Some more math stuff

Author: jakep-allenai

olmocr/bench/katex/render.py

@@ -69,10 +69,15 @@ def render_equation(
     eq_hash = get_equation_hash(equation, bg_color, text_color, font_size)
     cache_dir = get_cache_dir()
     cache_file = cache_dir / f"{eq_hash}.png"
+    cache_error_file = cache_dir / f"{eq_hash}_error"
 
     # Check if the equation is already cached
-    if use_cache and cache_file.exists():
-        return Image.open(cache_file)
+    if use_cache:
+        if cache_error_file.exists():
+            return None
+            
+        if cache_file.exists():
+            return Image.open(cache_file)
 
     # We need to escape backslashes for JavaScript string
     escaped_equation = equation.replace("\\", "\\\\")
@@ -86,9 +91,6 @@ def render_equation(
     if not os.path.exists(katex_css_path) or not os.path.exists(katex_js_path):
         raise FileNotFoundError(f"KaTeX files not found. Please ensure katex.min.css and katex.min.js are in {script_dir}")
 
-    # Temporary file to save the screenshot
-    temp_path = str(cache_file)
-    
     with sync_playwright() as p:
         # Launch a headless browser
         browser = p.chromium.launch()
@@ -155,9 +157,7 @@ def render_equation(
 
         if has_error:
             print(f"Error rendering equation: '{equation}'")
-            # Clean up any partially created cache file
-            if os.path.exists(temp_path):
-                os.remove(temp_path)
+            cache_error_file.touch()
             browser.close()
             return None
 
@@ -168,13 +168,13 @@ def render_equation(
         container = page.query_selector("#equation-container")
 
         # Take the screenshot
-        container.screenshot(path=temp_path)
+        container.screenshot(path=str(cache_file))
 
         # Close the browser
         browser.close()
 
         # Return the image as a Pillow Image
-        return Image.open(temp_path)
+        return Image.open(cache_file)
 
 def main():
     # Example equation: Einstein's famous equation

olmocr/bench/sample_data/chatgpt/mathfuncs_1.md

@@ -0,0 +1,30 @@
+The 20 Most Important Mathematical Equations
+
+A journey through the most elegant and influential formulas in mathematics
+
+1. Euler's Identity
+
+\[ e^{i\pi} + 1 = 0 \]
+
+Connects five fundamental constants \((e, i, \pi, 1, 0)\), revealing the profound relationship between exponential functions and trigonometry.
+
+2. Pythagorean Theorem
+
+\[ a^2 + b^2 = c^2 \]
+
+In right triangles, the hypotenuse squared equals the sum of the squares of the other sides. Cornerstone of geometry with applications in navigation and architecture.
+
+3. The Fundamental Theorem of Calculus
+
+\[ \int_{a}^{b} f(x) \, dx = F(b) - F(a) \]
+
+Establishes that differentiation and integration are inverse operations. If \( F \) is an antiderivative of \( f \), the definite integral equals \( F(b) - F(a) \). Revolutionized mathematical problem-solving.
+
+4. Maxwell's Equations
+
+\[ \nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0} \]
+\[ \nabla \cdot \mathbf{B} = 0 \]
+\[ \nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t} \]
+\[ \nabla \times \mathbf{B} = \mu_0 \mathbf{J} + \mu_0 \varepsilon_0 \frac{\partial \mathbf{E}}{\partial t} \]
+
+Unified electricity and magnetism as manifestations of the same force. Describes electromagnetic field behavior, predicting waves traveling at light speed. Enabled technologies from radio to smartphones.

olmocr/bench/sample_data/chatgpt45/mathfuncs_1.md

@@ -0,0 +1,22 @@
+The 20 Most Important Mathematical Equations
+
+A journey through the most elegant and influential formulas in mathematics
+
+1. Euler's Identity
+\[ e^{i\pi} + 1 = 0 \]
+Connects five fundamental constants (e, i, π, 1, 0), revealing the profound relationship between exponential functions and trigonometry.
+
+2. Pythagorean Theorem
+\[ a^2 + b^2 = c^2 \]
+In right triangles, the hypotenuse squared equals the sum of the squares of the other sides. Cornerstone of geometry with applications in navigation and architecture.
+
+3. The Fundamental Theorem of Calculus
+\[ \int_{a}^{b} f(x)\,dx = F(b) - F(a) \]
+Establishes that differentiation and integration are inverse operations. If F is an antiderivative of f, the definite integral equals F(b) - F(a). Revolutionized mathematical problem-solving.
+
+4. Maxwell's Equations
+\[ \nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0} \]
+\[ \nabla \cdot \mathbf{B} = 0 \]
+\[ \nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t} \]
+\[ \nabla \times \mathbf{B} = \mu_0 \mathbf{J} + \mu_0 \varepsilon_0 \frac{\partial \mathbf{E}}{\partial t} \]
+Unified electricity and magnetism as manifestations of the same force. Describes electromagnetic field behavior, predicting waves traveling at light speed. Enabled technologies from radio to smartphones.

