
5.1.159 uressolve
Syntax:
uressolve ( ideal_expression, int_expression, int_expression, int_expression )
Type:
 list
Purpose:
 computes all complex roots of a zerodimensional ideal.
Makes either use of the multipolynomial resultant of Macaulay (second argument
= 1), which works only for homogeneous ideals, or uses the sparse resultant
of Gelfand, Kapranov and Zelevinsky (second argument = 0).
The sparse resultant algorithm uses a mixed polyhedral subdivision of the
Minkowski sum of the Newton polytopes in order to construct the sparse
resultant matrix. Its determinant is a nonzero multiple of the sparse
resultant. The uresultant of B.\ L. van der Waerden and Laguerre's algorithm
are used to determine the complex roots.
The third argument defines the precision of the fractional part if the ground
field is the field of rational numbers, otherwise it will be ignored.
The fourth argument (can be 0, 1 or 2) gives the number of extra runs of
Laguerre's algorithm (with corrupted roots), leading to better results.
Note:
 If the ground field is the field of complex numbers, the elements of the list
are of type number, otherwise of type string.
See
laguerre;
mpresmat.
