[Merged by Bors] - feat(ring_theory/hahn_series): extend the domain of a Hahn series by an order_embedding
#7551
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…an `order_embedding` (#7551) Defines `hahn_series.emb_domain`, which extends the domain of a Hahn series by embedding it into a larger domain in an order-preserving way. Bundles `hahn_series.emb_domain` with additional properties as `emb_domain_linear_map`, `emb_domain_ring_hom`, and `emb_domain_alg_hom` under additional conditions. Defines the ring homomorphism `hahn_series.of_power_series` and the algebra homomorphism `hahn_series.of_power_series_alg`, which map power series to Hahn series over an ordered semiring using `hahn_series.emb_domain` with `nat.cast` as the embedding.
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Defines
hahn_series.emb_domain, which extends the domain of a Hahn series by embedding it into a larger domain in an order-preserving way.Bundles
hahn_series.emb_domainwith additional properties asemb_domain_linear_map,emb_domain_ring_hom, andemb_domain_alg_homunder additional conditions.Defines the ring homomorphism
hahn_series.of_power_seriesand the algebra homomorphismhahn_series.of_power_series_alg, which map power series to Hahn series over an ordered semiring usinghahn_series.emb_domainwithnat.castas the embedding.Later, I will prove that
hahn_series.of_power_seriesis the localization map from power series to Laurent series.