Bases of subalgebras of and

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• 作者：A. Assi^a ; ¹ ; ^{assi@univ-angers.fr" class="auth_mail" title="E-mail the corresponding author} ; P.A. Garcí ; a-Sá ; nchez^b ; ² ; ^{pedro@ugr.es" class="auth_mail" title="E-mail the corresponding author} ; V. Micale^c ; ^{vmicale@dmi.unict.it" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Bases of subalgebras ; Value semigroup ; Numerical semigroup
• 刊名：Journal of Symbolic Computation
• 出版年：2017
• 出版时间：March-April 2017
• 年：2017
• 卷：79
• 期：part_P1
• 页码：4-22
• 全文大小：502 K

文摘

Let 815&_mathId=si3.gif&_user=111111111&_pii=S0747717116300815&_rdoc=1&_issn=07477171&md5=82b172a5e918167a31cbd9b302dc0f44" title="Click to view the MathML source">f₁,…,f_s$f_1,\dots ,f_s$ be formal power series (respectively polynomials) in the variable x  . We study the semigroup of orders of the formal series in the algebra 815&_mathId=si4.gif&_user=111111111&_pii=S0747717116300815&_rdoc=1&_issn=07477171&md5=cab5b01ecf114a6a71341ec208b6da15" title="Click to view the MathML source">K〚f₁,…,f_s〛⊆K〚x〛$\mathbb{K}〚f_1,\dots ,f_s〛\subseteq \mathbb{K}〚x〛$ (respectively the semigroup of degrees of polynomials in 815&_mathId=si5.gif&_user=111111111&_pii=S0747717116300815&_rdoc=1&_issn=07477171&md5=d4ded970ba9bd1636a69de1e3fb3c72a" title="Click to view the MathML source">K[f₁,…,f_s]⊆K[x]$\mathbb{K}[f_1,\dots ,f_s]\subseteq \mathbb{K}[x]$). We give procedures to compute these semigroups and several applications. We prove in particular that the space curve parametrized by 815&_mathId=si3.gif&_user=111111111&_pii=S0747717116300815&_rdoc=1&_issn=07477171&md5=82b172a5e918167a31cbd9b302dc0f44" title="Click to view the MathML source">f₁,…,f_s$f_1,\dots ,f_s$ has a flat deformation into a monomial curve.