feat: add support for solving systems of linear equations and enhance solve method. fix #189

Author: arnog

CHANGELOG.md

@@ -2,6 +2,25 @@
 
 ### Improvements
 
+- **Systems of Linear Equations**: The `solve()` method now handles systems of
+  linear equations parsed from LaTeX `\begin{cases}...\end{cases}` environments.
+  Returns an object mapping variable names to their solutions.
+
+  ```javascript
+  const e = ce.parse('\\begin{cases}x+y=70\\\\2x-4y=80\\end{cases}');
+  const result = e.solve(['x', 'y']);
+  console.log(result.x.json);  // 60
+  console.log(result.y.json);  // 10
+
+  // 3x3 systems work too
+  const e2 = ce.parse('\\begin{cases}x+y+z=6\\\\2x+y-z=1\\\\x-y+2z=5\\end{cases}');
+  const result2 = e2.solve(['x', 'y', 'z']);
+  // → { x: 1, y: 2, z: 3 }
+  ```
+
+  Non-linear systems (containing `xy`, `x²`, etc.) and inconsistent systems
+  return `null`.
+
 - **Extended Sqrt Equation Solving**: The equation solver now handles sqrt
   equations of the form `√(f(x)) = g(x)` by squaring both sides and solving
   the resulting polynomial. Extraneous roots are automatically filtered.

src/compute-engine/boxed-expression/abstract-boxed-expression.ts

@@ -622,7 +622,7 @@ export abstract class _BoxedExpression implements BoxedExpression {
       | string
       | BoxedExpression
       | Iterable<BoxedExpression>
-  ): null | ReadonlyArray<BoxedExpression> {
+  ): null | ReadonlyArray<BoxedExpression> | Record<string, BoxedExpression> {
     return null;
   }
 

src/compute-engine/boxed-expression/boxed-function.ts

@@ -36,6 +36,7 @@ import {
 import { NumericValue } from '../numeric-value/types';
 
 import { findUnivariateRoots } from './solve';
+import { solveLinearSystem } from './solve-linear-system';
 import { replace } from './rules';
 import { negate } from './negate';
 import { Product } from './product';
@@ -904,8 +905,18 @@ export class BoxedFunction extends _BoxedExpression {
       | string
       | BoxedExpression
       | Iterable<BoxedExpression>
-  ): null | ReadonlyArray<BoxedExpression> {
+  ): null | ReadonlyArray<BoxedExpression> | Record<string, BoxedExpression> {
     const varNames = normalizedUnknownsForSolve(vars ?? this.unknowns);
+
+    // Handle List of equations (system of equations)
+    if (this.operator === 'List') {
+      const equations = this.ops;
+      if (equations && equations.every((eq) => eq.operator === 'Equal')) {
+        return solveLinearSystem([...equations], varNames);
+      }
+    }
+
+    // Existing univariate solving
     if (varNames.length !== 1) return null;
     return findUnivariateRoots(this, varNames[0]);
   }

src/compute-engine/boxed-expression/boxed-tensor.ts

@@ -359,6 +359,18 @@ export class BoxedTensor<T extends TensorDataType> extends _BoxedExpression {
     if (this._tensor && this._tensor.dtype !== 'expression') return this;
     return this.structural.N();
   }
+
+  solve(
+    vars?:
+      | Iterable<string>
+      | string
+      | BoxedExpression
+      | Iterable<BoxedExpression>
+  ): null | ReadonlyArray<BoxedExpression> | Record<string, BoxedExpression> {
+    // Delegate to the structural expression which may be a BoxedFunction
+    // that can handle system of equations
+    return this.structural.solve(vars);
+  }
 }
 
 export function isBoxedTensor(val: unknown): val is BoxedTensor<any> {