M. R. González-Dorrego, MadridSPAIN UniversidadAut ́onomadeMadrid
{"title":"基于Groebner基的数独解析","authors":"M. R. González-Dorrego, MadridSPAIN UniversidadAut ́onomadeMadrid","doi":"10.32603/2071-2340-3-5-21","DOIUrl":null,"url":null,"abstract":"We study the resolution of sudokus and generalized sudokus using Groebner basis. Let x1, . . . , x81 the 81 squares which form the sudoku, arranged from left to right and from top to bottom. Its solution will be (a1, . . . , a81), where ai is the number in the square associated to the variable xi . Let S be a sudoku with preassigned data {ci }i∈L , for L ⊂ {1, . . . ,81}. All the necessary information to solve the sudoku is contained in the algebraic set V(I+< {xi − ci }i∈L >). We shall use Groebner basis to find a solution and give a SAGE code for that purpose.","PeriodicalId":319537,"journal":{"name":"Computer Tools in Education","volume":"31 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Resolution of Sudokus Using Groebner Basis\",\"authors\":\"M. R. González-Dorrego, MadridSPAIN UniversidadAut ́onomadeMadrid\",\"doi\":\"10.32603/2071-2340-3-5-21\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the resolution of sudokus and generalized sudokus using Groebner basis. Let x1, . . . , x81 the 81 squares which form the sudoku, arranged from left to right and from top to bottom. Its solution will be (a1, . . . , a81), where ai is the number in the square associated to the variable xi . Let S be a sudoku with preassigned data {ci }i∈L , for L ⊂ {1, . . . ,81}. All the necessary information to solve the sudoku is contained in the algebraic set V(I+< {xi − ci }i∈L >). We shall use Groebner basis to find a solution and give a SAGE code for that purpose.\",\"PeriodicalId\":319537,\"journal\":{\"name\":\"Computer Tools in Education\",\"volume\":\"31 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-06-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computer Tools in Education\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.32603/2071-2340-3-5-21\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computer Tools in Education","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.32603/2071-2340-3-5-21","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We study the resolution of sudokus and generalized sudokus using Groebner basis. Let x1, . . . , x81 the 81 squares which form the sudoku, arranged from left to right and from top to bottom. Its solution will be (a1, . . . , a81), where ai is the number in the square associated to the variable xi . Let S be a sudoku with preassigned data {ci }i∈L , for L ⊂ {1, . . . ,81}. All the necessary information to solve the sudoku is contained in the algebraic set V(I+< {xi − ci }i∈L >). We shall use Groebner basis to find a solution and give a SAGE code for that purpose.
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