antipalindromic

Adjective

 * 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.
 * 2) Of a polynomial, being equivalent to the polynomial with reversed and additively inverted coefficients: $$\sum_{i=0}^n a_i x^i$$ is antipalindromic iff $$\sum_{i=0}^n a_i x^i = \sum_{i=0}^n -a_{n-i} x^i \Longleftrightarrow a_i = -a_{n-i}$$.
 * 3) Of a natural number, with respect to base $$b$$, being equivalent to the natural number whose digits are reversed and subtracted from $$b-1$$: $$\sum_{i=0}^n a_i b^i$$ is antipalindromic iff $$\sum_{i=0}^n a_i b^i = \sum_{i=0}^n \left( b - 1 - a_{n-i} \right) b^i \Longleftrightarrow a_i = b - 1 - a_{n-i}$$.
 * 1) Of a natural number, with respect to base $$b$$, being equivalent to the natural number whose digits are reversed and subtracted from $$b-1$$: $$\sum_{i=0}^n a_i b^i$$ is antipalindromic iff $$\sum_{i=0}^n a_i b^i = \sum_{i=0}^n \left( b - 1 - a_{n-i} \right) b^i \Longleftrightarrow a_i = b - 1 - a_{n-i}$$.