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junaid [2021/02/07 16:39] – created - external edit 127.0.0.1junaid [2023/02/23 17:55] (current) – [Procedure to classify the stably simple curve singularities] Dr. Atiq ur Rehman
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 {{ :dr-junaid-alam-khan.jpg?nolink |Dr Junaid Alam Khan}} {{ :dr-junaid-alam-khan.jpg?nolink |Dr Junaid Alam Khan}}
 +
 +==== 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.
 +
 +  * [[mathcity>files/junaid/Sasbi-Standard_Bases_of_Modules-Library.txt|Download Code in Text file]]
  
 ====Procedure to Classify the Hypersurface Singularities of Corank 3 in Positive Characteristics==== ====Procedure to Classify the Hypersurface Singularities of Corank 3 in Positive Characteristics====
-  * [[http://www.mathcity.org/files/junaid/Classify-Procedure.txt|Download Code in TXT file]]+ 
 +  * [[mathcity>files/junaid/Classify-Procedure.txt|Download Code in Text file]]
  
 ====Contact Map Germs==== ====Contact Map Germs====
-  * [[http://www.mathcity.org/files/junaid/Contact-Map-Germs.txt|Download Code in TXT file]]+ 
 +  * [[mathcity>files/junaid/Contact-Map-Germs.txt|Download Code in Text file]]
  
 ====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====
-  * [[http://www.mathcity.org/files/junaid/Right-uni-and-bimodal-in-+ve-char.txt|Download Code in TXT file]]+ 
 +  * [[mathcity>files/junaid/Right-uni-and-bimodal-in-+ve-char.txt|Download Code in Text file]]
  
 ====Procedure to classify the stably simple curve singularities==== ====Procedure to classify the stably simple curve singularities====
-  * [[http://www.mathcity.org/files/junaid/ClassifierSS.txt|Download Code in TXT file]]+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. 
 + 
 +  * [[mathcity>files/junaid/ClassifierSS.txt|Download Code in Text file]]
  
-====Procedures to  Compute  SH-bases of subalgebra ==== +====Procedures to Compute SH-bases of subalgebra ====
-  * SPDFICON [[http://www.mathcity.org/files/junaid/SH-basis_procedures.pdf|Download Code in PDF file]] +
-  * [[http://www.mathcity.org/files/junaid/SH-basis_procedures.txt|Download Code in TXT file]] +
-==== Subalgebra Analogue to Standard Basis for Ideal =====+
  
-  * SPDFICON [[mathcity>files/junaid/dn.php?file=SASBI_code.pdf|Download Code in PDF file]]+  * [[mathcity>files/junaid/SH-basis_procedures.txt|Download Code in Text file]] 
 +==== 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.
  
-  * [[mathcity>files/junaid/SASBI_code.txt|Download Code in TXT file]]+  * [[mathcity>files/junaid/Sasbi_Bases-Library.txt|Download Code in Text file]]
  
 ==== Further on Sagbi Basis Under Composition ==== ==== Further on Sagbi Basis Under Composition ====