bdd-mathematical-verification

BDD Mathematical Verification Skill

Overview

This skill enables Behavior-Driven Development (BDD) workflows for mathematics, combining:

1. Gherkin Specifications: Plain-text scenario definitions
2. RSpec Implementation: Executable Ruby verification code
3. mathpix-gem Integration: Automatic LaTeX extraction from images
4. Pattern Matching: Syntax-tree validation for mathematical expressions
5. Iterative Discovery: Cucumber features guide formula exploration

Core Components

1. Feature Specifications (Gherkin)

Feature: Mathematical Formula Extraction and Verification

  Scenario: Extract LaTeX from mathematical image
    Given I have a mathematical image file "quadratic.png"
    When I extract LaTeX using Mathpix
    Then I should get a LaTeX formula matching the pattern "ax^2 + bx + c"
    And the formula should be registered as an artifact

  Scenario: Verify quadratic formula in standard form
    Given a quadratic formula "x^2 - 5*x + 6"
    When I verify it is in standard form
    Then the coefficients should be [1, -5, 6]
    And it should be factorable as "(x - 2)(x - 3)"

  Scenario Outline: Verify binomial expansion
    Given a binomial expression "<binomial>"
    When I expand it using binomial theorem
    Then the result should match "<expanded>"
    And all terms should be present with correct signs

    Examples:
      | binomial  | expanded                    |
      | (x + 1)^2 | x^2 + 2*x + 1              |
      | (a - b)^3 | a^3 - 3*a^2*b + 3*a*b^2 - b^3 |
      | (2*x + 3)^2 | 4*x^2 + 12*x + 9         |

2. RSpec Implementation Blocks

describe "Mathematical Formula Verification" do

  describe "Formula Extraction" do
    context "with valid mathematical image" do
      it "extracts LaTeX representation" do
        # Extraction step
      end

      it "normalizes notation to standard form" do
        # Normalization step
      end
    end

    context "with multi-page document" do
      it "extracts all formulas in order" do
        # Batch processing
      end
    end
  end

  describe "Formula Verification" do
    context "with polynomial expressions" do
      it "matches pattern against syntax tree" do
        # Pattern matching verification
      end

      it "verifies algebraic equivalence" do
        # Equivalence checking
      end
    end

    context "with nested/complex expressions" do
      it "validates form requirement" do
        # Form verification (expanded/factored/etc)
      end
    end
  end

  describe "Scenario-Driven Discovery" do
    context "with parameterized examples" do
      it "verifies all example variations" do
        # Parameterized testing
      end
    end
  end
end