Interp - Maple Help

Interp

inert polynomial interpolation function

 Calling Sequence Interp(x, y, v) Interp(x, y)

Parameters

 x - list or Vector of independent values, x[1],..x[n] y - list or Vector of dependent values, y[1],..y[n] v - variable name to be used in polynomial

Description

 • 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.

Examples

 > $\mathrm{Interp}\left(\left[2,5,6\right],\left[9,8,3\right],x\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathbf{mod}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}11$
 ${8}{}{{x}}^{{2}}{+}{6}{}{x}{+}{9}$ (1)
 > $\mathrm{alias}\left(\mathrm{\alpha }=\mathrm{RootOf}\left({x}^{4}+x+1\right)\right)$
 ${\mathrm{\alpha }}$ (2)
 > $a≔\mathrm{Interp}\left(\left[0,1,\mathrm{\alpha }\right],\left[\mathrm{\alpha },{\mathrm{\alpha }}^{2},{\mathrm{\alpha }}^{3}\right],x\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathbf{mod}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}2$
 ${a}{≔}{{\mathrm{\alpha }}}^{{2}}{}{x}{+}{\mathrm{\alpha }}{}{x}{+}{{x}}^{{2}}{+}{\mathrm{\alpha }}{+}{x}$ (3)