| $NCGB$IntegerOverflow=False, 130
$NC$Binary$Dir$, 278 $NC$Binary$Name$, 278 $NC$Loaded$NCGB$, 278 $NC$LongLoadTime$, 278 aj[expr], 77 ajMat[u], 59 Aliases, 108 AllOrders[aListofPolynomials, aListofIndeterminants], 301 ASCII→ False, 203 BilinearQ[aFunction], 92 Cascade[P, K], 66 CEEP, 100 Chain[P], 66 ChangeNCMakeGBOptions[option,value] — need to update description, 299 CleanUp, 212 CleanUpBasisQ[] - Untested in 1999, 212 Clear[NCPAns], 226 ClearMonomialOrder[], 195 ClearMonomialOrderAll[], 197 ClearMonomialOrderN[n], 197 ClearUserSelect[], 209 co[expr], 78 CoIsometryQ[aSymbol], 88 coMat[u], 59 CommutativeAllQ[expr], 75 CommutativeQ[X], 75 CommuteEverything[expr], 73 ComplexCoordinates[expr], 72 ComplexD[expr, aVariable], 73 ComplexRules, 72 ConjugateLinearQ[aFunction], 93 ContinuousTimeQ[ System1], 119 CreateCategories[aListOfPolynomials, aName], 227 CriticalPoint[expr, aVariable], 57 DegreeCapSB→ aNumber1, 200 DegreeSumCapSB→ aNumber2, 200 Deselect→{} (DISABLED), 210 Diag[aMatrix], 66 DilationHalmos[x], 67 DirD, 56 DirectionalD[expr, aVariable, h], 56 DiscreteTimeQ[ System1], 119 Dual[ System1], 120 EquivalenceClasses[aListOfPolynomials] or EquivalenceClasses[aListOfPolynomials, Simpler], 301 ExpandNonCommutativeMultiply[expr], 47 ExpandQ[inv], 76 ExpandQ[tp], 77 FeedbackConnect[ System1, System2 ], 118 FinishedComputingBasisQ[] - Untested in 1999, 210 FunctionOnRules[Rules, Function1, Function2, (optional On)], 98 GBTEST, 243 GetCategory[aCharString,NCPAns], 226 GetCategory[aListOfVariables, NCPAns], 225 GrabIndeterminants[ aListOfPolynomialsOrRules], 51 GrabVariables[ aListOfPolynomialsOrRules ], 52 Grad[expr, aVariable], 56 GroebnerCutOffFlag[n_Integer], 302 GroebnerCutOffMin[n_Integer], 302 GroebnerCutOffSum[n_Integer], 302 History Off, 212 IdempotentQ[aFunction], 93 IntegerOverflow, 130 inv[x], 75 InverseSystem[ System1], 120 invL[x], 76 invQ[x], 76 invR[x], 76 IsometryQ[aSymbol], 88 IterationNumber[aList] or IterationNumber[ aNumber ] - UNTESTED 1999, 211 Keep[anInteger], 106 Kill[anInteger], 107 KillTeX[], 106 LeftQ[expr], 74 LinearQ[aFunction], 92 LookAtLongExpression[anExpression], 107 LookAtMatrix[aMatrix], 107 MakeGif[file,expression], 304 MatMult[x, y, …], 59 NCAddAdjoint, 137 NCAddAdjoint[aListOfExpressions], 223 NCAddTranspose, 137 NCAddTranspose[aListOfExpressions], 223 NCAllPermutationLDU[aMatrix], 64 NCAutomaticOrder, 137 NCAutomaticOrder[ aMonomialOrder, aListOfPolynomials ], 196 NCBackward[expr], 52 NCBorderVectorGather[alist,varlist] , 85 NCCheckPermutation[SizeOfMatrix, aListOfPermutations], 66 NCCoefficientList[Expression, aListOfIndeterminants], 267 NCCollect[expr, aListOfVariables], 48 NCCollectOnVars[ Y**A**B**Z + A**X+A**Y, {A,B}] , 201 NCCollectOnVars[aListOfExpressions, aListOfVariables], 