olmocr/bench/sample_data/gotocr/mathfuncs_1.md

@@ -0,0 +1,36 @@
+Made with
+The 20 Most Important Mathematical Equations
+A journey through the most elegant and influential formulas in mathematics
+1. Euler’s Identity
+2. Pythagorean Theorem
+e
+iττ + 1 = 0
+a2 + b2 = c2
+3. The Fundamental Theorem of Calculus
+4. Maxwell’s Equations
+Establishes that differentiation and integration are inverse
+operations. If F is an antiderivative of f, the definite integral
+equals F(b) - F(a). Revolutionized mathematical problem-
+solving.
+In right triangles, the hypotenuse squared equals the sum of
+the squares of the other sides. Cornerstone of geometry with
+applications in navigation and architecture.
+∇· E = ∂
+ε0
+∇· B = 0
+∇× E = −∂B
+∂t
+∇× B = µ0J + µ0ε0 ∂E
+∂t
+Unified electricity and magnetism as manifestations of the
+same force. Describes electromagnetic field behavior, predicting
+waves traveling at light speed. Enabled technologies from radio
+to smartphones.
+1. Euler’s Identity
+2. Pythagorean Theorem
+e
+iττ
++ 1 = 0
+a2 + b2 = c2
+3. The Fundamental THEorem of Calculus
+4. Maxwell’s Equations

olmocr/bench/sample_data/marker/mathfuncs_1.md

@@ -0,0 +1,17 @@
+## **The 20 Most Important Mathematical Equations**
+
+A journey through the most elegant and influential formulas in mathematics
+
+**1. Euler's Identity** Connects five fundamental constants (e, i, π, 1, 0), revealing the profound relationship between exponential functions and trigonometry. **2. Pythagorean Theorem** In right triangles, the hypotenuse squared equals the sum of the squares of the other sides. Cornerstone of geometry with applications in navigation and architecture. *e* + *iπ* 1 = 0 *a* + <sup>2</sup> *b* = <sup>2</sup> *c* 2
+
+## **3. The Fundamental Theorem of Calculus**
+
+## **4. Maxwell's Equations**
+
+$$\int\_{a}^{b} f(\mathbf{x}) \, d\mathbf{x} = F(b) - F(a)$$
+
+Establishes that differentiation and integration are inverse operations. If F is an antiderivative of f, the definite integral equals F(b) - F(a). Revolutionized mathematical problemsolving.
+
+∇ ⋅ **E** = *ε*0 *ρ* ∇ ⋅ **B** = 0 ∇ × **E** = − ∂*t* ∂**B** ∇ × **B** = *μ*0**J** + *μ*0*ε*<sup>0</sup> ∂*t* ∂**E**
+
+Unified electricity and magnetism as manifestations of the same force. Describes electromagnetic field behavior, predicting waves traveling at light speed. Enabled technologies from radio to smartphones.

olmocr/bench/sample_data/marker/mathfuncs_2.md

@@ -0,0 +1,17 @@
+## **The 20 Most Important Mathematical Equations**
+
+A journey through the most elegant and influential formulas in mathematics
+
+**1. Euler's Identity** Connects five fundamental constants (e, i, π, 1, 0), revealing the profound relationship between exponential functions and trigonometry. **2. Pythagorean Theorem** In right triangles, the hypotenuse squared equals the sum of the squares of the other sides. Cornerstone of geometry with applications in navigation and architecture. *e* + *iπ* 1 = 0 *a* + <sup>2</sup> *b* = <sup>2</sup> *c* 2
+
+## **3. The Fundamental Theorem of Calculus**
+
+## **4. Maxwell's Equations**
+
+$$\int\_{a}^{b} f(\mathbf{x}) \, d\mathbf{x} = F(b) - F(a)$$
+
+Establishes that differentiation and integration are inverse operations. If F is an antiderivative of f, the definite integral equals F(b) - F(a). Revolutionized mathematical problemsolving.
+
+∇ ⋅ **E** = *ε*0 *ρ* ∇ ⋅ **B** = 0 ∇ × **E** = − ∂*t* ∂**B** ∇ × **B** = *μ*0**J** + *μ*0*ε*<sup>0</sup> ∂*t* ∂**E**
+
+Unified electricity and magnetism as manifestations of the same force. Describes electromagnetic field behavior, predicting waves traveling at light speed. Enabled technologies from radio to smartphones.

