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Will this do? A = Table[a[i,j],{i,3},{j,3}]; Then you can have p[x_, y_] := Sum[Sum[A[[i, j]]*x^i*x^j, {j, 1, 3}], {i, 1, 3}]; and you will have e.g.: Dimensions[A] {3,3} This is essentially what bill s proposes, but I am wrapping the symbolic a[i,j] in a matrix A.


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Here is one way to keep everything symbolic: p[x_, y_] := Total@Flatten@Table[a[i, j] x^i y^j, {j, 1, 3}, {i, 1, 3}] p[3, 4] 12 a[1, 1] + 48 a[1, 2] + 192 a[1, 3] + 36 a[2, 1] + 144 a[2, 2] + 576 a[2, 3] + 108 a[3, 1] + 432 a[3, 2] + 1728 a[3, 3] Of course, you can assign values to the a[i,j] in order to get numerical values for the polynomial.



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