diff --git a/symja_android_library/doc/99-function-reference.md b/symja_android_library/doc/99-function-reference.md index a6f78fb415..fd41d28568 100644 --- a/symja_android_library/doc/99-function-reference.md +++ b/symja_android_library/doc/99-function-reference.md @@ -776,6 +776,7 @@ Functions in alphabetical order: * ✅ [Quotient](functions/Quotient.md) * ✅ [QuotientRemainder](functions/QuotientRemainder.md) * ✅ [Ramp](functions/Ramp.md) +* [RamseyNumber](functions/RamseyNumber.md) * ✅ [RandomChoice](functions/RandomChoice.md) * ✅ [RandomComplex](functions/RandomComplex.md) * ✅ [RandomGraph](functions/RandomGraph.md) diff --git a/symja_android_library/doc/functions/RamseyNumber.md b/symja_android_library/doc/functions/RamseyNumber.md new file mode 100644 index 0000000000..34413c09d4 --- /dev/null +++ b/symja_android_library/doc/functions/RamseyNumber.md @@ -0,0 +1,24 @@ +## RamseyNumber + +``` +RamseyNumber(r, s) +``` + +> returns the Ramsey number `R(r,s)`. Currently not all values are known for `1 <= r <= 4`. The function returns unevaluated if the value is unknown. + +See +* [Wikipedia - Ramsey's theorem](https://en.wikipedia.org/wiki/Ramsey's_theorem) +* [OEIS - A212954](https://oeis.org/A212954) + +### Examples + +``` +>> Table(RamseyNumber(1,j), {j,1,20}) +{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1} + +>> Table(RamseyNumber(2,j), {j,1,20}) +{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20} + +>> Table(RamseyNumber(i,j), {i,1,5},{j,i,10}) +{{1,1,1,1,1,1,1,1,1,1},{2,3,4,5,6,7,8,9,10},{6,9,14,18,23,28,36,RamseyNumber(3,10)},{18,25,RamseyNumber(4,6),RamseyNumber(4,7),RamseyNumber(4,8),RamseyNumber(4,9),RamseyNumber(4,10)}} +``` diff --git a/symja_android_library/matheclipse-core/src/main/java/org/matheclipse/core/builtin/NumberTheory.java b/symja_android_library/matheclipse-core/src/main/java/org/matheclipse/core/builtin/NumberTheory.java index f635db05c4..c2fd76c46f 100644 --- a/symja_android_library/matheclipse-core/src/main/java/org/matheclipse/core/builtin/NumberTheory.java +++ b/symja_android_library/matheclipse-core/src/main/java/org/matheclipse/core/builtin/NumberTheory.java @@ -4940,6 +4940,67 @@ public void setUp(final ISymbol newSymbol) { newSymbol.setAttributes(ISymbol.LISTABLE); } } + + private static class RamseyNumber extends AbstractFunctionEvaluator { + + @Override + public IExpr evaluate(final IAST ast, EvalEngine engine) { + int r = ast.arg1().toIntDefault(); + int s = ast.arg2().toIntDefault(); + if (r <= 0 || s <= 0) { + return F.NIL; + } + if (r > s) { + // symmetry across the diagonal: R(r, s) = R(s, r) + return F.binary(S.RamseyNumber, ast.arg2(), ast.arg1()); + } + // https://en.wikipedia.org/wiki/Ramsey%27s_theorem#Known_values) + switch (r) { + case 1: + return F.C1; + case 2: + return F.ZZ(s); + case 3: + switch (s) { + case 3: + return F.C6; + case 4: + return F.C9; + case 5: + return F.ZZ(14); + case 6: + return F.ZZ(18); + case 7: + return F.ZZ(23); + case 8: + return F.ZZ(28); + case 9: + return F.ZZ(36); + } + break; + case 4: + switch (s) { + case 4: + return F.ZZ(18); + case 5: + return F.ZZ(25); + } + break; + } + return F.NIL; + } + + @Override + public int[] expectedArgSize(IAST ast) { + return ARGS_2_2; + } + + @Override + public int status() { + return ImplementationStatus.PARTIAL_SUPPORT; + } + } + /** * * @@ -5599,6 +5660,7 @@ private static void init() { S.PrimitiveRoot.setEvaluator(new PrimitiveRoot()); S.PrimitiveRootList.setEvaluator(new PrimitiveRootList()); S.QuadraticIrrationalQ.setEvaluator(new QuadraticIrrationalQ()); + S.RamseyNumber.setEvaluator(new RamseyNumber()); S.Rationalize.setEvaluator(new Rationalize()); S.RootReduce.setEvaluator(new RootReduce()); S.SquareFreeQ.setEvaluator(new SquareFreeQ()); diff --git a/symja_android_library/matheclipse-core/src/main/java/org/matheclipse/core/convert/AST2Expr.java b/symja_android_library/matheclipse-core/src/main/java/org/matheclipse/core/convert/AST2Expr.java index c73ddade33..444bde3fcc 100644 --- a/symja_android_library/matheclipse-core/src/main/java/org/matheclipse/core/convert/AST2Expr.java +++ b/symja_android_library/matheclipse-core/src/main/java/org/matheclipse/core/convert/AST2Expr.java @@ -263,10 +263,10 @@ public class AST2Expr { "ProductLog", "Projection", "Protect", "PseudoInverse", "Put", "Pyramid", "QRDecomposition", "QuadraticIrrationalQ", "QuarticSolve", "Quantile", "Quantity", "QuantityDistribution", "QuantityMagnitude", "QuantityQ", "QuantityUnit", "Quartiles", "Quiet", "Quit", "Quotient", - "QuotientRemainder", "RadicalBox", "Ramp", "RandomChoice", "RandomComplex", "RandomInteger", - "RandomGraph", "RandomPermutation", "RandomPrime", "RandomReal", "RandomSample", - "RandomVariate", "Range", "RankedMax", "RankedMin", "Rational", "Rationalize", "RawBoxes", - "Re", "Read", "ReadList", "ReadString", "RealAbs", "RealDigits", "RealSign", + "QuotientRemainder", "RadicalBox", "Ramp", "RamseyNumber", "RandomChoice", "RandomComplex", + "RandomInteger", "RandomGraph", "RandomPermutation", "RandomPrime", "RandomReal", + "RandomSample", "RandomVariate", "Range", "RankedMax", "RankedMin", "Rational", "Rationalize", + "RawBoxes", "Re", "Read", "ReadList", "ReadString", "RealAbs", "RealDigits", "RealSign", "RealValuedNumericQ", "RealValuedNumberQ", "Reap", "Rectangle", "Reduce", "Refine", "RegularExpression", "ReIm", "ReleaseHold", "Remove", "RemoveDiacritics", "Repeated", "RepeatedNull", "RepeatedTiming", "Replace", "ReplaceAll", "ReplaceList", "ReplacePart", diff --git a/symja_android_library/matheclipse-core/src/main/java/org/matheclipse/core/expression/ID.java b/symja_android_library/matheclipse-core/src/main/java/org/matheclipse/core/expression/ID.java index ce34b52502..6becda84af 100644 --- a/symja_android_library/matheclipse-core/src/main/java/org/matheclipse/core/expression/ID.java +++ b/symja_android_library/matheclipse-core/src/main/java/org/matheclipse/core/expression/ID.java @@ -1210,424 +1210,425 @@ public class ID { public final static int QuotientRemainder = 1197; public final static int RadicalBox = 1198; public final static int Ramp = 1199; - public final static int RandomChoice = 1200; - public final static int RandomComplex = 1201; - public final static int RandomGraph = 1202; - public final static int RandomInteger = 1203; - public final static int RandomPermutation = 1204; - public final static int RandomPrime = 1205; - public final static int RandomReal = 1206; - public final static int RandomSample = 1207; - public final static int RandomVariate = 1208; - public final static int Range = 1209; - public final static int RankedMax = 1210; - public final static int RankedMin = 1211; - public final static int Rational = 1212; - public final static int Rationalize = 1213; - public final static int Rationals = 1214; - public final static int RawBoxes = 1215; - public final static int Re = 1216; - public final static int Read = 1217; - public final static int ReadList = 1218; - public final static int ReadProtected = 1219; - public final static int ReadString = 1220; - public final static int Real = 1221; - public final static int RealAbs = 1222; - public final static int RealDigits = 1223; - public final static int Reals = 1224; - public final static int RealSign = 1225; - public final static int RealValuedNumberQ = 1226; - public final static int RealValuedNumericQ = 1227; - public final static int Reap = 1228; - public final static int Record = 1229; - public final static int RecordSeparators = 1230; - public final static int Rectangle = 1231; - public final static int Red = 1232; - public final static int Reduce = 1233; - public final static int Refine = 1234; - public final static int RegularExpression = 1235; - public final static int ReIm = 1236; - public final static int ReleaseHold = 1237; - public final static int Remove = 1238; - public final static int RemoveDiacritics = 1239; - public final static int Repeated = 1240; - public final static int RepeatedNull = 1241; - public final static int RepeatedTiming = 1242; - public final static int Replace = 1243; - public final static int ReplaceAll = 1244; - public final static int ReplaceList = 1245; - public final static int ReplacePart = 1246; - public final static int ReplaceRepeated = 1247; - public final static int Rescale = 1248; - public final static int Rest = 1249; - public final static int Resultant = 1250; - public final static int Return = 1251; - public final