"` l P}&polyXY'algebra(mathcomp@()Notations$Init#Coq@%Logic$Init#Coq@*Logic_Type$Init#Coq@)Datatypes$Init#Coq@&Specif$Init#Coq@%Peano$Init#Coq@"Wf$Init#Coq@'Tactics$Init#Coq@%Tauto$Init#Coq@'Prelude$Init#Coq@)Notations$Init#Coq@0&v!D]hwnv %Logic$Init#Coq@0\͉!Ig)Datatypes$Init#Coq@0.i bYN Z*Logic_Type$Init#Coq@0 1jc6&Specif$Init#Coq@0;RWMi\N'Decimal$Init#Coq@0C涳N*ua#Nat$Init#Coq@0eʤģPSR蠠%Peano$Init#Coq@0 jha|ؠ"Wf$Init#Coq@0q+W,J+'Tactics$Init#Coq@0/9m+ a%Tauto$Init#Coq@0̂"&/rk0JqTttֱ$Bool#Coq@0j 2cZ`FW+ssrmatching#Coq@0L1T=>)ssreflect#ssr#Coq@0 zv)ssreflect(mathcomp@0tn|kN0 D/O&ssrfun#ssr#Coq@01 ZP"};o{,ssrnotations)ssreflect(mathcomp@0hPB &ssrfun)ssreflect(mathcomp@0âNO=(V'ssrbool#ssr#Coq@0X% 'ssrbool)ssreflect(mathcomp@0o: n߂Q&eqtype)ssreflect(mathcomp@0Wn"2&=zH0;&ssrnat)ssreflect(mathcomp@0ͧMy}yWߘ#seq)ssreflect(mathcomp@0=~(sV,Aڠ&choice)ssreflect(mathcomp@02*{;"W$^6#div)ssreflect(mathcomp@0W~ě o+ N'fintype)ssreflect(mathcomp@0ǒ3fp%tuple)ssreflect(mathcomp@0ýޑР&finfun)ssreflect(mathcomp@0ƜNtD砠$path)ssreflect(mathcomp@0*%)bhcFrY%bigop)ssreflect(mathcomp@0#z xW :G؂b%prime)ssreflect(mathcomp@0.wFbN_&finset)ssreflect(mathcomp@0 @$$~,B|XŠ(fingroup(mathcomp@0c"65rk(binomial)ssreflect(mathcomp@0io  } $perm(fingroup(mathcomp@0R 嫁_]U&ssralg'algebra(mathcomp@0ⴆg {PK(morphism(fingroup(mathcomp@0ď \n.v(,automorphism(fingroup(mathcomp@0$D^ V+b`Š(quotient(fingroup(mathcomp@0鰷 x<G@&action(fingroup(mathcomp@0wԦ-M:AB j3!&finalg'algebra(mathcomp@02!3 o'<%zmodp'algebra(mathcomp@0 SꮔnOA &matrix'algebra(mathcomp@0f±ƭ]p\)mxalgebra'algebra(mathcomp@04@%qp{$poly'algebra(mathcomp@0*%H,""6ɠ'polydiv'algebra(mathcomp@0ps2g}CaR젠&mxpoly'algebra(mathcomp@03?~="fJvQxeizf*+Р&polyXY'algebra(mathcomp@A*swapXY_key @@@)Datatypes$Init#Coq@@$unitUe@@@@@@AA@@A@*swapXY_def @!R&ssralg54@%GRing$Ring@$type;Y@!u$poly@'poly_of† @-poly_ringType%!A)ssreflect#ssrC@%phant)`@A 6@$sort;1G*@&horner 8')B6@(map_poly BpW    ?@%polyC;u&+4G@%polyX;u&@@b`QOO?S C3$ +k()7 7 7! 7 7 7"7 7 7 7 7 7 7&'Р(d:䠒(`@`pt@@@>=z~A*sRk\@A@@&swapXY @j@+locked_with/Ξ@JY=@Jg@C +k7 +L 7 7!T77&'G7 7%'Р XHX|$`@@@@@Ǡ1swapXY_unlockable @©@*unlockable|3@A!xm@9@J9i@&unlock:퀰>@6locked_with_unlockable!8߀KE@㩛  0+k7 7 +)L7 7!T7" 7 + L7 7!T7" 7 :'G7 7%'G7 7%'SpXP`cdD+@@@HAA*w|@@A@ABC@@%sizeY @%bigop%BigOp@ gЛ?