{"product_id":"standard-bases-and-primary-decomposition-von-afshan-sadiq","title":"Standard Bases and Primary Decomposition","description":"\u003cp\u003eThe theory of standard bases in polynomial rings with coefficients in a ring with respect to local orderings is developed. Then the generalization of F4-Algorithm for polynomial rings with coefficients in Euclidean rings is given. This algorithm computes successively a Gröbner basis replacing the reduction of one single s-polynomial in Buchberger's algorithm by the  simultaneous reduction of several polynomials.  And finally we present an algorithm to compute a primary decomposition of an ideal in a polynomial ring over the rings. For this purpose we use algorithms for primary decomposition in polynomial rings over the rationals resp. over finite fields, and the idea of Shimoyama--Yokoyama resp. Eisenbud--Hunecke--Vasconcelos to extract primary ideals from pseudo-primary ideals.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783846598528\"\u003e\u003ch3\u003eThe F4-Algorithm for Euclidean Rings and Efficient Algorithm for Primary Decomposition over Rings\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Softcover - 9783846598528","offer_id":39493508759645,"sku":"9783846598528","price":49.0,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/8309ff79-8d91-46eb-9d2b-1d7b8e9cf2d8.jpg?v=1748581422","url":"https:\/\/shop.autorenwelt.de\/en\/products\/standard-bases-and-primary-decomposition-von-afshan-sadiq","provider":"Autorenwelt Shop","version":"1.0","type":"link"}