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BUILT-IN MATHEMATICA SYMBOL
Root[f, k]
represents the exact k
root of the polynomial equation 
.
Root[{f1, f2, ...}, {k1, k2, ...}]
represents the last coordinate of the exact vector 
such that 
is the 
root of the polynomial equation 
.
Root[{f, x0}]
represents the exact root of the general equation 
near 
.
Root[{f, x0, n}]
represents n roots of the equation 
near 
.
Details and Options
- f must be a Function object such as
. - Root[f, k] is automatically reduced so that f has the smallest possible degree and smallest integer coefficients.
- The ordering used by Root[f, k] takes real roots to come before complex ones, and takes complex conjugate pairs of roots to be adjacent.
- The coefficients in the polynomial
can involve symbolic parameters. - For linear and quadratic polynomials
, Root[f, k] is automatically reduced to explicit rational or radical form. - For other polynomials, ToRadicals can be used to convert to explicit radicals.
- In Root[{f1, f2, ...}, {k1, k2, ...}],
must be a Function object with i formal parameters, and 
should be a polynomial in x of degree at least 
. - If for all i,
is a polynomial in 
with rational number coefficients, then RootReduce can be used to represent Root[{f1, f2, ...}, {k1, k2, ...}] in the Root[f, k] form. - Root[{f, x0}] represents an exact root of the general equation
, which can be transcendental. - In Root[{f, x0}],
must be an approximate real or complex number such that exactly one root of 
lies within the numerical region defined by its precision. - Root[{f, x0, n}] represents n roots, counting multiplicity, that lie within the numerical region defined by the precision of
. - N finds the approximate numerical value of a Root object.
- Operations such as Abs, Re, Round, and Less can be used on Root objects.
- Root[f, k] is treated as a numeric quantity if f contains no symbolic parameters.
- Root by default isolates the complex roots of a polynomial using validated numerical methods. SetOptions[Root, ExactRootIsolation->True] will make Root use symbolic methods that are usually much slower.
New in 3 | Last modified in 9
