On 13.07.2015 19:33, Nathann Cohen wrote:
I agree with Simon, although finding a nice expression like sqrt(2)+3^(1/3)
can be very costly deppending on how the algebraic number was constructed.
Yepyep. As Simon said we cannot always express algebraic numbers in
such a nice way, though..... Well, if you want to build such an object
*in Sage* then you must describe your value somehow, and it is also
stored internally somewhere.. And I wonder how, and whether we can
base the representation on this internal version of the value :-)
Anyways we could have such an expression for the cases where it is evident
from the number construction.
-1
I definitely prefer a uniform output.
If you want a symbolic representation then convert the element to
one from SR (symbolic ring). This is basically what you are asking with
"where it is evident" anyway...
Of course you could add a function which tries to do exactly that
but in my opinion the default output should have a "uniform" look
for a given parent. That way you also realize (better) over what
parent you are working with currently.
Sidenote: Another useful representation is the minimal polynomial +
exact bounds (maybe interval field element?) for a root location.
I implemented a proof of concept of such a field once where all elements
were displayed as their minimal polynomial + bounds for the root
location. Arithmetic operations like addition or multiplication can
be defined for the root polynomial. What is harder are the root location
bounds (+ irreducible parts of the polynomial) which have to
be recalculated I suppose.
Best
Jonas
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