The Interp function is a placeholder for polynomial interpolation. It is used in conjunction with mod and modp1.

The call Interp(x, y, v) mod p computes the polynomial of degree at most $n-1$ in the name v that interpolates the points (x[1],y[1]), (x[2], y[2]),..., (x[n], y[n]) mod p. The points must be from a finite field.

The call modp1(Interp(x, y), p) computes the interpolation polynomial in the modp1 representation where x and y must be lists.

All the independent values in x must be distinct.  In other words, a particular value modulo p must not occur more than once in x.

$\mathrm{Interp}\left(\left[2\,5\,6\right]\,\left[9\,8\,3\right]\,x\right)\mathbf{mod}11$

$8x^2+6x+9$

$\mathrm{alias}\left(\mathrm{\alpha }=\mathrm{RootOf}\left(x^4+x+1\right)\right)$

$\mathrm{\alpha }$

$a≔\mathrm{Interp}\left(\left[0\,1\,\mathrm{\alpha }\right]\,\left[\mathrm{\alpha }\,{\mathrm{\alpha }}^2\,{\mathrm{\alpha }}^3\right]\,x\right)\mathbf{mod}2$

$a≔{\mathrm{\alpha }}^{2}x+\mathrm{\alpha }x+x^2+\mathrm{\alpha }+x$