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Depth :: regularSequence

regularSequence -- generates a regular sequence

Synopsis

Description

Given a ring and an ideal, regularSequence attempts to generate a regular sequence contained in I. The algorithm is based on one found in Chapter 5.5 of W. Vasconcelos' book: Computational Methods in Commutative Algebra and Algebraic Geometry.
A = ZZ/5051[x, y, z];
I = ideal (x, x*y, y*z);
X = regularSequence(I,A)
isRegularSequence(X,A)
Here are examples with optional inputs:
A = ZZ/5051[x, y, z];
I = ideal (x, x*y, y*z);
regularSequence(I,A,Attempts=>1,Bound=>100,Sparseness=>.9)
Here are examples with the optional input Maximal => false:
x = symbol x; y = symbol y;
n = 2;
A = ZZ/101[x_(1,1)..x_(n,n),y_(1,1)..y_(n,n)];
X = transpose genericMatrix(A,n,n);
Y = transpose genericMatrix(A,y_(1,1),n,n);
b = ideal(X*Y - Y*X);
B = A/b;
regularSequence(B,Attempts=>1,Maximal=>false)

This symbol is provided by the package Depth.

Ways to use regularSequence :