-- -*- M2-comint -*- {* hash: 686966352 *} i1 : showClassStructure o1 = Type : AffineVariety Array AssociativeExpression BasicList BettiTally Boolean : false true CacheFunction CacheTable ChainComplex ChainComplexMap CoherentSheaf CompiledFunction : abs acos agm alarm ancestor any append apply applyKeys applyPairs applyValues ascii asin atan atan2 atEndOfFile BesselJ BesselY characters class clearEcho collectGarbage combine commandInterpreter concatenate connectionCount copy cos cosh cot coth cpuTime csc csch currentDirectory currentLineNumber currentTime deepSplice difference disassemble drop dumpdata echoOff echoOn eint erase erf erfc exec exp expm1 fileExists fileLength fileMode fileTime firstkey flagLookup floor fork format frames functionBody Gamma get getc getenv getGlobalSymbol getNetFile groupID hash hashTable horizontalJoin identity imaginaryPart installMethod instance isANumber isDirectory isFinite isGlobalSymbol isInfinite isInputFile isListener isOpen isOutputFile isReady isRegularFile join keys kill linkFile loaddata localDictionaries locate log log1p lookup lookupCount merge mergePairs mingle minimizeFilename minus mkdir mutable newClass newNetFile nextkey openDatabase openDatabaseOut openFiles openIn openInOut openListener openOut openOutAppend override pack pairs parent plus power powermod prepend printString processID protect pseudocode read readDirectory readlink realPart realpath recursionDepth regex registerFinalizer relativizeFilename remove removeDirectory removeFile reorganize reverse run scan scanPairs sec sech select separate sequence set setEcho setGroupID sin sinh size2 sleep splice sqrt stack substring symlinkFile take tally tan tanh times toCC toList toRR toSequence uncurry unsequence unstack utf8 values wait wrap xor youngest zeta CompiledFunctionBody CompiledFunctionClosure : chainComplex code commonest directSum EXAMPLE examples export exportMutable expression flatten gcd gradedModule gradedModuleMap hold html hypertext ideal info intersect isSorted lcm length makePackageIndex mathML max maxPosition methods min minPosition monomialIdeal net options package pretty runLengthEncode tex texMath toExternalString toString transpose undocumented unique vars ComplexField Constant : EulerConstant ii pi Database Descent Dictionary DocumentTag EngineRing Expression File : stderr stdio FilePosition ForestNode FractionField Function FunctionBody FunctionClosure : addEndFunction addStartFunction ancestors applicationDirectory applicationDirectorySuffix applyTable assert baseFilename beginDocumentation benchmark cacheValue ceiling centerString columnate delete demark End error even first getNonUnit getSymbol globalAssign globalAssignFunction globalAssignment globalReleaseFunction groebnerBasis infoHelp input integrate inversePermutation isPrimitive isTable jacobiTrudi last lines load makeDocumentTag method mod monoid monomialCurveIdeal needs notImplemented number odd on pager peek print same seeParsing showHtml stashValue subtable symmRing synonym SYNOPSIS syzygyScheme table temporaryFileName toAbsolutePath toE toLower toP toS toUpper tutorial uniform userSymbols vector zero GaloisField GeneralOrderedMonoid GlobalDictionary : OutputDictionary PackageDictionary GradedModule GradedModuleMap GroebnerBasis GroebnerBasisOptions HashTable HeaderType : Adjacent BinaryOperation Divide Equation FunctionApplication MatrixExpression Power RowExpression SparseMonomialVectorExpression SparseVectorExpression Subscript Superscript Table Ideal ImmutableType IndeterminateNumber : indeterminate IndexedVariable IndexedVariableTable InexactField InexactFieldFamily : CC RR InexactNumber InexactNumber * InfiniteNumber : infinity Keyword LibxmlAttribute LibxmlNode List LocalDictionary Manipulator : close closeIn closeOut endl flush Matrix MethodFunction : accumulate acosh acot addHook adjoint adjoint1 all ambient analyticSpread apropos asinh autoload baseName between binomial borel capture char clean coefficient coefficientRing coimage cokernel columnAdd columnMult columnPermute columnSwap commonRing comodule complement complete components compositions compress conductor cone conjugate content contract contract' conwayPolynomial cover coverMap debug decompose default degree degreeLength degrees degreesMonoid degreesRing denominator depth describe diagonalMatrix dictionary diff diff' dim discriminant dismiss divideByVariable doc eagonNorthcott elements eliminate endPackage entries euler eulers exponents Fano findSynonyms