I've been trying to use qepcad on the Sagecell and I have the following problem. If I run the following code:
var('a1, a2, a3, a4, d1, d2, d3, d4')
qf = qepcad_formula
F1 = qf.and_(
a1 >= 1,
a2 >= 1,
a3 >= 1,
a4 >= 1,
d1 >= 0,
d2 >= 0,
d3 >= 0,
d4 >= 0,
a1*d1 + a2*d2 + a3*d3 - a4*d4 == 0,
d1 + d2 < d3 + d4
)
qepcad(F1, solution = 'any-point')
Then I get a possible solution with {... 'd4' : 1}. However if I perform nearly the same computation, except with the condition d4 >= 0 changed to d4 >= 1, then I get an error:
var('a1, a2, a3, a4, d1, d2, d3, d4')
qf = qepcad_formula
F2 = qf.and_(
a1 >= 1,
a2 >= 1,
a3 >= 1,
a4 >= 1,
d1 >= 0,
d2 >= 0,
d3 >= 0,
d4 >= 1,
a1*d1 + a2*d2 + a3*d3 - a4*d4 == 0,
d1 + d2 < d3 + d4
)
qepcad(F2, solution = 'any-point')
which gives ... ValueError: input formula is false everywhere. However the solution to the first example is a valid solution to the second example so I'm not sure what's going on.
Any help would be greatly appreciated!
