Source-pinned research
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polynomial_tanh_bounded
Mathematical statement
For a polynomial P, show that P (tanh x) is bounded on the real line
Source project: Physlib
Person-level attribution pending.
Polynomial.Bivariate.degreeX_le_degreeX_sub_degreeX
Project documentation
If a non-zero bivariate polynomial f divides a non-zero bivariate polynomial g, then all the coefficients of the quoetient are non-zero. -/ @[grind .] lemma coeff_ne_zero {f q : F[X][Y]} (hg : q * f ≠ 0) : q.coeff ≠ 0 := (ne_zero_iff_coeffs_ne_zero q).1 (quotient_nezero hg) /- If q * f ≠ 0, then the X-degree of q is bounded above by the differen...
Source project: ArkLib
Person-level attribution pending.
Polynomial.Bivariate.exists_max_index_totalDegree
Mathematical statement
There exists a maximal Y-index achieving totalDegree. Above it, total-degree contributions are strictly smaller or the coefficient vanishes.
Source project: ArkLib
Person-level attribution pending.
Polynomial.Bivariate.totalDegree_mul
Mathematical statement
The total degree of the product of two bivariate polynomials is the sum of their total degrees.
Source project: ArkLib
Person-level attribution pending.
Polynomial.folding_polynomial_eq_sum_splitNth
Mathematical statement
foldingPolynomial in terms of splitNth when q = X ^ n.
Source project: ArkLib
Person-level attribution pending.
Polynomial.FoldingPolynomial.eq_zero_of_folding_polynomial_eq_zero
Mathematical statement
If the folding polynomial is zero then so is the original polynomial.
Source project: ArkLib
Person-level attribution pending.