proot - Maple Help

psqrt

square root of a polynomial

proot

nth root of a polynomial

 Calling Sequence psqrt(p) proot(p, n)

Parameters

 p - multivariate rational coefficients polynomial n - integer

Description

 • If p is a perfect square, psqrt returns a square root of p.  Otherwise it returns the name _NOSQRT.
 • If p is an nth power, proot(p, n) returns a nth root of p.  Otherwise proot returns the name _NOROOT.

Examples

 > $\mathrm{psqrt}\left(9\right)$
 ${3}$ (1)
 > $\mathrm{proot}\left(9,2\right)$
 ${3}$ (2)
 > $\mathrm{proot}\left(27,3\right)$
 ${3}$ (3)
 > $\mathrm{psqrt}\left({x}^{2}+2xy+{y}^{2}\right)$
 ${x}{+}{y}$ (4)
 > $\mathrm{psqrt}\left(9{x}^{2}+12xy+4{y}^{2}\right)$
 ${3}{}{x}{+}{2}{}{y}$ (5)
 > $\mathrm{proot}\left({x}^{3}+3{x}^{2}+3x+1,3\right)$
 ${x}{+}{1}$ (6)
 > $\mathrm{psqrt}\left({x}^{2}-{y}^{2}\right)$
 ${\mathrm{_NOSQRT}}$ (7)
 > $\mathrm{proot}\left(81{x}^{4}+108{x}^{3}+54{x}^{2}+12x+1,4\right)$
 ${3}{}{x}{+}{1}$ (8)
 > $\mathrm{psqrt}\left(x+y\right)$
 ${\mathrm{_NOSQRT}}$ (9)
 > $\mathrm{proot}\left(x+y,3\right)$
 ${\mathrm{_NOROOT}}$ (10)
 > $\mathrm{proot}\left({x}^{3}+{y}^{3},3\right)$
 ${\mathrm{_NOROOT}}$ (11)