static int Reverse = 1252; - public final static int RGBColor = 1253; - public final static int RiccatiSolve = 1254; - public final static int Riffle = 1255; - public final static int Right = 1256; - public final static int RightComposition = 1257; - public final static int RogersTanimotoDissimilarity = 1258; - public final static int RomanNumeral = 1259; - public final static int Root = 1260; - public final static int RootIntervals = 1261; - public final static int RootOf = 1262; - public final static int RootReduce = 1263; - public final static int Roots = 1264; - public final static int RotateLeft = 1265; - public final static int RotateRight = 1266; - public final static int RotationMatrix = 1267; - public final static int RotationTransform = 1268; - public final static int Round = 1269; - public final static int Row = 1270; - public final static int RowBox = 1271; - public final static int RowReduce = 1272; - public final static int RSolve = 1273; - public final static int RSolveValue = 1274; - public final static int Rule = 1275; - public final static int RuleDelayed = 1276; - public final static int RussellRaoDissimilarity = 1277; - public final static int SameObjectQ = 1278; - public final static int SameQ = 1279; - public final static int SameTest = 1280; - public final static int SASTriangle = 1281; - public final static int SatisfiabilityCount = 1282; - public final static int SatisfiabilityInstances = 1283; - public final static int SatisfiableQ = 1284; - public final static int SawtoothWave = 1285; - public final static int Scale = 1286; - public final static int Scaled = 1287; - public final static int ScalingFunctions = 1288; - public final static int ScalingTransform = 1289; - public final static int Scan = 1290; - public final static int SchurDecomposition = 1291; - public final static int Sec = 1292; - public final static int Sech = 1293; - public final static int Second = 1294; - public final static int SeedRandom = 1295; - public final static int Select = 1296; - public final static int SelectFirst = 1297; - public final static int SemanticImport = 1298; - public final static int SemanticImportString = 1299; - public final static int Sequence = 1300; - public final static int SequenceCases = 1301; - public final static int SequenceHold = 1302; - public final static int SequenceReplace = 1303; - public final static int SequenceSplit = 1304; - public final static int Series = 1305; - public final static int SeriesCoefficient = 1306; - public final static int SeriesData = 1307; - public final static int Set = 1308; - public final static int SetAttributes = 1309; - public final static int SetDelayed = 1310; - public final static int SetSystemOptions = 1311; - public final static int Share = 1312; - public final static int ShearingTransform = 1313; - public final static int Short = 1314; - public final static int Shortest = 1315; - public final static int Show = 1316; - public final static int Sign = 1317; - public final static int Signature = 1318; - public final static int SignCmp = 1319; - public final static int Simplex = 1320; - public final static int Simplify = 1321; - public final static int Sin = 1322; - public final static int Sinc = 1323; - public final static int SingularValueDecomposition = 1324; - public final static int SingularValueList = 1325; - public final static int Sinh = 1326; - public final static int SinhIntegral = 1327; - public final static int SinIntegral = 1328; - public final static int SixJSymbol = 1329; - public final static int Skewness = 1330; - public final static int Slot = 1331; - public final static int SlotAbsent = 1332; - public final static int SlotSequence = 1333; - public final static int Small = 1334; - public final static int SokalSneathDissimilarity = 1335; - public final static int Solve = 1336; - public final static int Sort = 1337; - public final static int SortBy = 1338; - public final static int Sow = 1339; - public final static int Span = 1340; - public final static int SparseArray = 1341; - public final static int Specularity = 1342; - public final static int Sphere = 1343; - public final static int SphericalBesselJ = 1344; - public final static int SphericalBesselY = 1345; - public final static int SphericalHankelH1 = 1346; - public final static int SphericalHankelH2 = 1347; - public final static int SphericalHarmonicY = 1348; - public final static int Split = 1349; - public final static int SplitBy = 1350; - public final static int SpotLight = 1351; - public final static int Sqrt = 1352; - public final static int SqrtBox = 1353; - public final static int SquaredEuclideanDistance = 1354; - public final static int SquareFreeQ = 1355; - public final static int SquareMatrixQ = 1356; - public final static int SSSTriangle = 1357; - public final static int Stack = 1358; - public final static int StackBegin = 1359; - public final static int StandardDeviation = 1360; - public final static int StandardForm = 1361; - public final static int Standardize = 1362; - public final static int StarGraph = 1363; - public final static int StartOfLine = 1364; - public final static int StartOfString = 1365; - public final static int StaticsVisible = 1366; - public final static int StieltjesGamma = 1367; - public final static int StirlingS1 = 1368; - public final static int StirlingS2 = 1369; - public final static int StreamPlot = 1370; - public final static int Strict = 1371; - public final static int String = 1372; - public final static int StringCases = 1373; - public final static int StringContainsQ = 1374; - public final static int StringCount = 1375; - public final static int StringDrop = 1376; - public final static int StringExpression = 1377; - public final static int StringForm = 1378; - public final static int StringFormat = 1379; - public final static int StringFreeQ = 1380; - public final static int StringInsert = 1381; - public final static int StringJoin = 1382; - public final static int StringLength = 1383; - public final static int StringMatchQ = 1384; - public final static int StringPart = 1385; - public final static int StringPosition = 1386; - public final static int StringQ = 1387; - public final static int StringRepeat = 1388; - public final static int StringReplace = 1389; - public final static int StringReverse = 1390; - public final static int StringRiffle = 1391; - public final static int StringSplit = 1392; - public final static int StringTake = 1393; - public final static int StringTemplate = 1394; - public final static int StringToByteArray = 1395; - public final static int StringToStream = 1396; - public final static int StringTrim = 1397; - public final static int Structure = 1398; - public final static int StruveH = 1399; - public final static int StruveL = 1400; - public final static int StudentTDistribution = 1401; - public final static int Style = 1402; - public final static int StyleForm = 1403; - public final static int Subdivide = 1404; - public final static int Subfactorial = 1405; - public final static int Subscript = 1406; - public final static int SubscriptBox = 1407; - public final static int SubsetQ = 1408; - public final static int Subsets = 1409; - public final static int Subsuperscript = 1410; - public final static int SubsuperscriptBox = 1411; - public final static int Subtract = 1412; - public final static int SubtractFrom = 1413; - public final static int SubtractSides = 1414; - public final static int Sum = 1415; - public final static int Summary = 1416; - public final static int Superscript = 1417; - public final static int SuperscriptBox = 1418; - public final static int Surd = 1419; - public final static int SurfaceArea = 1420; - public final static int SurfaceGraphics = 1421; - public final static int SurvivalFunction = 1422; - public final static int Switch = 1423; - public final static int Symbol = 1424; - public final static int SymbolName = 1425; - public final static int SymbolQ = 1426; - public final static int Symmetric = 1427; - public final static int SymmetricMatrixQ = 1428; - public final static int SyntaxLength = 1429; - public final static int SyntaxQ = 1430; - public final static int SystemDialogInput = 1431; - public final static int SystemOptions = 1432; - public final static int Table = 1433; - public final static int TableAlignments = 1434; - public final static int TableDepth = 1435; - public final static int TableDirections = 1436; - public final static int