The workhorse commands of a strategy are the NCProcess1 and NCProcess2 commands. These two commands fit the general mold of the NCProcess command. In particular, each option of NCProcess is also an option of NCProcess1 and NCProcess2. See §15.6.
In practice, the user runs NCProcess, then looks at the file fileName in order to get ideas for the next step. When the user decides on the next step, he can use some of the lists of Mathematica output in addition to some new relations as inputs for the next call to NCProcess. There are many options for NCProcess.
The command NCProcess calls NCMakeGB[aListOfPolynomials,iters]. NCMakeGB is an algorithm for producing a partial Gröbner basis. This produces many new relations whose solution set is the same as the solution set for aListOfPolynomials. Typically, many of the relations follow from other relations within the same output. There are many options for NCProcess which remove “mathematically redundant” relations before generating the spreadsheet in fileName and lists (2) and (3) of the Mathematica output. The various options as well as the default options for NCProcess are described in §19.
Here are some examples of how the NCProcess commands are called.
NCProcess1[aListOfPolys,2,"filname"]
list1 = NCProcess1[aListOfPolys,2,"filname", DegreeCap->8, DegreeSumCap->12] list2 = NCProcess2[aListOfPolys,2,"filname",UserSelect->anotherList, DegreeCap->6, DegreeSumCap->10] |