@#nat@'fintype&Finite@ X @/ordinal_finType#LE#seq$@$size'P4@'polyseqc*,A9@*index_enumZ5(%!i(@'ordinala@'@'bigbody0D@AH18TC-.R&ssrnat]@$maxn+kB@$boolZ'@AIPAN@#nth'D 'Zmodule@^$\M@(zmodType!1@$zero'}n5u@*nat_of_ord2ܵC@ H+k() +; 7 7! 7 7 7!7 7 L7 7!7 7 7!7 7 77#'77 7!7 7 7!7!7 7!7 7 7 7 7 7 77!7 7!L7 8'<q<H젒-ࠒXd|R,!p|$L0X|dpL접<ɐH@@@*'ssrboolA4[c@A:dޠRA4`ؠx@>9!ؠHA4eA@z@{A@ABCD@@ (poly_XaY @ !pة@)comp_poly̩q@#add'p@-poly_zmodTypeU|کȩ@$" +k()7 7 7 7 7 7! 7 7 7 7 7" 7 7&'PӠd%ࠒpt@'Ġ#@@@@N(poly_XmY @KIB@@#mul'p.54@20ࠒPdTࠒĠpKt@@@@@z.sub_annihilant @wunD!q&mxpolyw@)resultant1ъm@?j뺀BA:i@\*! +k()7 7 7 7! 7 7&'РMPhJpx@(@@%@@.div_annihilant @~:L8C@u?j잀0/@,)РuPopx@hP@@M@@ܠ,swapXY_polyC @@A׶%Logic@"eq @ǐ@@@A1GK@k@AB@@(swapXY_X @@"B)שݐ@@@@(swapXY_Y @@6C  2=@@@@2swapXY_is_additive @@ED(Additive@%axiomYɀ *V@@@2A1DHM@C@@ABC@@;+swapXY_addf @86@#mapC@A@ .w@8>DV)@NL,, @+k7 7 :'hX@@@iA@A@@n+coef_swapXY @@EkiZXI!jLؐD2쐩䐩d<?cB FkG@@@A)ZA@A7@A+ˠro@ABr@@A@@ABA+Qlv@ Az@"A@@ABCDE@@'swapXYK @@F&ssrfun@*involutive&j\@@@@@@ABC@@̠0swapXY_map_polyC @@GǶi@@M@@ܠ*swapXY_eq0 @@H׶Ʃ\&eqtype@%eq_op&@+poly_eqType1Q˩N @@r@@8swapXY_is_multiplicative @@(I)RMorphism@(mixin_of 9@@@%@A%A@'A5@AB#Ag@(A+@A)@*A @ABC+A8G0@2A8Go @A@=@AB0@2A4SOA@A5A4[d@9A4`w@ABC:"I@A?v`@ABCD@@-swapXY_linear @驚D@N(@: Y@U:EX'Lmodule@` O>Q5@ c@Bܼ@_Yϐ +k+ $7 L7 7 7 7 7 L 7 7"7 7 7 7 L @ 7 7 7  7  7  7"LL 7!L7 7!+27 7 7 T77 7 7 7 7  7 7# ''7 7 7$'<Eܠp+̠ՐTԠ:Pw0xݐې,@|D$@ lPD<䠒pސ\@@@@@Q1swapXY_lrmorphism @NLLH*LRMorphism@%clone=i0;E@-poly_lalgType\$bV@À@f@1b<hd(Lalgebra@(ringTypegׯWl4 {@(class_of @w@ 1!`@gf@%mixin&Us'@(lmodType+#1ਗ਼@$~ 7\@>`թ:A@[@o=t@Vn p+k+ Em7 L @ 7 7 7  7 7 7"LL7!L7 7!+7 7 7 T7 7 7 7  7 7 L 7 7" 7 7 n7 L @ 7 7 7 7 7 7"LL7!L7 7!+@7 7 7 T7 7 7 7  7 7 L7 7" 7 7 @ 7 7 7  7  7  7"LL 7!L7 7!+7 7 7 T77 7 7 7 7 L 7 7" 7 7 7 + #7 L 7 7  7 7 L 7 7"77 7 L @ 7 7 7  7  7 7"LL7!L7 7!+Z7 7 7 T7 7 7  7 7  7 7# ''7 7 7$'7 7 7$'7 7 7$''7 7 7$'Ljp L(̠!Ԡw| p:, \0kl< tlࠒiԠ@4tTHPDdD0$h4( t@hD$\(dX$h\H+ @`@xPPO0p@@@@@0swapXY_comp_poly @@#Kƶ!ِݐ}4~©<@@@AA@AB@@A}@t@ABCD@@$/max_size_coefXY @@KL!>@'is_true#œ@#leq+@+(u@@@U@AH@@C@ABC@@N4max_size_lead_coefXY @@uMKI:8)$  @@)lead_coef/` #l@@@@i.max_size_evalX @@NfdUSD?.%&1*L@$addn+,}#Nat@$pred `<E@@@@AAjp@p@AB@@A@a@A]@ @@ABCDE@@.max_size_evalC @@O0xsbY/e3\Ro@@@@A%@@AB@@A@@AB@-@@@ABCDE@@&sizeYE @@Pezy|Ր@@@@A@@E@@ABCD@@֠)sizeY_eq0 @@QѶa@*nat_eqType4X@@@\@@AB@@*sizeY_mulX @@Rשɩ@@@@/swapXY_poly_XaY @@&Sɩ#.|@@@@/swapXY_poly_XmY @@7T  ک4?