Mathematics Mechanization

Preface
PartIHistoricalDevelopments
ChapterIPolynomialEquations-SolvinginAncientTimes,MainlyinAncientChina
1.1ABriefDescriptionofHistoryofAncientChinaandMathematicsClassicsinAncientChina
1.2PolynomialEquations-SolvinginAncientChina
1.3PolynomialEquations-SolvinginAncientTimesbeyondChinaandtheProgramofDescartes
ChapterIIHistoricalDevelopmentofGeometryTheorem-ProvingandGeometryProblem-SolvinginAncientTimes
2.1GeometryTheorem-ProvingfromEuclidtoHilbert
2.2GeometryTheorem-ProvingintheComputerAge
2.3GeometryProblem-SolvingandGeometryTheorem-ProvinginAncientChina
PartIIPrinciplesandMethods
ChapterIIIAlgebraicVarieiesasZero-SetsandCharacteristic-SetMethod
3.1AffineandProjectiveSpaceExtendedPointsandSpecialization
3.2AlgebraicVarietiesandZero-Sets
3.3PolsetsandAscendingSets.PartialOrdering
3.4CharacteristicSetofaPolsetandtheWell-OrderingPrinciple
3.5Zero-DecompositionTheorems
3.6Variety-DecompositionTheorems
ChapterIVSomeTopicsinComputerAlgebra
4.1TuplesofIntegers
4.2Well-ArrangedBasisofaPolynomialIdeal
4.3Well-BehavedBasisofaPolynomialIdeal
4.4PropertiesofWell-BehavedBasisandItsRelationshipwithGroebnerBasis
4.5FaetorizationandCCDofMultivariatePolynomialsoverArbitraryExtensionFields
ChapterVSomeTopicsinComputationalAlgebraicGeometry
5.1SomeImportantCharactersofAlgebraicVarietiesComplexandRealVarieties
5.2AlgebraicCorrespondenceandChowForm
5.3ChernClassesandChernNumbersofanIrreducibleAlgebraicVarietywithArbitraryingularities
5.4AProjectionTheoremonQuasi-Varieties
5.5ExtremalPropertiesofRealPolynomials
Part111ApplicationsandExamples
ChapterVIApplicationstoPolynomialEquations-Solving
6.1BasicPrinciplesofPolynomialEquations-Solving:TheChar-SetMethod
6.2AHybridMethodofPolynomialEquations-Solving
6.3SolvingofProblemsinEnumerativeGeometry
6.4CentralConfigurationsinPlanetMotionsandVortexMotions
6.5SolvingofInverseKinematicEquationsinRobotics
ChapterVIIApplicationstoGeometryTheorem-Proving
7.1BasicPrinciplesofMechanicalGeometryTheorem-Proving
7.2MechanicalProvingofGeometryTheoremsofHilbertianType
7.3MechanicalProvingofGeometryTheoremsInvolvingEqualitiesAlone
7.4MechanicalProvingofGeometryTheoremsInvolvingInequalities
ChapterVIDiverseApplications
8.1ApplicationstoAutomatedDiscoveringofUnknownRelationsandAutomatedDeterminationofGeometryLoci
8.2ApplicationstoProblemsInvolvingInequalities,OptimizationProblems,andNonLinearProgramming
8.3Applicationsto4-BarLinkageDesign
8.4ApplicationstoSurface-FittingProbleminCAGD
8.5SomeMiscellaneousComplementsandExtensions
Bibliography
Index