ó ¡¼™\c@ súddlmZmZddlmZmZmZddlmZddl m Z m Z m Z ddl mZmZddlmZmZddlmZd„Zd e fd „ƒYZd „Zd efd „ƒYZdefd„ƒYZdefd„ƒYZdefd„ƒYZdefd„ƒYZdefd„ƒYZdefd„ƒYZde fd„ƒYZdefd„ƒYZ defd„ƒYZ!d efd!„ƒYZ"d"efd#„ƒYZ#d$efd%„ƒYZ$d&efd'„ƒYZ%d(S()iÿÿÿÿ(tprint_functiontdivision(tStsympifytcacheit(tAdd(tFunctiontArgumentIndexErrort _coeff_isneg(t factorialtRisingFactorial(texptlog(tsqrtcC s,t|ƒ}|jd„|jtƒDƒƒS(NcS s"i|]}|jtƒ|“qS((trewriteR (t.0th((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pys s (RtxreplacetatomstHyperbolicFunction(texpr((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyt_rewrite_hyperbolics_as_exp s  RcB seZdZeZRS(se Base class for hyperbolic functions. See Also ======== sinh, cosh, tanh, coth (t__name__t __module__t__doc__tTruet unbranched(((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRscC sÌxˆtj|ƒD]j}|tjtjkr9tj}Pq|jr|jƒ\}}|tjtjkrz|jrzPqzqqW|tj fS|tj tjtj}|tjtj|}|||fS(sÕ Split ARG into two parts, a "rest" and a multiple of I*pi/2. This assumes ARG to be an Add. The multiple of I*pi returned in the second position is always a Rational. Examples ======== >>> from sympy.functions.elementary.hyperbolic import _peeloff_ipi as peel >>> from sympy import pi, I >>> from sympy.abc import x, y >>> peel(x + I*pi/2) (x, I*pi/2) >>> peel(x + I*2*pi/3 + I*pi*y) (x + I*pi*y + I*pi/6, I*pi/2) ( Rt make_argsRtPit ImaginaryUnittOnetis_Mult as_two_termst is_RationaltZerotHalf(targtatKtptm1tm2((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyt _peeloff_ipi#s    tsinhcB sÑeZdZdd„Zdd„Zed„ƒZeed„ƒƒZ d„Z e d„Z e d„Z e d „Zd „Zd „Zd „Zd „Zd„Zd„Zd„Zd„Zd„Zd„ZRS(s¦ The hyperbolic sine function, `\frac{e^x - e^{-x}}{2}`. * sinh(x) -> Returns the hyperbolic sine of x See Also ======== cosh, tanh, asinh icC s0|dkrt|jdƒSt||ƒ‚dS(s@ Returns the first derivative of this function. iiN(tcoshtargsR(tselftargindex((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pytfdiffPs cC stS(s7 Returns the inverse of this function. (tasinh(R.R/((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pytinverseYscC sddlm}t|ƒ}|jr•|tjkr;tjS|tjkrQtjS|tjkrgtjS|tjkr}tjS|j rþ|| ƒ Sni|tj kr«tjS|j tj ƒ}|dk rÚtj ||ƒSt|ƒrò|| ƒ S|jr>t|ƒ\}}|r>t|ƒt|ƒt|ƒt|ƒSn|jtkrX|jdS|jtkr|jd}t|dƒt|dƒS|jtkrÂ|jd}|td|dƒS|jtkrþ|jd}dt|dƒt|dƒSdS(Niÿÿÿÿ(tsiniii(tsympyR3Rt is_NumberRtNaNtInfinitytNegativeInfinityR"t is_negativetComplexInfinitytas_coefficientRtNoneRtis_AddR*R+R,tfuncR1R-tacoshR tatanhtacoth(tclsR$R3ti_coefftxtm((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyteval_sF       +    cG sy|dks|ddkr#tjSt|ƒ}t|ƒdkrc|d}||d||dS||t|ƒSdS(sG Returns the next term in the Taylor series expansion. iiiþÿÿÿiN(RR"RtlenR (tnRDtprevious_termsR'((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyt taylor_terms  cC s|j|jdjƒƒS(Ni(R>R-t conjugate(R.((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyt_eval_conjugate¡scK sÐddlm}m}|jdjr_|rOt|d<|j||tjfS|tjfSn|r|jdj||j ƒ\}}n|jdj ƒ\}}t |ƒ||ƒt |ƒ||ƒfS(s@ Returns this function as a complex coordinate. iÿÿÿÿ(tcosR3itcomplex( R4RMR3R-tis_realtFalsetexpandRR"t as_real_imagR+R,(R.tdeepthintsRMR3tretim((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRR¤s (cK s*|jd||\}}||tjS(NRS(RRRR(R.RSRTtre_parttim_part((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyt_eval_expand_complexµscK só|r"|jdj||}n |jd}d}|jrS|jƒ\}}nV|jdtƒ\}}|tjk r©|j r©|tjk r©|}|d|}n|dk rét |ƒt |ƒt |ƒt |ƒjdtƒSt |ƒS(Nitrationalittrig( R-RQR<R=R t as_coeff_MulRRRt is_IntegerR+R,(R.RSRTR$RDtytcoefftterms((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyt_eval_expand_trig¹s  ' 4cK st|ƒt| ƒdS(Ni(R (R.R$tkwargs((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyt_eval_rewrite_as_tractableÊscK st|ƒt| ƒdS(Ni(R (R.R$Rb((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyt_eval_rewrite_as_expÍscK s$tj t|tjtjdƒS(Ni(RRR,R(R.R$Rb((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyt_eval_rewrite_as_coshÐscK s'ttj|ƒ}d|d|dS(Nii(ttanhRR#(R.R$Rbt tanh_half((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyt_eval_rewrite_as_tanhÓscK s'ttj|ƒ}d||ddS(Nii(tcothRR#(R.R$Rbt coth_half((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyt_eval_rewrite_as_coth×scC sbddlm}|jdj|ƒ}||jkrQ|d|ƒj|ƒrQ|S|j|ƒSdS(Niÿÿÿÿ(tOrderii(R4RlR-tas_leading_termt free_symbolstcontainsR>(R.RDRlR$((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyt_eval_as_leading_termÛs 'cC s|jdjrtSdS(Ni(R-ROR(R.((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyt _eval_is_realäscC s"|jdjr|jdjSdS(Ni(R-ROt is_positive(R.((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyt_eval_is_positiveèscC s"|jdjr|jdjSdS(Ni(R-ROR9(R.((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyt_eval_is_negativeìscC s|jd}|jrtSdS(Ni(R-t is_imaginaryR(R.R$((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyt_eval_is_finiteðs  (RRRR0R2t classmethodRFt staticmethodRRJRLRRRRYRaRcRdReRhRkRpRqRsRtRv(((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyR+Ds(  1            R,cB s³eZdZdd„Zed„ƒZeed„ƒƒZd„Z e d„Z e d„Z e d„Z d „Zd „Zd „Zd „Zd „Zd„Zd„Zd„ZRS(sª The hyperbolic cosine function, `\frac{e^x + e^{-x}}{2}`. * cosh(x) -> Returns the hyperbolic cosine of x See Also ======== sinh, tanh, acosh icC s0|dkrt|jdƒSt||ƒ‚dS(Nii(R+R-R(R.R/((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyR0s cC sãddlm}t|ƒ}|jr”|tjkr;tjS|tjkrQtjS|tjkrgtjS|tjkr}tj S|j rß|| ƒSnK|tj krªtjS|j tj ƒ}|dk rÒ||ƒSt|ƒré|| ƒS|jr5t|ƒ\}}|r5t|ƒt|ƒt|ƒt|ƒSn|jtkr]td|jddƒS|jtkrw|jdS|jtkr£dtd|jddƒS|jtkrß|jd}|t|dƒt|dƒSdS(Niÿÿÿÿ(RMiii(R4RMRR5RR6R7R8R"RR9R:R;RR<RR=R*R,R+R>R1R R-R?R@RA(RBR$RMRCRDRE((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRFsB        +  cG 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RfcB s¹eZdZdd„Zdd„Zed„ƒZeed„ƒƒZ d„Z e d„Z d„Z d „Zd „Zd „Zd „Zd „Zd„Zd„Zd„Zd„ZRS(s¯ The hyperbolic tangent function, `\frac{\sinh(x)}{\cosh(x)}`. * tanh(x) -> Returns the hyperbolic tangent of x See Also ======== sinh, cosh, atanh icC s;|dkr(tjt|jdƒdSt||ƒ‚dS(Niii(RRRfR-R(R.R/((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyR0›s cC stS(s7 Returns the inverse of this function. (R@(R.R/((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyR2¡scC sddlm}t|ƒ}|jr•|tjkr;tjS|tjkrQtjS|tjkrgtj S|tj kr}tj S|j r || ƒ Snx|tj kr«tjS|j tjƒ}|dk rùt|ƒrètj || ƒStj||ƒSt|ƒr|| ƒ S|jrgt|ƒ\}}|rgt|ƒ}|tj krWt|ƒSt|ƒSqgn|jtkr™|jd}|td|dƒS|jtkrÕ|jd}t|dƒt|dƒ|S|jtkrï|jdS|jtkr d|jdSdS(Niÿÿÿÿ(ttaniii(R4RzRR5RR6R7RR8t NegativeOneR"R9R:R;RR<RR=R*RfRiR>R1R-R R?R@RA(RBR$RzRCRDREttanhm((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRF§sN              cG sddlm}|dks,|ddkr3tjSt|ƒ}d|d}||dƒ}t|dƒ}||d||||SdS(Niÿÿÿÿ(t bernoulliiii(R4R}RR"RR (RHRDRIR}R%tBtF((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRJÜs cC s|j|jdjƒƒS(Ni(R>R-RK(R.