"` = !^y&mxpoly'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#div)ssreflect(mathcomp@0W~ě o+ N&choice)ssreflect(mathcomp@02*{;"W$^6'fintype)ssreflect(mathcomp@0ǒ3fp%tuple)ssreflect(mathcomp@0ýޑР&finfun)ssreflect(mathcomp@0ƜNtD砠$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{$poly'algebra(mathcomp@0*%H,""6ɠ'polydiv'algebra(mathcomp@0ps2g}CaR }Z]D䄕Y]DF6YР&mxpoly'algebra(mathcomp@A&rVpoly @!R&ssralg@%GRing$Ring@$type;Y@!d)Datatypes$Init#Coq@@#nat@!v&matrix!@"x@,@$sort;1GB$B(AA$poly;@:C!k8Р8@&option >v@AA@A@@@@@C!x&eqtype)ssreflect[@(sub_sort,4VW&ssrnat @#leq+?9D'fintype@/ordinal_subTypeE B:TE'@%insub&Ex"N!i2k@-fun_of_matrix f:a O@$zero'}n%zmodp@+Zp_zmodType/0Cok@(zmodType!뀐;@v@'poly_of†t^#ssr@%phant)`@AI +k() + 7&'7 +877=# R5'>L7 7 77 7#'7 7$'' 97%'+k7$'03ܠ^hIʐ@^AA@@AGA@p_@蠒N4@@@>=zAOx9!ؠHA@A4eAJ@A*sRk@ABC@@+coef_rVpoly @@@~Y%Logic@"eq @k_<@qSDs}oeco81@@@bA*'ssrbool@AA1DH#@:mA ůM@ABFA @IA1GK/@AH@@A)ZA@A @ABCDE@@۠/coef_rVpoly_ord @@Aնƶ]t@'ordinala@OFHMEhJd@@@2@A-@+@q@@ABCD@@,rVpoly_delta @@B  (Equality@ H@&eqTypeŏ{km@(delta_mx9<멚@#exp'p#@-poly_ringType%!@%polyX;u&@ @@@@A@@='rVpolyK @@ZCJH97&ssrfun@&cancelں7A1@Q=B @@@*A(?z@A@@ABg@hA|On@@lA@@ABCD@@i)poly_rV_K @@Dvtecfd@e@'is_true#œ>@$size'P7U簩נҐݰJ<^@@@@A@@AB@@A @@A @@A@ABCDE@@1poly_rV_is_linear @@E&Linear@%axiomJv@-poly_lmodType1m3@/matrix_zmodType1,@%scale(_@/matrix_lmodType. w{%Scale@)scale_law&fΘ9A@@Ð@$]@A'Lmodule@%{k:,é @$base%y6@%class&?ŀ搩#}AũM@@@@AA@E@ABB@@A@@AB=@?w=cA@A>:"I@A?v`@ABCDE@@#0poly_rV_additive @0.1-(Additive@#mapC@AЩR@ O.@( *$@UMр@.class_of_axiom#< %@""@`^OM/'! +k()hA7!L 7 7" 7!  7! 7 7" 7! 7 7 7" 7  77!77"7!77 7"7 7 7!:',x!dȠ t* *8A@tHPT`@@@A@A@@.poly_rV_linear @@hBܼ@Ap鐶@f`SV@ z 4+k()<7!L77"7!7!7 7"7! 7 7 7" 7  7 7!:'([pܠ`qqtA@DP(Ѐ@@@@@Ԡ0rVpoly_is_linear @@F߶Ω8@-poly_zmodTypeU|'7@¶@Ґ ;BwܐsLQ @@@I@AB@?@AB@<@A9@@ABC@}@A3@@@@ABCDE@@/rVpoly_additive @  Щ X>f@EթbHBש dJDBA{@X7@42#!԰S +k()X67!L7  7!  7! 7  7! 