Multivariate Lagrange Interpolation Over Finite Field

Answer

f~(x1,x2)=15x15x25+4x15x24+7x15x23+1x15x22+4x15x2+6x14x25+11x14x24+9x14x22+2x14x2+9x12x25+10x12x24+10x12x23+8x12x22+9x12x2+4x1x25+12x1x24+12x1x23+13x1x22+4x1x2+15x25+11x24+11x23+2x22+15x2+10x13x25+6x13x24+16x13x23+15x13x22+4x13x2+9x12x25+1x12x24+1x12x23+8x12x22+15x12x2+13x1x24+11x1x23+12x1x22+15x1x2\tilde f(x_1,x_2) = 15x_1^5x_2^5 + 4x_1^5x_2^4 + 7x_1^5x_2^3 + 1x_1^5x_2^2 + 4x_1^5x_2 + 6x_1^4x_2^5 + 11x_1^4x_2^4 + 9x_1^4x_2^2 + 2x_1^4x_2 + 9x_1^2x_2^5 + 10x_1^2x_2^4 + 10x_1^2x_2^3 + 8x_1^2x_2^2 + 9x_1^2x_2 + 4x_1x_2^5 + 12x_1x_2^4 + 12x_1x_2^3 + 13x_1x_2^2 + 4x_1x_2 + 15x_2^5 + 11x_2^4 + 11x_2^3 + 2x_2^2 + 15x_2 + 10x_1^3x_2^5 + 6x_1^3x_2^4 + 16x_1^3x_2^3 + 15x_1^3x_2^2 + 4x_1^3x_2 + 9x_1^2x_2^5 + 1x_1^2x_2^4 + 1x_1^2x_2^3 + 8x_1^2x_2^2 + 15x_1^2x_2 + 13x_1x_2^4 + 11x_1x_2^3 + 12x_1x_2^2 + 15x_1x_2