4
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According to following example,we can know the Mathematica classify every function in different aspect.

 EntityValue[
 Entity["WolframLanguageSymbol", "Image"], "FunctionalityAreas"]

Out[52]= {"ImageFunctions"}

EntityValue[
 Entity["WolframLanguageSymbol", "Plot"], "FunctionalityAreas"]

Out[53]= {"BasicFunctions", "PlottingFunctions"}

EntityValue[
 Entity["WolframLanguageSymbol", 
  "BilateralFilter"], "FunctionalityAreas"]

Out[54]= {"ImageFilterFunctions"}

But the question is how many types be classified in Mathematica.And what are these types?

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7
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In 10.4 there are 173 functionality areas.

funcAreas = 
  Sort@DeleteDuplicates@*Flatten@
    WolframLanguageData[WolframLanguageData[], "FunctionalityAreas"];

Length@funcAreas
(* 173 *)

A quick browser with Manipulate

Manipulate[
 Multicolumn[
  WolframLanguageData[
   EntityClass["WolframLanguageSymbol", {"FunctionalityArea", fooArea}]], 
  4],
 {fooArea, fooAreaList},
 Initialization :> {
   fooAreaList = Sort@DeleteDuplicates@*Flatten@  
      WolframLanguageData[WolframLanguageData[], "FunctionalityAreas"];}
]

enter image description here

Hope this helps.


Explicit list of "FunctionalityAreas" in 10.4 as OP is having firewall issues connecting to Wolfram Cloud.

