In this paper, we characterize the classification of unimodal maps from the plane to the plane with respect to [Formula: see text]-equivalence given by Rieger in terms of invariants. We recall the classification over an algebraically closed field of characteristic [Formula: see text]. On the basis of this characterization, we present an algorithm to compute the type of the unimodal maps from the plane to the plane without computing the normal form and also give its implementation in the computer algebra system Singular.
In this article, we correct the classification of unimodal map germs from the plane to the plane of Boardman symbol (2, 2) given by Dimca and Gibson. Also, we characterize this classification of unimodal map germs in terms of certain invariants. Moreover, on the basis of this characterization we present an algorithm to compute the type of unimodal map germs of the Boardman symbol (2, 2) without computing the normal form and give its implementation in the computer algebra system Singular [8].
The classification of contact simple map germs from (C2,0)→(C2,0) was given by Dimca and Gibson. In this article, we give a useful criteria to recognize this classification of contact simple map germs of holomorphic mappings with finite codimension. The recognition is based on the computation of explicit numerical invariants. By using this characterization, we implement an algorithm to compute the type of the contact simple map germs without computing the normal form and also give its implementation in the computer algebra system Singular.
<abstract><p>The classification and the geometry of corank one map germs from $ ({\mathbb{C}}^2, 0) \rightarrow ({\mathbb{C}}^3, 0) $ have been studied by Mond <sup>[<xref ref-type="bibr" rid="b1">1</xref>,<xref ref-type="bibr" rid="b2">2</xref>]</sup>. In this paper we characterize the classification of map germs of corank at most $ 1 $, in terms of certain invariants. Moreover, by using this characterization, we develop an algorithm to compute the type of map germs with out computing the normal form. Also, we give its implementation in the computer algebra system SINGULAR <sup>[<xref ref-type="bibr" rid="b15">15</xref>]</sup>.</p></abstract>
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