TableForm = 1437; - public final static int TableHeadings = 1438; - public final static int TableSpacing = 1439; - public final static int TagSet = 1440; - public final static int TagSetDelayed = 1441; - public final static int Take = 1442; - public final static int TakeLargest = 1443; - public final static int TakeLargestBy = 1444; - public final static int TakeSmallest = 1445; - public final static int TakeSmallestBy = 1446; - public final static int TakeWhile = 1447; - public final static int Tally = 1448; - public final static int Tan = 1449; - public final static int Tanh = 1450; - public final static int TargetFunctions = 1451; - public final static int TautologyQ = 1452; - public final static int Taylor = 1453; - public final static int TemplateApply = 1454; - public final static int TemplateExpression = 1455; - public final static int TemplateIf = 1456; - public final static int TemplateSlot = 1457; - public final static int TensorDimensions = 1458; - public final static int TensorProduct = 1459; - public final static int TensorRank = 1460; - public final static int TensorSymmetry = 1461; - public final static int TestID = 1462; - public final static int TestReport = 1463; - public final static int TestReportObject = 1464; - public final static int TestResultObject = 1465; - public final static int Tetrahedron = 1466; - public final static int TeXForm = 1467; - public final static int Text = 1468; - public final static int TextCell = 1469; - public final static int TextElement = 1470; - public final static int TextString = 1471; - public final static int TextStructure = 1472; - public final static int Thickness = 1473; - public final static int Thread = 1474; - public final static int ThreeJSymbol = 1475; - public final static int Through = 1476; - public final static int Throw = 1477; - public final static int Ticks = 1478; - public final static int TicksStyle = 1479; - public final static int TimeConstrained = 1480; - public final static int TimeObject = 1481; - public final static int TimeRemaining = 1482; - public final static int Times = 1483; - public final static int TimesBy = 1484; - public final static int TimeValue = 1485; - public final static int Timing = 1486; - public final static int Tiny = 1487; - public final static int ToBoxes = 1488; - public final static int ToCharacterCode = 1489; - public final static int Today = 1490; - public final static int ToeplitzMatrix = 1491; - public final static int ToExpression = 1492; - public final static int Together = 1493; - public final static int ToIntervalData = 1494; - public final static int ToLowerCase = 1495; - public final static int TooLarge = 1496; - public final static int Top = 1497; - public final static int ToPolarCoordinates = 1498; - public final static int ToRadicals = 1499; - public final static int ToSphericalCoordinates = 1500; - public final static int ToString = 1501; - public final static int Total = 1502; - public final static int ToUnicode = 1503; - public final static int ToUpperCase = 1504; - public final static int Tr = 1505; - public final static int Trace = 1506; - public final static int TraceForm = 1507; - public final static int TraditionalForm = 1508; - public final static int TransformationFunction = 1509; - public final static int TranslationTransform = 1510; - public final static int Transliterate = 1511; - public final static int Transpose = 1512; - public final static int TreeForm = 1513; - public final static int Triangle = 1514; - public final static int Trig = 1515; - public final static int TrigExpand = 1516; - public final static int TrigReduce = 1517; - public final static int TrigSimplifyFu = 1518; - public final static int TrigToExp = 1519; - public final static int True = 1520; - public final static int TrueQ = 1521; - public final static int TTest = 1522; - public final static int Tube = 1523; - public final static int TukeyWindow = 1524; - public final static int Tuples = 1525; - public final static int TwoWayRule = 1526; - public final static int Undefined = 1527; - public final static int Underflow = 1528; - public final static int Underoverscript = 1529; - public final static int UnderoverscriptBox = 1530; - public final static int Underscript = 1531; - public final static int UnderscriptBox = 1532; - public final static int UndirectedEdge = 1533; - public final static int Unequal = 1534; - public final static int UnequalTo = 1535; - public final static int Unevaluated = 1536; - public final static int UniformDistribution = 1537; - public final static int Union = 1538; - public final static int Unique = 1539; - public final static int UnitaryMatrixQ = 1540; - public final static int UnitConvert = 1541; - public final static int Unitize = 1542; - public final static int UnitStep = 1543; - public final static int UnitTriangle = 1544; - public final static int UnitVector = 1545; - public final static int UniverseAge = 1546; - public final static int Unknown = 1547; - public final static int Unprotect = 1548; - public final static int UnsameQ = 1549; - public final static int Unset = 1550; - public final static int UpperCaseQ = 1551; - public final static int UpperTriangularize = 1552; - public final static int UpperTriangularMatrixQ = 1553; - public final static int UpSet = 1554; - public final static int UpSetDelayed = 1555; - public final static int UpTo = 1556; - public final static int UpValues = 1557; - public final static int URLFetch = 1558; - public final static int UseTypeChecking = 1559; - public final static int ValueQ = 1560; - public final static int Values = 1561; - public final static int VandermondeMatrix = 1562; - public final static int Variable = 1563; - public final static int Variables = 1564; - public final static int Variance = 1565; - public final static int VectorAngle = 1566; - public final static int VectorGreater = 1567; - public final static int VectorGreaterEqual = 1568; - public final static int VectorLess = 1569; - public final static int VectorLessEqual = 1570; - public final static int VectorPlot = 1571; - public final static int VectorQ = 1572; - public final static int Vectors = 1573; - public final static int Verbatim = 1574; - public final static int VerificationTest = 1575; - public final static int VertexEccentricity = 1576; - public final static int VertexLabels = 1577; - public final static int VertexList = 1578; - public final static int VertexQ = 1579; - public final static int VertexShapeFunction = 1580; - public final static int VertexSize = 1581; - public final static int VertexStyle = 1582; - public final static int ViewPoint = 1583; - public final static int Volume = 1584; - public final static int WeaklyConnectedGraphQ = 1585; - public final static int WeberE = 1586; - public final static int WeibullDistribution = 1587; - public final static int WeierstrassHalfPeriods = 1588; - public final static int WeierstrassInvariants = 1589; - public final static int WeierstrassP = 1590; - public final static int WeierstrassPPrime = 1591; - public final static int WeightedAdjacencyMatrix = 1592; - public final static int WeightedData = 1593; - public final static int WeightedGraphQ = 1594; - public final static int WheelGraph = 1595; - public final static int Which = 1596; - public final static int While = 1597; - public final static int White = 1598; - public final static int Whitespace = 1599; - public final static int WhitespaceCharacter = 1600; - public final static int WhittakerM = 1601; - public final static int WhittakerW = 1602; - public final static int With = 1603; - public final static int Word = 1604; - public final static int WordBoundary = 1605; - public final static int WordCharacter = 1606; - public final static int WordSeparators = 1607; - public final static int Write = 1608; - public final static int WriteString = 1609; - public final static int Xnor = 1610; - public final static int Xor = 1611; - public final static int Yellow = 1612; - public final static int YuleDissimilarity = 1613; - public final static int ZeroSymmetric = 1614; - public final static int ZeroTest = 1615; - public final static int Zeta = 1616; - public final static int ZTransform = 1617; + public final static int RamseyNumber = 1200; + public final static int RandomChoice = 1201; + public final static int RandomComplex = 1202; + public final static int RandomGraph = 1203; + public final static int RandomInteger = 1204; + public