Index

$NCGB$IntegerOverflow=False, 288
$NC$Binary$Dir$, 669
$NC$Binary$Name$, 669
$NC$Loaded$NCGB$, 669
$NC$LongLoadTime$, 669


aj[expr], 182
ajMat[u], 145
Aliases, 237
AllOrders[aListofPolynomials, aListofIndeterminants], 717
ASCIIFalse, 478


BilinearQ[aFunction], 205


Cascade[P, K], 156
CEEP, 220
Chain[P], 157
ChangeNCMakeGBOptions[option,value] — need to update description, 713
CleanUp, 495
CleanUpBasisQ[] - Untested in 1999, 496
Clear[NCPAns], 533
ClearMonomialOrder[], 460
ClearMonomialOrderAll[], 463
ClearMonomialOrderN[n], 463
ClearUserSelect[], 492
co[expr], 182
CoIsometryQ[aSymbol], 199
coMat[u], 145
CommutativeAllQ[expr], 177
CommutativeQ[X], 177
CommuteEverything[expr], 175
ComplexCoordinates[expr], 172
ComplexD[expr, aVariable], 173
ComplexRules, 172
ConjugateLinearQ[aFunction], 206
ContinuousTimeQ[ System1], 260
CreateCategories[aListOfPolynomials, aName], 535
CriticalPoint[expr, aVariable], 138


DegreeCapSBaNumber1, 468
DegreeSumCapSBaNumber2, 468
Deselect→{} (DISABLED), 492
Diag[aMatrix], 156
DilationHalmos[x], 158
DirD, 137
DirectionalD[expr, aVariable, h], 137
DiscreteTimeQ[ System1], 261
Dual[ System1], 263


EquivalenceClasses[aListOfPolynomials] or EquivalenceClasses[aListOfPolynomials, Simpler], 718
ExpandNonCommutativeMultiply[expr], 121
ExpandQ[inv], 180
ExpandQ[tp], 181


FeedbackConnect[ System1, System2 ], 258
FinishedComputingBasisQ[] - Untested in 1999, 493
FunctionOnRules[Rules, Function1, Function2, (optional On)], 218


GBTEST, 581
GetCategory[aCharString,NCPAns], 533
GetCategory[aListOfVariables, NCPAns], 531
GrabIndeterminants[ aListOfPolynomialsOrRules], 128
GrabVariables[ aListOfPolynomialsOrRules ], 129
Grad[expr, aVariable], 138
GroebnerCutOffFlag[n_Integer], 718
GroebnerCutOffMin[n_Integer], 719
GroebnerCutOffSum[n_Integer], 719


History Off, 496


IdempotentQ[aFunction], 207
IntegerOverflow, 288
inv[x], 178
InverseSystem[ System1], 264
invL[x], 179
invQ[x], 180
invR[x], 179
IsometryQ[aSymbol], 198
IterationNumber[aList] or IterationNumber[ aNumber ] - UNTESTED 1999, 494


Keep[anInteger], 234
Kill[anInteger], 235
KillTeX[], 233


LeftQ[expr], 176
LinearQ[aFunction], 206
LookAtLongExpression[anExpression], 236
LookAtMatrix[aMatrix], 235