((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRLìscK söddlm}m}|jdjr_|rOt|d<|j||tjfS|tjfSn|r|jdj||j ƒ\}}n|jdj ƒ\}}t |ƒd||ƒd}t |ƒt |ƒ|||ƒ||ƒ|fS(Niÿÿÿÿ(RMR3iRNi( R4RMR3R-RORPRQRR"RRR+R,(R.RSRTRMR3RURVtdenom((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRRïs (cK s*t| ƒt|ƒ}}||||S(N(R (R.R$Rbtneg_exptpos_exp((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRcþscK s*t| ƒt|ƒ}}||||S(N(R (R.R$RbRR‚((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRdscK s-tjt|ƒttjtjd|ƒS(Ni(RRR+R(R.R$Rb((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRyscK s-tjttjtjd|ƒt|ƒS(Ni(RRR,R(R.R$Rb((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRe scK sdt|ƒS(Ni(Ri(R.R$Rb((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRk scC sbddlm}|jdj|ƒ}||jkrQ|d|ƒj|ƒrQ|S|j|ƒSdS(Niÿÿÿÿ(Rlii(R4RlR-RmRnRoR>(R.RDRlR$((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRps 'cC s|jdjrtSdS(Ni(R-ROR(R.((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRqscC s"|jdjr|jdjSdS(Ni(R-RORr(R.((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRsscC s"|jdjr|jdjSdS(Ni(R-ROR9(R.((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRt scC s|jd}|jrtSdS(Ni(R-ROR(R.R$((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRv$s  (RRRR0R2RwRFRxRRJRLRRRRcRdRyReRkRpRqRsRtRv(((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRfs$   5          RicB s§eZdZdd„Zdd„Zed„ƒZeed„ƒƒZ d„Z e d„Z d„Z d „Zd „Zd „Zd „Zd „Zd„Zd„ZRS(s The hyperbolic cotangent function, `\frac{\cosh(x)}{\sinh(x)}`. * coth(x) -> Returns the hyperbolic cotangent of x icC s8|dkr%dt|jdƒdSt||ƒ‚dS(Niiÿÿÿÿii(R+R-R(R.R/((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyR01s cC stS(s7 Returns the inverse of this function. (RA(R.R/((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyR27scC sddlm}t|ƒ}|jr•|tjkr;tjS|tjkrQtjS|tjkrgtj S|tj kr}tj S|j r || ƒ Snx|tj kr«tjS|j tjƒ}|dk rùt|ƒrçtj|| ƒStj ||ƒSt|ƒr|| ƒ S|jrgt|ƒ\}}|rgt|ƒ}|tj krWt|ƒSt|ƒSqgn|jtkr™|jd}td|dƒ|S|jtkrÕ|jd}|t|dƒt|dƒS|jtkród|jdS|jtkr |jdSdS(Niÿÿÿÿ(tcotiii(R4RƒRR5RR6R7RR8R{R"R:R9R;RR<RR=R*RiRfR>R1R-R R?R@RA(RBR$RƒRCRDREtcothm((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRF=sN             cG s™ddlm}|dkr*dt|ƒS|dksF|ddkrMtjSt|ƒ}||dƒ}t|dƒ}d|d||||SdS(Niÿÿÿÿ(R}iii(R4R}RRR"R (RHRDRIR}R~R((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRJrs  cC s|j|jdjƒƒS(Ni(R>R-RK(R.((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRL‚scK s÷ddlm}m}|jdjr_|rOt|d<|j||tjfS|tjfSn|r|jdj||j ƒ\}}n|jdj ƒ\}}t |ƒd||ƒd}t |ƒt |ƒ|||ƒ ||ƒ|fS(Niÿÿÿÿ(RMR3iRNi( R4RMR3R-RORPRQRR"RRR+R,(R.RSRTRMR3RURVR€((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRR…s (cK s*t| ƒt|ƒ}}||||S(N(R (R.R$RbRR‚((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRc”scK s*t| ƒt|ƒ}}||||S(N(R (R.R$RbRR‚((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRd˜scK s.tj ttjtjd|ƒt|ƒS(Ni(RRR+R(R.R$Rb((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRyœscK s.tj t|ƒttjtjd|ƒS(Ni(RRR,R(R.R$Rb((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyReŸscK sdt|ƒS(Ni(Rf(R.R$Rb((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRh¢scC s"|jdjr|jdjSdS(Ni(R-RORr(R.((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRs¥scC s"|jdjr|jdjSdS(Ni(R-ROR9(R.