final static int RandomPermutation = 1205; + public final static int RandomPrime = 1206; + public final static int RandomReal = 1207; + public final static int RandomSample = 1208; + public final static int RandomVariate = 1209; + public final static int Range = 1210; + public final static int RankedMax = 1211; + public final static int RankedMin = 1212; + public final static int Rational = 1213; + public final static int Rationalize = 1214; + public final static int Rationals = 1215; + public final static int RawBoxes = 1216; + public final static int Re = 1217; + public final static int Read = 1218; + public final static int ReadList = 1219; + public final static int ReadProtected = 1220; + public final static int ReadString = 1221; + public final static int Real = 1222; + public final static int RealAbs = 1223; + public final static int RealDigits = 1224; + public final static int Reals = 1225; + public final static int RealSign = 1226; + public final static int RealValuedNumberQ = 1227; + public final static int RealValuedNumericQ = 1228; + public final static int Reap = 1229; + public final static int Record = 1230; + public final static int RecordSeparators = 1231; + public final static int Rectangle = 1232; + public final static int Red = 1233; + public final static int Reduce = 1234; + public final static int Refine = 1235; + public final static int RegularExpression = 1236; + public final static int ReIm = 1237; + public final static int ReleaseHold = 1238; + public final static int Remove = 1239; + public final static int RemoveDiacritics = 1240; + public final static int Repeated = 1241; + public final static int RepeatedNull = 1242; + public final static int RepeatedTiming = 1243; + public final static int Replace = 1244; + public final static int ReplaceAll = 1245; + public final static int ReplaceList = 1246; + public final static int ReplacePart = 1247; + public final static int ReplaceRepeated = 1248; + public final static int Rescale = 1249; + public final static int Rest = 1250; + public final static int Resultant = 1251; + public final static int Return = 1252; + public final static int Reverse = 1253; + public final static int RGBColor = 1254; + public final static int RiccatiSolve = 1255; + public final static int Riffle = 1256; + public final static int Right = 1257; + public final static int RightComposition = 1258; + public final static int RogersTanimotoDissimilarity = 1259; + public final static int RomanNumeral = 1260; + public final static int Root = 1261; + public final static int RootIntervals = 1262; + public final static int RootOf = 1263; + public final static int RootReduce = 1264; + public final static int Roots = 1265; + public final static int RotateLeft = 1266; + public final static int RotateRight = 1267; + public final static int RotationMatrix = 1268; + public final static int RotationTransform = 1269; + public final static int Round = 1270; + public final static int Row = 1271; + public final static int RowBox = 1272; + public final static int RowReduce = 1273; + public final static int RSolve = 1274; + public final static int RSolveValue = 1275; + public final static int Rule = 1276; + public final static int RuleDelayed = 1277; + public final static int RussellRaoDissimilarity = 1278; + public final static int SameObjectQ = 1279; + public final static int SameQ = 1280; + public final static int SameTest = 1281; + public final static int SASTriangle = 1282; + public final static int SatisfiabilityCount = 1283; + public final static int SatisfiabilityInstances = 1284; + public final static int SatisfiableQ = 1285; + public final static int SawtoothWave = 1286; + public final static int Scale = 1287; + public final static int Scaled = 1288; + public final static int ScalingFunctions = 1289; + public final static int ScalingTransform = 1290; + public final static int Scan = 1291; + public final static int SchurDecomposition = 1292; + public final static int Sec = 1293; + public final static int Sech = 1294; + public final static int Second = 1295; + public final static int SeedRandom = 1296; + public final static int Select = 1297; + public final static int SelectFirst = 1298; + public final static int SemanticImport = 1299; + public final static int SemanticImportString = 1300; + public final static int Sequence = 1301; + public final static int SequenceCases = 1302; + public final static int SequenceHold = 1303; + public final static int SequenceReplace = 1304; + public final static int SequenceSplit = 1305; + public final static int Series = 1306; + public final static int SeriesCoefficient = 1307; + public final static int SeriesData = 1308; + public final static int Set = 1309; + public final static int SetAttributes = 1310; + public final static int SetDelayed = 1311; + public final static int SetSystemOptions = 1312; + public final static int Share = 1313; + public final static int ShearingTransform = 1314; + public final static int Short = 1315; + public final static int Shortest = 1316; + public final static int Show = 1317; + public final static int Sign = 1318; + public final static int Signature = 1319; + public final static int SignCmp = 1320; + public final static int Simplex = 1321; + public final static int Simplify = 1322; + public final static int Sin = 1323; + public final static int Sinc = 1324; + public final static int SingularValueDecomposition = 1325; + public final static int SingularValueList = 1326; + public final static int Sinh = 1327; + public final static int SinhIntegral = 1328; + public final static int SinIntegral = 1329; + public final static int SixJSymbol = 1330; + public final static int Skewness = 1331; + public final static int Slot = 1332; + public final static int SlotAbsent = 1333; + public final static int SlotSequence = 1334; + public final static int Small = 1335; + public final static int SokalSneathDissimilarity = 1336; + public final static int Solve = 1337; + public final static int Sort = 1338; + public final static int SortBy = 1339; + public final static int Sow = 1340; + public final static int Span = 1341; + public final static int SparseArray = 1342; + public final static int Specularity = 1343; + public final static int Sphere = 1344; + public final static int SphericalBesselJ = 1345; + public final static int SphericalBesselY = 1346; + public final static int SphericalHankelH1 = 1347; + public final static int SphericalHankelH2 = 1348; + public final static int SphericalHarmonicY = 1349; + public final static int Split = 1350; + public final static int SplitBy = 1351; + public final static int SpotLight = 1352; + public final static int Sqrt = 1353; + public final static int SqrtBox = 1354; + public final static int SquaredEuclideanDistance = 1355; + public final static int SquareFreeQ = 1356; + public final static int SquareMatrixQ = 1357; + public final static int SSSTriangle = 1358; + public final static int Stack = 1359; + public final static int StackBegin = 1360; + public final static int StandardDeviation = 1361; + public final static int StandardForm = 1362; + public final static int Standardize = 1363; + public final static int StarGraph = 1364; + public final static int StartOfLine = 1365; + public final static int StartOfString = 1366; + public final static int StaticsVisible = 1367; + public final static int StieltjesGamma = 1368; + public final static int StirlingS1 = 1369; + public final static int StirlingS2 = 1370; + public final static int StreamPlot = 1371; + public final static int Strict = 1372; + public final static int String = 1373; + public final static int StringCases = 1374; + public final static int StringContainsQ = 1375; + public final static int StringCount = 1376; + public final static int StringDrop = 1377; + public final static int StringExpression = 1378; + public final static int StringForm = 1379; + public final static int StringFormat = 1380; + public final static int StringFreeQ = 1381; + public final static int StringInsert = 1382; + public final static int StringJoin = 1383; + public final static int StringLength = 1384; + public final static int StringMatchQ = 1385; + public final static int StringPart = 1386; + public final static int StringPosition = 1387; + public final static int StringQ = 1388; + public final static int StringRepeat = 1389; + public final static int StringReplace = 1390; + public final static int StringReverse = 