It would be convenient to filter "solve" output based on "assume". Is
there an easy, generally applicable way to do this?
E.g.,
sage: var('a b t x y')
(a, b, t, x, y)
sage: assume(a>0,b>0,t>0)
sage: assumptions()
[a > 0, b > 0, t > 0]
sage: solve([y==(x^2-1)/2,x==a*t,y==b*t],x,y,t)
[[x == (b + sqrt(a^2 + b^2))/a, y == (b^2 + sqrt(a^2 + b^2)*b)/a^2, t
== (b + sqrt(a^2 + b^2))/a^2], [x == (b - sqrt(a^2 + b^2))/a, y ==
(b^2 - sqrt(a^2 + b^2)*b)/a^2, t == (b - sqrt(a^2 + b^2))/a^2]]
sage: bool((b - sqrt(a^2 + b^2))/a^2 > 0) # This shows the 2nd value
for t is not > 0
False
sage:
The second solution is not valid based on the assumptions. How best
to filter it? ... and in the general case?
Cheers,
Richard
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