Question: Why are polynomials including constants not factorized?


I have trouble in using the function factors. For example, I expect

factor(Pi*(t^2+1), {I});

to output


but instead the result is


This problem does not appear if Pi gets replaced by a general symbol:

factor(pi*(t^2+1), {I});

produces (as I expect it should)


The problem seems to be tied to symbols representing constants, as for example replacing Pi by Catalan also results in no factorization being performed. It further seems to be tied to specifying a splitting field, because


results in


Is this behaviour intended? Probably the reason is that the polynomial does not have algebraic coefficients (as it includes Pi). Indeed,


produces the error message

Error, (in factor) expecting a polynomial over an algebraic number field

But why does this error then not appear for the call factor(Pi*(t^2-1))? If this would assume complex coefficients, it should factor using I. Considering coefficients in an algebraic number field, also the original call factor(Pi*(t^2+1), {I}); should raise an error!?



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