Hi,
For the following ideal, dimension() returns 0,
{{{
R.<s0,s1>=QQbar[]
I=R.ideal([ s0 + 1, s0*s1 + s0 + s1 + 1, (-2)*s0 + 1, (-10)*s1 + 5, 5*s0^2
+ 10*s0*s1 ])
I.dimension()
}}}
but its variety is empty.
Also for any other ring, dimension() returns -1 for this ideal. Is this a
bug with dimension()? The documentation for dimension() doesn't seem to
mention the -1 case.
It provides the following example,
{{{
R.<x,y> = PolynomialRing(GF(2147483659),order='lex')
I = R.ideal([x*y,x*y+1])
I.dimension()
}}}
which yields dimension 0 for the ideal, yet the corresponding variety is
empty.
What is the expected behavior for dimension()? When the variety of the
ideal in question has no points is dimension() always supposed to return -1?
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