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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>
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119
examples/c++/rcf_example.cpp
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119
examples/c++/rcf_example.cpp
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/**
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\brief Example demonstrating the RCF (Real Closed Field) API in C++.
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This example shows how to use RCF numerals to work with:
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- Transcendental numbers (pi, e)
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- Algebraic numbers (roots of polynomials)
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- Infinitesimals
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- Exact real arithmetic
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*/
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#include <iostream>
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#include "z3++.h"
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using namespace z3;
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void rcf_basic_example() {
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std::cout << "RCF Basic Example\n";
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std::cout << "=================\n";
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context c;
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// Create pi and e
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rcf_num pi = rcf_pi(c);
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rcf_num e = rcf_e(c);
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std::cout << "pi = " << pi << "\n";
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std::cout << "e = " << e << "\n";
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// Arithmetic operations
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rcf_num sum = pi + e;
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rcf_num prod = pi * e;
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std::cout << "pi + e = " << sum << "\n";
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std::cout << "pi * e = " << prod << "\n";
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// Decimal approximations
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std::cout << "pi (10 decimals) = " << pi.to_decimal(10) << "\n";
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std::cout << "e (10 decimals) = " << e.to_decimal(10) << "\n";
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// Comparisons
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std::cout << "pi < e? " << (pi < e ? "yes" : "no") << "\n";
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std::cout << "pi > e? " << (pi > e ? "yes" : "no") << "\n";
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}
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void rcf_rational_example() {
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std::cout << "\nRCF Rational Example\n";
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std::cout << "====================\n";
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context c;
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// Create rational numbers
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rcf_num half(c, "1/2");
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rcf_num third(c, "1/3");
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std::cout << "1/2 = " << half << "\n";
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std::cout << "1/3 = " << third << "\n";
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// Arithmetic
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rcf_num sum = half + third;
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std::cout << "1/2 + 1/3 = " << sum << "\n";
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// Type queries
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std::cout << "Is 1/2 rational? " << (half.is_rational() ? "yes" : "no") << "\n";
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std::cout << "Is 1/2 algebraic? " << (half.is_algebraic() ? "yes" : "no") << "\n";
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}
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void rcf_roots_example() {
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std::cout << "\nRCF Roots Example\n";
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std::cout << "=================\n";
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context c;
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// Find roots of x^2 - 2 = 0
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// Polynomial: -2 + 0*x + 1*x^2
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std::vector<rcf_num> coeffs;
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coeffs.push_back(rcf_num(c, -2)); // constant term
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coeffs.push_back(rcf_num(c, 0)); // x coefficient
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coeffs.push_back(rcf_num(c, 1)); // x^2 coefficient
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std::vector<rcf_num> roots = rcf_roots(c, coeffs);
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std::cout << "Roots of x^2 - 2 = 0:\n";
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for (size_t i = 0; i < roots.size(); i++) {
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std::cout << " root[" << i << "] = " << roots[i] << "\n";
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std::cout << " decimal = " << roots[i].to_decimal(15) << "\n";
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std::cout << " is_algebraic = " << (roots[i].is_algebraic() ? "yes" : "no") << "\n";
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}
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}
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void rcf_infinitesimal_example() {
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std::cout << "\nRCF Infinitesimal Example\n";
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std::cout << "=========================\n";
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context c;
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// Create an infinitesimal
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rcf_num eps = rcf_infinitesimal(c);
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std::cout << "eps = " << eps << "\n";
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std::cout << "Is eps infinitesimal? " << (eps.is_infinitesimal() ? "yes" : "no") << "\n";
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// Infinitesimals are smaller than any positive real number
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rcf_num tiny(c, "1/1000000000");
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std::cout << "eps < 1/1000000000? " << (eps < tiny ? "yes" : "no") << "\n";
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}
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int main() {
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try {
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rcf_basic_example();
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rcf_rational_example();
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rcf_roots_example();
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rcf_infinitesimal_example();
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std::cout << "\nAll RCF examples completed successfully!\n";
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return 0;
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}
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catch (exception& e) {
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std::cerr << "Z3 exception: " << e << "\n";
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return 1;
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}
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}
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133
examples/dotnet/RCFExample.cs
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133
examples/dotnet/RCFExample.cs
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/**
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Example demonstrating the RCF (Real Closed Field) API in C#.
