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@teachinglab/omd

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omd

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# Simplification Utilities This module provides a collection of helper functions that are used throughout the simplification engine and rules. These utilities handle common tasks like creating nodes, manipulating expression trees, and formatting output. ## Core Functions #### `gcd(a, b)` - Calculates the greatest common divisor of two numbers. #### `createConstantNode(value, fontSize)` - Creates a new, fully initialized `omdConstantNode`. #### `createRationalNode(numerator, denominator, fontSize)` - Creates a new, fully initialized `omdRationalNode`, handling negative numerators and cases where the denominator is 1. #### `nodeToString(node)` - A robust function that converts any `omdNode` into a human-readable string, handling different node types and formatting them correctly. ## Expression Tree Manipulation #### `flattenSum(node, terms)` - A key utility that takes a nested tree of additions and subtractions (e.g., `a - (b + c)`) and flattens it into a linear list of terms, each with an associated sign. - **Parameters:** - `node`: The root of the expression to flatten. - `terms`: An array that will be populated with the term objects (`{ node, sign }`). #### `buildSumTree(terms, fontSize)` - The counterpart to `flattenSum`. It takes a list of terms (like the one produced by `flattenSum`) and reconstructs a valid, balanced `omdBinaryExpressionNode` tree from them. #### `_replaceNodeInTree(oldNode, newNode, currentRoot)` - An internal helper that safely replaces a node within the larger expression tree, handling parent-child connections and ensuring the tree remains valid. ## Polynomial and Monomial Helpers #### `expandPolynomialPower(terms, exponent, fontSize)` - Expands a polynomial raised to a power (e.g., `(a+b)^2`). It uses more specific helpers for common cases. #### `expandBinomialSquare(terms, fontSize)` - Expands `(a+b+...)^2`. #### `expandBinomialCube(terms, fontSize)` - Expands `(a+b)^3`. #### `expandBinomialFourth(terms, fontSize)` - Expands `(a+b)^4`. #### `multiplyTermArrays(terms1, terms2, fontSize)` - Performs polynomial multiplication by multiplying each term from the first array by each term from the second. ## Provenance Helpers #### `extractLeafNodes(node)` - Traverses an expression and returns an array of all its leaf nodes (constants and variables). This is used for detailed provenance tracking. #### `extractMonomialProvenance(termNode)` - A specialized function that separates the leaf nodes of a monomial into `coefficientNodes` and `variableNodes` for highly granular highlighting. #### `createMonomialWithGranularProvenance(...)` - Creates a monomial while assigning separate provenance chains to its coefficient and variable parts. ### See Also - [`omdSimplification`](./omdSimplification.md) - [`simplificationRules`](./simplificationRules.md)