¿How do I construct the real numbers from a basic magma?
I tried for hours and haven't found the way yet.
I invoked a Magmas() instance and got a kind of set containing "category of magmas", then I don't remember how, I added another element to it, but still doesn't resemble a magma.
I also tried creating a finite set A and a functor acting over it, but when I type
R1.<x> = A[]
I get
TypeError: '<' not supported between instances of 'str' and 'int'
So far so good, it seems that Sage is focused on specific interest areas, like graphs, symmetry groups and all that curricular stuff, but I don't find the way to open up to my means. It seems like it lacks enough modularity and that everything comes pre-constructed. I'm totally new in Sage and may be also in math. I'm still ignorant about the correct syntax of the language also. So please tell me what I'm doing wrong and if it is there any way to achieve what I want in Sage.
Magmas()does not return a single magma, but rather the category of all such. I don't see many examples of individual magmas created in the Sage library, but perhaps you could use https://doc.sagemath.org/html/en/refe... (source code https://github.com/sagemath/sage/blob...) as a template.Well that's something concrete, anyway, yet no succesor function, nor operations being defined.
Magmas need not have a successor function, just a product operation, at least as far as I understand it. The
productmethod defines the operation, although it is maybe not very interesting in this example.