zlacker

Simple examples demonstrate the idea of the system, but I would be more impressed if they took some of the more complex published math papers out there and successfully rendered the notation from those with Penrose. That, to me, would better prove that it can handle the complexity that often comes with mathematical concepts.

>>ColanR+(OP)
All the examples are just "sets represented as circles". Quite basic.

>>andrep+0d
Maybe the end representation is quite basic but I still think it’s a feat of programming to take a bunch of constraints and turn it into a representation that dynamically satisfies those constraints.

>>reikon+1e
I think the criticism is more that the examples only show a very simple case. What you described is indeed very cool, if only rich examples showed it off better.

>>ColanR+(OP)
You should read the paper! http://penrose.ink/media/Penrose_SIGGRAPH2020.pdf

They include:

* Vector spaces

* Function diagrams

* Geometric illustrations

* Polygonal meshes

* Ray tracing diagrams

The linked article is pretty much fluff, but the SIGGRAPH paper has the real content.

>>wcrich+uf
Already did! Those are all basic examples of those various concepts. How about something that 'mixes metaphors', so to speak? Mathematicians are a creative bunch.

E.g., fuzzy sets. [1] One of the most-cited math papers ever. How could I use Penrose to represent a continuum of grades of membership between sets?

[1] https://sci-hub.st/10.1016/S0019-9958(65)90241-X

>>ColanR+(OP)
I think this is a reasonable criticism, I didn't see it addressed in the paper, but one place where it complex examples wouldn't matter is when writing material for basic introductory courses. There this would be really good: it's a way of quickly and accurately producing large numbers of diagrams, automatically adjusting for changes, without drawing things by hand, and there are probably enough students that this would help if it just reduced the barrier to producing maths diagrams.

>>andrep+0d
Figures 1, 7, 17, 18, 19, 22, 24, and 29 from the web page are not sets as circles. The paper contains additional counterexamples.