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AIUI, you don't need to "compute" sqrt5 to high precision in order to use that closed form! Just "adjoin" it to Q and compute symbolically over Q(sqrt5).


Yes, and that symbolic computation is the same arithmetic as the original algorithm the author was complaining about.

Personally I like the version better where you explicitly work in terms of integers like a + or rational numbers like (a + )/c. https://observablehq.com/@jrus/zome-arithmetic very handy when working with the symmetry system of the icosahedron. https://observablehq.com/d/cae3fea57d7cf2d4


Nice. Thanks for that.


The computation over Q(sqrt(5)) is essentially identical to the matrix form.




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