The CoCoAIdeal class represents an ideal of polynomials over a given polynomial ring (See <a href="MatlabCoCoAPoly.html">Poly class</a>).
The constructor for a CoCoAIdeal can have two arguments:
- Generators: Array of polynomials
- Optional: 1/0 : 1 = Compute Groebner-Basis of Ideal
If no input is given the default ideal (1) over Q[x] is returned Generators should be a 1xn CoCoAPoly array. A nx1 array is transposed.
|gens||an array of polynomials|
|gBasis||the Groebner-Basis of an Ideal|
|numBasisElements||The number of basis elements. If gBasis is not yet computed the number of generators is stored.|
|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.|
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^2-1'); p2 = CoCoAPoly('y+x'); myIdeal = CoCoAIdeal([p1 p2]); </matlab>