Part VI
NCGB: LISTS OF COMMANDS AND OTHER DETAILS

18 Ordering on variables and monomials
 18.1 Lex Order: The simplest elimination order
 18.2 Graded lex ordering: A non-elimination order
 18.3 Multigraded lex ordering : A variety of elimination orders
 18.4 The list of commands
 18.5 Fancier Order Setting Commands
19 More NCProcess Options
 19.1 Creating small generating sets: RR→ True, RRByCat→ True, SB→ False, SBByCat→ True
 19.2 NCCollectOnVars
 19.3 Turning screen output off
 19.4 Output Options
 19.5 NCProcess Summary Table
20 Commands for Making and Using GB’s
 20.1 Simplification
 20.2 Making a Gröbner Basis and various options (with their defaults)
 20.3 Reduction
21 Commands for Making Small Bases for Ideals: Small Basis, Shrink Basis
 21.1 Brute Force: Shrinking
 21.2 Brute Force: Many shrinks
 21.3 First Example
 21.4 Second Example
 21.5 Smaller Bases and the Spreadsheet command
 21.6 How Small Basis commands relate to the similar NCProcess Options
22 Help in Typing Relations .
 22.1 Output notation for pseudoinverse and perp’s
23 Retrieving Categories and Regular Output
 23.1 Example
 23.2 Creating Categories
 23.3 RegularOutput[aListOfPolynomials,“fileName”]
 23.4 How to Really Change Regular Output
24 The Dimension of the Solution Set of a Set of Polynomial Equations
 24.1 The Commuting Case
 24.2 Noncommutative Case: Gelfand-Kirillov dimension
 24.3 References
 24.4 Commands
25 Commands which are not supported
 25.1 A Mathematica Groebner Basis Package Without C++
 25.2 NCXWholeProcess[ polys, orderList, fileName, grobIters]
26 Getting NCALGEBRA and NCGB
 26.1 Getting NCAlgebra and NCGB off the web
 26.2 Getting NCAlgebra and NCGB through anonymous ftp
 26.3 The last step
 26.4 The NC directory structure
 26.5 Directory structure of NCAlgebra alone
27 Testing your version of NCGB
 27.1 Beginners
 27.2 Turning On Screen Output
 27.3 More Testing for Developers - DOES NOT WORK 2001
28 References