{"title":"在马普尔中实现保留抽象的块矩阵","authors":"David J. Jeffrey, Stephen M. Watt","doi":"arxiv-2408.02112","DOIUrl":null,"url":null,"abstract":"A Maple implementation of partitioned matrices is described. A recursive\nblock data structure is used, with all operations preserving the block\nabstraction. These include constructor functions, ring operations such as\naddition and product, and inversion. The package is demonstrated by calculating\nthe PLU factorization of a block matrix.","PeriodicalId":501033,"journal":{"name":"arXiv - CS - Symbolic Computation","volume":"93 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"An Abstraction-Preserving Block Matrix Implementation in Maple\",\"authors\":\"David J. Jeffrey, Stephen M. Watt\",\"doi\":\"arxiv-2408.02112\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A Maple implementation of partitioned matrices is described. A recursive\\nblock data structure is used, with all operations preserving the block\\nabstraction. These include constructor functions, ring operations such as\\naddition and product, and inversion. The package is demonstrated by calculating\\nthe PLU factorization of a block matrix.\",\"PeriodicalId\":501033,\"journal\":{\"name\":\"arXiv - CS - Symbolic Computation\",\"volume\":\"93 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - CS - Symbolic Computation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2408.02112\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - CS - Symbolic Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.02112","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
介绍了分区矩阵的 Maple 实现。使用了递归块数据结构，所有操作都保留了块抽象。这些操作包括构造函数、环运算（如加法和乘积）和反转。通过计算分块矩阵的 PLU 因式分解，演示了该软件包。
An Abstraction-Preserving Block Matrix Implementation in Maple
A Maple implementation of partitioned matrices is described. A recursive
block data structure is used, with all operations preserving the block
abstraction. These include constructor functions, ring operations such as
addition and product, and inversion. The package is demonstrated by calculating
the PLU factorization of a block matrix.
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