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Optimize geometric-domain Lagrange evaluation - #116

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odraccir1 wants to merge 5 commits into
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Optimize geometric-domain Lagrange evaluation#116
odraccir1 wants to merge 5 commits into
masterfrom
ra/optimized_geometric_domain_lagrange

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@odraccir1

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Add reusable linear-time barycentric precomputation to geometric_sequence_domain.

For a domain of size (m):

Construction takes (O(m)) field operations and one field inversion.
Evaluating all Lagrange weights at one point takes (O(m)) operations and one inversion.
Evaluating at (k) points takes (O(mk)) after domain construction.
The PR also includes

batch_inverse which is needed for the algorithm.
calculation of vanishing polynomial in linear time using the recurrence relation from the Gaussian-Binomial theorem
Related to #113

@odraccir1 odraccir1 closed this Aug 6, 2026
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