algorithm - Polynomial multiplication in M2(R)? -

i trying implement fft-based multiplication algorithm in m2(r). algorithm gets input 2 polynoms elements given matrices, , builds product polynom. however, though algorithm should work, looks identical version wrote earlier on regular number, doesn't. coefficients off little.

i have not found articles on roots of unity in m2(c), have found(on paper) choosing eps = ((cos(2pi/n) , sin(2pi/n)) , ( sin(2pi/n) , cos(2pi/n))), nice cycle.

is there wrong in approach?

here code:

struct fft {      polyc to, aux[17][2], res[17][2], ac, bc, resc, resd, arga, argb;      void fft(polyc v, var depth, var n, polyc to, matc step) {         if(n == 1) {             to[0] = v[0];         } else {              matc eps = matchelper.i2;              //we "split" poly in 2             for(var i=0; i<n; i++)                 aux[depth+1][i&1][i>>1] = v[i];              //we recursively apply fft components             fft(aux[depth+1][0], depth+1, n/2, res[depth+1][0], step*step);             fft(aux[depth+1][1], depth+1, n/2, res[depth+1][1], step*step);              //we compute result n roots             for(var i=0; i<n/2; i++) {                 to[i] = res[depth+1][0][i] + eps * res[depth+1][1][i];                 to[n/2+i] = res[depth+1][0][i] - eps * res[depth+1][1][i];                 eps = eps * step;             }         }     }      void fftmultiply(poly res, poly a, poly b, var n1, var n2) {          var m;         for(m = 1; m <= 2*n1 || m <= 2*n2; m <<= 1);          for(var i=0; i<n1; i++) arga[i] = a[i];         for(var i=n1; i<m; i++) arga[i] = matchelper.o2;          for(var i=0; i<n2; i++) argb[i] = b[i];         for(var i=n2; i<m; i++) argb[i] = matchelper.o2;          matc step( complex(cos(2*pi/m), 0) , complex(0, sin(2*pi/m)),                    complex(0, sin(2*pi/m)) , complex(cos(2*pi/m), 0) );          fft(arga, 0, m, ac, step);         fft(argb, 0, m, bc, step);          for(var i=0; i<m; i++) {             rezc[i] = ac[i] * bc[i];         }          step.b = -step.b;         step.c = -step.c;          fft(rezc, 0, m, rezd, step);          for(var i=0; i<m; i++) {             // divided m , copied every element of resd res modulo number         }     } }; 

you can not expect method work if coefficient matrices not commute matrix step. working correctly, use diagonal matrix corresponding multiplication scalar exp(i*2*pi/m).