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Ordering on variables and
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Contents
Index
NCGB: LISTS OF COMMANDS AND OTHER DETAILS
Subsections
Ordering on variables and monomials
Lex Order: The simplest elimination order
Graded lex ordering: A non-elimination order
Multigraded lex ordering : A variety of elimination orders
The list of commands
SetMonomialOrder[aListOfListsOfIndeterminates, ...]
SetUnknowns[aListOfIndeterminates]
SetUnKnowns[aListOfVariables]
ClearMonomialOrder[]
PrintMonomialOrder[]
NCAutomaticOrder[ aMonomialOrder, aListOfPolynomials ]
Fancier Order Setting Commands
SetMonomialOrder[aListOfIndeterminants, n]
ClearMonomialOrderN[n]
ClearMonomialOrderAll[]
WhatIsMultiplicityOfGrading[]
WhatIsSetOfIndeterminants[n]
More NCProcess Options
Creating small generating sets: RR
, RRByCat
, SB
, SBByCat
SBFlatOrder
DegreeCapSB
and DegreeSumCapSB
NCCollectOnVars
NCCollectOnVars[aListOfExpressions, aListOfVariables]
The NCCollectOnVars option LeftAndRight
The NCProcess option NCCV
Turning screen output off
Output Options
Turning screen output off: PrintScreenOutput
TeX
ASCII
NCGBFastRegularOutput
NCShortFormulas
NCProcess Summary Table
Commands for Making and Using GB's
Simplification
NCSimplifyAll[expressions, startRelations, iterations]
NCSimplifyRationalX1[expressions, startRelations, iterations]
NCSimplifyRationalX1[expressions,startRelations]
NCSimplifyRationalX1[expressions,iterations]
NCSimplifyRationalX1[expressions]
Making a Gröbner Basis and various options (with their defaults)
NCMakeGB[aListOfPolynomials, iterations]
UserSelect
(Distinguishing important relations)
ClearUserSelect[]
Deselect
(DISABLED)
FinishedComputingBasisQ[] - Untested in 1999
WhatIsPartialGB[]
NCGBSetIntegerOverflow[False]
PartialBasis[aNumber] - Untested in 1999
IterationNumber[aList] or IterationNumber[ aNumber ] - UNTESTED 1999
CleanUp
SetCleanUpBasis[n] - Untested in 1999
CleanUpBasisQ[] - Untested in 1999
History Off
Correspondence to sections `Simplification' and `Reduction'
Setting Monomial Orders- See Chapter 21
ReinstateOrder[]
Reduction
Reduction[aListOfPolynomials, aListOfRules]
PolyToRule[aPolynomial]
RuleToPoly[aRule]
Commands for Making Small Bases for Ideals: Small Basis, Shrink Basis
Brute Force: Shrinking
SmallBasis[aListOfPolynomials, anotherListOfPolynomials, iter]
SmallBasisByCategory[aListOfPolynomials, iter]
ShrinkOutput[aListOfPolynomials,fileName]
Brute Force: Many shrinks
ShrinkBasis[aListOfPolynomials,iterations]
First Example
Second Example
Smaller Bases and the Spreadsheet command
How Small Basis commands relate to the similar NCProcess Options
Help in Typing Relations .
NCMakeRelations[aSpecialList, aSpecialList, ...]
Output notation for pseudoinverse and perp's
NCAddTranspose[aListOfExpressions]
NCAddAdjoint[aListOfExpressions]
Pulling important equations into your session from an
NCProcess
output - See
GetCategories
in §26.0.5.
Help in typing Monomial Orders - See NCAutomaticOrder Section 21.4.6
Retrieving Categories and Regular Output
GetCategory[aListOfVariables, NCPAns]
GetCategory[aCharString,NCPAns]
Clear[NCPAns]
Example
Creating Categories
CreateCategories[aListOfPolynomials, aName]
RegularOutput[aListOfPolynomials,``fileName"]
RegularOutput[aListOfPolynomials,``fileName"]
How to Really Change Regular Output
The Dimension of the Solution Set of a Set of Polynomial Equations
The Commuting Case
Noncommutative Case: Gelfand-Kirillov dimension
References
Commands
NCHilbertCoefficient[integer1, aListOfExpressions, integer2, anOption]
NCX1VectorDimension[alist]
Commands which are not supported
A Mathematica Groebner Basis Package Without C++
NCXWholeProcess[ polys, orderList, fileName, grobIters]
Getting NCALGEBRA and NCGB
Getting NCAlgebra and NCGB off the web
Getting NCAlgebra and NCGB through anonymous ftp
The ``.Z" file
The ``.gz" file
The ``.zip" file
Look at the document
The last step
The NC directory structure
Directory structure of NCAlgebra alone
Testing your version of NCGB
Beginners
Basic Tests
Fancy test program- DOES NOT WORK
Turning On Screen Output
More Testing for Developers - DOES NOT WORK 2001
Setting the Testing Environment
NCAlgebra Project 2002-09-09
,
RRByCat
, SB
, SBByCat
(Distinguishing important relations)
(DISABLED)
and
DegreeSumCapSB
