{"title":"在领域的灵感与极性HSV - RGB理论的颜色","authors":"J. Haluska","doi":"10.18778/7969-663-5.06","DOIUrl":null,"url":null,"abstract":"A three-polar, cf. T. Gregor, J. Halu\\v{s}ka, Lexicographical ordering and field operations in the complex plane. Stud. Mat. 41(2014), 123--133., $HSV-RGB$ Colour space $\\triangle$ was introduced and studied. It was equipped with operations of addition, subtraction, multiplication, and (partially) division. Achromatic Grey Hues form an ideal $\\mathfrak{S}$. Factorizing $\\triangle$ by the ideal $\\mathfrak{S}$, we obtain a field $\\triangle | \\mathfrak{S}$. An element (i.e an individual Colour) in $\\triangle | \\mathfrak{S}$ is a triplet of three triangular coefficients. The set of all triangular coefficients is a subset of a semi-field of parabolic-complex functions. For the parabolic-complex number set, cf.~A. A. Harkin--J. B. Harkin, Geometry of general complex numbers. Mathematics magazine, 77(2004), 118--129.","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2015-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"On fields inspired with the polar HSV -- RGB theory of Colour\",\"authors\":\"J. Haluska\",\"doi\":\"10.18778/7969-663-5.06\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A three-polar, cf. T. Gregor, J. Halu\\\\v{s}ka, Lexicographical ordering and field operations in the complex plane. Stud. Mat. 41(2014), 123--133., $HSV-RGB$ Colour space $\\\\triangle$ was introduced and studied. It was equipped with operations of addition, subtraction, multiplication, and (partially) division. Achromatic Grey Hues form an ideal $\\\\mathfrak{S}$. Factorizing $\\\\triangle$ by the ideal $\\\\mathfrak{S}$, we obtain a field $\\\\triangle | \\\\mathfrak{S}$. An element (i.e an individual Colour) in $\\\\triangle | \\\\mathfrak{S}$ is a triplet of three triangular coefficients. The set of all triangular coefficients is a subset of a semi-field of parabolic-complex functions. For the parabolic-complex number set, cf.~A. A. Harkin--J. B. Harkin, Geometry of general complex numbers. Mathematics magazine, 77(2004), 118--129.\",\"PeriodicalId\":429168,\"journal\":{\"name\":\"arXiv: History and Overview\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2015-11-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: History and Overview\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.18778/7969-663-5.06\",\"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: History and Overview","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.18778/7969-663-5.06","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On fields inspired with the polar HSV -- RGB theory of Colour
A three-polar, cf. T. Gregor, J. Halu\v{s}ka, Lexicographical ordering and field operations in the complex plane. Stud. Mat. 41(2014), 123--133., $HSV-RGB$ Colour space $\triangle$ was introduced and studied. It was equipped with operations of addition, subtraction, multiplication, and (partially) division. Achromatic Grey Hues form an ideal $\mathfrak{S}$. Factorizing $\triangle$ by the ideal $\mathfrak{S}$, we obtain a field $\triangle | \mathfrak{S}$. An element (i.e an individual Colour) in $\triangle | \mathfrak{S}$ is a triplet of three triangular coefficients. The set of all triangular coefficients is a subset of a semi-field of parabolic-complex functions. For the parabolic-complex number set, cf.~A. A. Harkin--J. B. Harkin, Geometry of general complex numbers. Mathematics magazine, 77(2004), 118--129.