{"AlgebraicFunctions", "AlignmentFunctions", "AngleFunctions", \
"AnnotationFunctions", "ArrayFunctions", "ArrowOperatorFunctions", \
"AskFunctions", "AssociationFunctions", "AstronomyFunctions", \
"AsynchronousTaskFunctions", "AutocompleteFunctions", \
"BasicFunctions", "BinaryDataFunctions", "BitFunctions", \
"BooleanFunctions", "BoxFunctions", "BoxOptions", "ButtonFunctions", \
"CalculusFunctions", "CDFFunctions", "CellFunctions", \
"ChartFunctions", "CloudFunctions", "ClusteringFunctions", \
"CodeActionFunctions", "CodeEvaluationFunctions", \
"CodeFlowFunctions", "CodeInterruptionFunctions", "ColorFunctions", \
"ComparisonOperatorFunctions", "CompileFunctions", \
"ComplexFunctions", "ContentObjectFunctions", \
"ContinuedFractionFunctions", "ContinuousFourierFunctions", \
"ControllerFunctions", "ControlObjectFunctions", \
"ControlObjectOptions", "ControlSystemFunctions", \
"CryptographyFunctions", "DatabinFunctions", "DatasetFunctions", \
"DateFunctions", "DebugFunctions", "DeviceFunctions", \
"DialogFunctions", "DirectoryFunctions", "DiscreteCalculusFunctions", \
"DiscreteFourierFunctions", "DomainFunctions", "DynamicFunctions", \
"EntityFunctions", "EnvironmentFunctions", "ExpressionSizeFunctions", \
"ExpressionTestingFunctions", "ExternalProcessFunctions", \
"ExtractionFunctions", "FileSystemFunctions", "FinanceFunctions", \
"FittingFunctions", "FontFunctions", "FormattingFunctions", \
"FormFunctions", "FractalFunctions", "FrontEndExecutionFunctions", \
"FrontEndFunctions", "FrontEndOptions", "FunctionFunctions", \
"Functions", "GaugeFunctions", "GeodesyFunctions", \
"GeoGraphicsFunctions", "GeoGraphicsPrimitiveFunctions", \
"GeometricTransformFunctions", "GlobalOptions", "GrammarFunctions", \
"GraphBooleanPropertyFunctions", "GraphDistributionFunctions", \
"GraphicsFunctions", "GraphicsPrimitiveFunctions", \
"GraphTheoryFunctions", "GroupTheoryFunctions", "HistogramFunctions", \
"HyperlinkFunctions", "ImageFilterFunctions", "ImageFunctions", \
"InfinityFunctions", "IntegerFunctions", "InterpolationFunctions", \
"InterpreterFunctions", "IntervalFunctions", "LegendFunctions", \
"LibraryLinkFunctions", "LinearAlgebraFunctions", "LinkFunctions", \
"ListFunctions", "LocalObjectFunctions", "LogicFunctions", \
"MachineFunctions", "MachineLearningFunctions", "MathFunctions", \
"MathFunctionWindows", "MathOperationFunctions", "MatrixFunctions", \
"MenuFunctions", "MessagesAndPrintingFunctions", "MinMaxFunctions", \
"ModuleFunctions", "NamedGraphFunctions", "NamedGroupFunctions", \
"NotebookFunctions", "NumberFieldFunctions", "NumberFunctions", \
"NumberTheoryFunctions", "NumericConstantFunctions", \
"NumericFunctions", "NumericsPrecisionFunctions", \
"OperatorFunctions", "OptionFunctions", "PackageFunctions", \
"PacketFunctions", "PacletFunctions", "PageFunctions", \
"PaletteFunctions", "ParallelFunctions", "PatternFunctions", \
"PermutationFunctions", "PlottingFunctions", "PolynomialFunctions", \
"QuantityFunctions", "QuantityVariableFunctions", \
"RationalFunctions", "RawExpressionFunctions", "RealFunctions", \
"RecurrenceFunctions", "RegionFunctions", "RestructuringFunctions", \
"RootFunctions", "RuleFunctions", "ScheduledTaskFunctions", \
"SeriesFunctions", "ServiceFunctions", "SetFunctions", \
"SignalProcessingFunctions", "SliderFunctions", "SolvingFunctions", \
"SoundFunctions", "SpecialSymbols", \
"StatisticalDistributionFunctions", "StatisticalProcessFunctions", \
"StatisticalTestFunctions", "StatisticsFunctions", "StreamFunctions", \
"StringFunctions", "StructuralFunctions", "StyleFunctions", \
"SymbolAssignmentFunctions", "SymbolContextFunctions", \
"SymbolFunctions", "SymbolInformationFunctions", \
"SymbolValueFunctions", "TemplateFunctions", "TensorFunctions", \
"TestFunctions", "TextStringFunctions", "TimeMemoryFunctions", \
"TimeSeriesFunctions", "TravelFunctions", "VectorCalculusFunctions", \
"VectorTeeOperatorFunctions", "ViewerFunctions", "WaveletFunctions", \
"WolframAlphaFunctions"}
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  • $\begingroup$ Thanks for your answer.But as the fire wall,WolframLanguageData[WolframLanguageData[], "FunctionalityAreas"] must be fail to run with my network.Any method to get the funcAreas?And if you show the funcAreas contain what something,I'll appreciate you very much. $\endgroup$ – yode Mar 23 '16 at 9:36
  • $\begingroup$ I can cost small amount of time connected to the wolfram-data.If I run you code,it will be this.So a good method to get the valus of a property can be is better for me.:) $\endgroup$ – yode Mar 23 '16 at 9:53
  • $\begingroup$ Sorry I disturb you again.Can you help me list all of MathFunctions?And I think you can filter it by WolframLanguageData[WolframLanguageData[], "FunctionalityAreas"] $\endgroup$ – yode Apr 14 '16 at 14:14
  • $\begingroup$ @yode It should be WolframLanguageData[ EntityClass[ "WolframLanguageSymbol", {"FunctionalityArea", "MathFunctions"}]] but this is returning an empty list at the moment from version 10.3. Not certain why that is the case as other functionality areas are returning list of functions. Might be a bug. Report it to WRI and see. $\endgroup$ – Edmund Apr 14 '16 at 17:08
  • $\begingroup$ I think this is a bug too.And I'll report it.But Select[WolframLanguageData[],MemberQ[WolframLanguageData[#,"FunctionalityAreas"],"MathFunctions"]&] maybe get it.Just for the network firewall.So I need some help.:) $\endgroup$ – yode Apr 14 '16 at 18:08
2
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In version 11.0.1,the function be splited $175$ kinds

EntityValue["WolframLanguageSymbol","FunctionalityAreas",DeleteDuplicates@*Flatten]