7  77" 77!7 7!7 7 7"7 7!:'(t},Pud A@PР`ࠒ*xw<@@@@\-rVpoly_linear @igXV7@OID@qo`^? +k()17!L7 7!7!7 7!7  7 7" 7 7!:'$ȠxDT0ؠӠhA@ŐĠdp@@@@@,Sylvester_mx @hꐩz3!qȐ"dSD@$addn+,}#Nat@$pred `<> @r~@&col_mx ÌCөMש\Sݩb@'lin1_mx=zA @A4eA#seq)ssreflect(mathcomp@@ABC@@-resultant_eq0 @@IZ.IntegralDomain@S@Q @HV{AGA@AjB\AB〰)Datatypes$Init#Coq@@$boolZ'@&eqtype)ssreflect(mathcomp@@%eq_op&@&eqType ԷJC݀QCBA@j'}nܐ^CkaB   @@ @B @Af\&ssralg'algebra(mathcomp@%GRing.IntegralDomain@(ringTypeV{C^'polydiv'algebra(mathcomp@$Pdiv'Idomain@$gcdpc'polydiv$#@ -CommonIdomain@ PhCBA@@@A@A AOx9!ؠHYAi@Aa@ABCAC@ A@A A@>?ޠfAv@ABA^@A вuXa@A A Գq\d@ An@ABCAY@A'@AAf@?y5k{A$@ABA>:"I~@A?v`@A B@{B$@?w=cB@ABCDEFG@@ )horner_mx @   @ C@"n' !A @ Cd    @,horner_morph>sRqЩ@(ringTypeV  @/matrix_ringType"-e   @)scalar_mx7l/   !a  #@.scalar_mx_commF    @ P>6 =42 A '  8 '/   +k() + 9 7 7!7 7!7 7#' 7#'Р6lL3x"2XI@@@@@ q2horner_mx_additive @ ~ld kb`M@%clone\r€$A ݐV ΐ@ n 䐩  (Lalgebra@ggׯmF \@-poly_lalgType\$ZJ@75 _ r i h@/horner_additive!z @3scalar_mx_rmorphismoz vq@\_q320!x @'phantom2"@@ Aq'  @YɀJI0 @  sONL +k()+ + E)   +   7 7!  7 7! 7 7L7 7!7 7 7 7 )+Z   7 7!  7 7! 7 77"7"L7 7!7 7 7 7# ''' 7#' 7#'((tH0TРeG(=Gࠒ=H< L`@@@@@ 3horner_mx_rmorphism @  穚  )RMorphism@1u$ީ V@  vv @0horner_rmorphismTp@1b< ig@  om&@(class_of @# @ 5# "1@0OF@- , +k()+ + B)   +   7 7!  7 7! 7 7L7 7!7 7 7 )+W   7 7!  7 7! 7 77"7"L7 7!7 7 7# ''' 7#' 7#'$(\<$H0< #h0BࠒUt@@@@@ ]+horner_mx_C @@ zJ jXP WNL)' ʰ  ) < 2@%polyC;u&+ := D  =@@@ @A@@ z+horner_mx_X @@ K um tki 氩 l G Z Q YI R@@@@ *horner_mxZ @@ L  }@(mixin_of=v^{T@-lmod_ringType.$<[ @/matrix_lAlgType2Я|@$base%y6@@@5k A @AA 4@ jA @AB @ @A 9@ @A@@@ABCDE@@ ͠0horner_mx_linear @ ȷ Ƿ 2@$packN(?>%YB 0@S(LCB 5@u0 G9MLg 75)Q@%applyX# @  ߩT]\Cw p+k()+P 7"L7 7!L7 7"L7 7"7 7!L 7 7"L 7 7"  7 7!L 7 7"L 7 7" 7 7"  7 7!L 7 7"L 7 7";7 7 L 7 7"77"7"7"L7 7!L7 7"7 7!7 7!L 7 7"L 7 7"  7 7!L 7 7"L 7 7"  7 7!L 7 7"L 7 7" 7 7"  7 7!L 7 7"L 7 7";7 7  7 7# ''8@ hD d@\8`<\  *4Lj$Ppl`x Y$ j,D:Du$,LHhhwt Bt @@@@@ /4horner_mx_lrmorphism @ <*" )  < 8*LRMorphism@=i06 @N O0=& M@^1    @4u @%mixin&U7@(lmodType+ @u~C _ @ r`M =@ |jb i`^A@ H=t@WQs +k()+_ M   7"L  7 7!L 7 7" 7 7!  7 7!7  7 7 L 7 7" 7 7 M   7"L  7 7!L 7 7" 7 7!  7 7!7  7 7 L7 7" 7 77 7!L7 7"7 7!7 7!7 7 7 L 7 7" 7 77" +y *   7"L  7 7! 7 7 L 7 7"77"7"L  7 7!L 7 7" 7 7!  7 7! 