+ ihRt^RIt^RIHtHtHtHtHt^RIH t H t H t H t H t HtHtHtHtHtHtHtHtHtHtHtHtHtHtHtHtHtHtH t H!t!H"t"H#t#H$t$H%t%H&t&H't'H(t(H)t)H*t*H+t+H,t,H-t-H.t.H/t/H0t0H1t1H2t2H3t3H4t4H5t5H6t6H7t7H8t8H9t9^RI:H;t;Ht>H?t?H@t@HAtAHBtBHCtCHDtDHEtEHFtFHGtGHHtHHItIHJtJHKtKHLtLHMtMHNtNHOtOHPtPHQtQHRtR] ]3tS]]3tT]!]3tU]"]3tV]#]$3tW]#]$]%3tXRtYRtZRt[R]3R lt\R t]]3R lt^R t_]3R lt`]3Rlta^]3Rltb^]3Rltc]3RltdR]3RlteRtf]3Rltg]3Rlth]3Rlti]3Rltj]3Rltk]3Rltl]3Rltm]3Rltn]3Rlto]3Rltp]3Rltq]3Rltr]3R lts]3R!ltt]3R"ltuR#tv]3R$ltw]3R%ltx]3R&lty]3R'ltzR(t{]3R)lt|]3R*lt}]3R+lt~]3R,lt]3R-lt]3R.lt]3R/lt]3R0lt]3R1lt]3R2lt]3R3lt]3R4lt]3R5lt]3R6lt]3R7lt]!R84t]!R94tR:t]3R;lt]3R<lt]3R=lt]3R>lt]3R?lt]3R@ltRGRAltRGRBltRGRCltRGRDlt]RE8Xd(^RIHuHuHt]Pt~]PtzR#R# ]]3d ]!RF4R#i;i)Hz- Low-level functions for complex arithmetic. N)MPZMPZ_ZEROMPZ_ONEMPZ_TWOBACKEND)1 round_floor round_ceiling round_downround_up round_nearest round_fastbitcountbctable normalize normalize1reciprocal_rndrshiftlshift giant_steps negative_rndto_strto_fixed from_man_exp from_floatto_floatfrom_intto_intfzerofoneftwofhalffinffninffnanfnonempf_absmpf_posmpf_negmpf_addmpf_submpf_mulmpf_div mpf_mul_int mpf_shiftmpf_sqrt mpf_hypot mpf_rdiv_int mpf_floormpf_ceilmpf_nintmpf_fracmpf_signmpf_hash ComplexResult)mpf_pimpf_expmpf_log mpf_cos_sin mpf_cosh_sinhmpf_tan mpf_pow_int mpf_log_hypotmpf_cos_sin_pimpf_phimpf_cosmpf_sin mpf_cos_pi mpf_sin_pimpf_atan mpf_atan2mpf_coshmpf_sinhmpf_tanhmpf_asinmpf_acos mpf_acosh mpf_nthroot mpf_fibonaccicBVwrV\9dR#V\9dR#R#)z2Check if either real or imaginary part is infiniteTF)_infszreims& s/Users/tonyclaw/.openclaw/workspace/skills/math-calculator/venv/lib/python3.14/site-packages/mpmath/libmp/libmpc.py mpc_is_infrW)s FB U{4 U{4 cBVwrV\9dR#V\9dR#R#)z9Check if either real or imaginary part is infinite or nanTF) _infs_nanrRs& rV mpc_is_infnanr[0s FB Yt Yt rXc Vwr4\W14pV^,'d,VR,\\V4V3/VB,R,#VR,\WA3/VB,R,#)z - jz + )rr')rSdpskwargsrTrUrss&&, rV mpc_to_strrb7s] FB B !uuEzF72;>v>>DDEzF25f55;;rXFcJVwr4\\W1V4\WAV44#N)complexr)rSstrictrndrTrUs&&& rVmpc_to_complexrh?s$ FB 8B,hr3.G HHrXct\PR8drVwr\V4\PP\V4,,pV^\PP ,,p\ V4#\\VRR74# \d\T4u#i;i)T)rf)rj) sys version_infor6 hash_infoimagwidthinthashrh OverflowError)rSrTrUhs& rVmpc_hashruCs 6! RL3==-- < < CMM''' (1v  q67 7 7N sBB76B7c&Vwr4V\WAV43#rdr'rSprecrgrTrUs&&& rV mpc_conjugaterzPs FB wr% %%rXcV\8g#rd)mpc_zero)rSs&rVmpc_is_nonzeror}Ts =rXcBVwrEVwrg\WFW#4\WWW#43#rdr(rSwryrgabcds&&&& rVmpc_addrW) DA DA 1 #WQ4%= ==rXc&VwrE\WAW#4V3#rdr)rSxryrgrrs&&&& rV mpc_add_mpfr\ DA 1 #Q &&rXcBVwrEVwrg\WFW#4\WWW#43#rdr)rs&&&& rVmpc_subr`rrXc&VwrE\WAW#4V3#rdr)rSpryrgrrs&&&& rV mpc_sub_mpfrerrXc:Vwr4\W1V4\WAV43#rd)r&rSryrgrrs&&& rVmpc_posri" DA 1C '!3"7 77rXc:Vwr4\W1V4\WAV43#rdrwrs&&& rVmpc_negrmrrXc6Vwr#\W!4\W143#rd)r-)rSnrrs&& rV mpc_shiftrqs DA Q?IaO ++rXc"Vwr4\W4W4#)zAAbsolute value of a complex number, |a+bi|. Returns an mpf value.)r/rs&&& rVmpc_absrus DA Q4 %%rXc"Vwr4\WCW4#)z3Argument of a complex number. Returns an mpf value.)rGrs&&& rVmpc_argr{s DA Q4 %%rXc:Vwr4\W1V4\WAV43#rd)r1rs&&& rV mpc_floorrs" DA Qc "Ias$; ;;rXc:Vwr4\W1V4\WAV43#rd)r2rs&&& rVmpc_ceilr" DA AS !8AS#9 99rXc:Vwr4\W1V4\WAV43#rd)r3rs&&& rVmpc_nintrrrXc:Vwr4\W1V4\WAV43#rd)r4rs&&& rVmpc_fracrrrXcVwrEVwrg\WF4p\WW4p \WG4p \WV4p \WW#4p \WW#4p W3#)z Complex multiplication. Returns the real and imaginary part of (a+bi)*(c+di), rounded to the specified precision. The rounding mode applies to the real and imaginary parts separately. )r*r)r()rSrryrgrrrrrqrsrTrUs&&&& rVmpc_mulrsU DA DA A A A A t !B t !B 6MrXcVwr4\W34p\WD4p\W4W4p\WVW4p\V^4p W3#)r*r)r-) rSryrgrrrrrrTrUs &&& rV mpc_squarersE DA A ATA t !B 1aB 6MrXc@VwrE\WAW#4p\WQW#4pWg3#rd)r*rSrryrgrrrTrUs&&&& rV mpc_mul_mpfrs( DA t !B t !B 6MrXcRVwrE\\WQW#44p\WAW#4pWg3#)z: Multiply the mpc value z by I*x where x is an mpf value. )r'r*)rSrryrgrrrTrUs&&&& rVmpc_mul_imag_mpfrs/ DA t) *B t !B 6MrXc@VwrE\WAW#4p\WQW#4pWg3#rd)r,)rSrryrgrrrTrUs&&&& rV mpc_mul_intrs( DA Q4 %B Q4 %B 6MrXcVwrEVwrgV^ ,p\\Wf4\Ww4V4p \\WF4\WW4V4p \\WV4\WG4V4p \WW#4\WW#43# )r(r*r)r+) rSrryrgrrrrwpmagtus &&&& rVmpc_divrst DA DA B '!