{"title":"An interactive console operating as background in a large computer system","authors":"S. Schlesinger, Lawrence Sashkin, C. Aumann","doi":"10.1145/2402536.2402554","DOIUrl":"https://doi.org/10.1145/2402536.2402554","url":null,"abstract":"In order to fill the gap between small desktop calculators and conventional computer programming, an interactive console system has been developed to permit engineers and mathematicians to solve small scale problems with a simple algebra-like language, EASY (Elementary Algebraic Solutions for You). In order to achieve effective operation at low cost, the consoles (IBM 2260) are supported as a low level background function on an IBM 360 Model 40 computer Attached Support Processor (ASP), which is simultaneously supplying data processing capability to support multiple printers, plotters, card readers and punches, auxiliary storage devices, and the monitoring and job scheduling for an attached IBM 360 Model 65 computer (Fig. 1).","PeriodicalId":148361,"journal":{"name":"Symposium on Interactive Systems for Experimental Applied Mathematics","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1967-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132818487","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":"Mathematical symbol processing","authors":"C. Abraham, T. Pearcey","doi":"10.1145/2402536.2402557","DOIUrl":"https://doi.org/10.1145/2402536.2402557","url":null,"abstract":"Most of the early efforts to write computer programs which perform symbolic mathematical operations were directed toward polynomial manipulation including their differentiation and integration [1, 2]. In 1961, Bernick et al. [3] produced an interpretive routine to provide multiple capabilities for a general class of mathematical expression. More recent programs belonging to the same class are FORMAC [4] and Formula ALGOL, [5] but both suffer various kinds of restrictions.","PeriodicalId":148361,"journal":{"name":"Symposium on Interactive Systems for Experimental Applied Mathematics","volume":"779 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1967-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123285429","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":"An implementation of automatic array arithmetic by a generalized push-down stack","authors":"J. Reinfelds","doi":"10.1145/2402536.2402583","DOIUrl":"https://doi.org/10.1145/2402536.2402583","url":null,"abstract":"One of the most fundamental and useful notions of mathematical analysis is the concept of a continuous, single valued function of one independent variable. By <i>y</i> = <i>f</i>(<i>x</i>) we mean that for every <i>x</i> in the range of <i>x</i>, defined as α ≤ x ≤ β, the mapping <i>f</i> provides us with a value in the domain of the function <i>y</i><sub>α</sub> ≤ <i>y</i> ≤ <i>y</i><sub>β</sub>, where <i>y</i><sub>α</sub> = <i>f</i>(<i>x</i><sub>α</sub>) and <i>y</i><sub>β</sub> = <i>f</i>(<i>x</i><sub>β</sub>). In a numerical computation we represent the part of the range of the independent variable, which is of interest to us, by a suitably chosen ordered set of <i>n</i> + 1 values (<i>x</i><sub>0</sub>, <i>x</i><sub>1</sub>, <i>x</i><sub>2</sub>, . . ., <i>x<sub>n</sub></i>), and a representation of any function over this range is then found by evaluating <i>y</i> = <i>f</i>(<i>x</i>) at these points, to obtain a corresponding ordered set of values (<i>y</i><sub>0</sub>, <i>y</i><sub>1</sub>, <i>y</i><sub>2</sub>, . . ., <i>y<sub>n</sub></i>). Because of the obvious analogy, these arrays of numbers representing continuous functions are often called vectors. However, a semantic problem arises when we discuss vectors of functions, such as the vector potential or the wind velocity patterns in the atmosphere. Therefore, I prefer to make a special case of the representations of continuous functions and refer to them as arrays rather than vectors.","PeriodicalId":148361,"journal":{"name":"Symposium on Interactive Systems for Experimental Applied Mathematics","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1967-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131558407","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":"Structure of a language for a numerical analysis problem solving system","authors":"Lawrence R. Symes, R. V. Roman","doi":"10.1145/2402536.2402543","DOIUrl":"https://doi.org/10.1145/2402536.2402543","url":null,"abstract":"The Numerical Analysis Problem Solving System (NAPSS) project has been undertaken at Purdue University to design and construct an interactive system for solving numerical problems [1]. The system is designed to accept input in a language which is very close to natural mathematical notation, and also to provide for the solution of problems without requiring specially trained programmers and numerical analysts.","PeriodicalId":148361,"journal":{"name":"Symposium on Interactive Systems for Experimental Applied Mathematics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1967-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126002043","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}