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junaid [2023/02/23 17:46] – [Subalgebra Analogue to Standard Basis for Ideal] Dr. Atiq ur Rehman | junaid [2023/02/23 17:55] (current) – [Procedure to classify the stably simple curve singularities] Dr. Atiq ur Rehman | ||
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+ | ==== Procedure to Compute Sasbi-Standard Bases==== | ||
+ | Let A=B_> be a localization of polynomial subalgebra B with respect to a local monomial ordering >. For a polynomial vector f in (R_>)^n (R_> is a localization of ring R with respect to >) and a finite set of polynomials vectors I in a module (A)^n, the following procedure computes a Sasbi-Standard weak normal form of f with respect to I over A. | ||
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+ | * [[mathcity> | ||
====Procedure to Classify the Hypersurface Singularities of Corank 3 in Positive Characteristics==== | ====Procedure to Classify the Hypersurface Singularities of Corank 3 in Positive Characteristics==== | ||
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====Contact Map Germs==== | ====Contact Map Germs==== | ||
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====Procedure to classify the right unimodal and bimodal Hypersurface singularities in positive characteristic by invariants==== | ====Procedure to classify the right unimodal and bimodal Hypersurface singularities in positive characteristic by invariants==== | ||
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====Procedure to classify the stably simple curve singularities==== | ====Procedure to classify the stably simple curve singularities==== | ||
- | | + | Remarks: Compute the Sagbi- basis of the Module. Compute the Semi-Group of the Algebra provided the input is Sagbi Bases of the Algebra. Compute the Semi-Module provided that the inputs are the Sagbi Bases of the Algebra resp. Module. |
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+ | ====Procedures to Compute SH-bases of subalgebra ==== | ||
- | ====Procedures to Compute | + | |
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- | * [[http:// | + | |
==== Procedure to Compute Sasbi Bases ===== | ==== Procedure to Compute Sasbi Bases ===== | ||
Let A=B_> be a localization of a polynomial subalgebra B with respect to a local monomial ordering >. For a polynomial f of R_> (a localization of ring R with respect to >) and a finite set of polynomials I in A, the following procedure computes a weak Sasbi normal form of f with respect to A. | Let A=B_> be a localization of a polynomial subalgebra B with respect to a local monomial ordering >. For a polynomial f of R_> (a localization of ring R with respect to >) and a finite set of polynomials I in A, the following procedure computes a weak Sasbi normal form of f with respect to A. |