Equation Counting Bug Fix

Equation Counting Bug Fix

Problem

The count_equations_in_file() function in book-metrics.py was significantly over-counting LaTeX equations. For example, a signal processing textbook showed 2,421 equations when the actual count was much lower.

Root Causes

The original implementation had two major bugs:

1. Double Counting Display Math

The original regex patterns:

inline = len(re.findall(r'\$[^$]+\$', content))      # Inline math
display = len(re.findall(r'\$\$[^$]+\$\$', content))  # Display math

When a display math equation like $$x = a + b$$ appeared in the content:

• The display pattern correctly matched $$x = a + b$$ (counted as 1)
• The inline pattern then matched $x = a + b$ (the content between the first and second $)
• The inline pattern also matched text between consecutive equations like $\n\n### Title\n$

This caused display math to be counted multiple times.

2. False Positives from Dollar Amounts

The inline pattern \$[^$]+\$ matched dollar amounts like:

• $500
• $1,000
• $25 to $75

These are not LaTeX equations but were being counted as such.

Solution

The fixed implementation:

def count_equations_in_file(self, markdown_file: Path) -> int:
    """Count LaTeX equations in a single markdown file."""
    try:
        with open(markdown_file, 'r', encoding='utf-8') as f:
            content = f.read()

            # Count display math: $$...$$ (must come first)
            display_matches = re.findall(r'\$\$[^$]+?\$\$', content, re.DOTALL)
            display = len(display_matches)

            # Remove all display math blocks to avoid double-counting
            content_no_display = re.sub(r'\$\$[^$]+?\$\$', '', content, flags=re.DOTALL)

            # Count inline math: $...$
            # Negative lookahead (?!\d) ensures we don't match dollar amounts like $500
            inline_matches = re.findall(r'\$(?!\d)([^\$]+?)\$', content_no_display)
            inline = len(inline_matches)

            return inline + display
    except Exception as e:
        print(f"Warning: Could not read {markdown_file}: {e}")
        return 0

Key Improvements

1. Prevent Double Counting: First count display math $$...$$, then remove all display math blocks from the content before counting inline math
2. Exclude Dollar Amounts: Use negative lookahead (?!\d) to ensure we don't match expressions like $500 where a digit immediately follows the opening $
3. Non-greedy Matching: Use +? instead of + for better handling of adjacent equations

Test Results

Created test file equation-count-test.md with:

• 5 display math equations
• 7 inline math equations
• Multiple dollar amounts (false positives)
• Total: 12 actual equations

Original Function Results

• Counted: 24 equations
• Error: +12 (100% over-count)
• Status: ❌ FAILED

Fixed Function Results

• Counted: 12 equations
• Error: 0
• Status: ✅ PASSED

Impact

For a typical intelligent textbook:

• Before: Counts could be 2-3x higher than actual
• After: Accurate counts that reflect actual LaTeX equation usage

This fix ensures the book metrics accurately represent the mathematical content in educational textbooks.

Files Modified

• src/book-metrics/book-metrics.py - Fixed count_equations_in_file() method
• src/book-metrics/equation-count-test.md - Test file with 12 known equations
• src/book-metrics/test-equation-count.py - Original test script
• src/book-metrics/test-equation-count-fixed.py - Test comparing original vs fixed versions

Testing

To verify the fix works:

cd src/book-metrics
python test-equation-count-fixed.py

Expected output: ✅ Fixed version PASSED!