Add unary function parsing and custom operator support

[psaegert]

Asked copilot to add support for unary and custom operators. The following is auto-generated. Still needs human review.
~ psaegert

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This pull request significantly expands the supported syntax of the expression tree generator to include custom operators/functions (with variable arity), improves the parsing and validation of expressions, and refactors the tree construction and rendering logic to handle arbitrary arity nodes. The UI and documentation are also updated to reflect these new capabilities.

Major parser and validation enhancements:

• Added support for custom operators/functions (e.g., #pi, #add(a,b), #clamp(x,a,b)) with arity detection and validation in infixToPostfix.js, including robust tokenization and validation logic for both standard and custom functions. [1] [2] [3]
• Improved error messaging and validation to inform users about supported functions and operators, and updated the error display to reflect new syntax options.

Expression tree construction and rendering:

• Refactored tree.js to support nodes with arbitrary arity (not just binary), including changes to the Node class, tree construction (constructTree), coordinate assignment, and drawing logic. This enables correct visualization of custom functions/operators with 0–3 arguments. [1] [2] [3]
• Updated the tree drawing code to dynamically size and position nodes and edges for n-ary trees, ensuring clarity for complex expressions. [1] [2]

UI and documentation updates:

• Expanded the list of sample expressions in canvas.js and updated the input placeholder in index.html to showcase new syntax. [1] [2]
• Updated the README.md with a detailed list of supported syntax and example expressions, providing clear guidance for users.

Other improvements:

• Removed forced lowercasing of input expressions to allow for case-sensitive custom operators/functions.

These changes collectively make the expression tree generator more flexible, powerful, and user-friendly, supporting a broader range of mathematical expressions and custom functions.

[Copilot]

Pull request overview

Expands the expression parser and tree renderer to support unary functions and custom #name(...) operators (variable arity), enabling visualization of n-ary expression trees in the existing canvas UI.

Changes:

• Added tokenization + validation for custom #... operators/functions (arity inferred from commas, max 3) and integrated them into infix→postfix conversion.
• Refactored tree construction/rendering from binary-only nodes to n-ary nodes with dynamic layout/drawing.
• Updated UI samples/placeholder and README to document and demonstrate the new syntax.

Reviewed changes

Copilot reviewed 5 out of 5 changed files in this pull request and generated 1 comment.

Show a summary per file

File	Description
infixToPostfix.js	Adds tokenizer, custom-function validation, and shunting-yard support for unary/custom function tokens.
tree.js	Updates Node model and algorithms (construction, layout, drawing) to support arbitrary arity.
canvas.js	Removes forced lowercasing and adds sample expressions + updated validation help text.
index.html	Updates input placeholder to show new syntax.
README.md	Documents supported syntax and provides examples for unary/custom operators.

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[Copilot]

tokenize() only skips literal spaces (current === ' '), but isValidExpression allows all whitespace via ALLOWED_CHARACTERS_REGEX (\s). As a result, tabs/newlines can pass the allowed-characters check but still fail tokenization. Consider skipping all whitespace in tokenize (e.g., /\s/), or tightening ALLOWED_CHARACTERS_REGEX to only allow spaces so validation is consistent.

Suggested change

	if (current === ' ') {
	if (/\s/.test(current)) {