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The text covers automatic simplification through formal goals and an algorithmic procedure, then develops core theory for integers, rational numbers, and fields. It progresses to single-variable polynomials, multivariate polynomials, resultants, side relations, and polynomial factorization, including classical and modern approaches, with supporting algorithms and references.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/computer-algebra-and-symbolic-computation-mathematical-methods/326571/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/computer-algebra-and-symbolic-computation-mathematical-methods/326571.png","ImageObject",300,407,{"name":92,"@type":93},"Hazel","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-07","2026-09-21",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",11,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What role do Computer Algebra Systems and MPL play in the book?","Question",{"text":113,"@type":114},"They provide a formal way to represent algebraic expressions and structure so that symbolic manipulation can be automated. MPL is presented as a pseudo-language for expressing mathematical objects for computation.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How does the text approach automatic simplification?",{"text":118,"@type":114},"It begins by stating the goal of automatic simplification, then introduces an automatic simplification algorithm. The discussion emphasizes expression structure and systematic reduction.",{"name":120,"@type":111,"acceptedAnswer":121},"Which polynomial operations and analysis techniques are covered?",{"text":122,"@type":114},"The book covers polynomial division, greatest common divisors, decomposition, resultants, simplification with side relations, and factorization. It also distinguishes approaches for classical and modern irreducible factorization.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},326571,1790673694,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":140,"language":141,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":67,"update_tm":145,"read_time":146,"preview_page_count":4},137441390410,"https://ap-avatar.wpscdn.com/avatar/2000252f4ab5702993?_k=1776741390130283984","J O E L S . C O H E N  \nComputer Algebra and Symbolic Computation  \nM a t h e m a t i c a l M e t h o d s  \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􀀑􀀛 ,􀀙 􀀆 􀀂􀀊-.􀀊􀀅􀀊 􀀝􀀂􀀕\\#􀀆!!􀀃􀀄 􀀛 &􀀛 /􀀃􀀅􀀙􀀆􀀛  \n0,􀀑􀀎􀀎􀀛􀀌􀀛1􀀏 􀀛􀀉􀀍􀀐􀀎 􀀔􀀋􀀋􀀔  \n􀀎􀀑􀀔-􀀇\\#􀀔􀀑 􀀔􀀋􀀋􀀔􀀋􀀔􀀏􀀐􀀑􀀎  \n􀀁􀀂􀀃􀀄􀀅􀀆􀀇 􀀃􀀄 􀀉􀀊􀀄􀀊􀀇􀀊  \n􀀋􀀌 􀀋􀀍 􀀋􀀎 􀀋􀀏 􀀋􀀐 􀀑􀀋 􀀒 􀀓 􀀌 􀀍 􀀎 􀀏 􀀐 􀀔 􀀑  \n􀀁􀀂􀀃 􀀅􀀆 􀀇􀀈􀀉􀀊 􀀋􀀌􀀍􀀎􀀃􀀆􀀏  \nvii  \nContents  \n1 Preface ix  \n1 Background Concepts 1  \n1.1 Computer Algebra Systems .................... 1  \n1.2 Mathematical Pseudo-Language (MPL) ............. 2  \n1.3 Automatic Simplification and Expression Structure ...... 5  \n1.4 General Polynomial Expressions ................. 11  \n1.5 Miscellaneous Operators ..................... 12  \n2 Integers, Rational Numbers, and Fields 17  \n2.1 The Integers ............................ 17  \n2.2 Rational Number Arithmetic ................... 37  \n2.3 Fields ................................ 44  \n3 Automatic Simplification 63  \n3.1 The Goal of Automatic Simplification .............. 63  \n3.2 An Automatic Simplification Algorithm ............. 91  \n4 Single Variable Polynomials 111  \n4.1 Elementary Concepts and Polynomial Division ......... 111  \n4.2 Greatest Common Divisors in F[x] ................ 126  \n4.3 Computations in Elementary Algebraic Number Fields .... 146  \n4.4 Partial Fraction Expansion in F(x) ................ 166  \nviii  \n5 Polynomial Decomposition 179  \n5.1 Theoretical Background .................... 180  \n5.2 A Decomposition Algorithm ................. 188  \n6 Multivariate Polynomials 201  \n6.1 Multivariate Polynomials and Integral Domains ....... 201  \n6.2 Polynomial Division and Expansion .............. 207  \n6.3 Greatest Common Divisors .................. 229  \n7 The Resultant 265  \n7.1 The Resultant Concept .................... 265  \n7.2 Polynomial Relations for Explicit Algebraic Numbers .... 289  \n8 Polynomial Simplification with Side Relations 297  \n8.1 Multiple Division and Reduction ............... 297  \n8.2 Equivalence, Simplification, and Ideals ........... 318  \n8.3 A Simplification Algorithm .................. 334  \n9 Polynomial Factorization 349  \n9.1 Square-Free Polynomials and Factorization ......... 350  \n9.2 Irreducible Factorization: The Classical Approach ..... 360  \n9.3 Factorization in Zp [x] ..................... 370  \n9.4 Irreducible Factorization: A Modern Approach ....... 399  \nBibliography 431  \nIndex 441","cbCaiejMTw8ciHjZ","https://ap.wps.com/l/cbCaiejMTw8ciHjZ","pdf",3279947,470,"English","# Preface\n# Background Concepts\n## Computer Algebra Systems\n## Mathematical Pseudo-Language (MPL)\n## Automatic Simplification and Expression Structure\n## General Polynomial Expressions\n## Miscellaneous Operators\n# Integers, Rational Numbers, and Fields\n## The Integers\n## Rational Number Arithmetic\n## Fields\n# Automatic Simplification\n## The Goal of Automatic Simplification\n## An Automatic Simplification Algorithm\n# Single Variable Polynomials\n## Elementary Concepts and Polynomial Division\n## Greatest Common Divisors in F[x]\n## Computations in Elementary Algebraic Number Fields\n## Partial Fraction Expansion in F(x)\n# Polynomial Decomposition\n## Theoretical Background\n## A Decomposition Algorithm\n# Multivariate Polynomials\n## Multivariate Polynomials and Integral Domains\n## Polynomial Division and Expansion\n## Greatest Common Divisors\n# The Resultant\n## The Resultant Concept\n## Polynomial Relations for Explicit Algebraic Numbers\n# Polynomial Simplification with Side Relations\n## Multiple Division and Reduction\n## Equivalence, Simplification, and Ideals\n## A Simplification Algorithm\n# Polynomial Factorization\n## Square-Free Polynomials and Factorization\n## Irreducible Factorization: The Classical Approach\n## Factorization in Zp [x]\n## Irreducible Factorization: A Modern Approach\n# Bibliography\n# Index","[{\"question\":\"What role do Computer Algebra Systems and MPL play in the book?\",\"answer\":\"They provide a formal way to represent algebraic expressions and structure so that symbolic manipulation can be automated. MPL is presented as a pseudo-language for expressing mathematical objects for computation.\"},{\"question\":\"How does the text approach automatic simplification?\",\"answer\":\"It begins by stating the goal of automatic simplification, then introduces an automatic simplification algorithm. The discussion emphasizes expression structure and systematic reduction.\"},{\"question\":\"Which polynomial operations and analysis techniques are covered?\",\"answer\":\"The book covers polynomial division, greatest common divisors, decomposition, resultants, simplification with side relations, and factorization. It also distinguishes approaches for classical and modern irreducible factorization.\"}]","Computer Algebra and Symbolic Computation - Mathematical Methods | PDF",1789974627,1184]