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It further covers core algorithmic ideas, recursive procedures, and case studies such as first-order ODEs and elementary integration operators, before treating polynomials, rational expressions, and exponential/trigonometric transformations, with references and 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Elementary Algorithms\u003Cbr>\u003Cbr>A K PETERS | J O E L S . C O H E N\u003Cbr>Computer Algebra and Symbolic Computation\u003Cbr>E l e m e n t a r y A l g o r i t h m s |\n| --- | --- | --- |\n\n􀀁􀀂􀀃􀀄􀀅􀀆􀀇􀀈 􀀊􀀋􀀌􀀇􀀍􀀈􀀎 􀀎􀀏􀀐 􀀑􀀒􀀃􀀍􀀂􀀋􀀓􀀔 􀀁􀀂􀀃􀀄􀀅􀀆􀀎􀀆􀀓􀀂􀀏  \n􀀁􀀂􀀃􀀄􀀅􀀆􀀇􀀈 􀀊􀀋􀀌􀀇􀀍􀀈􀀎 􀀎􀀏􀀐 􀀑􀀒􀀃􀀍􀀂􀀋􀀓􀀔 􀀁􀀂􀀃􀀄􀀅􀀆􀀎􀀆􀀓􀀂􀀏  \n􀀕􀀋􀀇􀀃􀀇􀀏􀀆􀀎􀀈􀀒 􀀊􀀋􀀌􀀂􀀈􀀓􀀆􀀖􀀃􀀗  \n􀀘􀀂􀀇􀀋 􀀑􀀙 􀀁􀀂􀀖􀀇􀀏  \n􀀁􀀂􀀃􀀄􀀅􀀆􀀇􀀂􀀈􀀆 􀀊􀀋 􀀌􀀊􀀇􀀃􀀍􀀆􀀂􀀅 􀀎􀀏􀀐􀀂􀀈􀀏􀀂􀀑􀀈􀀐􀀒􀀂􀀅􀀓􀀐􀀆􀀔 􀀊􀀋 􀀁􀀂􀀈􀀒􀀂􀀅  \n􀀁 􀀃 􀀄􀀅􀀆􀀅􀀇􀀈􀀉􀀊􀀆􀀋􀀌􀀍􀀎 􀀏􀀊􀀈􀀈􀀊􀀌􀀐􀀑􀀈􀀅􀀆􀀆􀀈  \n1􀀇􀀃􀀅􀀕􀀂􀀃􀀊􀀙􀀗 􀀚􀀊􀀙􀀆!􀀗 􀀊􀀄􀀇 􀀉􀀞!􀀅􀀕􀀜􀀆􀀂 􀀚􀀆􀀂2􀀃\\#􀀆 3''􀀃\\#􀀆, 4 􀀁􀀆􀀅􀀆􀀂!􀀗 5􀀅􀀇􀀛  \n􀀌􀀏 􀀚􀀕􀀞􀀅􀀖 ,2􀀆􀀄􀀞􀀆*􀀊􀀅􀀃\\#6􀀗 7, 􀀋􀀑􀀔􀀌􀀋 888􀀛􀀊6􀀝􀀆􀀅􀀆􀀂!􀀛\\#􀀕􀀜  \n􀀉􀀕􀀝\"􀀂􀀃 􀀖􀀅 9 􀀐􀀋􀀋􀀐 \" , 4 􀀁􀀆􀀅􀀆􀀂!􀀗 5􀀅􀀇􀀛  \n,􀀙􀀙 􀀂􀀃 􀀖􀀅! 􀀂􀀆!􀀆􀀂2􀀆􀀇􀀛 *􀀕 􀀝􀀊􀀂􀀅 􀀕' 􀀅􀀖􀀆 􀀜􀀊􀀅􀀆􀀂􀀃􀀊􀀙 􀀝􀀂􀀕􀀅􀀆\\#􀀅􀀆􀀇 \" 􀀅􀀖􀀃! \\#􀀕􀀝\"􀀂􀀃 􀀖􀀅 􀀄􀀕􀀅􀀃\\#􀀆􀀜􀀊\" 􀀆 􀀂􀀆􀀝􀀂􀀕􀀇􀀞\\#􀀆􀀇 􀀕􀀂 􀀞􀀅􀀃􀀙􀀃:􀀆􀀇 􀀃􀀄 􀀊􀀄\" '􀀕􀀂􀀜􀀗 􀀆􀀙􀀆\\#􀀅􀀂􀀕􀀄􀀃\\# 􀀕􀀂 􀀜􀀆\\#􀀖􀀊􀀄􀀃\\#􀀊􀀙􀀗 􀀃􀀄\\#􀀙􀀞􀀇􀀃􀀄􀀝􀀖􀀕􀀅􀀕\\#􀀕􀀝\"􀀃􀀄 􀀗 􀀂􀀆\\#􀀕􀀂􀀇􀀃􀀄 􀀗 􀀕􀀂 \" 􀀊􀀄\" 􀀃􀀄'􀀕􀀂􀀜􀀊􀀅􀀃􀀕􀀄 !􀀅􀀕􀀂􀀊 􀀆 􀀊􀀄􀀇 􀀂􀀆􀀅􀀂􀀃􀀆2􀀊􀀙 !\"!􀀅􀀆􀀜􀀗 8􀀃􀀅􀀖􀀕􀀞􀀅 8􀀂􀀃􀀅􀀅􀀆􀀄 􀀝􀀆􀀂􀀜􀀃!!􀀃􀀕􀀄 '􀀂􀀕􀀜 􀀅􀀖􀀆 \\#􀀕􀀝\"􀀂􀀃 􀀖􀀅 􀀕8􀀄􀀆􀀂􀀛  \n􀀁􀀂􀀃􀀄􀀅􀀄􀀆 􀀈􀀉 􀀊􀀈􀀋􀀌􀀄􀀍􀀎􀀎 􀀊􀀅􀀏􀀅􀀐􀀈􀀌􀀂􀀋􀀌􀀑􀀂􀀋􀀑􀀒􀀓􀀃􀀐􀀂􀀔􀀅􀀏􀀂􀀈􀀋 􀀕􀀅􀀏􀀅  \n􀀉􀀕􀀖􀀆􀀄􀀗 􀀘􀀕􀀆􀀙 􀀚􀀛  \n􀀉􀀕􀀜􀀝􀀞􀀅􀀆􀀂 􀀊􀀙 􀀆 􀀂􀀊 􀀊􀀄􀀇 !\"􀀜 􀀕􀀙􀀃\\# \\#􀀕􀀜􀀝􀀞􀀅􀀊􀀅􀀃􀀕􀀄 $ 􀀆􀀙􀀆􀀜􀀆􀀄􀀅􀀊􀀂\"􀀊􀀙 􀀕􀀂􀀃􀀅􀀖􀀜! % 􀀘􀀕􀀆􀀙 􀀚􀀛 􀀉􀀕􀀖􀀆􀀄  \n􀀝􀀛 \\#􀀜􀀛  \n&􀀄\\#􀀙􀀞􀀇􀀆! 􀀃 􀀙􀀃􀀕 􀀂􀀊􀀝􀀖􀀃\\#􀀊􀀙 􀀂􀀆'􀀆􀀂􀀆􀀄\\#􀀆! 􀀊􀀄􀀇 􀀃􀀄􀀇􀀆(􀀛  \n&􀀚)* 􀀑+􀀍􀀌􀀓􀀓􀀑+􀀑􀀍􀀓+􀀌  \n􀀑􀀛 ,􀀙 􀀆 􀀂􀀊-.􀀊􀀅􀀊 􀀝􀀂􀀕\\#􀀆!!􀀃􀀄 􀀛 &􀀛 /􀀃􀀅􀀙􀀆􀀛  \n0,􀀑􀀍􀀍􀀛􀀔􀀛1􀀎 􀀛􀀉􀀌􀀏􀀍 􀀐􀀋􀀋􀀐  \n􀀍􀀑􀀐-􀀇\\#􀀐􀀑 􀀐􀀋􀀋􀀑􀀋􀀍􀀍􀀑􀀍􀀒  \n􀀁􀀂􀀃􀀄􀀅􀀆􀀇 􀀃􀀄 􀀉􀀊􀀄􀀊􀀇􀀊  \n􀀋􀀌 􀀋􀀍 􀀋􀀎 􀀋􀀏 􀀋􀀐 􀀑􀀋 􀀒 􀀓 􀀔 􀀌 􀀍 􀀎 􀀏 􀀐 􀀑  \n􀀁􀀂 􀀄􀀅 􀀆􀀇􀀈􀀉 􀀊􀀋􀀌􀀍􀀎􀀅􀀏  \nContents  \nPreface ix  \n1 Introduction to Computer Algebra 1  \n1.1 Computer Algebra and Computer Algebra Systems ..... 1  \n1.2 Applications of Computer Algebra .............. 