ɩ]$@@@@q@AB@@#)poly_XaY0 @@JU F @@@@@6)poly_XmY0 @@]V31Y!@@N@@D*swapXY_map @@kWA&ssralg'algebra(mathcomp@%GRingB@A;Y@!S!f(Additive@"C@ @!뀐BA)ssreflect#ssr#Coq@@%phant)`@A@;@E;1GB=u$poly'algebra(mathcomp@@x†   @@{%!C)ssreflect#ssr#Coq@@%phant)`@A&ssralg*%GRing$Ring@$sort;1G)!%Logic$Init#Coq@@"eq @C  @U9iC$poly'algebra(mathcomp@@(map_poly BpW\D_CDC@%applyX#@BA.DC8DC$Ð@BSDA@@@>9!ؠH@A1DH{zy@@A A1GK@A4eA#seq)ssreflect(mathcomp@@>=zA*sRk)ssreflect#ssr#Coq@@ABC@@i-horner_swapXY @@Xfd`'ComRing@_C@^\T@VUSg W@GCd`>nQJ@pK  @+horner_eval4pT@@@-sA@AA|@A@ABA@ Ax@A@@ABC@@A@@AB@@A@@AB2@@@5kB@ABCDEF@@Ƞ,horner_polyC @@Y_VBA?8A?6<@@@AJ@@O@ABC@@ߠ.horner2_swapXY @@ ZvmY!yboRJtt| ͩ  @@@,@ACA@@@|@ABCD@@ /horner_poly_XaY @@ 3[ !vՐʩ8ְ Ӑ@@@O@@6@ABC@@ -/horner_poly_XmY @@ T\ *Ķ!!R{ % @@@@ C-size_poly_XaY @@ j] @ > :.IntegralDomain@ 9S@@ 6 @V{ - +@  4~6 $ @ ޠ @( /  @@@  fA@q@  kB@ABC@@ ,poly_XaY_eq0 @@ ^ }=t4& ᐩk)* d琩q-@@@A @@AB@@ -size_poly_XmY @@ _ ZQy`CWC>=@@9@@ ,poly_XmY_eq0 @@ ` md԰ԩҰ0/,@@&@@ 2lead_coef_poly_XaY @@ a }t䰩.&fob qfrc@@@`@A@@AB IA(?z@ N@A.@-@@d@ABCDE@@ ᠠ7sub_annihilant_in_ideal @@ b g ̠  @ÐB  @֐Ѡ ǐ &Specif @$sig2#6@ +@$prodt@  ϐE    "uvN@#andЖw@ J  F \@#fst  4 $ 8 (  ,   3.p & & {@#snd ) .ME\ Gؐ*H ; @@ C \n5 G I kI x h | lA  ! 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N r Y#*[@G) W {R, d. fF  i3k `@@@@AB@CA@AB@@A .@@@D@ABCDE@@ /sub_annihilantP @@ c ~uG n OpO@ @$negb[ /@f :@ P Hy s G@{ yy M} ` XI 갩d © ^@#opp'p e@@@}@AA@@A$@j@ @ABCD@@ 3sub_annihilant_neq0 @@ Dd ڶ Ѷ<@XC;0 ۩  3@cNF/   2mX 6@&eqType Է&İ& ͩ  @@@@ B>?ޠ B@AB@@ W7div_annihilant_in_ideal @@ ~e T K v@q@_TK55L  ~ !멚 @ A S  ,  % Iΐ@@@@ |3div_annihilant_neq0 @@ f y9 p0 @_@Z @K4"t  L C jȐ[2TS@@P@@ /div_annihilantP @@ g!E  %Field@ 2 a@   @?$=ԉ  @ |2᱀  A  u   x   OO@방㐩 X , @ -e 9 @D@g| v HK@ PMU@  b ZK ީ Y@ # m eV  ư d - w o`J Ұ ư  t@#inv'p|@,unitRingType<̀ @@@@Al%9 #A @A @AB @ E@A@ 2@d#1 ,B @ABCD@@ A3map_sub_annihilantP @@ hh!F$FtoEʰ @ @ 6 ک ' ש <ީ - x<@6w  J@Cv ː Uy@  5} +tv S@? @  B 8wy `@|L   N D㐐K o@ #, `}@@@|A@A}@z@AB@ @A @@ '@z@ABCDE@@ 3map_div_annihilantP @@ iwus n @i d@c@W@䰩N Q #Q@ ̩ ʩ K`ɶ@ ɩ ǩ FCg  F >L N 3LScU @4ک s ]~נ_ N@@Q@@ /root_annihilant @@ &j[^\ 1 ǐE     АȐ#pEx ϰ   F ȰG©Iĩ @   Ơ ҩ  @Z E   @ @-algebraicOver =)Z @ © ^@#ex2М@ ,J η!r% n fM *  7P u ^@3 D@$root:ʀ\B :< V X  @@@?@ 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