What’s a lagrange base?
if , otherwise.
Arkworks has the formula to construct a lagrange base:
Evaluate all Lagrange polynomials at to get the lagrange coefficients. Define the following as
- : The coset we are in, with generator and offset
- : The size of the coset
- : The vanishing polynomial for .
- : A sequence of values, where , and
We then compute as
However, if in , both the numerator and denominator equal 0 when i corresponds to the value tau equals, and the coefficient is 0 everywhere else. We handle this case separately, and we can easily detect by checking if the vanishing poly is 0.
following this, for we have:
- and so on