201 NCCollectSymmetric[expr], 48 NCCompose[aVerySpecialList], 97 NCContinueMakeGB[iterationNumber], 298 NCConvexityRegion[afunction,alistOfVars,opts], 81 NCCV→ True, 202 NCDecompose[expr, listofsymbols], 97 NCExpand, 47 NCForward[expr], 52 NCGBFastRegularOutput→ False, 203 NCGBMmaDiagnostics[ True], 202 NCGBMmaDiagnostics[False], 244 NCGBSetIntegerOverflow[False], 211 NCGBSetIntegerOverflow[True], 130 NCGuts, 85 NCHessian[afunction, {X1,H1},…,{Xk,Hk} ], 58 NCHilbertCoefficient[integer1, aListOfExpressions, integer2, anOption], 233 NCIndependenceCheck[aListofLists,variable], 84 NCInverse[aSquareMatrix], 64 NCLDUDecomposition[aMatrix, Options], 64 NCMakeGB Options CleanUp → True, 212 NCMakeGB[{},iters], 131 NCMakeGB[aListOfPolynomials, iterations], 209 NCMakeGB[polys, iters], 200 NCMakeGB[-b + x ** y , x ** a-1,4], 191 NCMakeRelations, 136 NCMakeRelations[aSpecialList, aSpecialList, ...], 222 NCMatrixOfQuadratic[  , {H1,…,Hn} ] ,
83
NCMatrixToPermutation[aMatrix], 65 NCMonomial[expr], 53 NCMToMatMult[expr], 60 NCPermutationMatrix[aListOfIntegers], 65 NCProcess[aListOfPolynomials,iterations,fileName, Options ], 161 NCReconstructFromTermArray[anArray], 96 NCSetNC, 86 NCSetOutput[ optionlist,…], 102 NCShortFormulas→-1, 203 NCSimplify1Rational[expr], 55 NCSimplify2Rational[expr], 56 NCSimplifyAll[expressions, startRelations, iterations], 207 NCSimplifyRational[ expr ], NCSimplify1Rational[ expr ], and NCSimplify2Rational[ expr ], 55 NCSimplifyRationalX1[expressions, startRelations, iterations], 208 NCSolve[expr1==expr2,var], 49 NCStrongCollect[expr, aListOfVariables], | 48
NCStrongProduct1, 85 NCStrongProduct2, 86 NCTermArray[expr,aList,anArray], 95 NCTermsOfDegree[expr,aListOfVariables,indices], 49 NCTeX[], 104 NCTeXForm[exp], 103 NCUnMonomial[expr], 53 NCX1VectorDimension[alist], 234 NCXAllPossibleChangeOfVariables[ aListOfPolynomials], 271 NCXFindChangeOfVariables[ aListofPolynomials, anInteger, aString, Options], 269 NCXMultiplyByMonomials[ aVerySpecialList], 270 NCXPossibleChangeOfVariables[ aListofPolynomials, Options], 270 NCXRepresent[aListOfExpressions, aListOfVariables, aListOfDims, aListOfFunctions, aListOfExtraRules], 274 NoTeX[], 105 NumbersFromHistory[aPolynomial,history], 252 OverrideInverse, 77 ParallelConnect[ System1, System2 ], 118 PartialBasis[aNumber] - Untested in 1999, 211 PolyToRule, 132 PolyToRule[aPolynomial], 214 PolyToRule[RuleToPoly[r]]=r, 136 PolyToRule[a**x-1, b-x], 192 PrintMonomialOrder[], 196 PrintScreenOutput → True, 202 PrintScreenOutput → False, 203 PrintSreenOutput → False, 244 ProjectionQ[S], 90 RandomMatrix[m,n,min,max,options], 99 Redheffer[P], 67 Reduction[aListOfPolynomials, aListOfRules], 214 Reduction[, ], 136 RegularOutput[aListOfPolynomials,“fileName], 