7 7  7 7# '''D]x|\<X4lHpL T4x5XS`H (,&`<8x|@p  ȠdGmh@TX 48@@@@@ )powers_mx @     Щ s  e@$muln+]]  J  v    0 Q 7   f @%mxvec>$~  ǰ p } 0 ^ @  ض   հ- + +k() +7 997!7 7 7# '()L7 7 #7!7 7!7"997 7 7997!77 7 7#'4<pА ٰH| j } 䠒 F|\ |3TA@  Ā@@@ /@ @AB@@ +-horner_rVpoly @@ HM 8& %!m )!u t    %   ԩ       *@&vec_mx|o (xx 3@%mulmx>$# ) * ! @&g    0@@@@AA @@AB @@A A @ A4[c%bigop @ABC:dޠR A'j r@ ArߠA y@A A@A4`ؠx@ABA5@ @A @ A4[d@ABC A4`w@ A5[%@A @ 3@AB @?y5k A @AA @A }@ B@ABCDEF@@ ,char_poly_mx @  !n    u u @'p         (@#opp'p     @&map_mx!  ^ O   @  ϶$ "  $+k()7 L7!7 7 7 7"7! 7 7 7" 7 7 7"7&'0 &P d  )Ԡyx. Ƞ+pC  Q@@@ AEƠ @A@@ )char_poly @ a _  ݩ _@p q@ki _ `+k() 7" 7 7&' L @l@@@@@ (.size_char_poly @@EN53" %  r   @:%8@@@ A1A)E @A x@ LA6 @AB @ @A QA@ SA@ UA@ WA@ABCDE@@ S/char_poly_monic @@pO`^MD 鐩 @&in_mem&0R/@#memڕ @,predPredType>h` ũ@+has_quality.=jF ̩B@%monic;o0@@@F@A @ @AB @ A0 O@AH@ @ABC A*ˠ @ .@A @K@AI@H@G@ABCDE@@ /char_poly_trace @@P@ 0@wx   k  _<v  4 @'mxtrace߀ @@@ dA*Z @A gA*נ @ kA*ɔ @ABXA@O@AM@\A6Xa@ABC IA+Ql@ OA+ˠr@A@ @AB @ Q@AT@R@ABCDL@ @A A@X@AB@ V@A @ @ABC L@@A@@A@ AZ@ Ak@ABCDEF@@ -char_poly_det @@ QOM [   k ȩl@#mul'p.© ĩM 婚w@#one'ptߩ o@@@@A A@ A@ABQ@Ag@AA`@A[@ABCA@@A@@ABA8R@ @A AKd@ c@ABCD `@ @A@@AB;@:@A @>Ah@ABC?Ac@ @ACA1FdJ @ h@AB @IA4SOA@A@@]@OA8OO@ABCDEFG@@M1mx_poly_ring_isom @@jRZ.@P;Y@F@ȐBA @"ex @ 0m@ @0OF@@@M"-eSCBW)ssreflect#ssr#Coq@@%phant)`@A@$@5"x@ O" >A@;1G-A _>Fu PA"Q#phiVPCBXCBJ@<7C63CAA1mu/,@{SR@@$and4@&ssrfun#ssr#Coq@@)bijectiveق@ @$\M @n!뀐됩DCDC@91@ͩ͠թ  AB&ssralg%GRing'Zmodule@$sort$\M $Ring@(zmodType!뀐:DhaEEDPЩOQ @착 吩LLݠ ېذ ''B"@d7l/qE)Datatypes$Init#Coq@@#nat@BDA$poly'algebra(mathcomp@@(map_poly BpWELED&matrix'algebra(mathcomp@@7l/E3DA©x@w"x@ DDCG 萩ᐩŐ~EDЩϐѐz@lgeb̩] x[Xl ~BR@&map_mx! WE 3E , _v@ ;u&+EDDA *ŠEDA*<5Р DCƩ'fintype)ssreflect@'ordinala@D E%)Datatypes$Init#Coq@@#nat@ @%;1GH @ f: H/ ) #seq)ssreflect(mathcomp@@U'D  w)HG  HG Ӡ) 7Щ> / = D3 A4@&!:> . .SIC' W WEDACBIՐ H䀐 H `hਗ਼q hP yS |DCBA@@@gA(x0a@AjA @lA @ABmA4[c%bigop)ssreflect(mathcomp@@xA4`ؠx @A{A5@:dޠR'fintype)ssreflect(mathcomp@Aj@ABC Ag 4@A#@AA@A@ABA8G0'@A8Go,@AkA@mA7@ABCDnA1@D@uA@AvA1FdJ@zA@AB{A @~A4SOAB@AA4[dE@A4`wI@ABCA5[L@A7ZtR@A A@ AEƠ@AB A @ A@A A@ A @A A@ A@ A@ABCDEFG@@r/Cayley_Hamilton @@S :h @j逰 B BA BA pxCB@75CBA@%8 TC,BA CB@@@ WA e@A 0A S@ 2A ?