The “Modulus” feature of the IrreduciblePolynomialQ function doesn’t work as expected :
Try the provided sample :
IrreduciblePolynomialQ[{x^3+1, x^3+x+1}, Modulus → 2]
which is interpreted as :
IrreduciblePolynomialQ[{x^3+1, x^3+x+1}, abs(x)->2]
While the “Modulus” feature of the PolynomialGCD works fine.
(1) Don’t put “bug report” in a subject header. It is often the case that the behavior being reported is not in fact a bug. This sort of thing requires actual corroboration.
(2) In this particular example, the behavior reported is not a bug. It can’t be, for one thing, since no actual result is shown.
(3) I have no idea what is meant by the part “which is interpreted as…”. How does “abs(x)” enter into the matter?
(4) Here is the actual result (and this should have been included in the post).
IrreduciblePolynomialQ[{x^3 + 1, x^3 + x + 1}, Modulus -> 2]
(* Out[469]= {False, True} *)
(5) And here is corroboration that it is correct.
Factor[{x^3 + 1, x^3 + x + 1}, Modulus -> 2]
(* Out[470]= {(1 + x) (1 + x + x^2), 1 + x + x^3} *)
(6) Maybe I forgot to mention this, but it is really bad form to assume one has found a bug and put that into a subject heading.
Well said. I guess one of the moderators will change it… @Vitaliy Kaurov ?
I think the original post meant that Wolfram|Alpha doesn’t do anything useful with the input in question.
In general, not all Wolfram Language inputs will be understood and executed in Wolfram|Alpha. One may be better off using the Wolfram Cloud for actual computation.
Bug was debugged from title.