fittingIdeal flip fold frac fraction fromDual gbRemove gbSnapshot gcdCoefficients genera generateAssertions generator genericMatrix genericSkewMatrix genericSymmetricMatrix genus getChangeMatrix getWWW gramm heft height hilbertFunction Hom homogenize homomorphism httpHeaders icFractions icMap icPIdeal image index indices inducesWellDefinedMap insert installAssignmentMethod installHilbertFunction instances inverse irreducibleCharacteristicSeries irreducibleDecomposition isAffineRing isBorel isCommutative isConstant isDirectSum isField isFreeModule isHomogeneous isIdeal isInjective isIsomorphism isLinearType isModule isMonomialIdeal isNormal isPolynomialRing isPrimary isPrime isPseudoprime isQuotientModule isQuotientOf isQuotientRing isReal isRing isSkewCommutative isSquareFree isSubmodule isSubquotient isSubset isSurjective isUnit isWellDefined jacobian koszul leadCoefficient leadComponent leadMonomial leadTerm liftable listForm listSymbols lngamma LUdecomposition makeDirectory makeS2 match member memoize methodOptions minimalPrimes module monomialSubideal multidegree multiplicity newCoordinateSystem norm nullhomotopy numColumns numerator numeric numgens numRows ofClass packageTemplate pad part partition partitions parts pdim peek' permanents permutations pfaffians pivots poincare poincareN poly positions precision preimage presentation product profile Proj projectiveHilbertPolynomial promote pseudoRemainder quotient' quotientRemainder quotientRemainder' rank reduceHilbert reductionNumber relations remainder remainder' removeHook removeLowestDimension replace reshape resultant ring rotate round rowAdd rowMult rowPermute rowSwap runHooks scanKeys scanLines scanValues schreyerOrder schurRing searchPath selectInSubring selectVariables separateRegexp setRandomSeed setup setupEmacs sheaf sheafHom show simpleDocFrob singularLocus size someTerms source Spec standardForm standardPairs sublists submatrix submatrix' subquotient subsets substitute sum super support switch sylvesterMatrix symmetricPower target tensorAssociativity terms TEST toDual toField topCoefficients topComponents trace truncate truncateOutput ultimate unbag universalEmbedding use value variety wedgeProduct weightRange whichGm width Wikipedia MethodFunctionWithOptions : annihilator associatedGradedRing associatedPrimes basis betti check codim coefficients cohomology copyDirectory copyFile cotangentSheaf determinant distinguished distinguishedAndMult document dual eigenvalues eigenvectors extend exteriorPower factor fillMatrix findFiles flattenRing forceGB gb gcdLLL generators getPackage GF graphIdeal graphRing Grassmannian hermite hilbertPolynomial hilbertSeries homology icFracP idealizer independentSets inducedMap installPackage integralClosure isLLL isReduction kernel kernelLLL lift LLL loadPackage localize map markedGB matrix mingens minimalPresentation minimalReduction minors modulo monomials moveFile mutableIdentity mutableMatrix needsPackage netList newPackage newRing normalCone position primaryComponent primaryDecomposition prune pushForward quotient radical random randomMutableMatrix reesAlgebra reesIdeal regularity resolution ringFromFractions rsort saturate Schubert showTex smithNormalForm solve sort sortColumns specialFiber specialFiberIdeal status SVD symlinkDirectory symmetricAlgebra symmetricKernel syz tangentCone tangentSheaf tensor trim uninstallPackage Module ModuleMap Monoid MonoidElement MonomialIdeal MutableHashTable MutableList MutableMatrix Net NetFile Nothing Number OneExpression Option OptionTable OrderedMonoid Package : Classic ConwayPolynomials Core Elimination IntegralClosure LLLBases Parsing PrimaryDecomposition ReesAlgebra SchurRings SimpleDoc TangentCone Text User Partition PolynomialRing ProjectiveHilbertPolynomial ProjectiveVariety Pseudocode QuotientRing RealField Resolution Ring : QQ ZZ RingElement RingFamily RingMap SchurRing SchurRingIndexedVariableTable ScriptedFunctor : Ext HH hh id OO sheafExt Tor SelfInitializingType : Bag Command : clearAll clearOutput edit exit help listLocalSymbols listUserSymbols profileSummary quit restart showClassStructure showStructure showUserStructure viewHelp Eliminate Hybrid LowerBound ProductOrder PushforwardComputation URL VerticalList Sequence Set SheafOfRings String SumOfTwists Symbol Tally Thing Time TreeNode Variety Vector VirtualTally VisibleList WrapperType : Holder Minus NonAssociativeProduct Parenthesize Product Sum ZeroExpression o1 : 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