@AB A@ A@A A E@ A @AB A P@ WA t@A XA{@ ZA d@ \A P@ABCDE@@⠠4eigenvalue_root_char @@T!F %Field@2 a@KPߩ^@2᱀BAAȩ&ssralg'algebra(mathcomp@%GRing%Field@$sort2᱀C 2 O)mxalgebra'algebra(mathcomp@@*eigenvalue%DCBA|@$root:ʀL@ $=ԉD DCBA@@@ A @A VA @d#1 A @AB A @ A @A A @ A@ABC A @ A @A A @HAZc? q@ABKA]@NAU@AOA5n~`a@SAW@ABCD A @ A @A A @ A)@AB A&@ A5EtIr@A A @ A @ABC A @ A @A A @ A @AB A;@ A;@A A9@ A @AB A @ A @CBl%9 !@ B @ABCDEFG@@6degree_mxminpoly_proof @@U%Field@2 a@   @2᱀GG@O @K[)mxalgebra@&mxrankd[]s*@+comRingType)e@@@d#1Bl%9@A@@ޠ0degree_mxminpoly @BA ط 8@'ex_minnCl/B@W-oF  T@RQ  H鐐  +k() 7" +7%' !97 7997!977%'>蠒Pl?̠>@@@@@5mxminpoly_nonconstant @@3Vzy  p󩚠v@I+ @@@㳠LA4@AA@Ao@ABo@@@_@ABCD@@8+minpoly_mx1 @@UW +2 )ΐ@%submx ثL'  i&@ ($=ԉ    O ,#8@@@Ad@AA@@A@@@ABCD@@g/minpoly_mx_free @@Xʶ Za X@(row_freeMڀ7V/!@@@@}-horner_mx_mem @@Y pw n׶{ؠ9ӐK`mǩz o % % YlcB[n @@@D@AC@A@ABKA@NA1@D@A@C@ABC&@@A@@ABO@%@AN@@AB@@@@ABCDEF@@-mx_inv_horner @  !By  y:x< \ \@&pinvmxKƙfG <@54 ˶ +,' +k()i3   7"   7 79 97!   7" 7   9 9 7 7 77"997!77 7 7" 7 7&',@蠒'&tJ4hPLA@@@@A@@8@ABC@@.mx_inv_horner0 @@.Zut   k}mΩhҩs@k~os  Oߐ@@@@A9@@@ABC@@6.mx_inv_hornerK @@S[ )0 '}"  @А}d  3 " * 7)@@@A@AR@@AB@@Ah@@@ABCD@@e+minpoly_mxM @@\ȶ X_ V/!CT+  @4IV 9O%,>@@UbZ0K`mȠdoI n-\E&#@@@A@AJ@@AB @I@A@F@@ABCD@@/minpoly_mx_ring @@]  D@&mxring~ h@@@A@A @^@A>?ޠA@@B@ABCD@@Ϡ)mxminpoly @32 ɷ )+5O@#opp'pư @KJ  Aא L+k()7"7 7!7"7 7 7 7! 7" 7 7 7 7 7" 7 7 7 7&', ʐXːܠޠdڠ L|tc85q,@@@@@.size_mxminpoly @@:^  wܩޠܩ@a / @@@p@A>@@@ABC@@;/mxminpoly_monic @@X_ .5 ,ѐX.ݐ0ذ2@@@}A@A~A@@ABA@@A@c@A@@@ABCDE@@`2size_mod_mxminpoly @@}`ö SZ Q^Hvr(UnitRing@ N#| @,unitRingType(@+idomainTypeF@'polydiv$Pdiv@$modpB+IdomainDefs@ ht@@@A@ @@ABC@@/mx_root_minpoly @@a      b !d- @@@e@Ad@ @AB@@A9@c@@ABCD@@ˠ.horner_rVpolyK @@b/. 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C0 (@ǰ< @nzw@s/R  " i @fB%u'l H ␶@ql @! ?]:BAB c@; OJq @ ;@&horner 8NP@@@A@A@@@F@ABCD@@֠3integral_root_monic @@zѶҶ۶@o 72"   z  u(@?@xS #Bx'z)R@zz |z@@@A@A@@AB@J@A@@A @@@ABCDE@@,integral_opp @@<{,$ζ@x@""ܩީ@Xr @@@|@@@ABC@@B/integral_horner @@_|O=;>9G@H4@AM 8.B -50@"G7b(@@@@n,integral_sub @@}{igjes@]9@8%IM@yҰceA@@@@@AB@@,integral_add @@~[8xT@@2+ |)X@@@@9@AB@@,integral_mul @@rOk@2@IB! 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