olmocr/bench/sample_data/marker/mathfuncs_3.md

@@ -0,0 +1,17 @@
+## **The 20 Most Important Mathematical Equations**
+
+A journey through the most elegant and influential formulas in mathematics
+
+**1. Euler's Identity** Connects five fundamental constants (e, i, π, 1, 0), revealing the profound relationship between exponential functions and trigonometry. **2. Pythagorean Theorem** In right triangles, the hypotenuse squared equals the sum of the squares of the other sides. Cornerstone of geometry with applications in navigation and architecture. *e* + *iπ* 1 = 0 *a* + <sup>2</sup> *b* = <sup>2</sup> *c* 2
+
+## **3. The Fundamental Theorem of Calculus**
+
+## **4. Maxwell's Equations**
+
+$$\int\_{a}^{b} f(\mathbf{x}) \, d\mathbf{x} = F(b) - F(a)$$
+
+Establishes that differentiation and integration are inverse operations. If F is an antiderivative of f, the definite integral equals F(b) - F(a). Revolutionized mathematical problemsolving.
+
+∇ ⋅ **E** = *ε*0 *ρ* ∇ ⋅ **B** = 0 ∇ × **E** = − ∂*t* ∂**B** ∇ × **B** = *μ*0**J** + *μ*0*ε*<sup>0</sup> ∂*t* ∂**E**
+
+Unified electricity and magnetism as manifestations of the same force. Describes electromagnetic field behavior, predicting waves traveling at light speed. Enabled technologies from radio to smartphones.

olmocr/bench/sample_data/marker/mathfuncs_4.md

@@ -0,0 +1,17 @@
+## **The 20 Most Important Mathematical Equations**
+
+A journey through the most elegant and influential formulas in mathematics
+
+**1. Euler's Identity** Connects five fundamental constants (e, i, π, 1, 0), revealing the profound relationship between exponential functions and trigonometry. **2. Pythagorean Theorem** In right triangles, the hypotenuse squared equals the sum of the squares of the other sides. Cornerstone of geometry with applications in navigation and architecture. *e* + *iπ* 1 = 0 *a* + <sup>2</sup> *b* = <sup>2</sup> *c* 2
+
+## **3. The Fundamental Theorem of Calculus**
+
+## **4. Maxwell's Equations**
+
+$$\int\_{a}^{b} f(\mathbf{x}) \, d\mathbf{x} = F(b) - F(a)$$
+
+Establishes that differentiation and integration are inverse operations. If F is an antiderivative of f, the definite integral equals F(b) - F(a). Revolutionized mathematical problemsolving.
+
+∇ ⋅ **E** = *ε*0 *ρ* ∇ ⋅ **B** = 0 ∇ × **E** = − ∂*t* ∂**B** ∇ × **B** = *μ*0**J** + *μ*0*ε*<sup>0</sup> ∂*t* ∂**E**
+
+Unified electricity and magnetism as manifestations of the same force. Describes electromagnetic field behavior, predicting waves traveling at light speed. Enabled technologies from radio to smartphones.

olmocr/bench/sample_data/marker/mathfuncs_5.md

@@ -0,0 +1,17 @@
+## **The 20 Most Important Mathematical Equations**
+
+A journey through the most elegant and influential formulas in mathematics
+
+**1. Euler's Identity** Connects five fundamental constants (e, i, π, 1, 0), revealing the profound relationship between exponential functions and trigonometry. **2. Pythagorean Theorem** In right triangles, the hypotenuse squared equals the sum of the squares of the other sides. Cornerstone of geometry with applications in navigation and architecture. *e* + *iπ* 1 = 0 *a* + <sup>2</sup> *b* = <sup>2</sup> *c* 2
+
+## **3. The Fundamental Theorem of Calculus**
+
+## **4. Maxwell's Equations**
+
+$$\int\_{a}^{b} f(\mathbf{x}) \, d\mathbf{x} = F(b) - F(a)$$
+
+Establishes that differentiation and integration are inverse operations. If F is an antiderivative of f, the definite integral equals F(b) - F(a). Revolutionized mathematical problemsolving.
+
+∇ ⋅ **E** = *ε*0 *ρ* ∇ ⋅ **B** = 0 ∇ × **E** = − ∂*t* ∂**B** ∇ × **B** = *μ*0**J** + *μ*0*ε*<sup>0</sup> ∂*t* ∂**E**
+
+Unified electricity and magnetism as manifestations of the same force. Describes electromagnetic field behavior, predicting waves traveling at light speed. Enabled technologies from radio to smartphones.

