Circle Polynomials

In STARK protocols, the computation trace is organized into columns and represented as polynomials. This section explains how Stwo represents and manipulates polynomials over the circle, covering both point-value (evaluations) and coefficient representations.

This section is organized as follows:

• Columns: How computation trace data is stored in columns, including both base field and secure field representations.
• Circle Evaluations and Polynomials: Point-value and coefficient representations of polynomials, their mathematical foundations, and conversion between forms.
• Secure Evaluations and Polynomials: Extension to secure field polynomials using the quartic extension QM31, with implementation details.