Add RCF (Real Closed Field) bindings to C++, Java, C#, and TypeScript (#8171)

* Initial plan * Add RCF (Real Closed Field) bindings to C++ API Co-authored-by: NikolajBjorner <3085284+NikolajBjorner@users.noreply.github.com> * Add RCF (Real Closed Field) bindings to Java API Co-authored-by: NikolajBjorner <3085284+NikolajBjorner@users.noreply.github.com> * Add RCF (Real Closed Field) bindings to C# (.NET) API Co-authored-by: NikolajBjorner <3085284+NikolajBjorner@users.noreply.github.com> * Add RCF (Real Closed Field) example for TypeScript/JavaScript API Co-authored-by: NikolajBjorner <3085284+NikolajBjorner@users.noreply.github.com> * Add comprehensive RCF implementation summary documentation Co-authored-by: NikolajBjorner <3085284+NikolajBjorner@users.noreply.github.com> --------- Co-authored-by: copilot-swe-agent[bot] <198982749+Copilot@users.noreply.github.com> Co-authored-by: NikolajBjorner <3085284+NikolajBjorner@users.noreply.github.com>
2026-01-18 16:28:56 +00:00 · 2026-01-12 16:34:42 -08:00 · 2026-01-12 16:34:42 -08:00 · bd0eba812d
commit bd0eba812d
parent cfd40d2588
8 changed files with 1874 additions and 0 deletions
--- a/examples/java/RCFExample.java
+++ b/examples/java/RCFExample.java
@ -0,0 +1,119 @@
+/**
+   Example demonstrating the RCF (Real Closed Field) API in Java.
+   
+   This example shows how to use RCF numerals to work with:
+   - Transcendental numbers (pi, e)
+   - Algebraic numbers (roots of polynomials)
+   - Infinitesimals
+   - Exact real arithmetic
+*/
+
+package com.microsoft.z3;
+
+public class RCFExample {
+    
+    public static void rcfBasicExample() {
+        System.out.println("RCF Basic Example");
+        System.out.println("=================");
+        
+        try (Context ctx = new Context()) {
+            // Create pi and e
+            RCFNum pi = RCFNum.mkPi(ctx);
+            RCFNum e = RCFNum.mkE(ctx);
+            
+            System.out.println("pi = " + pi);
+            System.out.println("e = " + e);
+            
+            // Arithmetic operations
+            RCFNum sum = pi.add(e);
+            RCFNum prod = pi.mul(e);
+            
+            System.out.println("pi + e = " + sum);
+            System.out.println("pi * e = " + prod);
+            
+            // Decimal approximations
+            System.out.println("pi (10 decimals) = " + pi.toDecimal(10));
+            System.out.println("e (10 decimals) = " + e.toDecimal(10));
+            
+            // Comparisons
+            System.out.println("pi < e? " + (pi.lt(e) ? "yes" : "no"));
+            System.out.println("pi > e? " + (pi.gt(e) ? "yes" : "no"));
+        }
+    }
+    
+    public static void rcfRationalExample() {
+        System.out.println("\nRCF Rational Example");
+        System.out.println("====================");
+        
+        try (Context ctx = new Context()) {
+            // Create rational numbers
+            RCFNum half = new RCFNum(ctx, "1/2");
+            RCFNum third = new RCFNum(ctx, "1/3");
+            
+            System.out.println("1/2 = " + half);
+            System.out.println("1/3 = " + third);
+            
+            // Arithmetic
+            RCFNum sum = half.add(third);
+            System.out.println("1/2 + 1/3 = " + sum);
+            
+            // Type queries
+            System.out.println("Is 1/2 rational? " + (half.isRational() ? "yes" : "no"));
+            System.out.println("Is 1/2 algebraic? " + (half.isAlgebraic() ? "yes" : "no"));
+        }
+    }
+    
+    public static void rcfRootsExample() {
+        System.out.println("\nRCF Roots Example");
+        System.out.println("=================");
+        
+        try (Context ctx = new Context()) {
+            // Find roots of x^2 - 2 = 0
+            // Polynomial: -2 + 0*x + 1*x^2
+            RCFNum[] coeffs = new RCFNum[] {
+                new RCFNum(ctx, -2),   // constant term
+                new RCFNum(ctx, 0),    // x coefficient
+                new RCFNum(ctx, 1)     // x^2 coefficient
+            };
+            
+            RCFNum[] roots = RCFNum.mkRoots(ctx, coeffs);
+            
+            System.out.println("Roots of x^2 - 2 = 0:");
+            for (int i = 0; i < roots.length; i++) {
+                System.out.println("  root[" + i + "] = " + roots[i]);
+                System.out.println("  decimal = " + roots[i].toDecimal(15));
+                System.out.println("  is_algebraic = " + (roots[i].isAlgebraic() ? "yes" : "no"));
+            }
+        }
+    }
+    
+    public static void rcfInfinitesimalExample() {
+        System.out.println("\nRCF Infinitesimal Example");
+        System.out.println("=========================");
+        
+        try (Context ctx = new Context()) {
+            // Create an infinitesimal
+            RCFNum eps = RCFNum.mkInfinitesimal(ctx);
+            System.out.println("eps = " + eps);
+            System.out.println("Is eps infinitesimal? " + (eps.isInfinitesimal() ? "yes" : "no"));
+            
+            // Infinitesimals are smaller than any positive real number
+            RCFNum tiny = new RCFNum(ctx, "1/1000000000");
+            System.out.println("eps < 1/1000000000? " + (eps.lt(tiny) ? "yes" : "no"));
+        }
+    }
+    
+    public static void main(String[] args) {
+        try {
+            rcfBasicExample();
+            rcfRationalExample();
+            rcfRootsExample();
+            rcfInfinitesimalExample();
+            
+            System.out.println("\nAll RCF examples completed successfully!");
+        } catch (Exception e) {
+            System.err.println("Error: " + e.getMessage());
+            e.printStackTrace();
+        }
+    }
+}