{"title":"使用mathematica自动向量空间证明","authors":"Aaron E. Naiman","doi":"10.1145/3572865.3572866","DOIUrl":null,"url":null,"abstract":"We present Mathematica tools for proving or disproving whether a set of objects constitutes a vector space. When necessary axioms are upheld, the relationships between the variables are presented. When the axioms fail, intuitive counterexamples are shown. A number of different kinds of vectors are demonstrated, with varying types of vector addition and scalar multiplication as well. All of the calculations are performed in an automated fashion.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"56 1","pages":"1 - 13"},"PeriodicalIF":0.4000,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Automated vector space proofs using mathematica\",\"authors\":\"Aaron E. Naiman\",\"doi\":\"10.1145/3572865.3572866\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present Mathematica tools for proving or disproving whether a set of objects constitutes a vector space. When necessary axioms are upheld, the relationships between the variables are presented. When the axioms fail, intuitive counterexamples are shown. A number of different kinds of vectors are demonstrated, with varying types of vector addition and scalar multiplication as well. All of the calculations are performed in an automated fashion.\",\"PeriodicalId\":41965,\"journal\":{\"name\":\"ACM Communications in Computer Algebra\",\"volume\":\"56 1\",\"pages\":\"1 - 13\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2022-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACM Communications in Computer Algebra\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/3572865.3572866\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACM Communications in Computer Algebra","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3572865.3572866","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
We present Mathematica tools for proving or disproving whether a set of objects constitutes a vector space. When necessary axioms are upheld, the relationships between the variables are presented. When the axioms fail, intuitive counterexamples are shown. A number of different kinds of vectors are demonstrated, with varying types of vector addition and scalar multiplication as well. All of the calculations are performed in an automated fashion.
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