linear: implement P0 PLU decomposition with unified result type

[Ezrnest]

Motivation

• Implement the P0 work item to provide a robust PLU/LUP decomposition entry for exact (non-floating) linear algebra.
• Introduce a unified decomposition result type so consumers can access P, L, U, pivot indices and rank in a single object.
• Provide a field-context API for decompPLU to complement existing decompLU and enable pivoting when leading elements are zero.

Description

• Add PLUDecompositionResult<T> containing P, L, U, and pivots with a computed rank property in src/main/kotlin/.../Matrix.kt.
• Add the extension API Matrix<T>.decompPLU() which delegates to MatrixImpl.decompPLU(this, model) in Matrix.kt.
• Implement MatrixImpl.decompPLU(m: Matrix<T>, mc: Field<T>) performing row pivot selection, row swaps on U and P, updating L accordingly, and returning PLUDecompositionResult in src/main/kotlin/.../MatrixImpl.kt.
• Add unit tests decompPLUOfSquareMatrix and decompPLUHandlesZeroLeadingPivotByRowSwap in src/test/kotlin/linear/MatrixTest.kt to validate P*A == L*U, pivot/rank consistency and row-swap behavior.

Testing

• Attempted to run targeted tests linear.MatrixTest.decompPLUOfSquareMatrix and linear.MatrixTest.decompPLUHandlesZeroLeadingPivotByRowSwap via the Gradle wrapper, but the wrapper download failed due to a network connection refusal so the tests could not be executed in this environment.
• Project changes include the new tests and compile-time code; CI or a local run with working network should execute the added tests (decompPLUOfSquareMatrix, decompPLUHandlesZeroLeadingPivotByRowSwap) to verify correctness.

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[chatgpt-codex-connector]

Preserve PLU invariants when a pivot column is all zero

In decompPLU, the early continue when column k has no non-zero candidate skips initialization of lower[k,k] and abandons pivot tracking for that step. On rank-deficient inputs with a zero leading column but non-zero entries later in the row (for example [[0,1],[0,0]]), this yields P=I and U=A but leaves row k of L zeroed, so P*A != L*U, and pivots/rank underreport the matrix rank. This should handle zero-pivot columns without breaking the decomposition identity.

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