Basic Arithmetic

[:days4/projects/: Other SAGE Days 4 Project]

Test cases Read these as "an element of and an element of "

  1. \mathbf{Z}[x]/\mathbf{Z} \in \mathbf{Q}[x] (not Frac(\mathbf{Z}[x]))

  2. \mathbf{Q} + \mathbf{Z}[x] \in \mathbf{Q}[x] and \mathbf{Z}/5\mathbf{Z} + \mathbf{Z}[x] \in \mathbf{Z}/5\mathbf{Z}[x]

  3. \mathbf{Q} * \mathbf{Z}[x] \in \mathbf{Q}[x]

  4. \mathbf{Q} * \mathbf{Z}/5\mathbf{Z} error due to no morphism from all of \mathbf{Q} into \mathbf{Z}/5\mathbf{Z}.

  5. \mathbf{Z}[x] + \mathbf{Z}[y] error due to unknown relation between x and y and ambiguous order

  6. \mathbf{Q}[\zeta_m] + \mathbf{Q}[\zeta_n] \in \mathbf{Q}[\zeta_{lcm(m,n)}] as cyclotomic fields are created with an embedding into \bar{\mathbf{Q}}

  7. \mathbf{F}_{p^n} + \mathbf{F}_{p^m} works using Conway polynomials

  8. \mathbf{Z}[x] + \mathbf{Q}[y] same as 5 (minus the symmetry concerns)

Proposed model

One can view most desired natural coersions as functorial operations from some simpler base object. E.g.

Other