antipalindromic

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adjective

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.

“x²-1 is an antipalindromic polynomial.”

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Meanings

adjectiveantipalindromic (not comparable)
  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.
    1. not comparablemathematicsOf 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.

      x²-1 is an antipalindromic polynomial.

    2. not comparablemathematicsOf 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.

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

Cite this entry
APA

antipalindromic. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/antipalindromic

MLA

“antipalindromic.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/antipalindromic. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. “antipalindromic,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/antipalindromic.

Source: antipalindromic on Wiktionary, CC BY-SA 4.0.