MakeGif[file,expression], 724
MatMult[x, y, ], 144


NCAddAdjoint, 320
NCAddAdjoint[aListOfExpressions], 526
NCAddTranspose, 320
NCAddTranspose[aListOfExpressions], 526
NCAllPermutationLDU[aMatrix], 153
NCAutomaticOrder, 323
NCAutomaticOrder[ aMonomialOrder, aListOfPolynomials ], 461
NCBackward[expr], 130
NCBorderVectorGather[alist,varlist] , 192
NCCheckPermutation[SizeOfMatrix, aListOfPermutations], 155
NCCoefficientList[Expression, aListOfIndeterminants], 643
NCCollect[expr, aListOfVariables], 122
NCCollectOnVars[ Y**A**B**Z + A**X+A**Y, {A,B}] , 472
NCCollectOnVars[aListOfExpressions, aListOfVariables], 472
NCCollectSymmetric[expr], 123
NCCompose[aVerySpecialList], 215
NCContinueMakeGB[iterationNumber], 710
NCConvexityRegion[afunction,alistOfVars,opts], 186
NCCVTrue, 476
NCDecompose[expr, listofsymbols], 215
NCExpand, 121
NCForward[expr], 131
NCGBFastRegularOutputFalse, 479
NCGBMmaDiagnostics[ True], 477
NCGBMmaDiagnostics[False], 583
NCGBSetIntegerOverflow[False], 494
NCGBSetIntegerOverflow[True], 288
NCGuts, 193
NCHessian[afunction, {X1,H1},,{Xk,Hk} ], 140
NCHilbertCoefficient[integer1, aListOfExpressions, integer2, anOption], 552
NCIndependenceCheck[aListofLists,variable], 190
NCInverse[aSquareMatrix], 153
NCLDUDecomposition[aMatrix, Options], 152
NCMakeGB Options
    CleanUp True, 495
NCMakeGB[{},iters], 294
NCMakeGB[aListOfPolynomials, iterations], 491
NCMakeGB[polys, iters], 469
NCMakeGB[-b + x ** y , x ** a-1,4], 449
NCMakeRelations, 319
NCMakeRelations[aSpecialList, aSpecialList, ...], 525
NCMatrixOfQuadratic[ Q, {H1,,Hn} ] , 188
NCMatrixToPermutation[aMatrix], 155
NCMonomial[expr], 132
NCMToMatMult[expr], 147
NCPermutationMatrix[aListOfIntegers], 154
NCProcess[aListOfPolynomials,iterations,fileName, Options ], 378
NCReconstructFromTermArray[anArray], 212
NCSetNC, 195
NCSetOutput[ optionlist,], 227
NCShortFormulas→-1, 479
NCSimplify1Rational[expr], 135
NCSimplify2Rational[expr], 136
NCSimplifyAll[expressions, startRelations, iterations], 488
NCSimplifyRational[ expr ], NCSimplify1Rational[ expr ], and NCSimplify2Rational[ expr ], 134
NCSimplifyRationalX1[expressions, startRelations, iterations], 489
NCSolve[expr1==expr2,var], 124
NCStrongCollect[expr, aListOfVariables],
122
NCStrongProduct1, 194
NCStrongProduct2, 195
NCTermArray[expr,aList,anArray], 210
NCTermsOfDegree[expr,aListOfVariables,indices], 123
NCTeX[], 230
NCTeXForm[exp], 228
NCUnMonomial[expr], 132
NCX1VectorDimension[alist], 552
NCXAllPossibleChangeOfVariables[ aListOfPolynomials], 649
NCXFindChangeOfVariables[ aListofPolynomials, anInteger, aString, Options], 646
NCXMultiplyByMonomials[ aVerySpecialList], 648
NCXPossibleChangeOfVariables[ aListofPolynomials, Options], 647
NCXRepresent[aListOfExpressions, aListOfVariables, aListOfDims, aListOfFunctions, aListOfExtraRules], 654
NoTeX[], 232
NumbersFromHistory[aPolynomial,history], 603


OverrideInverse, 181


ParallelConnect[ System1, System2 ], 259
PartialBasis[aNumber] - Untested in 1999, 494
PolyToRule, 298
PolyToRule[aPolynomial], 499
PolyToRule[RuleToPoly[r]]=r, 316
PolyToRule[a**x-1, b-x], 450
PrintMonomialOrder[], 460
PrintScreenOutput True, 477
PrintScreenOutput False, 478
PrintSreenOutput False, 583
ProjectionQ[S], 201


