Multivariate Lagrange Interpolation Over Finite Field

Answer

f(x1,x2)=15x2+2x1x2+2x22+8x1x22+7x12x2+11x23+6x1x23+16x12x22+4x13x2+11x24+8x1x24+11x12x23+15x13x22+2x14x2+15x25+4x1x25+11x12x24+16x13x23+9x14x22+4x15x2+x12x25+6x13x24+x15x22+10x13x25+11x14x24+7x15x23+6x14x25+4x15x24+15x15x25f(x_1,x_2) = 15x_{2} + 2x_{1}x_{2} + 2x_{2}^{2} + 8x_{1}x_{2}^{2} + 7x_{1}^{2}x_{2} + 11x_{2}^{3} + 6x_{1}x_{2}^{3} + 16x_{1}^{2}x_{2}^{2} + 4x_{1}^{3}x_{2} + 11x_{2}^{4} + 8x_{1}x_{2}^{4} + 11x_{1}^{2}x_{2}^{3} + 15x_{1}^{3}x_{2}^{2} + 2x_{1}^{4}x_{2} + 15x_{2}^{5} + 4x_{1}x_{2}^{5} + 11x_{1}^{2}x_{2}^{4} + 16x_{1}^{3}x_{2}^{3} + 9x_{1}^{4}x_{2}^{2} + 4x_{1}^{5}x_{2} + x_{1}^{2}x_{2}^{5} + 6x_{1}^{3}x_{2}^{4} + x_{1}^{5}x_{2}^{2} + 10x_{1}^{3}x_{2}^{5} + 11x_{1}^{4}x_{2}^{4} + 7x_{1}^{5}x_{2}^{3} + 6x_{1}^{4}x_{2}^{5} + 4x_{1}^{5}x_{2}^{4} + 15x_{1}^{5}x_{2}^{5}

Evaluation

f(f())== 00