Sagemath claims that some assumption are inconsistent

asked 2023-05-16 13:19:43 +0200

Cyrille gravatar image

Sagemath says that my assumption about $A$ and $B$ are inconsistent in the following code

var ('p θ A B ds')
bool((p - 1)^2*p*θ^2*A  - ((p - 1)*θ + 1)^2*(p - 1)*B<0)

but $(p - 1)^2>0$, $p>0$ $θ^2>0$ so $A<0$ make the first term negative. For the second, for the same type of reasons, we arrive to the fact that both hypothesis are necessary to arrive to a negative formula. So I do not understand the SageMath claim.

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For p=1 your expression is zero

achrzesz gravatar imageachrzesz ( 2023-05-16 13:57:00 +0200 )edit