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Mirrors > Home > MPE Home > Th. List > Mathboxes > cytpfn | Structured version Visualization version GIF version |
Description: Functionality of the cyclotomic polynomial sequence. (Contributed by Stefan O'Rear, 5-Sep-2015.) |
Ref | Expression |
---|---|
cytpfn | ⊢ CytP Fn ℕ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ovex 7183 | . 2 ⊢ ((mulGrp‘(Poly1‘ℂfld)) Σg (𝑟 ∈ (◡(od‘((mulGrp‘ℂfld) ↾s (ℂ ∖ {0}))) “ {𝑛}) ↦ ((var1‘ℂfld)(-g‘(Poly1‘ℂfld))((algSc‘(Poly1‘ℂfld))‘𝑟)))) ∈ V | |
2 | df-cytp 39796 | . 2 ⊢ CytP = (𝑛 ∈ ℕ ↦ ((mulGrp‘(Poly1‘ℂfld)) Σg (𝑟 ∈ (◡(od‘((mulGrp‘ℂfld) ↾s (ℂ ∖ {0}))) “ {𝑛}) ↦ ((var1‘ℂfld)(-g‘(Poly1‘ℂfld))((algSc‘(Poly1‘ℂfld))‘𝑟))))) | |
3 | 1, 2 | fnmpti 6485 | 1 ⊢ CytP Fn ℕ |
Colors of variables: wff setvar class |
Syntax hints: ∖ cdif 3932 {csn 4560 ↦ cmpt 5138 ◡ccnv 5548 “ cima 5552 Fn wfn 6344 ‘cfv 6349 (class class class)co 7150 ℂcc 10529 0cc0 10531 ℕcn 11632 ↾s cress 16478 Σg cgsu 16708 -gcsg 18099 odcod 18646 mulGrpcmgp 19233 algSccascl 20078 var1cv1 20338 Poly1cpl1 20339 ℂfldccnfld 20539 CytPccytp 39795 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1907 ax-6 1966 ax-7 2011 ax-8 2112 ax-9 2120 ax-10 2141 ax-11 2157 ax-12 2173 ax-ext 2793 ax-sep 5195 ax-nul 5202 ax-pr 5321 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3an 1085 df-tru 1536 df-ex 1777 df-nf 1781 df-sb 2066 df-mo 2618 df-eu 2650 df-clab 2800 df-cleq 2814 df-clel 2893 df-nfc 2963 df-ral 3143 df-rex 3144 df-rab 3147 df-v 3496 df-sbc 3772 df-dif 3938 df-un 3940 df-in 3942 df-ss 3951 df-nul 4291 df-if 4467 df-sn 4561 df-pr 4563 df-op 4567 df-uni 4832 df-br 5059 df-opab 5121 df-mpt 5139 df-id 5454 df-xp 5555 df-rel 5556 df-cnv 5557 df-co 5558 df-dm 5559 df-iota 6308 df-fun 6351 df-fn 6352 df-fv 6357 df-ov 7153 df-cytp 39796 |
This theorem is referenced by: (None) |
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