ApCoCoA:MatlabCoCoAIdeal
Introduction
The CoCoAIdeal class represents an ideal of polynomials over a given polynomial ring (See <a href="MatlabCoCoAPoly.html">Poly class</a>).
Constructor
The constructor for a CoCoAIdeal can have two arguments:
 Generators: Array of polynomials
 Optional: 1/0 : 1 = Compute GroebnerBasis of Ideal
If no input is given the default ideal (1) over Q[x[1]] is returned Generators should be a 1xn CoCoAPoly array. A nx1 array is transposed.
Attributes
basering  A CoCoARing 
gens  an array of polynomials 
gBasis  the GroebnerBasis of an Ideal 
numBasisElements  The number of basis elements. If gBasis is not yet computed the number of generators is stored. 
Methods
Method  Operator  Description 
computeGBasis  computes the GBasis of the given Ideal and returns a new ideal with the same set of generators and the computed GBasis.  
computeLT  computes the leading term of the ideal. Returns a CoCoAPoly.  
display  Is used by Matlab to print a CoCoAIdeal to the command window. E.g. when a command is not terminated by a ';'.  
eq  ==  Compares two ideals. Returns 1 if all generators are equal. 
ge  >=  Compares two ideals according to their leading term. Returns 1 if first ideal is greater equal the second ideal. 
get  Returns the attributes of an ideal. Syntax: get(idealVar, 'Keyword'), where idealVar is a CoCoAIdeal and 'Keyword' is one of the keywords: 

gt  >  Compares two ideals according to their leading term. Returns 1 if first ideal is greater than the second ideal. 
isContained  Returns 1 if the first ideal is contained in the second ideal.  
isElem  Returns 1 if the polynomial (2. argument) is in the ideal (1. argument)  
le  <=  Compares two ideals according to their leading term. Returns 1 if first ideal is less equal the second ideal. 
lt  <  Compares two ideals according to their leading term. Returns 1 if first ideal is less than the second ideal. 
ne  ~=  returns NOT eq. 
Examples
A collection of examples is provided in the file TestCoCoAIdeal.m. This file defines the function TestCoCoAIdeal which will run and display many examples. A few common examples are presented below.
 Ideal generated by two polynomials.
<matlab> p1 = CoCoAPoly('x^21'); p2 = CoCoAPoly('y+x'); myIdeal = CoCoAIdeal([p1 p2]); </matlab>