De Computis et Scripturis & Problem of Points (1494)

Models Pacioli’s Venetian Giornale and Quaderno grande (Part I, Distinctio IX, Tractatus XI, fols. 198v–210v) in exact l. s. g. p. money of account, verifies the oriented incidence conservation law \(\mathbf{1}^T B = \mathbf{0}^T\) and skew-symmetric flow \(F^T = -F\), executes the Pro e Danno \(\to\) Cavedal \(\to\) Bilancio del libro closing cycle, and compares Pacioli’s 1494 balla and three-player balestrare stake divisions (fol. 197r–197v) against Pascal and Fermat’s 1654 combinatorial expectation.

"""Runnable CLI demonstration of Pacioli's Venetian *Quaderno* & *Problem of Points* (1494).

        Displays Rich tables verifying:
        1. Chronological Venetian *Giornale* entries (``Per // A``) in ``l. s. g. p.`` money of account,
        2. Pre-closing *Summa summarum* trial balance and skew-symmetric conservation ``F + F^T = 0``,
        3. Cap. 27 & Cap. 34 closing cycle (*Pro e Danno* -> *Cavedal* -> *Bilancio del libro*),
        4. Pacioli's 1494 *Problem of Points* (*balla* & *balestrare*, fol. 197r–197v) vs. Pascal–Fermat.
        """

        from __future__ import annotations

        import sys
        from pathlib import Path

        _SRC = Path(__file__).resolve().parents[1] / "src"
        if str(_SRC) not in sys.path:
            sys.path.insert(0, str(_SRC))

        import sympy as sp  # noqa: E402
        from rich.console import Console  # noqa: E402
        from rich.table import Table  # noqa: E402

        from geometor.pacioli.ledger_conservation import (  # noqa: E402
            build_venetian_merchant_quaderno_1493,
            compare_problem_of_points,
        )


        def run_demo() -> None:
            """Execute and print the Venetian *Quaderno* and *Problem of Points* showcase."""
            console = Console()
            console.rule("[bold gold1]Fra Luca Pacioli • Summa Dist. IX (1494) — De Computis et Scripturis")

            ledger = build_venetian_merchant_quaderno_1493()

            giornale_table = Table(title="Venetian Giornale (Nov. 1493, al modo de Vinegia, fol. 201v)")
            giornale_table.add_column("#", justify="right", style="cyan")
            giornale_table.add_column("Date", style="white")
            giornale_table.add_column("Per (Dare / Debtor)", style="green")
            giornale_table.add_column("A (Avere / Creditor)", style="yellow")
            giornale_table.add_column("l. s. g. p.", justify="right", style="bold white")

            for ent in ledger.entries:
                giornale_table.add_row(
                    str(ent.entry_no),
                    ent.date,
                    ent.debit_account,
                    ent.credit_account,
                    ent.amount.format_venetian(),
                )
            console.print(giornale_table)

            tb = ledger.trial_balance()
            mat_b = ledger.incidence_matrix()
            flow_f = ledger.skew_symmetric_flow_matrix()
            is_skew = flow_f + flow_f.T == sp.zeros(flow_f.rows, flow_f.cols)

            quaderno_table = Table(title="Pre-Closing Quaderno Grande — Summa Summarum (Ducati a oro)")
            quaderno_table.add_column("Carta", justify="right", style="cyan")
            quaderno_table.add_column("Account", style="white")
            quaderno_table.add_column("Dare", justify="right", style="green")
            quaderno_table.add_column("Avere", justify="right", style="yellow")
            quaderno_table.add_column("Net Dare", justify="right", style="magenta")

            for acc in tb.accounts:
                quaderno_table.add_row(
                    str(acc.folio),
                    acc.name,
                    str(acc.dare_ducati),
                    str(acc.avere_ducati),
                    str(acc.net_dare_ducati),
                )
            quaderno_table.add_section()
            quaderno_table.add_row(
                "Σ",
                "SUMMA SUMMARUM",
                f"[bold]{tb.summa_dare_ducati}[/bold]",
                f"[bold]{tb.summa_avere_ducati}[/bold]",
                f"[bold]{tb.net_conservation_sum}[/bold]",
            )
            console.print(quaderno_table)

            net_profit = ledger.close_to_bilancio()
            closed_tb = ledger.trial_balance()
            console.print(
                f"[bold]Conservation Laws Verified:[/bold] "
                f"Incidence B shape={mat_b.shape}, Fᵀ = -F is [green]{is_skew}[/green], "
                f"Cassa non-negative is [green]{tb.cassa_non_negative}[/green], "
                f"Net Profit to Cavedal = [yellow]{net_profit} ducati[/yellow], "
                f"Post-Bilancio Summa = {closed_tb.summa_dare_ducati} = {closed_tb.summa_avere_ducati}\n"
            )

            points_table = Table(
                title="Fol. 197r–197v: Problem of Points — Pacioli (1494) vs. Pascal–Fermat (1654)"
            )
            points_table.add_column("Contest (Target = 6, Stake = 10 ducats)", style="cyan")
            points_table.add_column("Pacioli 1494 Shares", style="yellow")
            points_table.add_column("Pascal–Fermat Shares", style="bold green")
            points_table.add_column("Discrepancy (PF - Pacioli)", style="magenta")

            for label, scores in [("Balla 2-player (5, 3)", (5, 3)), ("Balestrare 3-player (4, 3, 2)", (4, 3, 2))]:
                cmp = compare_problem_of_points(6, scores, 10)
                points_table.add_row(
                    label,
                    ", ".join(str(x) for x in cmp.pacioli_shares),
                    ", ".join(str(x) for x in cmp.pascal_fermat_shares),
                    ", ".join(str(x) for x in cmp.discrepancies),
                )
            console.print(points_table)


        if __name__ == "__main__":
            run_demo()