olmocr/bench/sample_data/olmocr_base_temp0_1/mathfuncs_1.md

@@ -0,0 +1,19 @@
+# The 20 Most Important Mathematical Equations
+
+A journey through the most elegant and influential formulas in mathematics
+
+| 1. Euler's Identity | 2. Pythagorean Theorem |
+|--------------------|------------------------|
+| \( e^{i\pi} + 1 = 0 \) | \( a^2 + b^2 = c^2 \) |
+
+Connects five fundamental constants (e, i, π, 1, 0), revealing the profound relationship between exponential functions and trigonometry.
+
+In right triangles, the hypotenuse squared equals the sum of the squares of the other sides. Cornerstone of geometry with applications in navigation and architecture.
+
+| 3. The Fundamental Theorem of Calculus | 4. Maxwell's Equations |
+|----------------------------------------|------------------------|
+| \( \int_{a}^{b} f(x) \, dx = F(b) - F(a) \) | \( \nabla \cdot \mathbf{E} = \frac{Q}{\varepsilon_0} \) |
+
+Establishes that differentiation and integration are inverse operations. If \( F \) is an antiderivative of \( f \), the definite integral equals \( F(b) - F(a) \). Revolutionized mathematical problem-solving.
+
+Unified electricity and magnetism as manifestations of the same force. Describes electromagnetic field behavior, predicting waves traveling at light speed. Enabled technologies from radio to smartphones.

olmocr/bench/sample_data/olmocr_base_temp0_1/mathfuncs_2.md

@@ -0,0 +1,19 @@
+# The 20 Most Important Mathematical Equations
+
+A journey through the most elegant and influential formulas in mathematics
+
+| 1. Euler's Identity | 2. Pythagorean Theorem |
+|---------------------|------------------------|
+| \( e^{i\pi} + 1 = 0 \) | \( a^2 + b^2 = c^2 \) |
+
+Connects five fundamental constants (e, i, π, 1, 0), revealing the profound relationship between exponential functions and trigonometry.
+
+In right triangles, the hypotenuse squared equals the sum of the squares of the other sides. Cornerstone of geometry with applications in navigation and architecture.
+
+| 3. The Fundamental Theorem of Calculus | 4. Maxwell's Equations |
+|----------------------------------------|------------------------|
+| \[ \int_{a}^{b} f(x) \, dx = F(b) - F(a) \] | \[ \nabla \cdot \mathbf{E} = \frac{Q}{\varepsilon_0} \] |
+
+Establishes that differentiation and integration are inverse operations. If \( F \) is an antiderivative of \( f \), the definite integral equals \( F(b) - F(a) \). Revolutionized mathematical problem-solving.
+
+Unified electricity and magnetism as manifestations of the same force. Describes electromagnetic field behavior, predicting waves traveling at light speed. Enabled technologies from radio to smartphones.

olmocr/bench/sample_data/olmocr_base_temp0_1/mathfuncs_3.md

@@ -0,0 +1,19 @@
+# The 20 Most Important Mathematical Equations
+
+A journey through the most elegant and influential formulas in mathematics
+
+| 1. Euler's Identity | 2. Pythagorean Theorem |
+|--------------------|------------------------|
+| \( e^{i\pi} + 1 = 0 \) | \( a^2 + b^2 = c^2 \) |
+
+Connects five fundamental constants (e, i, π, 1, 0), revealing the profound relationship between exponential functions and trigonometry.
+
+In right triangles, the hypotenuse squared equals the sum of the squares of the other sides. Cornerstone of geometry with applications in navigation and architecture.
+
+| 3. The Fundamental Theorem of Calculus | 4. Maxwell's Equations |
+|----------------------------------------|------------------------|
+| \( \int_{a}^{b} f(x) \, dx = F(b) - F(a) \) | \( \nabla \cdot \mathbf{E} = \frac{Q}{\varepsilon_0} \) |
+
+Establishes that differentiation and integration are inverse operations. If \( F \) is an antiderivative of \( f \), the definite integral equals \( F(b) - F(a) \). Revolutionized mathematical problem-solving.
+
+Unified electricity and magnetism as manifestations of the same force. Describes electromagnetic field behavior, predicting waves traveling at light speed. Enabled technologies from radio to smartphones.

