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Let $d$ be the cyclotomic derivation of $k[X]$, and let $\\Delta$ be the factorisable derivation of $k[Y]$ associated with $d$, that is, $d(x_j)=x_{j+1}$ and $\\Delta(y_j)=y_j(y_{j+1}-y_j)$ for all $j\\in\\mathbb Z_n$. We describe polynomial constants and rational constants of these derivations. We prove, among others, that the field of constants of $d$ is a field of rational functions over $k$ in $n-\\f(n)$ var"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1301.6251","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-01-26T13:27:44Z","cross_cats_sorted":[],"title_canon_sha256":"3ed66022cce39bb98ea377f87fe3381b9bf553e739b694c1a801448150f08bb2","abstract_canon_sha256":"b220abbef5114323b0db0bb3dfd89ed0554afcedd5bc925fb5d9eac302faaca5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:58.241140Z","signature_b64":"HLdFSeDzx7vMP6RMEitP8vzh9rEsUTAeb+2GehLB9svYQ6GX7iZUiOugmJhPhtcs55KBXEcR+mDWU7b99S7EBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f2b6add2b95a08745e8a07aeba71a1d7bea99ae48249b4e8f8a3b8214290eae","last_reissued_at":"2026-05-18T03:10:58.240332Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:58.240332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Constants of cyclotomic derivations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Andrzej Nowicki, Jean Moulin Ollagnier","submitted_at":"2013-01-26T13:27:44Z","abstract_excerpt":"Let $k[X]=k[x_0,...,x_{n-1}]$ and $k[Y]=k[y_0,...,y_{n-1}]$ be the polynomial rings in $n\\geqslant 3$ variables over a field $k$ of characteristic zero containing the $n$-th roots of unity. Let $d$ be the cyclotomic derivation of $k[X]$, and let $\\Delta$ be the factorisable derivation of $k[Y]$ associated with $d$, that is, $d(x_j)=x_{j+1}$ and $\\Delta(y_j)=y_j(y_{j+1}-y_j)$ for all $j\\in\\mathbb Z_n$. We describe polynomial constants and rational constants of these derivations. 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