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This example shows how to use RCF numerals to work with:
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- Transcendental numbers (pi, e)
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- Algebraic numbers (roots of polynomials)
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- Infinitesimals
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- Exact real arithmetic
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*/
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using Microsoft.Z3;
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using System;
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class RCFExample
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{
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static void RcfBasicExample()
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{
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Console.WriteLine("RCF Basic Example");
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Console.WriteLine("=================");
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using (Context ctx = new Context())
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{
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// Create pi and e
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RCFNum pi = RCFNum.MkPi(ctx);
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RCFNum e = RCFNum.MkE(ctx);
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Console.WriteLine("pi = " + pi);
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Console.WriteLine("e = " + e);
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// Arithmetic operations
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RCFNum sum = pi + e;
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RCFNum prod = pi * e;
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Console.WriteLine("pi + e = " + sum);
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Console.WriteLine("pi * e = " + prod);
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// Decimal approximations
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Console.WriteLine("pi (10 decimals) = " + pi.ToDecimal(10));
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Console.WriteLine("e (10 decimals) = " + e.ToDecimal(10));
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// Comparisons
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Console.WriteLine("pi < e? " + (pi < e ? "yes" : "no"));
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Console.WriteLine("pi > e? " + (pi > e ? "yes" : "no"));
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}
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}
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static void RcfRationalExample()
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{
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Console.WriteLine("\nRCF Rational Example");
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Console.WriteLine("====================");
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using (Context ctx = new Context())
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{
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// Create rational numbers
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RCFNum half = new RCFNum(ctx, "1/2");
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RCFNum third = new RCFNum(ctx, "1/3");
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Console.WriteLine("1/2 = " + half);
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Console.WriteLine("1/3 = " + third);
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// Arithmetic
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RCFNum sum = half + third;
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Console.WriteLine("1/2 + 1/3 = " + sum);
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// Type queries
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Console.WriteLine("Is 1/2 rational? " + (half.IsRational() ? "yes" : "no"));
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Console.WriteLine("Is 1/2 algebraic? " + (half.IsAlgebraic() ? "yes" : "no"));
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}
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}
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static void RcfRootsExample()
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{
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Console.WriteLine("\nRCF Roots Example");
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Console.WriteLine("=================");
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using (Context ctx = new Context())
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{
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// Find roots of x^2 - 2 = 0
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// Polynomial: -2 + 0*x + 1*x^2
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RCFNum[] coeffs = new RCFNum[] {
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new RCFNum(ctx, -2), // constant term
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new RCFNum(ctx, 0), // x coefficient
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new RCFNum(ctx, 1) // x^2 coefficient
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};
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RCFNum[] roots = RCFNum.MkRoots(ctx, coeffs);
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Console.WriteLine("Roots of x^2 - 2 = 0:");
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for (int i = 0; i < roots.Length; i++)
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{
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Console.WriteLine(" root[" + i + "] = " + roots[i]);
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Console.WriteLine(" decimal = " + roots[i].ToDecimal(15));
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Console.WriteLine(" is_algebraic = " + (roots[i].IsAlgebraic() ? "yes" : "no"));
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}
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}
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}
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static void RcfInfinitesimalExample()
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{
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Console.WriteLine("\nRCF Infinitesimal Example");
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Console.WriteLine("=========================");
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using (Context ctx = new Context())
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{
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// Create an infinitesimal
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RCFNum eps = RCFNum.MkInfinitesimal(ctx);
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Console.WriteLine("eps = " + eps);
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Console.WriteLine("Is eps infinitesimal? " + (eps.IsInfinitesimal() ? "yes" : "no"));
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// Infinitesimals are smaller than any positive real number
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RCFNum tiny = new RCFNum(ctx, "1/1000000000");
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Console.WriteLine("eps < 1/1000000000? " + (eps < tiny ? "yes" : "no"));
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}
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}
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static void Main(string[] args)
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{
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try
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{
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RcfBasicExample();
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RcfRationalExample();
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RcfRootsExample();
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RcfInfinitesimalExample();
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Console.WriteLine("\nAll RCF examples completed successfully!");
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}
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catch (Exception ex)
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{
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Console.Error.WriteLine("Error: " + ex.Message);
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Console.Error.WriteLine(ex.StackTrace);
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}
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}
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}
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119
examples/java/RCFExample.java
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119
examples/java/RCFExample.java
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/**
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Example demonstrating the RCF (Real Closed Field) API in Java.
