From dd167db661b125411770d2a1869f9b72e65f47f7 Mon Sep 17 00:00:00 2001
From: Matt McKay <mmcky@users.noreply.github.com>
Date: Fri, 16 Jan 2026 10:09:31 +1100
Subject: [PATCH] Fix SymPy overflow error using Rational for exact computation

The sympy code was using float values (A=2.0, alpha=0.3, delta=0.5) which
caused 'OverflowError: mpz too large to convert to float' during symbolic
computation.

This fix:
- Imports Rational from sympy
- Defines A_sym, alpha_sym, delta_sym as Rational values for exact computation
- Uses float() when printing s_star for display

This matches the fix in the production lecture-python-intro repository.
---
 lectures/solow.md | 13 +++++++++----
 1 file changed, 9 insertions(+), 4 deletions(-)

diff --git a/lectures/solow.md b/lectures/solow.md
index ee02b8b..4e8180e 100644
--- a/lectures/solow.md
+++ b/lectures/solow.md
@@ -510,13 +510,18 @@ plt.show()
 One can also try to solve this mathematically by differentiating $c^*(s)$ and solve for $\frac{d}{ds}c^*(s)=0$ using [sympy](https://www.sympy.org/en/index.html).
 
 ```{code-cell} ipython3
-from sympy import solve, Symbol
+from sympy import solve, Symbol, Rational
 ```
 
 ```{code-cell} ipython3
+# Use Rational for exact symbolic computation to avoid overflow
+A_sym = Rational(2)
+alpha_sym = Rational(3, 10)
+delta_sym = Rational(1, 2)
+
 s_symbol = Symbol('s', real=True)
-k = ((s_symbol * A) / delta)**(1/(1 - alpha))
-c = (1 - s_symbol) * A * k ** alpha
+k = ((s_symbol * A_sym) / delta_sym)**(1/(1 - alpha_sym))
+c = (1 - s_symbol) * A_sym * k ** alpha_sym
 ```
 
 Let's differentiate $c$ and solve using [sympy.solve](https://docs.sympy.org/latest/modules/solvers/solvers.html#sympy.solvers.solvers.solve)
@@ -524,7 +529,7 @@ Let's differentiate $c$ and solve using [sympy.solve](https://docs.sympy.org/lat
 ```{code-cell} ipython3
 # Solve using sympy
 s_star = solve(c.diff())[0]
-print(f"s_star = {s_star}")
+print(f"s_star = {float(s_star)}")
 ```
 
 Incidentally, the rate of savings which maximizes steady state level of per capita consumption is called the [Golden Rule savings rate](https://en.wikipedia.org/wiki/Golden_Rule_savings_rate).