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document {
Key => {(roots, RingElement), roots, [(roots,RingElement),Unique], [(roots,RingElement),Precision] },
Headline => "compute the roots of a polynomial",
Usage => "roots p",
Inputs => {
"p" => "a univariate polynomial over ZZ, QQ, RR or CC.",
Precision => { "the number of precision bits used to compute the roots.", "The default ", TO "precision", " is 53 bits for polynomials over ", TO "ZZ", " or ", TO "QQ", " and the same as the coefficient ring for ", TT "RR[x]", " or ", TT "CC[x]", "." },
Unique => Boolean => { "whether to return multiple roots one or multiple times." },
},
Outputs => {List => {"The roots of p each one represented as an elements of ", TO "CC", ".", }},
EXAMPLE {
"RR_100[x]",
"p = x^13 + 5*x^9 + 7*x^4 + x +1",
"roots p",
"o3#0",
},
EXAMPLE {
"ZZ[x]",
"p = x^13 + 5*x^9 + 7*x^4 + x +1",
"roots(p^2, Precision=>150, Unique=>true)",
"o7#0",
},
PARA {
"The roots are computed using ", TO "MPSolve", ".",
},
}
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