From 2d824f394e8c3148e95b3374fb9903f6032ba3e6 Mon Sep 17 00:00:00 2001 From: Cyril Cohen Date: Thu, 25 Aug 2016 01:38:44 +0200 Subject: Enriched numClosedFieldType so that it factors a lot of theory from both complex and algC. The definitions of 'i, conjC, Re, Im, n.-root, sqrtC and their theory have been moved to the numClosedFieldType structure in ssrnum. This covers boths the uses in algC and complex.v. To that end the numClosedFieldType structure has been enriched with conjugation and 'i. Note that 'i can be deduced from the property of algebraic closure and is only here to let the user chose which definitional equality should hold on 'i. Same thing for conjC that could be written `|x|^+2/x, the only nontrivial (up to my knowledge) property is the fact that conjugation is a ring morphism. --- mathcomp/odd_order/PFsection3.v | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) (limited to 'mathcomp/odd_order/PFsection3.v') diff --git a/mathcomp/odd_order/PFsection3.v b/mathcomp/odd_order/PFsection3.v index cb55ae4..9011122 100644 --- a/mathcomp/odd_order/PFsection3.v +++ b/mathcomp/odd_order/PFsection3.v @@ -1360,7 +1360,7 @@ have{oxi_00} oxi_i0 i j i0: '[xi_ i j, xi_ i0 0] = ((i == i0) && (j == 0))%:R. by rewrite cfdotC Xi0_X0j // conjC0. have [-> | nzi2] := altP (i2 =P 0); first exact: oxi_0j. have [-> | nzj2] := altP (j2 =P 0); first exact: oxi_i0. -rewrite cfdotC eq_sym; apply: canLR conjCK _; rewrite rmorph_nat. +rewrite cfdotC eq_sym; apply: canLR (@conjCK _) _; rewrite rmorph_nat. have [-> | nzi1] := altP (i1 =P 0); first exact: oxi_0j. have [-> | nzj1] := altP (j1 =P 0); first exact: oxi_i0. have ->: xi_ i1 j1 = beta i1 j1 + xi_ i1 0 + xi_ 0 j1 by rewrite /xi_ !ifN. -- cgit v1.2.3