228 ReinstateOrder[], 213 RemoveRedundant[], 258 RemoveRedundant[aListOfPolynomials,history], 259 RemoveRedundentByCategory[ aListOfPolynomials, history], 259 RemoveRedundentByCategory[], 259 RR→ True, 199 RRByCat→ True, 199 RuleToPoly[aRule], 214 RuleToPoly[PolyToRule[r]]=r, 136 SaveRules[expression, ’optional tag → message’], 98 SaveRulesQ[], 98 SB→ False, 199 SBByCat→ True, 199 SBFlatOrder→ False, 199 SchurComplementBtm[M], 67 SchurComplementTop[M], 67 See[aListOfIntegers], 106 SeeTeX[] or SeeTeX[anInteger], 105 SelfAdjointQ[aSymbol], 87 SeriesConnect[ System1, System2 ], 118 SesquilinearQ[aFunction], 91 SetBilinear[Functions], 91 SetCleanUpBasis[n] - Untested in 1999, 212 SetCoIsometry[Symbols], 88 SetCommutative[a, b, c, …], 74 SetCommutingFunctions[ aFunction, anotherFunction], 94 SetCommutingOperators[b,c], 74 SetConjugateLinear[Functions], 92 SetIdempotent[Functions], 93 SetInv[a, b, c, …], 86 SetIsometry[Symbols], 87 SetKnowns[A,B], 201 SetLinear[Functions], 92 SetMonomialOrder[aListOfIndeterminants, n], 197 SetMonomialOrder[aListOfListsOfIndeterminates, ...], 194 SetMonomialOrder[A,B,a,b,f], 193 SetNonCommutative[A, B, C, …], 73 SetNonCommutativeMultiplyAntihomomorphism[ Functions], 94 SetProjection[Symbols], 89 SetRecordHistory[False], 212, 213 SetRecordHistory[True] , 213 SetSelfAdjoint[Symbols], 87 SetSesquilinear[Functions], 91 SetSignature[Symbols], 90 SetUnitary[Symbols], 89 SetUnknowns[aListOfIndeterminates], 195 SetUnKnowns[aListOfVariables] , 195 SetUnknowns[X,Y,Z], 201 ShrinkBasis[aListOfPolynomials,iterations], 218 ShrinkOutput[aListOfPolynomials,fileName], 217 SignatureQ[Symbol], 90 SmallBasis[aListOfPolynomials, anotherListOfPolynomials, iter], 216 SmallBasisByCategory[aListOfPolynomials, iter], 217 SortMonomials[aListOfVariables], 298 SortRelations[aListOfRules], 298 Substitute[expr,aListOfRules,(Optional On)], 50 SubstituteAll[expr, aListOfRules, (optional On)], 51 SubstituteSingleReplace[expr, aListOfRules, (optional On)], 50 SubstituteSymmetric[expr, aListOfRules, (optional On)], 50 SupressAllCOutput→ False (very little outp ut to the screen), 297 SupressCOutput→ False (less output to the screen ), 297 Testing NCGB: GBTEST, 243 TeX→ True, 203 TimesToNCM[expr], 60 ToHTMLString[expression], 303 tp[expr], 77 tpMat[u], 60 TransferFunction[ System1], 120 Transform[expr,aListOfRules], 51 UnitaryQ[aSymbol], 89 UniversalBasis[aListOfPolynomials, NumberOfIterations], 302 UserSelect→{}(Distinguishing important relations), 209 WhatAreGBNumbers[], 251 WhatAreNumbers[], 252 WhatIsHistory[aListOfIntegers], 253 WhatIsKludgeHistory[aListOfIntegers], 253 WhatIsMultiplicityOfGrading[], 197 WhatIsPartialGB[], 210 WhatIsPartialGB[aListOfIntegers], 252 WhatIsSetOfIndeterminants[n], 197 |