"""Executable examples for Chapters 9 and 10 (SymPy and Z3).

Run from the repository root with the locked environment:

    uv run python content/examples/math/tool-chapters/ch09_10_sympy_z3_demo.py

Illustrative teaching script. It is not an evidence-bundle producer; the
engine's recorded results come from src/math_engine/adapters/.
"""

import sympy
import z3
from sympy import expand, factor, simplify, sqrt, symbols, together

print("sympy", sympy.__version__, "z3", z3.get_version_string())

# --- Chapter 9: SymPy -------------------------------------------------------
v = symbols("v", real=True)
gamma = 1 / sqrt(1 - v**2)
residual = simplify(together(gamma**2 * (1 - v**2) - 1))
print("ch9 gamma residual (symbolic v):", residual)
print("ch9 same residual at v=2 (outside |v|<1):", simplify(residual.subs(v, 2)))
print("ch9 gamma^2(1-v^2)-1 at v=2 directly:",
      simplify((gamma**2 * (1 - v**2) - 1).subs(v, 2)))

t, x, g = symbols("t x gamma", real=True)
boost = expand((g * (t - v * x)) ** 2 - (g * (x - v * t)) ** 2 - (t**2 - x**2))
print("ch9 algebraic residual, factored:", factor(boost))
tt, xx, vv = symbols("t x v", real=True)
print("ch9 shear residual, factored:", factor(tt**2 - (xx + vv * tt) ** 2 - (tt**2 - xx**2)))

# --- Chapter 10: Z3 ---------------------------------------------------------
T, X, V, G = z3.Reals("t x v gamma")
goal_negation = (G * (T - V * X)) ** 2 - (G * (X - V * T)) ** 2 != T * T - X * X

with_hyp = z3.Solver()
with_hyp.add(G * G * (1 - V * V) == 1)
with_hyp.add(goal_negation)
print("ch10 negation WITH gamma hypothesis:", with_hyp.check())

no_hyp = z3.Solver()
no_hyp.add(goal_negation)
print("ch10 negation WITHOUT gamma hypothesis:", no_hyp.check())
print("ch10 model:", no_hyp.model())