antipalindromic

Definitions

1. Being equivalent to the object whose constituents or parameters are reversed in order and mapped by some involution, particularly the inversion operator of a quasigroup.
   not-comparable
2. Of a polynomial, being equivalent to the polynomial with reversed and additively inverted coefficients: ∑ᵢ₌₀ⁿa_ixⁱ is antipalindromic iff ∑ᵢ₌₀ⁿa_ixⁱ=∑ᵢ₌₀ⁿ-a_n-ixⁱ⟺a_i=-a_n-i.
   not-comparable
3. Of a natural number, with respect to base b, being equivalent to the natural number whose digits are reversed and subtracted from b-1: ∑ᵢ₌₀ⁿa_ibⁱ is antipalindromic iff ∑ᵢ₌₀ⁿa_ibⁱ=∑ᵢ₌₀ⁿ(b-1-a_n-i)bⁱ⟺a_i=b-1-a_n-i.
   not-comparable

Examples

“x²-1 is an antipalindromic polynomial.”

“1728#95;#123;10#125; is an antipalindromic number⟳ with respect⟳ to base⟳ 10.”

CEFR level