(%o180) [[x = 1/2,y = 1],[x = 9/8,y = 9/8],[x = 1,y = 1/2],[x = 0,y = 0]]
the system seems to have 4 (real) solutions.
`? algsys' says:
The method is as follows:
(1) First the equations are factored and split into subsystems.
(2) For each subsystem <S_i>, an equation <E> and a variable <x>
are selected. The variable is chosen to have lowest nonzero
degree. Then the resultant of <E> and <E_j> with respect to <x>
is computed for each of the remaining equations <E_j> in the
subsystem <S_i>. This yields a new subsystem <S_i'> in one fewer
variables, as <x> has been eliminated. The process now returns to
so `algsys' uses the resultant of the two polynomial with respect to x or y. i do this by hand:
(resultant with respect to x gives a similar result)
this gives 6 additional solution for y that can be found by sove. if i substitute such an y in the original polyomial the resulting polynomials in x have degree 4 and are also solvable. why don't `algsys' or `solve' don't find these solution?
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