1391; + public final static int StringRiffle = 1392; + public final static int StringSplit = 1393; + public final static int StringTake = 1394; + public final static int StringTemplate = 1395; + public final static int StringToByteArray = 1396; + public final static int StringToStream = 1397; + public final static int StringTrim = 1398; + public final static int Structure = 1399; + public final static int StruveH = 1400; + public final static int StruveL = 1401; + public final static int StudentTDistribution = 1402; + public final static int Style = 1403; + public final static int StyleForm = 1404; + public final static int Subdivide = 1405; + public final static int Subfactorial = 1406; + public final static int Subscript = 1407; + public final static int SubscriptBox = 1408; + public final static int SubsetQ = 1409; + public final static int Subsets = 1410; + public final static int Subsuperscript = 1411; + public final static int SubsuperscriptBox = 1412; + public final static int Subtract = 1413; + public final static int SubtractFrom = 1414; + public final static int SubtractSides = 1415; + public final static int Sum = 1416; + public final static int Summary = 1417; + public final static int Superscript = 1418; + public final static int SuperscriptBox = 1419; + public final static int Surd = 1420; + public final static int SurfaceArea = 1421; + public final static int SurfaceGraphics = 1422; + public final static int SurvivalFunction = 1423; + public final static int Switch = 1424; + public final static int Symbol = 1425; + public final static int SymbolName = 1426; + public final static int SymbolQ = 1427; + public final static int Symmetric = 1428; + public final static int SymmetricMatrixQ = 1429; + public final static int SyntaxLength = 1430; + public final static int SyntaxQ = 1431; + public final static int SystemDialogInput = 1432; + public final static int SystemOptions = 1433; + public final static int Table = 1434; + public final static int TableAlignments = 1435; + public final static int TableDepth = 1436; + public final static int TableDirections = 1437; + public final static int TableForm = 1438; + public final static int TableHeadings = 1439; + public final static int TableSpacing = 1440; + public final static int TagSet = 1441; + public final static int TagSetDelayed = 1442; + public final static int Take = 1443; + public final static int TakeLargest = 1444; + public final static int TakeLargestBy = 1445; + public final static int TakeSmallest = 1446; + public final static int TakeSmallestBy = 1447; + public final static int TakeWhile = 1448; + public final static int Tally = 1449; + public final static int Tan = 1450; + public final static int Tanh = 1451; + public final static int TargetFunctions = 1452; + public final static int TautologyQ = 1453; + public final static int Taylor = 1454; + public final static int TemplateApply = 1455; + public final static int TemplateExpression = 1456; + public final static int TemplateIf = 1457; + public final static int TemplateSlot = 1458; + public final static int TensorDimensions = 1459; + public final static int TensorProduct = 1460; + public final static int TensorRank = 1461; + public final static int TensorSymmetry = 1462; + public final static int TestID = 1463; + public final static int TestReport = 1464; + public final static int TestReportObject = 1465; + public final static int TestResultObject = 1466; + public final static int Tetrahedron = 1467; + public final static int TeXForm = 1468; + public final static int Text = 1469; + public final static int TextCell = 1470; + public final static int TextElement = 1471; + public final static int TextString = 1472; + public final static int TextStructure = 1473; + public final static int Thickness = 1474; + public final static int Thread = 1475; + public final static int ThreeJSymbol = 1476; + public final static int Through = 1477; + public final static int Throw = 1478; + public final static int Ticks = 1479; + public final static int TicksStyle = 1480; + public final static int TimeConstrained = 1481; + public final static int TimeObject = 1482; + public final static int TimeRemaining = 1483; + public final static int Times = 1484; + public final static int TimesBy = 1485; + public final static int TimeValue = 1486; + public final static int Timing = 1487; + public final static int Tiny = 1488; + public final static int ToBoxes = 1489; + public final static int ToCharacterCode = 1490; + public final static int Today = 1491; + public final static int ToeplitzMatrix = 1492; + public final static int ToExpression = 1493; + public final static int Together = 1494; + public final static int ToIntervalData = 1495; + public final static int ToLowerCase = 1496; + public final static int TooLarge = 1497; + public final static int Top = 1498; + public final static int ToPolarCoordinates = 1499; + public final static int ToRadicals = 1500; + public final static int ToSphericalCoordinates = 1501; + public final static int ToString = 1502; + public final static int Total = 1503; + public final static int ToUnicode = 1504; + public final static int ToUpperCase = 1505; + public final static int Tr = 1506; + public final static int Trace = 1507; + public final static int TraceForm = 1508; + public final static int TraditionalForm = 1509; + public final static int TransformationFunction = 1510; + public final static int TranslationTransform = 1511; + public final static int Transliterate = 1512; + public final static int Transpose = 1513; + public final static int TreeForm = 1514; + public final static int Triangle = 1515; + public final static int Trig = 1516; + public final static int TrigExpand = 1517; + public final static int TrigReduce = 1518; + public final static int TrigSimplifyFu = 1519; + public final static int TrigToExp = 1520; + public final static int True = 1521; + public final static int TrueQ = 1522; + public final static int TTest = 1523; + public final static int Tube = 1524; + public final static int TukeyWindow = 1525; + public final static int Tuples = 1526; + public final static int TwoWayRule = 1527; + public final static int Undefined = 1528; + public final static int Underflow = 1529; + public final static int Underoverscript = 1530; + public final static int UnderoverscriptBox = 1531; + public final static int Underscript = 1532; + public final static int UnderscriptBox = 1533; + public final static int UndirectedEdge = 1534; + public final static int Unequal = 1535; + public final static int UnequalTo = 1536; + public final static int Unevaluated = 1537; + public final static int UniformDistribution = 1538; + public final static int Union = 1539; + public final static int Unique = 1540; + public final static int UnitaryMatrixQ = 1541; + public final static int UnitConvert = 1542; + public final static int Unitize = 1543; + public final static int UnitStep = 1544; + public final static int UnitTriangle = 1545; + public final static int UnitVector = 1546; + public final static int UniverseAge = 1547; + public final static int Unknown = 1548; + public final static int Unprotect = 1549; + public final static int UnsameQ = 1550; + public final static int Unset = 1551; + public final static int UpperCaseQ = 1552; + public final static int UpperTriangularize = 1553; + public final static int UpperTriangularMatrixQ = 1554; + public final static int UpSet = 1555; + public final static int UpSetDelayed = 1556; + public final static int UpTo = 1557; + public final static int UpValues = 1558; + public final static int URLFetch = 1559; + public final static int UseTypeChecking = 1560; + public final static int ValueQ = 1561; + public final static int Values = 1562; + public final static int VandermondeMatrix = 1563; + public final static int Variable = 1564; + public final static int Variables = 1565; + public final static int Variance = 1566; + public final static int VectorAngle = 1567; + public final static int VectorGreater = 1568; + public final static int VectorGreaterEqual = 1569; + public final static int VectorLess = 1570; + public final static int VectorLessEqual = 1571; + public final static int VectorPlot = 1572; + public final static int VectorQ = 1573; + public final static int Vectors = 1574; + public final static int Verbatim = 1575; + public final static int VerificationTest = 1576; + public final static int VertexEccentricity = 