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

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* 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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src/api/js/examples/low-level/rcf-example.ts Normal file
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/**
* Example demonstrating the RCF (Real Closed Field) API in TypeScript.
*
* This example shows how to use RCF numerals to work with:
* - Transcendental numbers (pi, e)
* - Algebraic numbers (roots of polynomials)
* - Infinitesimals
* - Exact real arithmetic
*
* Note: The RCF API is exposed at the low-level API layer.
* Import from 'z3-solver' for low-level access.
*/
import { init } from 'z3-solver';
async function rcfBasicExample() {
console.log('RCF Basic Example');
console.log('=================');
const { Z3 } = await init();
const ctx = Z3.mk_context_rc(Z3.mk_config());
try {
// Create pi and e
const pi = Z3.rcf_mk_pi(ctx);
const e = Z3.rcf_mk_e(ctx);
console.log('pi =', Z3.rcf_num_to_string(ctx, pi, false, false));
console.log('e =', Z3.rcf_num_to_string(ctx, e, false, false));
// Arithmetic operations
const sum = Z3.rcf_add(ctx, pi, e);
const prod = Z3.rcf_mul(ctx, pi, e);
console.log('pi + e =', Z3.rcf_num_to_string(ctx, sum, false, false));
console.log('pi * e =', Z3.rcf_num_to_string(ctx, prod, false, false));
// Decimal approximations
console.log('pi (10 decimals) =', Z3.rcf_num_to_decimal_string(ctx, pi, 10));
console.log('e (10 decimals) =', Z3.rcf_num_to_decimal_string(ctx, e, 10));
// Comparisons
console.log('pi < e?', Z3.rcf_lt(ctx, pi, e) ? 'yes' : 'no');
console.log('pi > e?', Z3.rcf_gt(ctx, pi, e) ? 'yes' : 'no');
// Cleanup
Z3.rcf_del(ctx, pi);
Z3.rcf_del(ctx, e);
Z3.rcf_del(ctx, sum);
Z3.rcf_del(ctx, prod);
} finally {
Z3.del_context(ctx);
}
}
async function rcfRationalExample() {
console.log('\nRCF Rational Example');
console.log('====================');
const { Z3 } = await init();
const ctx = Z3.mk_context_rc(Z3.mk_config());
try {
// Create rational numbers
const half = Z3.rcf_mk_rational(ctx, '1/2');
const third = Z3.rcf_mk_rational(ctx, '1/3');
console.log('1/2 =', Z3.rcf_num_to_string(ctx, half, false, false));
console.log('1/3 =', Z3.rcf_num_to_string(ctx, third, false, false));
// Arithmetic
const sum = Z3.rcf_add(ctx, half, third);
console.log('1/2 + 1/3 =', Z3.rcf_num_to_string(ctx, sum, false, false));
// Type queries
console.log('Is 1/2 rational?', Z3.rcf_is_rational(ctx, half) ? 'yes' : 'no');
console.log('Is 1/2 algebraic?', Z3.rcf_is_algebraic(ctx, half) ? 'yes' : 'no');
// Cleanup
Z3.rcf_del(ctx, half);
Z3.rcf_del(ctx, third);
Z3.rcf_del(ctx, sum);
} finally {
Z3.del_context(ctx);
}
}
async function rcfRootsExample() {
console.log('\nRCF Roots Example');
console.log('=================');
const { Z3 } = await init();
const ctx = Z3.mk_context_rc(Z3.mk_config());
try {
// Find roots of x^2 - 2 = 0
// Polynomial: -2 + 0*x + 1*x^2
const coeffs = [
Z3.rcf_mk_small_int(ctx, -2), // constant term
Z3.rcf_mk_small_int(ctx, 0), // x coefficient
Z3.rcf_mk_small_int(ctx, 1) // x^2 coefficient
];
const roots = new Array(coeffs.length);
const numRoots = Z3.rcf_mk_roots(ctx, coeffs, roots);
console.log('Roots of x^2 - 2 = 0:');
for (let i = 0; i < numRoots; i++) {
console.log(` root[${i}] =`, Z3.rcf_num_to_string(ctx, roots[i], false, false));
console.log(` decimal =`, Z3.rcf_num_to_decimal_string(ctx, roots[i], 15));
console.log(` is_algebraic =`, Z3.rcf_is_algebraic(ctx, roots[i]) ? 'yes' : 'no');
}
// Cleanup
for (const coeff of coeffs) {
Z3.rcf_del(ctx, coeff);
}
for (let i = 0; i < numRoots; i++) {
Z3.rcf_del(ctx, roots[i]);
}
} finally {
Z3.del_context(ctx);
}
}
async function rcfInfinitesimalExample() {
console.log('\nRCF Infinitesimal Example');
console.log('=========================');
const { Z3 } = await init();
const ctx = Z3.mk_context_rc(Z3.mk_config());
try {
// Create an infinitesimal
const eps = Z3.rcf_mk_infinitesimal(ctx);
console.log('eps =', Z3.rcf_num_to_string(ctx, eps, false, false));
console.log('Is eps infinitesimal?', Z3.rcf_is_infinitesimal(ctx, eps) ? 'yes' : 'no');
// Infinitesimals are smaller than any positive real number
const tiny = Z3.rcf_mk_rational(ctx, '1/1000000000');
console.log('eps < 1/1000000000?', Z3.rcf_lt(ctx, eps, tiny) ? 'yes' : 'no');
// Cleanup
Z3.rcf_del(ctx, eps);
Z3.rcf_del(ctx, tiny);
} finally {
Z3.del_context(ctx);
}
}
async function main() {
try {
await rcfBasicExample();
await rcfRationalExample();
await rcfRootsExample();
await rcfInfinitesimalExample();
console.log('\nAll RCF examples completed successfully!');
} catch (error) {
console.error('Error:', error);
throw error;
}
}
main();