Theorems · Definition · order theory

HahnEmbedding.Partial.evalCoeff

{K : Type u_1} →
  [inst : DivisionRing K] →
    [inst_1 : LinearOrder K] →
      [inst_2 : IsOrderedRing K] →
        [inst_3 : Archimedean K] →
          {M : Type u_2} →
            [inst_4 : AddCommGroup M] →
              [inst_5 : LinearOrder M] →
                [inst_6 : IsOrderedAddMonoid M] →
                  [inst_7 : Module K M] →
                    [inst_8 : IsOrderedModule K M] →
                      {R : Type u_3} →
                        [inst_9 : AddCommGroup R] →
                          [inst_10 : LinearOrder R] →
                            [inst_11 : Module K R] →
                              {seed : HahnEmbedding.Seed K M R} →
                                HahnEmbedding.Partial seed → M → FiniteArchimedeanClass M → R

Evaluate coefficients of the HahnSeries given an arbitrary input that's not necessarily in f's domain. The coefficient is picked from y that is "close enough" to x (their difference is in a higher ArchimedeanClass). If no such y exists (in other words, x is "isolated"), set the coefficient to 0. This doesn't immediately extend f's domain to the entire module in a consistent way. Such extension isn't necessarily linear.

Defined in

Mathlib.Algebra.Order.Module.HahnEmbedding

Cited by

8 results in Mathlib

Foundations

Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingLinearOrderIsOrderedRingArchimedeanAddCommGroupLinearOrderIsOrderedAddMonoidModuleIsOrderedModuleAddCommGroupLinearOrderModule