### 5.1.74 laguerre

`Syntax:`
  `laguerre (` poly_expression `)`
  `laguerre (` poly_expression `,` int_expression `,` int_expression `)`
`Type:`
  list
`Purpose:`
  In characteristic 0:
  computes all complex roots of a univariate polynomial using Laguerre's algorithm. The second argument defines the precision of the fractional part if the ground field is the field of rational numbers, otherwise it will be ignored (default: 10). third argument (can be 0, 1 or 2) gives the number of extra runs for Laguerre's algorithm (with corrupted roots), leading to better results (default: 1).
  In characteristic p:
  computes all roots of a univariate polynomial using factorization
`Note:`
  If the ground field is the field of complex numbers, the elements of the list are of type number, otherwise of type string.
`Example:`

      ring rs1=0,(x,y),lp;
      poly f=15x5+x3+x2-10;
      laguerre(f);
      ==> [1]:
      ==>    0.8924637479
      ==> [2]:
      ==>    (-0.7392783383+I*0.5355190078)
      ==> [3]:
      ==>    (-0.7392783383-I*0.5355190078)
      ==> [4]:
      ==>    (0.2930464644-I*0.9003002396)
      ==> [5]:
      ==>    (0.2930464644+I*0.9003002396)
      laguerre(f,30,2);
      ==> [1]:
      ==>    0.892463747926447366650738925573
      ==> [2]:
      ==>    (-0.739278338347345779837700592458+I*0.535519007804239739420495882967)
      ==> [3]:
      ==>    (-0.739278338347345779837700592458-I*0.535519007804239739420495882967)
      ==> [4]:
      ==>    (0.293046464384122096512331129672-I*0.90030023962350314542842479521)
      ==> [5]:
      ==>    (0.293046464384122096512331129672+I*0.90030023962350314542842479521)

User manual for Singular version 4.4.1, 2025, generated by texi2html.