[CAES] (x^4-4*x^3+2*x^2+4*x+4) Exact factorization of Quartic Polynomial

[Anders]

To factorize generally ALL QUARTIC polynomial exactly you would need to solve the roots exactly by for instance using the formula posted on Wiki here:
https://upload.wikimedia.org/wikipedia/c...ormula.svg

Then Prime need to simplify/reduce until the roots cannot be simplified any more and lastly put it back in a factorized form. To implement this internal simplification of this large formula (for the general case) in CAS would likely be very challenging and likely also be very resource intensive and time consuming when executed. For wolfram running in the cloud using many magnitudes more CPU and memory it does not matter. However, not even Wolfram resolves generally for all polynomials (just some special classes of polynomials). So in the trade off when choosing what to implement on a constrained handheld platform, competing with other function candidates for the same flash memory space, CPU time (and man hour implementation time), general exact QUARTIC polynomial factorization would be difficult to justify.

But, for the sake of argument, let's say we discover and implement some low resource efficient great simplification algorithm. Just look at the exact general formula, using the link above. Imagine if you have a polynomial with some poorly correlated factors a, b, c, d, e, (not hard to construct - just make sure the inner roots do not come out nicely), resulting in some really complicated irreducible roots, and what this formula would look like - it would be totally incomprehensible for humans and totally useless in practical work.

(For the special cases when you have rational roots the factor() function works, but it is a very special case. You can implement many simple special cases that can be made to produce simpler outputs but they are not general.)