Implemented RamseyNumber(r,s) function

axkr · Nov 6, 2023 · 77816fb · 77816fb
1 parent 8200e10
commit 77816fb
Show file tree

Hide file tree

Showing 9 changed files with 733 additions and 607 deletions.
diff --git 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:
 * &#x2705; [Quotient](functions/Quotient.md)
 * &#x2705; [QuotientRemainder](functions/QuotientRemainder.md)
 * &#x2705; [Ramp](functions/Ramp.md)
+* [RamseyNumber](functions/RamseyNumber.md)
 * &#x2705; [RandomChoice](functions/RandomChoice.md)
 * &#x2705; [RandomComplex](functions/RandomComplex.md)
 * &#x2705; [RandomGraph](functions/RandomGraph.md)

diff --git a/symja_android_library/doc/functions/RamseyNumber.md 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/...oid_library/matheclipse-core/src/main/java/org/matheclipse/core/builtin/NumberTheory.java b/...oid_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/...android_library/matheclipse-core/src/main/java/org/matheclipse/core/convert/AST2Expr.java b/...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",