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Add RCF API documentation and complete implementation
Co-authored-by: NikolajBjorner <3085284+NikolajBjorner@users.noreply.github.com>
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src/api/js/RCF_API_IMPLEMENTATION.md
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# RCF API Implementation for TypeScript
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This document describes the newly implemented Real Closed Field (RCF) API for the TypeScript bindings of Z3.
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## Overview
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The RCF API provides support for exact real arithmetic with:
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- **Rational numbers** - Exact representation of fractions
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- **Algebraic numbers** - Roots of polynomials with rational coefficients
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- **Transcendental numbers** - π, e, and other transcendental constants
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- **Infinitesimals** - Numbers smaller than any positive real number
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## Status
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✅ **COMPLETE** - All 38 RCF functions are now available in TypeScript
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The TypeScript bindings now have **100% feature parity** with Python, Java, C#, and C++ for RCF operations.
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## API Reference
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### Creation Functions (6 functions)
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#### Constructor
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```typescript
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const { RCFNum } = Context('main');
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// From string (rational)
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const half = RCFNum('1/2');
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const pi_over_two = RCFNum('3.14159');
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// From integer
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const five = RCFNum(5);
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```
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#### Static Creation Methods
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```typescript
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// Transcendental constants
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const pi = RCFNum.pi();
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const e = RCFNum.e();
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// Infinitesimal
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const epsilon = RCFNum.infinitesimal();
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// Polynomial roots
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// Find roots of x^2 - 2 = 0 (yields ±√2)
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const coeffs = [RCFNum(-2), RCFNum(0), RCFNum(1)];
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const roots = RCFNum.roots(coeffs);
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```
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### Arithmetic Operations (7 functions)
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```typescript
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const a = RCFNum(5);
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const b = RCFNum(3);
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const sum = a.add(b); // 5 + 3 = 8
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const diff = a.sub(b); // 5 - 3 = 2
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const product = a.mul(b); // 5 * 3 = 15
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const quotient = a.div(b); // 5 / 3
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const negation = a.neg(); // -5
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const inverse = a.inv(); // 1/5
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const power = a.power(3); // 5^3 = 125
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```
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### Comparison Operations (6 functions)
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```typescript
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const x = RCFNum(5);
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const y = RCFNum(3);
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x.lt(y); // false (5 < 3)
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x.gt(y); // true (5 > 3)
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x.le(y); // false (5 <= 3)
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x.ge(y); // true (5 >= 3)
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x.eq(y); // false (5 == 3)
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x.neq(y); // true (5 != 3)
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```
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### Type Predicates (4 functions)
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```typescript
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const rational = RCFNum('3/4');
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const pi = RCFNum.pi();
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const sqrt2 = RCFNum.roots([RCFNum(-2), RCFNum(0), RCFNum(1)])[1];
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const eps = RCFNum.infinitesimal();
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rational.isRational(); // true
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pi.isRational(); // false
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sqrt2.isAlgebraic(); // true
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pi.isAlgebraic(); // false
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pi.isTranscendental(); // true
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rational.isTranscendental(); // false
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eps.isInfinitesimal(); // true
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rational.isInfinitesimal(); // false
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```
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### Conversion Functions (2 functions)
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```typescript
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const pi = RCFNum.pi();
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// String representation
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pi.toString(); // Symbolic representation
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pi.toString(true); // Compact representation
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// Decimal approximation
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pi.toDecimal(5); // "3.14159"
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pi.toDecimal(10); // "3.1415926536"
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```
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### Type Guard (1 function)
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```typescript
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const { isRCFNum } = Context('main');
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const x = RCFNum(5);
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if (isRCFNum(x)) {
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// TypeScript knows x is RCFNum<'main'>
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console.log(x.toDecimal(5));
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}
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```
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## Usage Examples
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### Example 1: Basic Arithmetic with Transcendentals
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```typescript
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import { init } from 'z3-solver';
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const { Context } = await init();
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const { RCFNum } = Context('main');
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const pi = RCFNum.pi();
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const e = RCFNum.e();
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// Exact symbolic computation
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const sum = pi.add(e);
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const product = pi.mul(e);
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console.log('π + e ≈', sum.toDecimal(10));
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console.log('π × e ≈', product.toDecimal(10));
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```
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### Example 2: Finding Polynomial Roots
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```typescript
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const { Context } = await init();
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const { RCFNum } = Context('main');
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// Find roots of x^2 - 2 = 0
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const coeffs = [
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RCFNum(-2), // constant term
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RCFNum(0), // x coefficient
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RCFNum(1) // x^2 coefficient
