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The Eval function is a placeholder for evaluation at a point. The expression a is evaluated at x=n (x1=n1, x2=n2, ... for the multivariate case).

To perform an evaluation of an expression or a polynomial over the rational numbers, use the eval command.

You can enter the command Eval using either the 1-D or 2-D calling sequence. For example, Eval(x^7 + x + 1, x=1) is equivalent to $\genfrac{}{}{0ex}{}{\left(x^7+x+1\right)}{\phantom{x=1}}|\genfrac{}{}{0ex}{}{\phantom{\left(x^7+x+1\right)}}{x=1}$.

The call Eval(a, x=n) mod p evaluates the polynomial a at x=n modulo p. The polynomial a must be a multivariate polynomial over a finite field. For this calling sequence, a can also be a Matrix or Vector of polynomials.

The call modp1(Eval(a, n), p) evaluates the polynomial a at x=n modulo p where a must be a univariate polynomial in the modp1 representation, with n an integer and p an integer > 1.

$\mathrm{Eval}\left(x^7+x+1\,x=1\right)$

$\genfrac{}{}{0ex}{}{\left(x^7+x+1\right)}{\phantom{x=1}}|\genfrac{}{}{0ex}{}{\phantom{\left(x^7+x+1\right)}}{x=1}$

$\mathrm{value}\left(\right)$

$3$

$\mathrm{Eval}\left(x^2+y\,\left\{x=3\,y=2\right\}\right)\mathbf{mod}5$

$1$

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

$a≔x^4+\mathrm{\alpha }{x}^2+1$

$a≔x^4+\mathrm{\alpha }{x}^2+1$

$\mathrm{Eval}\left(a\,x=\mathrm{\alpha }\right)\mathbf{mod}5$

${\mathrm{\alpha }}^3+4\mathrm{\alpha }$

$\mathrm{Eval}\left(\mathrm{int}\left(f\left(x\right)\,x\right)\,x=y\right)$

$\genfrac{}{}{0ex}{}{\int f\left(x\right)\ⅆx}{\phantom{x=y}}|\genfrac{}{}{0ex}{}{\phantom{\int f\left(x\right)\ⅆx}}{x=y}$

$\mathrm{Eval}\left(\mathrm{Matrix}\left(\left[\left[x^2+y\right]\right]\right)\,\left\{x=3\,y=2\right\}\right)\mathbf{mod}5$

$\left[\begin{array}{c}1\end{array}\right]$