Unwanted behavior cubic equations with assumptions

Questions
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1

Hello everyone. I am trying to solve a generic cubic equation with generic coefficients a,b,c,d and if I do so using Solve, I get the customary formula that I expect. However, if I set global assumptions:

$Assumptions = Element[a|b|c|d, Reals]

I get a definitely unwanted

ConditionalExpression[Root[d + c #1 + b #1^2 + a #1^3 &, 1], Or[
And[a > 0, c > 
   0, ((-2) a^(-2)) b^3 + ((9/a) b) ... ]]

you get the gist. This is just a toy equation, the one I’m actually trying to solve exhibits a similar phenomenon. Without assumptions it prints a solution, whereas if I add assumptions it keeps running without returning anything - I quit the kernel after 20 minutes. What am I doing wrong?

2

See Here: https://mathematica.stackexchange.com/questions/237193/behavior-of-solve-with-assumptions-changed-in-12-2

maybe helps

Regards

3

Thanks. It doesn’t, because by passing assumptions just inside the call to Solve, I still get useless conditional expressions.