{CodeInterruptionSymbols,ChannelSymbols,MessagesAndPrintingSymbols,RestructuringSymbols,AsynchronousTaskSymbols,AudioSymbols,DirectorySymbols,StreamSymbols,BinaryDataSymbols,CloudSymbols,NotebookSymbols,FrontEndSymbols,MachineSymbols,CompileSymbols,ParallelSymbols,SymbolContextSymbols,HyperlinkSymbols,LinkSymbols,DateSymbols,LocalObjectSymbols,DynamicSymbols,ServiceSymbols,EntitySymbols,FileSystemSymbols,FontSymbols,GeodesySymbols,EnvironmentSymbols,ImageSymbols,DeviceSymbols,InterpreterSymbols,LibraryLinkSymbols,NumericsPrecisionSymbols,MathFunctions,RootSymbols,BasicSymbols,PackageSymbols,PlottingSymbols,RegionSymbols,ScheduledTaskSymbols,SoundSymbols,TemplateSymbols,TimeMemorySymbols,QuantitySymbols,GraphicsPrimitiveSymbols,StatisticalProcessSymbols,NamedGroupSymbols,AlignmentSymbols,ComplexSymbols,StatisticsSymbols,GraphicsSymbols,OptionSymbols,FormSymbols,ListSymbols,ControlObjectSymbols,CodeEvaluationSymbols,GraphBooleanPropertySymbols,SymbolAssignmentSymbols,GraphTheorySymbols,TimeSeriesSymbols,BoxSymbols,BoxOptions,PacletSymbols,ControlSystemSymbols,GeometricTransformSymbols,SpecialSymbols,AlgebraicSymbols,BooleanSymbols,CellSymbols,GrammarSymbols,StringSymbols,CDFSymbols,PatternSymbols,AstronomySymbols,MachineLearningSymbols,StatisticalTestSymbols,OperatorSymbols,GaugeSymbols,ControlObjectOptions,AnnotationSymbols,FinanceSymbols,LinearAlgebraSymbols,TensorSymbols,SetSymbols,VectorCalculusSymbols,StatisticalDistributionSymbols,MinMaxSymbols,ArraySymbols,MatrixSymbols,AskSymbols,AssociationSymbols,WolframAlphaSymbols,PolynomialSymbols,FrontEndOptions,AutocompleteSymbols,SignalProcessingSymbols,ChartSymbols,LegendSymbols,GraphDistributionSymbols,MathFunctionWindows,StyleSymbols,NetSymbols,WaveletSymbols,PacketSymbols,ExpressionTestingSymbols,ImageFilterSymbols,HistogramSymbols,ClusteringSymbols,BitSymbols,ColorSymbols,CodeActionSymbols,ModuleSymbols,TextStringSymbols,CodeFlowSymbols,NamedGraphSymbols,ButtonSymbols,ExpressionSizeSymbols,CalculusSymbols,FractalSymbols,RecurrenceSymbols,NumericConstantSymbols,GroupTheorySymbols,NumberTheorySymbols,DialogSymbols,SliderSymbols,ExtractionSymbols,InfinitySymbols,FunctionSymbols,SeriesSymbols,FittingSymbols,LogicSymbols,SymbolInformationSymbols,SearchSymbols,ContinuedFractionSymbols,ControllerSymbols,DatabinSymbols,PaletteSymbols,PermutationSymbols,SolvingSymbols,AngleSymbols,DatasetSymbols,GeoGraphicsPrimitiveSymbols,CryptographySymbols,MenuSymbols,DiscreteCalculusSymbols,NumericSymbols,IntegerSymbols,FormattingSymbols,RuleSymbols,ComparisonOperatorSymbols,ArrowOperatorSymbols,VectorTeeOperatorSymbols,SymbolValueSymbols,GeoGraphicsSymbols,DebugSymbols,DomainSymbols,QuantityVariableSymbols,NumberFieldSymbols,GlobalOptions,ViewerSymbols,ContinuousFourierSymbols,DiscreteFourierSymbols,FrontEndExecutionSymbols,InterpolationSymbols,StructuralSymbols,PageSymbols,RawExpressionSymbols,IntervalSymbols,ExternalProcessSymbols,RealSymbols,UndocumentedSymbols,NumberSymbols,Symbols,ResourceSymbols,TestSymbols,TravelSymbols}

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