Question: What does the output of eliminate mean?

I was using "eliminate" to combine a set of equations removing some variables and getting a clearly wrong result. So I looked at the docs and the first example, and I find I don't understand its result either. Here is the example:

sol:=eliminate( {x^2+y^2-1=0, x^3-y^2*x+x*y-3=0}, x); # eliminate x from this set & leave one eqn of y

This returns:

which is the same as in the docs. My understanding is that the 1st set is the equation for x in terms of the other variables and the last set is the resultant eqn with x eliminated. Now I check by substitution of x in the original eqn:

simplify(subs(op(1,sol),x^3-y^2*x+x*y-3));

and I get

clearly not what was returned from eliminate; although its expression is in here. Note that I can replace "=0" in the equations by something else (a variable) and find the result of eliminate still disagrees with the substitution.

What am I missing??

Mac Dude




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