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This example shows how to use RCF numerals to work with:
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- Transcendental numbers (pi, e)
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- Algebraic numbers (roots of polynomials)
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- Infinitesimals
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- Exact real arithmetic
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*/
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package com.microsoft.z3;
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public class RCFExample {
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public static void rcfBasicExample() {
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System.out.println("RCF Basic Example");
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System.out.println("=================");
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try (Context ctx = new Context()) {
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// Create pi and e
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RCFNum pi = RCFNum.mkPi(ctx);
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RCFNum e = RCFNum.mkE(ctx);
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System.out.println("pi = " + pi);
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System.out.println("e = " + e);
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// Arithmetic operations
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RCFNum sum = pi.add(e);
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RCFNum prod = pi.mul(e);
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System.out.println("pi + e = " + sum);
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System.out.println("pi * e = " + prod);
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// Decimal approximations
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System.out.println("pi (10 decimals) = " + pi.toDecimal(10));
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System.out.println("e (10 decimals) = " + e.toDecimal(10));
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// Comparisons
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System.out.println("pi < e? " + (pi.lt(e) ? "yes" : "no"));
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System.out.println("pi > e? " + (pi.gt(e) ? "yes" : "no"));
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}
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}
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public static void rcfRationalExample() {
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System.out.println("\nRCF Rational Example");
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System.out.println("====================");
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try (Context ctx = new Context()) {
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// Create rational numbers
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RCFNum half = new RCFNum(ctx, "1/2");
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RCFNum third = new RCFNum(ctx, "1/3");
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System.out.println("1/2 = " + half);
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System.out.println("1/3 = " + third);
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// Arithmetic
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RCFNum sum = half.add(third);
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System.out.println("1/2 + 1/3 = " + sum);
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// Type queries
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System.out.println("Is 1/2 rational? " + (half.isRational() ? "yes" : "no"));
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System.out.println("Is 1/2 algebraic? " + (half.isAlgebraic() ? "yes" : "no"));
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}
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}
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public static void rcfRootsExample() {
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System.out.println("\nRCF Roots Example");
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System.out.println("=================");
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try (Context ctx = new Context()) {
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// Find roots of x^2 - 2 = 0
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// Polynomial: -2 + 0*x + 1*x^2
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RCFNum[] coeffs = new RCFNum[] {
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new RCFNum(ctx, -2), // constant term
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new RCFNum(ctx, 0), // x coefficient
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new RCFNum(ctx, 1) // x^2 coefficient
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};
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RCFNum[] roots = RCFNum.mkRoots(ctx, coeffs);
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System.out.println("Roots of x^2 - 2 = 0:");
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for (int i = 0; i < roots.length; i++) {
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System.out.println(" root[" + i + "] = " + roots[i]);
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System.out.println(" decimal = " + roots[i].toDecimal(15));
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System.out.println(" is_algebraic = " + (roots[i].isAlgebraic() ? "yes" : "no"));
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}
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}
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}
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public static void rcfInfinitesimalExample() {
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System.out.println("\nRCF Infinitesimal Example");
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System.out.println("=========================");
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try (Context ctx = new Context()) {
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// Create an infinitesimal
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RCFNum eps = RCFNum.mkInfinitesimal(ctx);
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System.out.println("eps = " + eps);
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System.out.println("Is eps infinitesimal? " + (eps.isInfinitesimal() ? "yes" : "no"));
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// Infinitesimals are smaller than any positive real number
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RCFNum tiny = new RCFNum(ctx, "1/1000000000");
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System.out.println("eps < 1/1000000000? " + (eps.lt(tiny) ? "yes" : "no"));
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}
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}
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public static void main(String[] args) {
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try {
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rcfBasicExample();
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rcfRationalExample();
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rcfRootsExample();
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rcfInfinitesimalExample();
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System.out.println("\nAll RCF examples completed successfully!");
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} catch (Exception e) {
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System.err.println("Error: " + e.getMessage());
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e.printStackTrace();
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}
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}
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}
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