I'm trying to use Sage to determine if a collection of (polynomial) inequalities has a solution or not. Ideally, I think I should use qepcad but I am having problems getting it to install. I thought I would try to see if standalone Sage would do the trick and began working with the solve function to get familiar with it. Already I'm running into very weird results. For example I run the following code:
x,y = var('x,y')
circ = x**2 + y**2 == 1
line = y == x
badIneq = y > 1
Now, if I execute
solve([circ, line], x)
it returns [] instead of the two solutions I expect. Furthermore, the code
assume(x,'real')
assume(y,'real')
solve([circ, badIneq], x)
is expected to return no solutions but instead it returns [[y - 1 > 0, x^2 + y^2 - 1 == 0]].
I must be doing something wrong but I can't figure out what it is. Thanks.
