Theory and more details

• Background on Ideals and Gröbner Bases
  • The Reduction Process
  • The Basis Algorithm
• A Gröbner Basis Theorem on Elimination Ideals
• Finding a small generating set for an ideal
  • The need to consider small generating sets
  • Preview of operations
  • The SmallBasis Operation
    • Approximation of the SmallBasis operation
  • The ShrinkBasis Operation
  • Gröbner Graph: Background for the RemoveRedundant Operation
    • Gröbner Basis Background
    • The graph
    • Definition of a Gröbner Graph
  • The RemoveRedundant operation
  • Respect for categories
    • Idealized shrinking by category
    • Practical shrinking by category
  • Remove Redundant Protected
• Speeding up runs
  • DegreeCap and DegreeSumCap
  • Monomial Orders vs. Run time
• Details of NCProcess
  • NCProcess1 command
  • NCProcess2 command
• Adjoints
• Example of discovering
• Formal descriptions of pure lex and multigraded lex
  • An ordering on
  • Formal description of pure lex
  • Formal description of multigraded lex
• Engineering motivation for the Control Problem (not for publication)
  • System definitions
  • Energy balance equations