classroom","authors":"B. Char, K. Geddes, G. Gonnet, B. J. Marshman, P. Ponzo","doi":"10.1145/32439.32467","DOIUrl":"https://doi.org/10.1145/32439.32467","url":null,"abstract":"Unrestricted usage of the computer algebra system Maple was made available to many sections of undergraduate mathematics classes in 1985 as part of an on-going investigation into the uses of computers in mathematics education. The paper discusses some of the results of the experiment as it has proceeded so far, as well as directions for future work.","PeriodicalId":314618,"journal":{"name":"Symposium on Symbolic and Algebraic Manipulation","volume":"40 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":"127317137","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}
In this paper an attempt is made to correct the misconception of several authors [1] that there exists a method by Upensky (based on Vincent's theorem) for the isolation of the real roots of a polynomial equation with rational coefficients. Despite Uspensky's claim, in the preface of his book [2], that he invented this method, we show that what Upensky actually did was to take Vincent's method and double its computing time. Upensky must not have understood Vincent's method probably because he was not aware of Budan's theorem [3]. In view of the above, it is historically incorrect to attribute Vincent's method to Upensky.
{"title":"There is no “Uspensky's method.”","authors":"A. Akritas","doi":"10.1145/32439.32457","DOIUrl":"https://doi.org/10.1145/32439.32457","url":null,"abstract":"In this paper an attempt is made to correct the misconception of several authors [1] that there exists a method by Upensky (based on Vincent's theorem) for the isolation of the real roots of a polynomial equation with rational coefficients. Despite Uspensky's claim, in the preface of his book [2], that he invented this method, we show that what Upensky actually did was to take Vincent's method and double its computing time. Upensky must not have understood Vincent's method probably because he was not aware of Budan's theorem [3]. In view of the above, it is historically incorrect to attribute Vincent's method to Upensky.","PeriodicalId":314618,"journal":{"name":"Symposium on Symbolic and Algebraic Manipulation","volume":"87 4 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":"116672474","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}
We describe the methods available in the current REDUCE system for introducing new mathematical domains, and illustrate these by discussing several new domains that significantly increase the power of the overall system.
{"title":"Enlarging the REDUCE domain of computation","authors":"R. Bradford, A. C. Hearn, J. Padget, E. Schrüfer","doi":"10.1145/32439.32460","DOIUrl":"https://doi.org/10.1145/32439.32460","url":null,"abstract":"We describe the methods available in the current REDUCE system for introducing new mathematical domains, and illustrate these by discussing several new domains that significantly increase the power of the overall system.","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":"122726242","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}
In simplifying an algebraic expression, human often applies multiterm rewriting rules cleverly. This paper describes a simple multiterm rewriting algorithm which simulates human simplification naively. The algorithm is simple but seems to be quite useful for many applications.
{"title":"Simplification of algebraic expression by multiterm rewriting rules","authors":"Tateaki Sasaki","doi":"10.1145/32439.32463","DOIUrl":"https://doi.org/10.1145/32439.32463","url":null,"abstract":"In simplifying an algebraic expression, human often applies multiterm rewriting rules cleverly. This paper describes a simple multiterm rewriting algorithm which simulates human simplification naively. The algorithm is simple but seems to be quite useful for many applications.","PeriodicalId":314618,"journal":{"name":"Symposium on Symbolic and Algebraic Manipulation","volume":"38 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":"122798681","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}
An implementation in the Maple system of Buchberger's algorithm for computing Gröbner bases is described. The efficiency of the algorithm is significantly affected by choices of polynomial representations, by the use of criteria, and by the type of coefficient arithmetic used for polynomial reductions. The improvement possible through a slightly modified application of the criteria is demonstrated by presenting time and space statistics for some sample problems. A fraction-free method for polynomial reduction is presented. Timings on problems with integer and polynomial coefficients show that a fraction-free approach is recommended.
{"title":"On implementing Buchberger's algorithm for Grobner bases","authors":"S. R. Czapor, K. Geddes","doi":"10.1145/32439.32486","DOIUrl":"https://doi.org/10.1145/32439.32486","url":null,"abstract":"An implementation in the Maple system of Buchberger's algorithm for computing Gröbner bases is described. The efficiency of the algorithm is significantly affected by choices of polynomial representations, by the use of criteria, and by the type of coefficient arithmetic used for polynomial reductions. The improvement possible through a slightly modified application of the criteria is demonstrated by presenting time and space statistics for some sample problems. A fraction-free method for polynomial reduction is presented. Timings on problems with integer and polynomial coefficients show that a fraction-free approach is recommended.","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":"129906358","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}
We apply the elimination property of Gröbner bases with respect to pure lexicographic ordering to solve systems of algebraic equations. We suggest reasons for this approach to be faster than the resultant technique, and give examples and timings that show that it is indeed faster, and more correct, than MACSYMA's solve.
{"title":"Gsolve: a faster algorithm for solving systems of algebraic equations","authors":"M. Bronstein","doi":"10.1145/32439.32489","DOIUrl":"https://doi.org/10.1145/32439.32489","url":null,"abstract":"We apply the elimination property of Gröbner bases with respect to pure lexicographic ordering to solve systems of algebraic equations. We suggest reasons for this approach to be faster than the resultant technique, and give examples and timings that show that it is indeed faster, and more correct, than MACSYMA's solve.","PeriodicalId":314618,"journal":{"name":"Symposium on Symbolic and Algebraic Manipulation","volume":"1 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":"122935817","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}
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