I once collected some amusing examples from Pari, Sage and Magma related to their different concepts of coercion. It can lead to all sorts of mathematical stupidity.
I concluded that trying to model maths this way is like trying to put a carpet down in a room with a wonky floor. You can locally get it quite flat, but once you get near a region that no one has flattened it's as crumpled as a Chinese Shar-pei. After a little more research I discovered that maths papers weren't any better. Bill. On Thursday, 1 October 2015 21:35:37 UTC+2, Bill Page wrote: > > 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-...@googlegroups.com <javascript:>> wrote: > > > > > > On 1 October 2015 at 20:23, William Stein <wst...@gmail.com > <javascript:>> 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.) > > > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
