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solveSystem -- solutions to a system of equalities

Synopsis

Description

i1 : R = QQ[x,y,z]

o1 = R

o1 : PolynomialRing
 
i2 : I = ideal(x+3*y^2-2*z, x^2-2*y-z, 3*x-4*y+5*z^2)

              2            2             2
o2 = ideal (3y  + x - 2z, x  - 2y - z, 5z  + 3x - 4y)

o2 : Ideal of R
 
i3 : M = solveSystem(I)

o3 = Tally{{-.286867+1.04128*ii, -.106152-.664903*ii, -.789675+.732385*ii} =>
           {-.286867-1.04128*ii, -.106152+.664903*ii, -.789675-.732385*ii} =>
           {-2.02148, 1.29357, 1.49925} => 1
           {.2419+1.1525*ii, -.675624+.694806*ii, .081518-.832036*ii} => 1
           {.2419-1.1525*ii, -.675624-.694806*ii, .081518+.832036*ii} => 1
           {0, 0, 0} => 1
           {1.05571+.941279*ii, .134991+.63069*ii, -.041468+.726052*ii} => 1
           {1.05571-.941279*ii, .134991-.63069*ii, -.041468-.726052*ii} => 1
     ------------------------------------------------------------------------
     1}
     1

o3 : Tally

Caveat

the procedure involves computation over inexact fields. If numerical errors occur, then the multiplicities of the solutions may be not reliable.

See also

Ways to use solveSystem :

For the programmer

The object solveSystem is a method function with options.