- 3C galB/A galB/A 1 "GA$$; ;;rXc@VwrE\WAW#4p\WQW#4pWg3#)zCalculate z/p where p is real)r+rs&&&& rV mpc_div_mpfrs( DA t !B t !B 6MrXcVwr4\\W34\WD4V^ ,4p\W5W4p\\WEW44pWg3#)zCalculate 1/z efficientlyr(r*r+r')rSryrgrrmrTrUs&&& rVmpc_reciprocalrsG DA WQ\$r'2A t !B t) *B 6MrXcVwrE\\WD4\WU4V^ ,4p\\W@4WbV4p\\\WP44WbV4pWx3#)z)Calculate p/z where p is real efficientlyr) rrSryrgrrrrTrUs &&&& rV mpc_mpf_divrsS DA WQ\473A q ,B & 5B 6MrXc^p^pV'dqV^,'d3W0,WA,, W@,W1,,rCV^,pW,W,, ^V,V,rV^,pKxW43#)zcComplex integer power: computes (a+b*I)**n exactly for nonnegative n (a and b must be Python ints).)rrrwrewims&&& rVcomplex_int_powrsa C C q55usu}cecem FAsQSy!A#a%1 a 8OrXc V^,\8Xd\W^,W#4#\\\ W^ ,4W^ ,4W#4#r)r mpc_pow_mpfmpc_exprmpc_log)rSrryrgs&&&&rVmpc_powrs?tu}1dD.. 7712g.7;T GGrXc VwrErgV^8d"\VRV,WV,,W#4#VR8Xd.\W^ ,4p\VRV,V,W#4#\\\ W^ ,4W^ ,4W#4#)r]) mpc_pow_intmpc_sqrtrrr) rSrryrgpsignpmanpexppbcsqrtzs &&&& rVrrs{E qy1rEkTZ8$DD rzG$52+"4d@@ ;wqr'2ABw? KKrXc VwrEV\8Xd\WAW#4\3#V\8Xdd\WQW#4pV^,pV^8Xd V\3#V^8Xd \V3#V^8Xd\V4\3#V^8Xd\\V43#V^8Xd\#V^8Xd \ WV4#V^8Xd \ WV4#VR8Xd \ WV4#V^8d\ \W)V^,4W#4#VwrxrVwrrV'dV)pV 'dV )p W, p\V4pVV\W4,,pVR8diV^8d W,pT p M W),p T p \WV4wpp\V\W,4W#4p\V\W,4W#4pVV3#\\\W^ ,4W^ ,4W#4#)i'r)rr>r'mpc_onerrrrabsmaxrrrqrrr)rSrryrgrrvasignamanaexpabcbsignbmanbexpbbcdeabs_de exact_sizerTrUs&&&& rVrrs DAEz1+U22Ez d ( Q 6e8O !V!8O !V1:u$ $ !V'!*$ $Avg~Avgas++Avj#..Bw~as331u^K2tAv$>JJEE dUd dUd B WFFS]*+JE 6 KDD cNDD Q/B "c!&k4 5 "c!&k4 52v ;wqr'2ABw? KKrXcVwr4V\8XdOV\8XdW43#V^,'d\\V4W4p\V3#\W1V4pV\3#V^,pV^,'gV\\ W43V4W74p\ VR4p \WV4p\ V^4p \W4p \ WKW4pWe3#\\ W43V4W74p\ VR4p \WV4p\ V^4p \W4p \ WKW4pV^,'d\V4p\V4pWe3#)zComplex square root (principal branch). We have sqrt(a+bi) = sqrt((r+a)/2) + b/sqrt(2*(r+a))*i where r = abs(a+bi), when a+bi is not a negative real number.r)rr.r'r(rr-r+r)) rSryrgrrrUrTrrrrrs &&& rVrr's2 DAEz :6M Q44'!*d0B2; !3'B;  bB Q44 WaVR(! 