Hi! On 24 Apr., 19:03, "Nathan O'Treally" <not.rea...@online.de> wrote: > What really would be nice, too, were a chart (or multple charts) > showing the dependencies, i.e. the "parent" relation(s), so one could > easily see potential coercion target domains, what domains are > "incompatible" etc.
I think I have once seen a graph of classes in Sage, and how they depend on / inherit from each other. But Parents are different from classes. They are "creative" in the linguistic sense. Hence, you can create arbitrarily complex parent structures: PolynomialRing(MatrixSpace(FractionField(PolynomialRing(ZZ,'x')), 2),'y') etc.So, it seems impossible to me to simply list all parents. However, one could try to depict something that happens in the background: There are so-called ConstructionFunctors. For example: sage: R.<x,y> = QQ[] sage: R.construction() (MPoly[x,y], Rational Field) sage: QQ.construction() (FractionField, Integer Ring) So, in order to construct R, one starts with the integers (which is "godgiven") and forms its fraction field. The result are the rationals. And to these, a constructor for a "Multivariate Polynomial Ring in x and y" is applied. These construction functors are also used in the coercion model: If you have parent structures X and Y and want to find a common parent, then you take the constructions of X and Y and try to merge it. So, if X is QQ and Y is ZZ['t'] then you want to merge the FractionField constructor and the "polynomial ring in t"-constructor, applied to ZZ in both cases. Now, the construction functors have a specific precedence. And that means: Sage will *first* apply the fraction field and then the polynomial ring constructor. The result is QQ['t'], the "pushout" of QQ and Z['t']. sage: pushout(QQ,ZZ['t']) Univariate Polynomial Ring in t over Rational Field It might be possible/nice to depict the currently available construction functors and the rules for them. I don't know how to do it, but I think it would indeed improve the understanding of coercion. Cheers, Simon -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
