Source-pinned research

Research proof index

Search theorem names, mathematical ideas, modules, topics, projects, and role-labelled researchers. Open a result for its complete indexed Lean declaration and source record.

This index contains 423 research declarations. Search 10,000 more complete Mathlib declarations.

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Project-declaredLean 4.31.0

Poly Fold nat Degree le

Polynomial.FoldingPolynomial.polyFold_natDegree_le

Plain-language statement

The degree bound of polyFold in terms of the degree of the original polynomial and k.

cryptographyproof systemscoding theory

Source project: ArkLib

Person-level attribution pending.

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Project-declaredLean 4.31.0

Poly Fold step

Polynomial.FoldingPolynomial.polyFold_step

Plain-language statement

Recursive case of polyFold: when 0 < k ≤ f.natDegree, polyFold f k r = C ((f %ₘ X^k).eval r) + X * polyFold (f /ₘ X^k) k r.

cryptographyproof systemscoding theory

Source project: ArkLib

Person-level attribution pending.

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Project-declaredLean 4.31.0

Indicator eq 1 of neg empty empty of pos nonempty

Polynomial.indicator_eq_1_of_neg_empty_empty_of_pos_nonempty

Plain-language statement

The indicator polynomial is a constant one polynomial if the set neg is empty while pos is not.

cryptographyproof systemscoding theory

Source project: ArkLib

Person-level attribution pending.

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Project-declaredLean 4.31.0

Indicator eq 1 on pos

Polynomial.indicator_eq_1_on_pos

Plain-language statement

Indicator evaluated on an element of pos is equal to 1.

cryptographyproof systemscoding theory

Source project: ArkLib

Person-level attribution pending.

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Project-declaredLean 4.31.0

Indicator ne zero of pos nonempty

Polynomial.indicator_ne_zero_of_pos_nonempty

Plain-language statement

If pos is non-empty then the indicator polynomial is the constant zero polynomial.

cryptographyproof systemscoding theory

Source project: ArkLib

Person-level attribution pending.

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Project-declaredLean 4.31.0

Split Nth of sum comp

Polynomial.splitNth_of_sum_comp

Plain-language statement

splitNth is the left inverse of the n-way recombination: splitting the polynomial ∑ j, X^j * (u j)(X^n) recovers u i for each component i.

cryptographyproof systemscoding theory

Source project: ArkLib

Person-level attribution pending.

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