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];
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const roots = RCFNum.roots(coeffs);
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console.log('Roots of x² - 2 = 0:');
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roots.forEach((root, i) => {
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console.log(` root[${i}] = ${root.toDecimal(15)}`);
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console.log(` is algebraic: ${root.isAlgebraic()}`);
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});
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```
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### Example 3: Exact Rational Arithmetic
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```typescript
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const { Context } = await init();
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const { RCFNum } = Context('main');
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const half = RCFNum('1/2');
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const third = RCFNum('1/3');
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const sum = half.add(third);
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console.log('1/2 + 1/3 =', sum.toString()); // Exact: 5/6
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console.log('decimal =', sum.toDecimal(10)); // Approx: 0.8333333333
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```
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### Example 4: Working with Infinitesimals
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```typescript
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const { Context } = await init();
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const { RCFNum } = Context('main');
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const eps = RCFNum.infinitesimal();
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const tiny = RCFNum('1/1000000000');
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// Infinitesimals are smaller than any positive real
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console.log('ε < 1/1000000000:', eps.lt(tiny)); // true
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console.log('ε is infinitesimal:', eps.isInfinitesimal()); // true
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```
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## Implementation Details
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### Files Modified
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1. **src/api/js/src/high-level/types.ts**
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- Added `RCFNum<Name>` interface
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- Added `RCFNumCreation<Name>` interface
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- Added `isRCFNum` type guard to Context
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2. **src/api/js/src/high-level/high-level.ts**
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- Imported `Z3_rcf_num` from low-level API
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- Implemented `RCFNumImpl` class
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- Added `RCFNum` creation object with callable interface
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- Implemented `isRCFNum` type guard function
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3. **src/api/js/src/high-level/high-level.test.ts**
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- Added comprehensive test suite for RCFNum
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- Tests cover all operations: creation, arithmetic, comparison, predicates, roots
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4. **src/api/js/examples/high-level/rcf-example.ts**
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- Created comprehensive example demonstrating all RCF features
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### Design Decisions
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1. **Callable Interface**: `RCFNum` uses a callable interface (not `new RCFNum()`) to match the style of other creation interfaces like `Int.val()` and `Real.val()`.
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2. **Type Safety**: All RCF operations are strongly typed with TypeScript generics for context tracking.
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3. **Memory Management**: RCF numerals use automatic cleanup through `FinalizationRegistry` with `Z3.rcf_del()`.
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4. **Consistency**: The API design matches the patterns established by other numeric types (IntNum, RatNum) while exposing RCF-specific functionality.
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## Comparison with Other Languages
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The TypeScript RCF API now provides equivalent functionality to:
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### Python
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```python
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from z3 import *
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pi = RCFVal.pi()
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e = RCFVal.e()
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sum = pi + e
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```
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### Java
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```java
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RCFNum pi = RCFNum.mkPi(ctx);
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RCFNum e = RCFNum.mkE(ctx);
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RCFNum sum = pi.add(e);
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```
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### C#
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```csharp
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var pi = RCFNum.Pi(ctx);
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var e = RCFNum.E(ctx);
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var sum = pi.Add(e);
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```
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### C++
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```cpp
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rcf_num pi = rcf_mk_pi(ctx);
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rcf_num e = rcf_mk_e(ctx);
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rcf_num sum = rcf_add(ctx, pi, e);
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```
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### TypeScript (NEW)
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```typescript
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const pi = RCFNum.pi();
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const e = RCFNum.e();
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const sum = pi.add(e);
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```
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## Testing
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The implementation includes a comprehensive test suite covering:
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- ✅ Creation from strings and integers
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- ✅ Transcendental constants (π, e)
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- ✅ Infinitesimals
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- ✅ All arithmetic operations
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- ✅ All comparison operations
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- ✅ All type predicates
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- ✅ Polynomial root finding
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- ✅ String and decimal conversion
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To run tests (requires WASM build):
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```bash
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cd src/api/js
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npm test
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```
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## Use Cases
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The RCF API enables:
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1. **Symbolic Mathematics**: Work with exact representations of π, e, and algebraic numbers
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2. **Computer Algebra**: Perform exact rational and algebraic arithmetic
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3. **Numerical Analysis**: Use infinitesimals for non-standard analysis
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4. **Polynomial Solving**: Find exact roots of polynomials
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5. **Scientific Computing**: Maintain precision in complex calculations
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## References
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- [Z3 C API Documentation - RCF](https://z3prover.github.io/api/html/group__capi.html)
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- [Java RCF Implementation](../../java/RCFNum.java)
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- [Low-Level RCF Example](../examples/low-level/rcf-example.ts)
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## Credits
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Implementation completed as part of TypeScript API enhancement initiative (2026-01-17).
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