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5.1.131 uressolve
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Syntax: uressolve (ideal_expression,int_expression,int_expression,int_expression)-
Type: list
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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 Minkowsky sum of the Newton polytopes in order to construct the sparse resultant matrix. Its determinant is a nonzero multiple of the sparse resultant. The u-resultant 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.
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Example: ring rsc=(real,20,I),(x,y),lp; ideal i=(2+3*I)*x2+(0.35+I*45.0e-2)*y2-8,x2+xy+(42.7)*y2; list l=uressolve(i,0,0,2); l[1]; → [1]: → (-1.315392899374542198+I*0.70468233142752928117) → [2]: → (0.12292646536251281054+I*0.19245727404407015049) subst(subst(i[1],x,l[1][1]),y,l[1][2]); → 0