Resources

Video Presentation

Watch the visual explanation of berkeDet, meryemSign, and meryemPer:

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Benchmark & Verification Scripts

Everything in the paper is executable. Fixed seeds; correctness asserted in-script. All are single-file Python, ready for Google Colab (CPU runtime).

• verify.py — determinants vs LU (orders 1–10), structural lex-order and sign checks
• colab_sign_benchmark.py — isolated sign generation: meryemSign vs inversion count, merge parity, and Narayana + $O(1)$ flip
• colab_benchmark.py — serial end-to-end Leibniz determinant, four methods
• colab_parallel_benchmark.py — vectorized tree vs chains: permutations, signs, and the full exact determinant

Preprint Repositories

Quick Start (Python)

Copy this code, paste it into any Python environment (such as online-python.com), and run it. Full code with detailed comments is on the Algorithm page.

def meryemSign(n):
    b = [1]
    for e in range(1, n):
        c = b[:]
        for d in range(e):
            if d % 2 == 0:
                f = [-x for x in c]
            else:
                f = c[:]
            b.extend(f)
    return b

def meryemPer(n):
    a = [[1]]
    for b in range(2, n + 1):
        c = list(range(1, b + 1))
        d = []
        for f in c:
            g = [e for e in c if e != f]
            for h in a:
                j = [g[i - 1] for i in h]
                d.append([f] + j)
        a = d
    return a

def berkeDet(matrix):
    n = len(matrix)
    signs = meryemSign(n)
    perms = meryemPer(n)
    det = 0
    for sign, perm in zip(signs, perms):
        product = 1
        for i in range(n):
            product *= matrix[i][perm[i] - 1]
        det += sign * product
    return det

# Try it!
A = [[6, 1, 1],
     [4, -2, 5],
     [2, 8, 7]]

print("Determinant:", berkeDet(A))  # Output: -306

Citation

If you use berkeDet in your work, please cite:

Gülmen, B., Gülmen, M., & Gülmen, Ö. (2026).
berkeDet: A Dual Iterative Algorithm for Exact Determinant
Computation via Block Replication and Index Mapping (Version 3).
Zenodo. https://doi.org/10.5281/zenodo.21326563

Version History

• Version 3 (July 2026) — Complete rewrite. Isolated sign-generation benchmarks (~100× / 350–400× / 15–18×); formal parallel-complexity analysis (factorial tree, work–span model: span $O(n)$ vs chains' $\Omega(n!)$); vectorized NumPy implementations with benchmarks (6× over C itertools; $S_{12}$ signs in 0.19 s; vectorized determinant 15× over SJT); verification extended to order 10; the serial n=10 crossover vs SJT explained and resolved.
• Version 2 (April 2026) — Strengthened meryemPer analysis with explicit comparison to naive (suffix sort) and optimized (Narayana Pandita) lexicographic generators. Added sort-free column to comparison table. Updated title.
• Version 1 (February 2026) — Initial release.