In FriCAS
(1) -> x:Polynomial(Integer)
Type: Void
(2) -> x + 1/2
1
(2) x + -
2
Type: Polynomial(Fraction(Integer))
On 1 October 2015 at 15:28, 'Bill Hart' via sage-devel
<sage-devel@googlegroups.com> wrote:
>
>
> On 1 October 2015 at 20:23, William Stein <wst...@gmail.com> wrote:
> <SNIP>
>
>> By the way, look at how coercion "works" in Magma:
>>
>> $ magma
>> Magma V2.18-5 Thu Oct 1 2015 16:59:12 on compute3-us [Seed =
>> 629019987]
>> Type ? for help. Type <Ctrl>-D to quit.
>> > R<x> := PolynomialRing(IntegerRing());
>> > x + 1/2;
>>
>> >> x + 1/2;
>> ^
>> Runtime error in '+': Bad argument types
>> Argument types given: RngUPolElt[RngInt], FldRatElt
>
>
> We are call this "complex coercion" in our Nemo discussions
>
> [...as opposed to simple coercion:
>
> R, x = PolynomialRing(QQ, "x")
> K, a = NumberField(x^3 + 3x + 1,"a")
>
> a + 1/2 # simple coercion since the result lives in K
> ]
>
> It's definitely quite easy to add complex coercion in Nemo/Julia (via Julia
> generic catchall functions), but I'm resisting it quite obstinately for the
> time being.
>
> One reason is that it easily leads to functions that are not
> type-consistent. You can quite easily write functions whose output type
> depends on the values, rather than the types of the inputs. This completely
> screws with type inference and Jit compilation, though Julia does allow it.
>
> Since Nemo focuses on highly performant generics for the time being, I'm
> trying to avoid introducing complex coercions, at least until we have a very
> fast core. (Though naturally, mathematicians are keen to introduce this
> feature as soon as possible, since it is basically germane to any real
> mathematics.)
>
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