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removing file to deal with build issue
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
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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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