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Here is the output

sage: var('c,u,v',domain=RR);assume(v>0,u>0,c>u,c>v);
(c, u, v)
sage: assumptions()
[v > 0, u > 0, c > u, c > v]
sage: bool(c^2 - u*v >= 0)
False
sage: bool(c^2 - u^2 >= 0)
True
sage: bool(c^2 - v^2 >= 0)
True

I don't see how c^2 - v*u can not be larger than or equal to zero. Why does this happen? Is there a workaround?

Here is the output

sage: var('c,u,v',domain=RR);assume(v>0,u>0,c>u,c>v);
(c, u, v)
sage: assumptions()
[v > 0, u > 0, c > u, c > v]
sage: bool(c^2 - u*v >= 0)
False
sage: bool(c^2 - u^2 >= 0)
True
sage: bool(c^2 - v^2 >= 0)
True

I don't see how c^2 - v*u can not be larger than or equal to zero. Why does this happen? Is there a workaround?