The ispoly function returns true if the input expression f is a polynomial of exactly degree n in the variable x, and false otherwise.  If successful, it assigns the remaining (optional) arguments the coefficients of degree 0, 1, ..., n.

Note, unlike the type function (with the linear, quadratic, cubic, or quartic option) in Maple, the ispoly function ensures that the coefficient of degree n is non-zero.

The second argument may be one of the keywords linear, quadratic, cubic, or quartic which can be used instead of integers 1, 2, 3, 4, respectively.

$f≔ax+b$

$f≔ax+b$

$\mathrm{ispoly}\left(f\,\mathrm{quadratic}\,x\right)$

$\mathrm{false}$

$\mathrm{ispoly}\left(f\,\mathrm{linear}\,x\,'\mathrm{a0}'\,'\mathrm{a1}'\right)$

$\mathrm{true}$

$\mathrm{a0},\mathrm{a1}$

$b,a$

$f≔a\left(a-1\right)x^2-a^2{x}^2+a{x}^2+a\left(a-1\right)x+ax$

$f≔a\left(a-1\right)x^2-a^2{x}^2+a{x}^2+a\left(a-1\right)x+ax$

$\mathrm{ispoly}\left(f\,\mathrm{quadratic}\,x\,'\mathrm{a0}'\,'\mathrm{a1}'\,'\mathrm{a2}'\right)$

$\mathrm{false}$

$\mathrm{ispoly}\left(f\,\mathrm{linear}\,x\,'\mathrm{a0}'\,'\mathrm{a1}'\right)$

$\mathrm{true}$

$\mathrm{a0},\mathrm{a1}$

$0,a\left(a-1\right)+a$

$f≔x^6-2x^3+3$

$f≔x^6-2x^3+3$

$\mathrm{ispoly}\left(f\,6\,x\,\mathrm{seq}\left(\mathrm{evaln}\left(a\left[i\right]\right)\,i=0..6\right)\right)$

$\mathrm{true}$

$\mathrm{seq}\left(a\left[i\right]\,i=0..6\right)$

$3,0,0,\mathrm{-2},0,0,1$