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
• simplificationRules