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D.8.2.1 laguerre_solve

Procedure from library solve.lib (see solve_lib).

Usage:
laguerre_solve(f [, m, l, n, s] ); f = polynomial,
m, l, n, s = integers (control parameters of the method)
m: precision of output in digits ( 4 <= m), if basering is not ring of complex numbers;
l: precision of internal computation in decimal digits ( l >=8 ) only if the basering is not complex or complex with smaller precision;
n: control of multiplicity of roots or of splitting of f into squarefree factors
n < 0, no split of f (good, if all roots are simple)
n >= 0, try to split
n = 0, return only different roots
n > 0, find all roots (with multiplicity)
s: s != 0, returns ERROR if | f(root) | > 0.1^m (when computing in the current ring)
( default: m, l, n, s = 8, 30, 1, 0 )

Assume:
f is a univariate polynomial;
basering has characteristic 0 and is either complex or without parameters.

Return:
list of (complex) roots of the polynomial f, depending on n. The entries of the result are of type
string: if the basering is not complex,
number: otherwise.

Note:
If printlevel >0: displays comments ( default = 0 ).
If s != 0 and if the procedure stops with ERROR, try a higher internal precision m.

Example:
 


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