0 a  as # aO a_ Q4 % 6M GQFB' / a  as # aO a_ Q4 % Q44BB 6MrXc8^2p\\WW$,, 44p\\WW$,, 44pVRV,,RV, ,pVPpVPp \ \V44p\ \V 44p ^ p Tp Tp\WCV ,4EFmp\WV^, 4wpp\VV^, V ,V, V, 4p\VV^, V ,V, V, 4pVV,VV,,W,, p\WV, 4p\WV, 4pVV,VV,,V, pV)V,VV,,V, pVV,V,pVV,V,pVV^, \WV , 4,,V,pVV^, \WV , 4,,V,p Tp EKp W3# \ d^\ YT4p\ Yd4p\ T4p \^Y4p \YV3T \3T4wr\T4p\T 4p ELi;i)2y?g?)rqrrealrorrsrr0rrrrrr)rrrrystarta1b1rrTrUfnnthextraprevpextra1rre2im2r4apbprecimcrebimbs&&&& rVmpc_nthroot_fixedrKs E VAag~ & 'B VAag~ & 'B  "r'\SU # VV VV R\ R\ E E F U +"21Q3/SS1Q3+/F23S1Q3+/F23#gCQZ 0 Aax  Aax Cx"s("q(sSy28#)axBaxBQqS&uW--- 1QqS&uW--- 1, 6M5  b  b  a[1b("C<7 BZ BZsAH11A$JJcVwrEV^,^8Xd V\8Xd\WAW#4pV\3#V^8dnV^8Xd\#V^8Xd\WE3W#4#VR8Xd\ \WE3W#4#\ WE3V)V^,\ V,4p\ \WrV4#V^8:d\RV^ ,,4pVwrrVwrpp\WE3V4pVR,VR,,R8drVR,VR,,V8dV\WH4p\WX4p\VVW4wpp^ p\Wh)V, W4p\VV)V, W4pVV3#\V4pV^ ,^ ,p\^VV4p\WE3V\3W4wpp\V^,V^,V^,V^,W#4p\V^,V^,V^,V^,W#4pVV3#)ze Complex n-th root. Use Newton method as in the real case when it is faster, otherwise use z**(1/n) g333333?ri)rrNrrr mpc_nthrootrrqrrrrrr0rr)rSrryrgrrrTinverseprec2rrrrrrrrpfafbfrUrrrs&&&& rVrrrs DAtqyQ%Z t )E{1u 6N 6A64- - 77QFD6 6qfqb$q&.2EFws33BwC4"9%&!"T!"T3 aUD ! b6BrF?S bfr"vo&<!#B!#B&r2q8FBEb&,;Bb5&,;Br6M !B GbLE q"e $C aVc5\5 6FB 2a5"Q%A1t 9B 2a5"Q%A1t 9B r6MrXc\V^W4#)z Complex cubic root. )rrSryrgs&&&rVmpc_cbrtr s q!T ''rXcVwr4V\8Xd \WAV4#V\8Xd\W1V4\3#\W1^,V4p\WA^,V4wrg\WVW4p\WWW4p W3#)aJ Complex exponential function. We use the direct formula exp(a+bi) = exp(a) * (cos(b) + sin(b)*i) for the computation. This formula is very nice because it is pefectly stable; since we just do real multiplications, the only numerical errors that can creep in are single-ulp rounding errors. The formula is efficient since mpmath's real exp is quite fast and since we can compute cos and sin simultaneously. It is no problem if a and b are large; if the implementations of exp/cos/sin are accurate and efficient for all real numbers, then so is this function for all complex numbers. )rr;r9r*) rSryrgrrrrrrTrUs &&& rVrrsy DAEz1C((Ezq$e++ !!VS !C qq&# &DA  #B  #B 6MrXcV\V^,V^,W4p\WV4pW43#r])r?rrxs&&& rVrrs+ qtQqT4 -B # B 6MrXcVwr4V\8Xd\W1V4\3#V\8Xd\WAV4\3#V^,p\W54wrg\ WE4wr\ WhW4p \ WyW4p V \ V 43#)a?Complex cosine. The formula used is cos(a+bi) = cos(a)*cosh(b) - sin(a)*sinh(b)*i. The same comments apply as for the complex exp: only real multiplications are pewrormed, so no cancellation errors are possible. The formula is also efficient since we can compute both pairs (cos, sin) and (cosh, sinh) in single stwps.)rrBrHr;r<r*r' rSryrgrrrrrchshrTrUs &&& rVmpc_cosrs DAEzq$e++Ez%u,, B q DA 1 !FB  "B  "B wr{?rXcVwr4V\8Xd\W1V4\3#V\8Xd\\WAV43#V^,p\W54wrg\ WE4wr\ WxW4p \ WiW4p W3#)z{Complex sine. We have sin(a+bi) = sin(a)*cosh(b) + cos(a)*sinh(b)*i. See the docstring for mpc_cos for additional comments.)rrCrIr;r<r*rs &&& rVmpc_sinrs} DAEzq$e++Ezhq,,, B q DA 1 !FB  "B  "B 6MrXc`Vwr4VwrVrxVwrrV\8Xd\W1V4\3#V\8Xd\\WAV43#V^,p \V^4p\V^4p\ W=4wr\ WM4wpp\ VVV 4p\VVW4p\VVW4pVV3#)z_Complex tangent. Computed as tan(a+bi) = sin(2a)/M + sinh(2b)/M*i where M = cos(2a) + cosh(2b).)rr=rJr-r;r<r(r+)rSryrgrrrrrrrrrrrrrrrrrTrUs&&& rVmpc_tanrs DAEEEz'!3/66Ez%!3!777 B!QA!QA q DA 1 !FB !R C C #B S$ $B r6MrXcVVwr4V\8Xd\W1V4\3#\V\V^,4V^,4pV\8Xd\ WAV4\3#V^,p\ W54wrg\ WE4wr\WhW4p \WyW4p V \V 43#)rrDr*r8rHr@r<r'rs &&& rV mpc_cos_pirs DAEz!3'..6$q&>46*AEz%u,, B ! DA 1 !FB  "B  "B wr{?rXcBVwr4V\8Xd\W1V4\3#\V\V^,4V^,4pV\8Xd\\ WAV43#V^,p\ W54wrg\ WE4wr\WxW4p \WiW4p W3#r)rrEr*r8rIr@r<rs &&& rV mpc_sin_pirs DAEz!3'..6$q&>46*AEzhq,,, B ! DA 1 !FB  "B  "B 6MrXctVwr4V\8Xd\WAV4wrVV\3\V33#V\8Xd\W1V4wrxV\3V\33#V^,p \W94wrx\WI4wrV\WuW4p \WW4p \WW4p \WvW4p V \ V 43W33#))rr<r;r*r')rSryrgrrrrrrrcrecimsresims&&& rV mpc_cos_sinr%s DAEzq,E{UBK''Ez1C(5zAu:%% B q DA 1 !FB ! #C ! #C ! #C ! #C   **rXcVwr4V\8Xd\W1V4wrVV\3V\33#\V\V^,4V^,4pV\8Xd\ WAV4wrxV\3\V33#V^,p \W94wrV\ WI4wrx\WWW4p \WhW4p \WgW4p \WXW4p V \ V 43W33#r)rr@r*r8r<r')rSryrgrrrrrrrr!r"r#r$s&&& rVmpc_cos_sin_pir'%s DAEzas+5zAu:%%6$q&>46*AEzq,E{UBK'' B ! DA 1 !FB ! #C ! #C ! #C ! #C   **rXc8Vwr4\V\V43W4#)z:Complex hyperbolic cosine. Computed as cosh(z) = cos(z*i).)rr'rs&&& rVmpc_coshr)7s DA Awqz?D ..rXc.Vwr4\WC3W4wrCW43#)z;Complex hyperbolic sine. Computed as sinh(z) = -i*sin(z*i).)rrs&&& rVmpc_sinhr+< DA A64 %DA 4KrXc.Vwr4\WC3W4wrCW43#)z>Complex hyperbolic tangent. Computed as tanh(z) = -i*tan(z*i).)rrs&&& rVmpc_tanhr.Br,rXchVwr4V^,p\\WE4\V43p\\WE4V3p\ We4p\ Wu4p \ WW4wr4\\ VR44\ VR43p V ^,\8Xd!\V4'dV ^,\3p V #r) r(rr'r)rrr-r#rWr) rSryrgrrrryl1l2rs &&& rVmpc_atanr5Is DA Bagaj(AaaA B B 24 %DA !B )Ab/1A tt| 1 qT5M HrXg:pΈ?g?c  VwrEV^ ,pV\8Xd\\\V4V4pV^,'g,V^8Xd\ WAV4\3#\ WAV4\3#V^,'dL\ W4p\\V4W4p V^8XdV\V 43#\\VR44V 3#\WAV4p V^8Xd \V 3#\ W4p\VR4\V 43#^;rV^,'d\V4p^p V^,'d\V4p^p \\WF4p\\WF4p \WV4p \WuV4p\\WV4R4p\WOV4p\WUV4p\\VV4^,'g$V^8Xd\ VV4pEMI\ VV4pEM;\WV4pV^,'g\V\WV4V4p \WV4p\\V\V VV4V4R4pV^8Xd"\\\!VV4WF4V4pM\\V\!VV4V4V4pM\V\WV4V4p \V\WV4V4p\\V VV4R4p\V\!VV4V4pV^8Xd\\VWF4V4pM\\VVV4V4p\\"W4^,'g\V\WV4V4p\V4^,'d2\WV4p\VVV4p\\VVV4R4pM#\WV4p\\VVV4R4p\V\V\V4V4p\%\\\V\!VV4V4V4V4pM<\!\\WV4\V4V4p\%\VVV4V4pV 'd*V^8Xd\\ V4VV4pM \V4pV 'gV^8Xd \V4pV 'dV^8Xd \V4p\'V^,V^,V^,V^,W4p\'V^,V^,V^,V^,W4pVV3#)acomplex acos for n = 0, asin for n = 1 The algorithm is described in T.E. Hull, T.F. Fairgrieve and P.T.P. Tang 'Implementing the Complex Arcsine and Arcosine Functions using Exception Handling', ACM Trans. on Math. Software Vol. 23 (1997), p299 The complex acos and asin can be defined as acos(z) = acos(beta) - I*sign(a)* log(alpha + sqrt(alpha**2 -1)) asin(z) = asin(beta) + I*sign(a)* log(alpha + sqrt(alpha**2 -1)) where z = a + I*b alpha = (1/2)*(r + s); beta = (1/2)*(r - s) = a/alpha r = sqrt((a+1)**2 + y**2); s = sqrt((a-1)**2 + y**2) These expressions are rewritten in different ways in different regions, delimited by two crossovers alpha_crossover and beta_crossover, and by abs(a) <= 1, in order to improve the numerical accuracy. r)rr)rr%rLrKr8rMr'r-r(r/r+r*beta_crossoverrFr.alpha_crossoverr:r)rSryrgrrrrampirrrrrralphabetab2rTAxrc1c2Am1rUs&&&& rV acos_asinrB_s[" DA