On 30 Jul 2016 12:46, "Jori Mäntysalo" <jori.mantys...@uta.fi> wrote: > > On Sat, 30 Jul 2016, John Cremona wrote: > >> Can we keep certify() for functions that return True/False, or possibly >> return None if ok and raise an error otherwise (as in an assert statement >> ); and only use certificate() for functions that return some sort of >> certificate? There are primality certificates, for example. > > > Ouh. Sounds very hard to remember two almost same keyword. > > What kind of certificates we have: > > - Dimension of poset and breadth of lattice are integers. There are always certificate that can we attach to those: for dimension it is realizers, i.e. a set of n linear orders, that actually show that the dimension is at most n; for breadth it is set of n elements showing that the breadth is at least n. > > - For planarity of grahp we can get "no"-certificate: a Kuratowski minor. Mathematically there exists also "yes"-certificate, i.e. the drawing on a plane. > > - If a lattice is dismantlable or not, there are both "yes" and "no" certificates: the dismantling order or a crown subposet. > > - If a lattice is relatively complemented or not, there is "no"-certificate: elements a,b,c so that b is the only element covering only a and covered by only c. There is no meaningful "yes"-certificate. > > - And for example is_prime can have only "yes"-certificate, i.e. two integers.
? A "no" certificate could be a single integer, a nontrivial divisor. A "yes" certificate is also possible though more complicated: see the Wikipedia entry for 'primality certificate '. Note also that Magma provides primality certificates (and remember Sage's Mission Statement! ) > > - If a finite lattice is not modular, we could have either by-definition "no"-certificate, i.e. elements not obeying modular law, or lattice-theoretic "no"-certificate, i.e. a pentangon sublattice. > > So, this can be a little complicated. > > -- > Jori Mäntysalo -- 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 https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