10  \n2 Elementary Concepts of Computer Algebra 29  \n2.1 Mathematical Pseudo-language (MPL) ........... 29  \n2.2 Expression Evaluation ..................... 49  \n2.3 Mathematical Programs .................... 58  \n2.4 Sets and Lists ......................... 68  \n3 Recursive Structure of Mathematical Expressions 77  \n3.1 Recursive Definitions and Algorithms ............. 77  \n3.2 Expression Structure and Trees ................ 84  \n3.3 Structure-Based Operators .................. 108  \n4 Elementary Mathematical Algorithms 119  \n4.1 Mathematical Algorithms ................... 119  \n4.2 MPL’s Algorithmic Language ................. 132  \n4.3 Case Study: First Order Ordinary Differential Equations .. 156  \n5 Recursive Algorithms 171  \n5.1 A Computational View of Recursion ............. 171  \n5.2 Recursive Procedures ..................... 176  \n5.3 Case Study: Elementary Integration Operator ........ 199  \nvii  \nviii Contents  \n6 Structure of Polynomials and Rational Expressions 213  \n6.1 Single Variable Polynomials .................. 214  \n6.2 General Polynomial Expressions ............... 223  \n6.3 Relationships Between Generalized Variables ........ 242  \n6.4 Manipulation of General Polynomial Expressions ...... 247  \n6.5 General Rational Expressions ................. 259  \n7 Exponential and Trigonometric Transformations 275  \n7.1 Exponential and Trigonometric Expansion .......... 275  \n7.2 Exponential and Trigonometric Contraction ......... 289  \nBibliography 307  \nIndex 316","cbCairjnWX1CvIZW","https://ap.wps.com/l/cbCairjnWX1CvIZW","pdf",2314113,344,"English","# Preface\n# Introduction to Computer Algebra\n## Computer Algebra and Computer Algebra Systems\n## Applications of Computer Algebra\n# Elementary Concepts of Computer Algebra\n## Mathematical Pseudo-language (MPL)\n## Expression Evaluation\n## Mathematical Programs\n## Sets and Lists\n# Recursive Structure of Mathematical Expressions\n## Recursive Definitions and Algorithms\n## Expression Structure and Trees\n## Structure-Based Operators\n# Elementary Mathematical Algorithms\n## Mathematical Algorithms\n## MPL’s Algorithmic Language\n## Case Study: First Order Ordinary Differential Equations\n# Recursive Algorithms\n## A Computational View of Recursion\n## Recursive Procedures\n## Case Study: Elementary Integration Operator\n# Structure of Polynomials and Rational Expressions\n## Single Variable Polynomials\n## General Polynomial Expressions\n## Relationships Between Generalized Variables\n## Manipulation of General Polynomial Expressions\n## General Rational Expressions\n# Exponential and Trigonometric Transformations\n## Exponential and Trigonometric Expansion\n## Exponential and Trigonometric Contraction\n# Bibliography\n# Index","[{\"question\":\"What is mathematical pseudo-language (MPL) used for in this book?\",\"answer\":\"MPL provides an algorithmic pseudo-language for working with computer algebra systems, supporting how expressions are evaluated and manipulated in subsequent sections.\"},{\"question\":\"How does the book explain the recursive structure of mathematical expressions?\",\"answer\":\"It presents recursive definitions and algorithms, then connects expression structure to trees and introduces operators derived from structural patterns.\"},{\"question\":\"Which topics are covered in the later chapters on expressions?\",\"answer\":\"Later chapters address polynomials and rational expressions, followed by exponential and trigonometric transformations, including expansion and contraction techniques.\"}]","Computer Algebra and Symbolic Computation - Elementary Algorithms - Preface | PDF",1789975606,867]