BEz T71:r *!uuAv-u44-u44ttD&gaj$46wqz>)"9R#45q88as+6 !8O*B$R,gaj88Ett AJtt AJ q B q B"A"A gaB' ,E 1R D b B >4 ,Q / / 6$#B$#BUr "!uu GA2.3Ar"A72wq!R'8"=rBBAvghr2&6>Cga"b)92>C GA2.3AGA2.3A71a,b1BHR,b1BAvgb!0"5gaR0"5 ?E .q 1 1 R+R 0 2;q>>#BR$BGBB/4C#BGBB/4C S'%r2B 7 WT73R0@"#ErJB OggeB7rBB G WUB+R 0 6R,BB Q!V R[ a R[ 2a5"Q%A1t 9B 2a5"Q%A1t 9B r6MrXc\WV^4#rrBr s&&&rVmpc_acosrE Qc1 %%rXc\WV^4#rrDr s&&&rVmpc_asinrHrFrXcVVwr4\V\V43W4wr4\V4V3#rd)rHr'rs&&& rV mpc_asinhrJs- DA a_d 0DA 1:q=rXc\WV4wr4V^,'g V\8Xd\V4V3#V\V43#r)rErr'rs&&& rV mpc_acoshrLs= AS !DAttqEzqz1}'!*}rXcV^,p\V\V4p\\W4p\WC4p\WS4p\ \WEV4R4pV^,\ 8Xd!\ V4'd\V^,3pV#r0)rrrrrr#rWr)rSryrgrrrrs&&& rV mpc_atanhrNsq B7BAAAA'!#R(A tt| 1 AaDM HrXcVwr4V\8Xd\W1V4\3#\\V^,V^,,4\V^,V^,,44pW,^,p\ V4p\ \ V^4\V4p\V\3W4p \W4p \WV4p \WV4p \WW4p V #)rk) rrOrrrAr(r-r$rrrrr) rSryrgrTrUsizerrrrrs &&& rV mpc_fibonaccirQ s FB U{b,e44 s2a5A;RU2a5[!1 2D r B A !Q+AE A"A1AbAbAA$$A HrXc\hrdr7rryrgs&&&rVmpf_expjrU rXcVwr4V\8Xd \W1V4#V\8Xd\\V4W4\3#\\V4V^ ,4p\W1^ ,4wrg\ WVW4p\ WWW4pW43#r)rr;r9r'r*)rSryrgrTrUeyrrs&&& rVmpc_expjrYs} FB U{2S)) U{wr{D.55 d2g &B r7 #DA  "B  "B 6MrXc\hrdrSrTs&&&rV mpf_expjpir[(rVrXcVwr4V\8Xd \W1V4#VwrVrxV^ ,p V'dV \^Wx,4, p \\ \ V 4WI44pV\8Xd\ WAV4\3#\ WA^ ,4p \W1^ ,4wr\ WW4p\ WW4pW43#r)rr@rr'r*r8r9) rSryrgrTrUsignmanexpbcrrXrrs &&& rV mpc_expjpira+s FB U{b,,Ds bB  c!SVn R, -B U{r%u,, "W B "2g &DA  "B  "B 6MrXsagez&Warning: Sage imports in libmpc failed)f)__doc__rlbackendrrrrrlibmpfrrr r r r r rrrrrrrrrrrrrrrrrrr r!r"r#r$r%r&r'r(r)r*r+r,r-r.r/r0r1r2r3r4r5r6r7 libelefunr8r9r:r;r<r=r>r?r@rArBrCrDrErFrGrHrIrJrKrLrMrNrOrr|mpc_twompc_halfrQrZrWr[rbrhrurzr}rrrrrrrrrrrrrrrrrrrrrrrrrrrrrr rrrrrrrr%r'r)r+r.r5r7r8rBrErHrJrLrNrQrUrYr[rasage.libs.mpmath.ext_libmplibsmpmath ext_libmp_lbmp ImportErrorAttributeErrorprintrrXrVrrsG ==              + %< + 5> u  5$  <# I  *&'> !+'j> *'$8j8,$& $& &<%:%:%: '$'!+ &0!+ ' <!+!+!+ 'H !+L!+&LP%"H%N!+'R%( $6$ $($ $&' ' (+"!++$%/ % %% &F#S/FP%&%&& &&   *   $ f822-->>   (8 678s3$II0/I0