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Description

This PR adds a comprehensive mathematical proof for two key optimization points in the Lagrange interpolator implementation:

  1. The formula v_inv[0] = m*h^{m-1} - Proven by analyzing the product representation and leveraging properties of multiplicative groups
  2. The recurrence relation v_inv[i] = g^{-1} * v_inv[i-1] - Derived through algebraic manipulation and group theory properties

These optimizations significantly reduce the computational cost of Lagrange interpolation by avoiding redundant calculations and leveraging mathematical properties of finite fields.

closes: #XXXX


Before we can merge this PR, please make sure that all the following items have been
checked off. If any of the checklist items are not applicable, please leave them but
write a little note why.

  • Targeted PR against correct branch (master)
  • Linked to Github issue with discussion and accepted design OR have an explanation in the PR that describes this work.
  • Wrote unit tests (N/A - Documentation

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