1577; + public final static int VertexLabels = 1578; + public final static int VertexList = 1579; + public final static int VertexQ = 1580; + public final static int VertexShapeFunction = 1581; + public final static int VertexSize = 1582; + public final static int VertexStyle = 1583; + public final static int ViewPoint = 1584; + public final static int Volume = 1585; + public final static int WeaklyConnectedGraphQ = 1586; + public final static int WeberE = 1587; + public final static int WeibullDistribution = 1588; + public final static int WeierstrassHalfPeriods = 1589; + public final static int WeierstrassInvariants = 1590; + public final static int WeierstrassP = 1591; + public final static int WeierstrassPPrime = 1592; + public final static int WeightedAdjacencyMatrix = 1593; + public final static int WeightedData = 1594; + public final static int WeightedGraphQ = 1595; + public final static int WheelGraph = 1596; + public final static int Which = 1597; + public final static int While = 1598; + public final static int White = 1599; + public final static int Whitespace = 1600; + public final static int WhitespaceCharacter = 1601; + public final static int WhittakerM = 1602; + public final static int WhittakerW = 1603; + public final static int With = 1604; + public final static int Word = 1605; + public final static int WordBoundary = 1606; + public final static int WordCharacter = 1607; + public final static int WordSeparators = 1608; + public final static int Write = 1609; + public final static int WriteString = 1610; + public final static int Xnor = 1611; + public final static int Xor = 1612; + public final static int Yellow = 1613; + public final static int YuleDissimilarity = 1614; + public final static int ZeroSymmetric = 1615; + public final static int ZeroTest = 1616; + public final static int Zeta = 1617; + public final static int ZTransform = 1618; /** * Generated by class: org.matheclipse.core.preprocessor.FunctionIDGenerator @@ -1899,90 +1900,89 @@ public class ID { "Quantity", "QuantityDistribution", "QuantityMagnitude", "QuantityQ", "QuantityUnit", "QuarticSolve", // "Quartiles", "Quiet", "Quit", "Quotient", "QuotientRemainder", "RadicalBox", // - "Ramp", "RandomChoice", "RandomComplex", "RandomGraph", "RandomInteger", "RandomPermutation", // - "RandomPrime", "RandomReal", "RandomSample", "RandomVariate", "Range", "RankedMax", // - "RankedMin", "Rational", "Rationalize", "Rationals", "RawBoxes", "Re", // - "Read", "ReadList", "ReadProtected", "ReadString", "Real", "RealAbs", // - "RealDigits", "Reals", "RealSign", "RealValuedNumberQ", "RealValuedNumericQ", "Reap", // - "Record", "RecordSeparators", "Rectangle", "Red", "Reduce", "Refine", // - "RegularExpression", "ReIm", "ReleaseHold", "Remove", "RemoveDiacritics", "Repeated", // - "RepeatedNull", "RepeatedTiming", "Replace", "ReplaceAll", "ReplaceList", "ReplacePart", // - "ReplaceRepeated", "Rescale", "Rest", "Resultant", "Return", "Reverse", // - "RGBColor", "RiccatiSolve", "Riffle", "Right", "RightComposition", - "RogersTanimotoDissimilarity", // - "RomanNumeral", "Root", "RootIntervals", "RootOf", "RootReduce", "Roots", // - "RotateLeft", "RotateRight", "RotationMatrix", "RotationTransform", "Round", "Row", // - "RowBox", "RowReduce", "RSolve", "RSolveValue", "Rule", "RuleDelayed", // - "RussellRaoDissimilarity", "SameObjectQ", "SameQ", "SameTest", "SASTriangle", - "SatisfiabilityCount", // - "SatisfiabilityInstances", "SatisfiableQ", "SawtoothWave", "Scale", "Scaled", - "ScalingFunctions", // - "ScalingTransform", "Scan", "SchurDecomposition", "Sec", "Sech", "Second", // - "SeedRandom", "Select", "SelectFirst", "SemanticImport", "SemanticImportString", "Sequence", // - "SequenceCases", "SequenceHold", "SequenceReplace", "SequenceSplit", "Series", - "SeriesCoefficient", // - "SeriesData", "Set", "SetAttributes", "SetDelayed", "SetSystemOptions", "Share", // - "ShearingTransform", "Short", "Shortest", "Show", "Sign", "Signature", // - "SignCmp", "Simplex", "Simplify", "Sin", "Sinc", "SingularValueDecomposition", // - "SingularValueList", "Sinh", "SinhIntegral", "SinIntegral", "SixJSymbol", "Skewness", // - "Slot", "SlotAbsent", "SlotSequence", "Small", "SokalSneathDissimilarity", "Solve", // - "Sort", "SortBy", "Sow", "Span", "SparseArray", "Specularity", // - "Sphere", "SphericalBesselJ", "SphericalBesselY", "SphericalHankelH1", "SphericalHankelH2", - "SphericalHarmonicY", // - "Split", "SplitBy", "SpotLight", "Sqrt", "SqrtBox", "SquaredEuclideanDistance", // - "SquareFreeQ", "SquareMatrixQ", "SSSTriangle", "Stack", "StackBegin", "StandardDeviation", // - "StandardForm", "Standardize", "StarGraph", "StartOfLine", "StartOfString", "StaticsVisible", // - "StieltjesGamma", "StirlingS1", "StirlingS2", "StreamPlot", "Strict", "String", // - "StringCases", "StringContainsQ", "StringCount", "StringDrop", "StringExpression", - "StringForm", // - "StringFormat", "StringFreeQ", "StringInsert", "StringJoin", "StringLength", "StringMatchQ", // - "StringPart", "StringPosition", "StringQ", "StringRepeat", "StringReplace", "StringReverse", // - "StringRiffle", "StringSplit", "StringTake", "StringTemplate", "StringToByteArray", - "StringToStream", // - "StringTrim", "Structure", "StruveH", "StruveL", "StudentTDistribution", "Style", // - "StyleForm", "Subdivide", "Subfactorial", "Subscript", "SubscriptBox", "SubsetQ", // - "Subsets", "Subsuperscript", "SubsuperscriptBox", "Subtract", "SubtractFrom", "SubtractSides", // - "Sum", "Summary", "Superscript", "SuperscriptBox", "Surd", "SurfaceArea", // - "SurfaceGraphics", "SurvivalFunction", "Switch", "Symbol", "SymbolName", "SymbolQ", // - "Symmetric", "SymmetricMatrixQ", "SyntaxLength", "SyntaxQ", "SystemDialogInput", - "SystemOptions", // - "Table", "TableAlignments", "TableDepth", "TableDirections", "TableForm", "TableHeadings", // - "TableSpacing", "TagSet", "TagSetDelayed", "Take", "TakeLargest", "TakeLargestBy", // - "TakeSmallest", "TakeSmallestBy", "TakeWhile", "Tally", "Tan", "Tanh", // - "TargetFunctions", "TautologyQ", "Taylor", "TemplateApply", "TemplateExpression", - "TemplateIf", // - "TemplateSlot", "TensorDimensions", "TensorProduct", "TensorRank", "TensorSymmetry", "TestID", // - "TestReport", "TestReportObject", "TestResultObject", "Tetrahedron", "TeXForm", "Text", // - "TextCell", "TextElement", "TextString", "TextStructure", "Thickness", "Thread", // - "ThreeJSymbol", "Through", "Throw", "Ticks", "TicksStyle", "TimeConstrained", // - "TimeObject", "TimeRemaining", "Times", "TimesBy", "TimeValue", "Timing", // - "Tiny", "ToBoxes", "ToCharacterCode", "Today", "ToeplitzMatrix", "ToExpression", // - "Together", "ToIntervalData", "ToLowerCase", "TooLarge", "Top", "ToPolarCoordinates", // - "ToRadicals", "ToSphericalCoordinates", "ToString", "Total", "ToUnicode", "ToUpperCase", // - "Tr", "Trace", "TraceForm", "TraditionalForm", "TransformationFunction", - "TranslationTransform", // - "Transliterate", "Transpose", "TreeForm", "Triangle", "Trig", "TrigExpand", // - "TrigReduce", "TrigSimplifyFu", "TrigToExp", "True", "TrueQ", "TTest", // - "Tube", "TukeyWindow", "Tuples", "TwoWayRule", "Undefined", "Underflow", // - "Underoverscript", "UnderoverscriptBox", "Underscript", "UnderscriptBox", "UndirectedEdge", - "Unequal", // - "UnequalTo", "Unevaluated", "UniformDistribution", "Union", "Unique", "UnitaryMatrixQ", // - "UnitConvert", "Unitize", "UnitStep", "UnitTriangle", "UnitVector", "UniverseAge", // - "Unknown", "Unprotect", "UnsameQ", "Unset", "UpperCaseQ", "UpperTriangularize", // - "UpperTriangularMatrixQ", "UpSet", "UpSetDelayed", "UpTo", "UpValues", "URLFetch", // - "UseTypeChecking", "ValueQ", "Values", "VandermondeMatrix", "Variable", "Variables", // - "Variance", "VectorAngle", "VectorGreater", "VectorGreaterEqual", "VectorLess", - "VectorLessEqual", // - "VectorPlot", "VectorQ", "Vectors", "Verbatim", "VerificationTest", "VertexEccentricity", // - "VertexLabels", "VertexList", "VertexQ", "VertexShapeFunction", "VertexSize", "VertexStyle", // - "ViewPoint", "Volume", "WeaklyConnectedGraphQ", "WeberE", "WeibullDistribution", - "WeierstrassHalfPeriods", // - "WeierstrassInvariants", "WeierstrassP", "WeierstrassPPrime", "WeightedAdjacencyMatrix", - "WeightedData", "WeightedGraphQ", // - "WheelGraph", "Which", "While", "White", "Whitespace", "WhitespaceCharacter", // - "WhittakerM", "WhittakerW", "With", "Word", "WordBoundary", "WordCharacter", // - "WordSeparators", "Write", "WriteString", "Xnor", "Xor", "Yellow", // - "YuleDissimilarity", "ZeroSymmetric", "ZeroTest", "Zeta", "ZTransform"}; + "Ramp", "RamseyNumber", "RandomChoice", "RandomComplex", "RandomGraph", "RandomInteger", // + "RandomPermutation", "RandomPrime", "RandomReal", "RandomSample", "RandomVariate", "Range", // + "RankedMax", "RankedMin", "Rational", "Rationalize", "Rationals", "RawBoxes", // + "Re", "Read", "ReadList", "ReadProtected", "ReadString", "Real", // + "RealAbs", "RealDigits", "Reals", "RealSign", "RealValuedNumberQ", "RealValuedNumericQ", // + "Reap", "Record", "RecordSeparators", "Rectangle", "Red", "Reduce", // + "Refine", "RegularExpression", "ReIm", "ReleaseHold", "Remove", "RemoveDiacritics", // + "Repeated", "RepeatedNull", "RepeatedTiming", "Replace", "ReplaceAll", "ReplaceList", // + "ReplacePart", "ReplaceRepeated", "Rescale", "Rest", "Resultant", "Return", // + "Reverse", "RGBColor", "RiccatiSolve", "Riffle", "Right", "RightComposition", // + "RogersTanimotoDissimilarity", "RomanNumeral", "Root", "RootIntervals", "RootOf", + "RootReduce", // + "Roots", "RotateLeft", "RotateRight", "RotationMatrix", "RotationTransform", "Round", // + "Row", "RowBox", "RowReduce", "RSolve", "RSolveValue", "Rule", // + "RuleDelayed", "RussellRaoDissimilarity", "SameObjectQ", "SameQ", "SameTest", "SASTriangle", // + "SatisfiabilityCount", "SatisfiabilityInstances", "SatisfiableQ", "SawtoothWave", "Scale", + "Scaled", // + "ScalingFunctions", "ScalingTransform", "Scan", "SchurDecomposition", "Sec", "Sech", // + "Second", "SeedRandom", "Select", "SelectFirst", "SemanticImport", "SemanticImportString", // + "Sequence", "SequenceCases", "SequenceHold", "SequenceReplace", "SequenceSplit", "Series", // + "SeriesCoefficient", "SeriesData", "Set", "SetAttributes", "SetDelayed", "SetSystemOptions", // + "Share", "ShearingTransform", "Short", "Shortest", "Show", "Sign", // + "Signature", "SignCmp", "Simplex", "Simplify", "Sin", "Sinc", // + "SingularValueDecomposition", "SingularValueList", "Sinh", "SinhIntegral", "SinIntegral", + "SixJSymbol", // + "Skewness", "Slot", "SlotAbsent", "SlotSequence", "Small", "SokalSneathDissimilarity", // + "Solve", "Sort", "SortBy", "Sow", "Span", "SparseArray", // + "Specularity", "Sphere", "SphericalBesselJ", "SphericalBesselY", "SphericalHankelH1", + "SphericalHankelH2", // + "SphericalHarmonicY", "Split", "SplitBy", "SpotLight", "Sqrt", "SqrtBox", // + "SquaredEuclideanDistance", "SquareFreeQ", "SquareMatrixQ", "SSSTriangle", "Stack", + "StackBegin", // + "StandardDeviation", "StandardForm", "Standardize", "StarGraph", "StartOfLine", + "StartOfString", // + "StaticsVisible", "StieltjesGamma", "StirlingS1", "StirlingS2", "StreamPlot", "Strict", // + "String", "StringCases", "StringContainsQ", "StringCount", "StringDrop", "StringExpression", // + "StringForm", "StringFormat", "StringFreeQ", "StringInsert", "StringJoin", "StringLength", // + "StringMatchQ", "StringPart", "StringPosition", "StringQ", "StringRepeat", "StringReplace", // + "StringReverse", "StringRiffle", "StringSplit", "StringTake", "StringTemplate", + "StringToByteArray", // + "StringToStream", "StringTrim", "Structure", "StruveH", "StruveL", "StudentTDistribution", // + "Style", "StyleForm", "Subdivide", "Subfactorial", "Subscript", "SubscriptBox", // + "SubsetQ", "Subsets", "Subsuperscript", "SubsuperscriptBox", "Subtract", "SubtractFrom", // + "SubtractSides", "Sum", "Summary", "Superscript", "SuperscriptBox", "Surd", // + "SurfaceArea", "SurfaceGraphics", "SurvivalFunction", "Switch", "Symbol", "SymbolName", // + "SymbolQ", "Symmetric", "SymmetricMatrixQ", "SyntaxLength", "SyntaxQ", "SystemDialogInput", // + "SystemOptions", "Table", "TableAlignments", "TableDepth", "TableDirections", "TableForm", // + "TableHeadings", "TableSpacing", "TagSet", "TagSetDelayed", "Take", "TakeLargest", // + "TakeLargestBy", "TakeSmallest", "TakeSmallestBy", "TakeWhile", "Tally", "Tan", // + "Tanh", "TargetFunctions", "TautologyQ", "Taylor", "TemplateApply", "TemplateExpression", // + "TemplateIf", "TemplateSlot", "TensorDimensions", "TensorProduct", "TensorRank", + "TensorSymmetry", // + "TestID", "TestReport", "TestReportObject", "TestResultObject", "Tetrahedron", "TeXForm", // + "Text", "TextCell", "TextElement", "TextString", "TextStructure", "Thickness", // + "Thread", "ThreeJSymbol", "Through", "Throw", "Ticks", "TicksStyle", // + "TimeConstrained", "TimeObject", "TimeRemaining", "Times", "TimesBy", "TimeValue", // + "Timing", "Tiny", "ToBoxes", "ToCharacterCode", "Today", "ToeplitzMatrix", // + "ToExpression", "Together", "ToIntervalData", "ToLowerCase", "TooLarge", "Top", // + "ToPolarCoordinates", "ToRadicals", "ToSphericalCoordinates", "ToString", "Total", + "ToUnicode", // + "ToUpperCase", "Tr", "Trace", "TraceForm", "TraditionalForm", "TransformationFunction", // + "TranslationTransform", "Transliterate", "Transpose", "TreeForm", "Triangle", "Trig", // + "TrigExpand", "TrigReduce", "TrigSimplifyFu", "TrigToExp", "True", "TrueQ", // + "TTest", "Tube", "TukeyWindow", "Tuples", "TwoWayRule", "Undefined", // + "Underflow", "Underoverscript", "UnderoverscriptBox", "Underscript", "UnderscriptBox", + "UndirectedEdge", // + "Unequal", "UnequalTo", "Unevaluated", "UniformDistribution", "Union", "Unique", // + "UnitaryMatrixQ", "UnitConvert", "Unitize", "UnitStep", "UnitTriangle", "UnitVector", // + "UniverseAge", "Unknown", "Unprotect", "UnsameQ", "Unset", "UpperCaseQ", // + "UpperTriangularize", "UpperTriangularMatrixQ", "UpSet", "UpSetDelayed", "UpTo", "UpValues", // + "URLFetch", "UseTypeChecking", "ValueQ", "Values", "VandermondeMatrix", "Variable", // + "Variables", "Variance", "VectorAngle", "VectorGreater", "VectorGreaterEqual", "VectorLess", // + "VectorLessEqual", "VectorPlot", "VectorQ", "Vectors", "Verbatim", "VerificationTest", // + "VertexEccentricity", "VertexLabels", "VertexList", "VertexQ", "VertexShapeFunction", + "VertexSize", // + "VertexStyle", "ViewPoint", "Volume", "WeaklyConnectedGraphQ", "WeberE", + "WeibullDistribution", // + "WeierstrassHalfPeriods", "WeierstrassInvariants", "WeierstrassP", "WeierstrassPPrime", + "WeightedAdjacencyMatrix", "WeightedData", // + "WeightedGraphQ", "WheelGraph", "Which", "While", "White", "Whitespace", // + "WhitespaceCharacter", "WhittakerM", "WhittakerW", "With", "Word", "WordBoundary", // + "WordCharacter", "WordSeparators", "Write", "WriteString", "Xnor", "Xor", // + "Yellow", "YuleDissimilarity", "ZeroSymmetric", "ZeroTest", "Zeta", "ZTransform"}; /** * Generated by class: org.matheclipse.core.preprocessor.FunctionIDGenerator @@ -1996,147 +1996,147 @@ public class ID { 240, 386, 212, 0, 167, 551, 26, 431, 53, 1033, 694, // 57, 98, 139, 181, 0, 0, 0, 0, 0, 592, 747, // 0, 0, 677, 127, 0, 27, 40, 119, 0, 155, 844, // - 394, 67, 616, 698, 190, 80, 183, 271, 343, 438, 536, // - 592, 182, 669, 638, 713, 809, 908, 1091, 283, 550, 108, // + 394, 67, 616, 698, 187, 80, 183, 271, 343, 438, 536, // + 592, 182, 669, 638, 713, 809, 908, 1090, 283, 550, 108, // 161, 336, 858, 777, 811, 1074, 0, 218, 103, 73, 36, // 42, 0, 87, 0, 106, 243, 378, 0, 467, 56, 0, // 0, 61, 0, 0, 0, 0, 0, 0, 0, 0, 0, // - 1948, 0, 0, 236, 259, 155, 12, 107, 128, 0, 128, // + 1945, 0, 0, 236, 259, 155, 12, 107, 128, 0, 128, // 1488, 264, 588, 729, 31, 473, 252, 407, 569, 659, 720, // 107, 748, 235, 1260, 0, 99, 74, 163, 33, 234, 946, // 369, 1145, 1275, 26, 54, 0, 0, 172, 0, 0, 0, // - 0, 110, 164, 137, 258, 0, 0, 920, 1008, 1026, 1218, // - 1272, 1308, 0, 0, 1387, 1543, 0, 0, 0, 1956, 125, // - 215, 0, 1294, 0, 0, 0, 48, 0, 282, 265, 0, // + 0, 107, 161, 134, 258, 0, 0, 920, 1008, 1026, 1218, // + 1272, 1308, 0, 0, 1387, 1543, 0, 0, 0, 1953, 125, // + 215, 0, 1294, 0, 0, 0, 48, 0, 282, 262, 0, // 172, 484, 0, 87, 169, 229, 293, 367, 543, 99, 1196, // 667, 602, 279, 1394, 1684, 467, 250, 0, 0, 1375, 178, // 0, 0, 990, 360, 310, 1289, 1377, 362, 422, 221, 679, // - 1426, 1050, 704, 102, 0, 1174, 0, 223, 264, 150, 29, // + 1426, 1050, 704, 102, 0, 1173, 0, 220, 261, 150, 29, // 155, 300, 1190, 0, 130, 0, 294, 318, 1213, 836, 916, // 0, 0, 0, 0, 1486, 0, 267, 54, 729, 1594, 125, // - 822, 0, 61, 721, 0, 1967, 1731, 1242, 316, 1675, 473, // + 822, 0, 61, 721, 0, 1964, 1731, 1229, 316, 1675, 473, // 543, 894, 281, 980, 1205, 1238, 0, 1785, 108, 52, 94, // - 156, 132, 333, 592, 1009, 1974, 910, 496, 634, 704, 773, // - 1294, 1633, 243, 1215, 1650, 233, 364, 