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).
为了填补小型桌面计算器和传统计算机编程之间的空白，一种交互式控制台系统已经被开发出来，允许工程师和数学家用一种简单的类似代数的语言来解决小规模的问题，EASY (Elementary Algebraic Solutions for You)。为了以低成本实现有效的操作，控制台(IBM 2260)作为IBM 360 Model 40计算机附加支持处理器(ASP)的低级后台功能得到支持，该处理器同时提供数据处理能力，以支持多台打印机，绘图仪，读卡器和打孔机，辅助存储设备以及附加的IBM 360 Model 65计算机的监控和作业调度(图1)。
{"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}
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.
{"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}
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 y = f(x) we mean that for every x in the range of x, defined as α ≤ x ≤ β, the mapping f provides us with a value in the domain of the function yα ≤ y ≤ yβ, where yα = f(xα) and yβ = f(xβ). 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 n + 1 values (x0, x1, x2, . . ., xn), and a representation of any function over this range is then found by evaluating y = f(x) at these points, to obtain a corresponding ordered set of values (y0, y1, y2, . . ., yn). 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.
{"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}
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.
普渡大学已经开展了数值分析问题解决系统(Numerical Analysis Problem Solving System, NAPSS)项目，旨在设计和构建一个用于解决数值问题的交互式系统[1]。该系统的设计目的是接受一种非常接近自然数学符号的语言输入，并且不需要经过专门训练的程序员和数值分析人员就能解决问题。
{"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}
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