RandomMatrix[m,n,min,max,options], 219
Redheffer[P], 157
Reduction[aListOfPolynomials, aListOfRules], 498
Reduction[, ], 317
RegularOutput[aListOfPolynomials,“fileName], 536
ReinstateOrder[], 497
RemoveRedundant[], 615
RemoveRedundant[aListOfPolynomials,history], 615
RemoveRedundentByCategory[ aListOfPolynomials, history], 616
RemoveRedundentByCategory[], 616
RRTrue, 467
RRByCatTrue, 467
RuleToPoly[aRule], 499
RuleToPoly[PolyToRule[r]]=r, 316


SaveRules[expression, ’optional tag message’], 216
SaveRulesQ[], 217
SBFalse, 467
SBByCatTrue, 467
SBFlatOrderFalse, 468
SchurComplementBtm[M], 159
SchurComplementTop[M], 158
See[aListOfIntegers], 233
SeeTeX[] or SeeTeX[anInteger], 232
SelfAdjointQ[aSymbol], 197
SeriesConnect[ System1, System2 ], 258
SesquilinearQ[aFunction], 204
SetBilinear[Functions], 204
SetCleanUpBasis[n] - Untested in 1999, 495
SetCoIsometry[Symbols], 199
SetCommutative[a, b, c, ], 175
SetCommutingFunctions[ aFunction, anotherFunction], 208
SetCommutingOperators[b,c], 176
SetConjugateLinear[Functions], 206
SetIdempotent[Functions], 207
SetInv[a, b, c, ], 196
SetIsometry[Symbols], 198
SetKnowns[A,B], 472
SetLinear[Functions], 205
SetMonomialOrder[aListOfIndeterminants, n], 462
SetMonomialOrder[aListOfListsOfIndeterminates, ...], 458
SetMonomialOrder[A,B,a,b,f], 455
SetNonCommutative[A, B, C, ], 174
SetNonCommutativeMultiplyAntihomomorphism[ Functions], 209
SetProjection[Symbols], 201
SetRecordHistory[False], 496
SetRecordHistory[True] , 496
SetSelfAdjoint[Symbols], 197
SetSesquilinear[Functions], 203
SetSignature[Symbols], 202
SetUnitary[Symbols], 200
SetUnknowns[aListOfIndeterminates], 459
SetUnKnowns[aListOfVariables] , 460
SetUnknowns[X,Y,Z], 472
ShrinkBasis[aListOfPolynomials,iterations], 507
ShrinkOutput[aListOfPolynomials,fileName], 506
SignatureQ[Symbol], 202
SmallBasis[aListOfPolynomials, anotherListOfPolynomials, iter], 505
SmallBasisByCategory[aListOfPolynomials, iter], 505
SortMonomials[aListOfVariables], 712
SortRelations[aListOfRules], 712
Substitute[expr,aListOfRules,(Optional On)], 125
SubstituteAll[expr, aListOfRules, (optional On)], 126
SubstituteSingleReplace[expr, aListOfRules, (optional On)], 126
SubstituteSymmetric[expr, aListOfRules, (optional On)], 125
SupressAllCOutputFalse (very little outp ut to the screen), 710
SupressCOutputFalse (less output to the screen ), 709


Testing NCGB: GBTEST, 581
TeXTrue, 478
TimesToNCM[expr], 147
ToHTMLString[expression], 723
tp[expr], 182
tpMat[u], 146
TransferFunction[ System1], 262
Transform[expr,aListOfRules], 127


UnitaryQ[aSymbol], 200
UniversalBasis[aListOfPolynomials, NumberOfIterations], 718
UserSelect→{}(Distinguishing important relations), 491


WhatAreGBNumbers[], 602
WhatAreNumbers[], 602
WhatIsHistory[aListOfIntegers], 604
WhatIsKludgeHistory[aListOfIntegers], 605
WhatIsMultiplicityOfGrading[], 463
WhatIsPartialGB[], 493
WhatIsPartialGB[aListOfIntegers], 603
WhatIsSetOfIndeterminants[n], 464