139, 1764, 1382, 1890, // - 1984, 532, 3338, 329, 359, 1298, 1485, 1916, 322, 1104, 366, // + 156, 132, 330, 592, 1009, 1971, 910, 496, 634, 704, 773, // + 1294, 1633, 243, 1214, 1649, 233, 364, 139, 1763, 1381, 1890, // + 1984, 532, 3338, 329, 359, 1298, 1484, 1915, 322, 1104, 366, // 59, 0, 201, 290, 482, 404, 174, 445, 0, 0, 0, // - 86, 131, 165, 1160, 1333, 410, 0, 0, 635, 497, 776, // - 0, 0, 2004, 2142, 2243, 2277, 2323, 0, 1141, 1994, 1984, // - 324, 86, 1378, 1452, 1472, 1562, 346, 0, 0, 0, 444, // - 50, 1234, 0, 348, 411, 1658, 1389, 0, 0, 1409, 0, // + 86, 131, 165, 1160, 1333, 407, 0, 0, 635, 494, 776, // + 0, 0, 2004, 2142, 2243, 2277, 2323, 0, 1141, 1991, 1981, // + 321, 86, 1378, 1452, 1472, 1562, 346, 0, 0, 0, 444, // + 50, 1234, 0, 348, 411, 1658, 1390, 0, 0, 1409, 0, // 0, 0, 374, 0, 292, 12, 3459, 587, 31, 452, 2346, // - 0, 0, 0, 0, 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2683, 1018, 2034, 2125, 6879, 0, 366, 6894, 5459, 0, // - 0, 45, 2635, 0, 0, 5652, 5601, 341, 137, 1121, 0, // - 0, 5406, 0, 0, 7043, 3040, 2079, 2118, 0, 0, 1389, // - 2728, 1469, 0, 2020, 7034, 0, 0, 0, 687, 0, 0, // - 2165, 2305, 7378, 7569, 7618, 7678, 7727, 7785, 7256, 3201, 3350, // - 0, 4437, 12, 2769, 0, 2879, 2898, 634, 894, 970, 726, // - 0, 48, 0, 0, 1182, 797, 1220, 0, 0, 2916, 0, // - 0, 2180, 80, 2280, 3246, 0, 0, 3073, 212, 3194, 5772, // - 6817, 112, 3221, 0, 191, 2976, 1150, 5256, 3027, 4232, 275, // - 3123, 0, 0, 5332, 4127, 5386, 3107, 7864, 3174, 3223, 5479, // - 3306, 3342, 0, 1138, 1165, 0, 5590, 819, 0, 0, 47, // - 54, 49, 35, 0, 4558, 7087, 1296, 0, 2806, 0, 0, // - 2664, 0, 0, 0, 0, 0, 4650, 0, 3424, 7188, 7972, // - 2380, 1477, 424, 932, 1030, 0, 5775, 0, 0, 321, 4717, // - 2469, 3270, 5831, 1537, 2554, 2634, 0, 2720, 1221, 0, 1577, // - 1168, 5890, 0, 4587, 7420, 5959, 1054, 1097, 1106, 1115, 0, // - 1635, 0, 0, 180, 1960, 0, 2026, 2078, 0, 0, 0, // - 0, 1331, 2101, 1148, 7516, 2045, 2081, 2119, 2163, 2121, 0, // - 2143, 458, 3497, 3570, 0, 0, 0, 1605, 1657, 3621, 0, // - 0, 0, 614, 1251, 1288, 4743, 4816, 0, 2933, 0, 0, // - 2217, 14}; + 0, 704, 0, 122, 244, 361, 338, 439, 471, 588, 759, // + 6477, 5471, 5572, 5617, 4856, 4967, 0, 0, 4952, 910, 0, // + 0, 1152, 0, 732, 1521, 0, 803, 1275, 1300, 2626, 0, // + 588, 979, 0, 17, 306, 0, 5088, 1431, 0, 0, 1473, // + 1555, 2701, 5686, 5860, 5919, 6062, 6179, 6632, 6245, 960, 2779, // + 6290, 19, 4905, 6375, 0, 6316, 2289, 652, 4176, 64, 0, // + 5056, 367, 6476, 6553, 226, 1032, 1635, 0, 0, 4997, 0, // + 0, 1611, 1660, 2370, 565, 4089, 0, 114, 4143, 4228, 4306, // + 860, 0, 1099, 0, 1055, 1808, 5071, 2532, 2692, 0, 796, // + 6633, 6670, 25, 21, 1689, 35, 0, 211, 322, 1309, 1362, // + 1629, 1813, 389, 1932, 1994, 18, 1105, 353, 0, 0, 5135, // + 2458, 5292, 0, 193, 2797, 2970, 5178, 5205, 3069, 1530, 1422, // + 113, 6706, 0, 0, 0, 0, 2512, 95, 1893, 1990, 2836, // + 0, 168, 0, 1119, 890, 1104, 958, 1019, 1147, 6763, 6835, // + 0, 5361, 0, 651, 5114, 1349, 145, 2914, 2962, 6803, 0, // + 6845, 423, 0, 0, 0, 2001, 5249, 5369, 0, 0, 0, // + 1149, 1302, 1229, 1345, 1379, 1406, 1461, 1501, 1624, 1723, 1788, // + 1844, 1933, 1969, 0, 2049, 2126, 2277, 2297, 2437, 2499, 2749, // + 2656, 1195, 2683, 1018, 2034, 2125, 6879, 0, 366, 6894, 5460, // + 0, 0, 45, 2635, 0, 0, 5652, 5601, 341, 137, 1121, // + 0, 0, 5406, 0, 0, 7043, 3040, 2072, 2111, 0, 0, // + 1389, 2728, 1469, 0, 2015, 7034, 0, 0, 0, 687, 0, // + 0, 2159, 2299, 7378, 7569, 7618, 7678, 7727, 7785, 7256, 3199, // + 3348, 0, 4437, 12, 2769, 0, 2879, 2898, 634, 894, 970, // + 726, 0, 48, 0, 0, 1182, 797, 1220, 0, 0, 2916, // + 0, 0, 2173, 80, 2273, 3246, 0, 0, 3073, 212, 3194, // + 5772, 6817, 112, 3221, 0, 191, 2976, 1150, 5256, 3027, 4232, // + 275, 3123, 0, 0, 5332, 4127, 5386, 3107, 7864, 3174, 3223, // + 5479, 3306, 3342, 0, 1138, 1165, 0, 5590, 819, 0, 0, // + 47, 54, 49, 35, 0, 4558, 7087, 1296, 0, 2806, 0, // + 0, 2664, 0, 0, 0, 0, 0, 4650, 0, 3424, 7188, // + 7972, 2374, 1477, 424, 932, 1030, 0, 5775, 0, 0, 321, // + 4717, 2463, 3270, 5831, 1537, 2549, 2629, 0, 2715, 1221, 0, // + 1577, 1168, 5890, 0, 4587, 7420, 5959, 1054, 1097, 1106, 1115, // + 0, 1635, 0, 0, 180, 1957, 0, 2023, 2075, 0, 0, // + 0, 0, 1331, 2098, 1148, 7516, 2045, 2081, 2119, 2163, 2118, // + 0, 2140, 458, 3497, 3571, 0, 0, 0, 1605, 1657, 3622, // + 0, 0, 0, 614, 1251, 1288, 4743, 4816, 0, 2933, 0, // + 0, 2217, 14}; public final static Map STRING_TO_ID_MAP = new TreeMap(); diff --git a/symja_android_library/matheclipse-core/src/main/java/org/matheclipse/core/expression/S.java b/symja_android_library/matheclipse-core/src/main/java/org/matheclipse/core/expression/S.java index 09ac60b7c0..cebfa245c9 100644 --- a/symja_android_library/matheclipse-core/src/main/java/org/matheclipse/core/expression/S.java +++ b/symja_android_library/matheclipse-core/src/main/java/org/matheclipse/core/expression/S.java @@ -8504,6 +8504,9 @@ public static IBuiltInSymbol symbol(int id) { */ public final static IBuiltInSymbol Ramp = S.initFinalSymbol("Ramp", ID.Ramp); + public final static IBuiltInSymbol RamseyNumber = + S.initFinalSymbol("RamseyNumber", ID.RamseyNumber); + /** * RandomChoice({item1, item2, item3,...}) - randomly picks one `item` from items. * diff --git a/symja_android_library/matheclipse-core/src/main/resources/doc/99-function-reference.md b/symja_android_library/matheclipse-core/src/main/resources/doc/99-function-reference.md index a6f78fb415..fd41d28568 100644 --- a/symja_android_library/matheclipse-core/src/main/resources/doc/99-function-reference.md +++ b/symja_android_library/matheclipse-core/src/main/resources/doc/99-function-reference.md @@ -776,6 +776,7 @@ Functions in alphabetical order: * ✅ [Quotient](functions/Quotient.md) * ✅ [QuotientRemainder](functions/QuotientRemainder.md) * ✅ [Ramp](functions/Ramp.md) +* [RamseyNumber](functions/RamseyNumber.md) * ✅ [RandomChoice](functions/RandomChoice.md) * ✅ [RandomComplex](functions/RandomComplex.md) * ✅ [RandomGraph](functions/RandomGraph.md) diff --git a/symja_android_library/matheclipse-core/src/main/resources/doc/functions/RamseyNumber.md b/symja_android_library/matheclipse-core/src/main/resources/doc/functions/RamseyNumber.md new file mode 100644 index 0000000000..34413c09d4 --- /dev/null +++ b/symja_android_library/matheclipse-core/src/main/resources/doc/functions/RamseyNumber.md @@ -0,0 +1,24 @@ +## RamseyNumber + +``` +RamseyNumber(r, s) +``` + +> returns the Ramsey number `R(r,s)`. Currently not all values are known for `1 <= r <= 4`. The function returns unevaluated if the value is unknown. + +See +* [Wikipedia - Ramsey's theorem](https://en.wikipedia.org/wiki/Ramsey's_theorem) +* [OEIS - A212954](https://oeis.org/A212954) + +### Examples + +``` +>> Table(RamseyNumber(1,j), {j,1,20}) +{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1} + +>> Table(RamseyNumber(2,j), {j,1,20}) +{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20} + +>> Table(RamseyNumber(i,j), {i,1,5},{j,i,10}) +{{1,1,1,1,1,1,1,1,1,1},{2,3,4,5,6,7,8,9,10},{6,9,14,18,23,28,36,RamseyNumber(3,10)},{18,25,RamseyNumber(4,6),RamseyNumber(4,7),RamseyNumber(4,8),RamseyNumber(4,9),RamseyNumber(4,10)}} +``` diff --git a/symja_android_library/matheclipse-core/src/test/java/org/matheclipse/core/system/LowercaseTestCase.java b/symja_android_library/matheclipse-core/src/test/java/org/matheclipse/core/system/LowercaseTestCase.java index e03e5d5f21..dd1fa4d77f 100644 --- a/symja_android_library/matheclipse-core/src/test/java/org/matheclipse/core/system/LowercaseTestCase.java +++ b/symja_android_library/matheclipse-core/src/test/java/org/matheclipse/core/system/LowercaseTestCase.java @@ -5253,6 +5253,17 @@ public void testDedekindNumber() { + "286386577668298411128469151667598498812366,DedekindNumber(10),DedekindNumber(11)}"); } + public void testRamseyNumber() { + check("Table(RamseyNumber(1,j), {j,1,20})", // + "{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}"); + check("Table(RamseyNumber(2,j), {j,1,20})", // + "{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}"); + check("Table(RamseyNumber(i,j), {i,1,4},{j,i,10})", // + "{{1,1,1,1,1,1,1,1,1,1},{2,3,4,5,6,7,8,9,10},{6,9,14,18,23,28,36,RamseyNumber(3,\n" // + + "10)},{18,25,RamseyNumber(4,6),RamseyNumber(4,7),RamseyNumber(4,8),RamseyNumber(4,\n" // + + "9),RamseyNumber(4,10)}}"); + } + public void testDenominator() { check("Denominator(ConditionalExpression(a/13,Element(C1,Integers)))", // "1");