olmocr/bench/sample_data/olmocr_base_temp0_1/mathfuncs_4.md

@@ -0,0 +1,19 @@
+# The 20 Most Important Mathematical Equations
+
+A journey through the most elegant and influential formulas in mathematics
+
+| 1. Euler's Identity | 2. Pythagorean Theorem |
+|--------------------|------------------------|
+| \( e^{i\pi} + 1 = 0 \) | \( a^2 + b^2 = c^2 \) |
+
+Connects five fundamental constants (e, i, π, 1, 0), revealing the profound relationship between exponential functions and trigonometry.
+
+In right triangles, the hypotenuse squared equals the sum of the squares of the other sides. Cornerstone of geometry with applications in navigation and architecture.
+
+| 3. The Fundamental Theorem of Calculus | 4. Maxwell's Equations |
+|----------------------------------------|------------------------|
+| \( \int_{a}^{b} f(x) \, dx = F(b) - F(a) \) | \( \nabla \cdot \mathbf{E} = \frac{Q}{\varepsilon_0} \) |
+
+Establishes that differentiation and integration are inverse operations. If F is an antiderivative of f, the definite integral equals F(b) - F(a). Revolutionized mathematical problem-solving.
+
+Unified electricity and magnetism as manifestations of the same force. Describes electromagnetic field behavior, predicting waves traveling at light speed. Enabled technologies from radio to smartphones.

olmocr/bench/sample_data/olmocr_base_temp0_1/mathfuncs_5.md

@@ -0,0 +1,19 @@
+# The 20 Most Important Mathematical Equations
+
+A journey through the most elegant and influential formulas in mathematics
+
+| 1. Euler's Identity | 2. Pythagorean Theorem |
+|--------------------|------------------------|
+| \( e^{i\pi} + 1 = 0 \) | \( a^2 + b^2 = c^2 \) |
+
+Connects five fundamental constants (e, i, π, 1, 0), revealing the profound relationship between exponential functions and trigonometry.
+
+In right triangles, the hypotenuse squared equals the sum of the squares of the other sides. Cornerstone of geometry with applications in navigation and architecture.
+
+| 3. The Fundamental Theorem of Calculus | 4. Maxwell's Equations |
+|----------------------------------------|------------------------|
+| \( \int_{a}^{b} f(x) \, dx = F(b) - F(a) \) | \( \nabla \cdot \mathbf{E} = \frac{Q}{\varepsilon_0} \) |
+
+Establishes that differentiation and integration are inverse operations. If \( F \) is an antiderivative of \( f \), the definite integral equals \( F(b) - F(a) \). Revolutionized mathematical problem-solving.
+
+Unified electricity and magnetism as manifestations of the same force. Describes electromagnetic field behavior, predicting waves traveling at light speed. Enabled technologies from radio to smartphones.

olmocr/bench/sample_data/olmocr_base_temp0_8/mathfuncs_1.md

@@ -0,0 +1,42 @@
+# The 20 Most Important Mathematical Equations
+
+A journey through the most elegant and influential formulas in mathematics
+
+---
+
+**1. Euler's Identity**
+
+\[ e^{i\pi} + 1 = 0 \]
+
+Connects five fundamental constants (\(e, i, \pi, 1, 0\)), revealing the profound relationship between exponential functions and trigonometry.
+
+---
+
+**2. Pythagorean Theorem**
+
+\[ a^2 + b^2 = c^2 \]
+
+In right triangles, the hypotenuse squared equals the sum of the squares of the other sides. Cornerstone of geometry with applications in navigation and architecture.
+
+---
+
+**3. The Fundamental Theorem of Calculus**
+
+\[ \int_a^b f(x) \, dx = F(b) - F(a) \]
+
+Establishes that differentiation and integration are inverse operations. If \(F\) is an antiderivative of \(f\), the definite integral equals \(F(b) - F(a)\). Revolutionized mathematical problem-solving.
+
+---
+
+**4. Maxwell's Equations**
+
+\[
+\begin{align*}
+\nabla \cdot \mathbf{E} &= \frac{Q}{\varepsilon_0} \\
+\nabla \cdot \mathbf{B} &= 0 \\
+\n\nabla \times \mathbf{E} &= -\frac{\partial \mathbf{B}}{\partial t} \\
+\n\nabla \times \mathbf{B} &= \mu_0 \mathbf{J} + \mu_0 \varepsilon_0 \frac{\partial \mathbf{E}}{\partial t}
+\end{align*}
+\]
+
+Unified electricity and magnetism as manifestations of the same force. Describes electromagnetic field behavior, predicting waves traveling at light speed. Enabled technologies from radio to smartphones.