((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRt©scC sfddlm}|jdj|ƒ}||jkrU|d|ƒj|ƒrUd|S|j|ƒSdS(Niÿÿÿÿ(Rlii(R4RlR-RmRnRoR>(R.RDRlR$((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRp­s '(RRRR0R2RwRFRxRRJRLRRRRcRdRyReRhRsRtRp(((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRi*s   5         tReciprocalHyperbolicFunctioncB sªeZdZdZdZdZed„ƒZd„Z d„Z d„Z d„Z d„Z d„Zd„Zed „Zd „Zed „Zd „Zd „Zd„ZRS(s=Base class for reciprocal functions of hyperbolic functions. cC sŽ|jƒr8|jr || ƒS|jr8|| ƒ Sn|jj|ƒ}t|dƒrv|jƒ|krv|jdS|dk rŠd|S|S(NR2ii( tcould_extract_minus_signt_is_event_is_oddt_reciprocal_ofRFthasattrR2R-R<(RBR$tt((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRF¿s    ! cO s,|j|jdƒ}t||ƒ||ŽS(Ni(R‰R-tgetattr(R.t method_nameR-Rbto((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyt_call_reciprocalÌscO s-|j|||Ž}|dk r)d|S|S(Ni(RR<(R.RR-RbR‹((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyt_calculate_reciprocalÑscC s?|j||ƒ}|dk r;||j|ƒkr;d|SdS(Ni(RR<R‰(R.RR$R‹((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyt_rewrite_reciprocal×s!cK s|jd|ƒS(NRd(R‘(R.R$Rb((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRdÞscK s|jd|ƒS(NRc(R‘(R.R$Rb((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRcáscK s|jd|ƒS(NRh(R‘(R.R$Rb((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRhäscK s|jd|ƒS(NRk(R‘(R.R$Rb((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRkçscK s$d|j|jdƒj||S(Nii(R‰R-RR(R.RSRT((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRRêscC s|j|jdjƒƒS(Ni(R>R-RK(R.((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRLíscK s*|jdt|\}}|tj|S(NRS(RRRRR(R.RSRTRWRX((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRYðscC s!d|j|jdƒj|ƒS(Nii(R‰R-Rp(R.RD((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRpôscC s|j|jdƒjS(Ni(R‰R-RO(R.((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRq÷scC sd|j|jdƒjS(Nii(R‰R-t is_finite(R.((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRvúsN(RRRR<R‰R‡RˆRwRFRRR‘RdRcRhRkRRRRLRYRpRqRv(((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyR…·s$            tcschcB s_eZdZeZeZdd„Zee d„ƒƒZ d„Z d„Z d„Z d„ZRS(sÀ The hyperbolic cosecant function, `\frac{2}{e^x - e^{-x}}` * csch(x) -> Returns the hyperbolic cosecant of x See Also ======== sinh, cosh, tanh, sech, asinh, acosh icC sB|dkr/t|jdƒ t|jdƒSt||ƒ‚dS(s? Returns the first derivative of this function iiN(RiR-R“R(R.R/((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyR0 s #cG sddlm}|dkr*dt|ƒS|dksF|ddkrMtjSt|ƒ}||dƒ}t|dƒ}ddd|||||SdS(sF Returns the next term in the Taylor series expansion iÿÿÿÿ(R}iiiN(R4R}RRR"R (RHRDRIR}R~R((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRJs  cK s#tjt|tjtjdƒS(Ni(RRR,R(R.R$Rb((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRe)scC s"|jdjr|jdjSdS(Ni(R-RORr(R.((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRs,scC s"|jdjr|jdjSdS(Ni(R-ROR9(R.((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRt0scC s)ddlj}|j|jdjƒƒS(Niÿÿÿÿi(tsage.alltallR“R-t_sage_(R.tsage((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyR–4s(RRRR+R‰RRˆR0RxRRJReRsRtR–(((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyR“þs     tsechcB sVeZdZeZeZdd„Zee d„ƒƒZ d„Z d„Z d„Z RS(s The hyperbolic secant function, `\frac{2}{e^x + e^{-x}}` * sech(x) -> Returns the hyperbolic secant of x See Also ======== sinh, cosh, tanh, coth, csch, asinh, acosh icC sB|dkr/t|jdƒ t|jdƒSt||ƒ‚dS(Nii(RfR-R˜R(R.R/((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyR0Hs #cG s_ddlm}|dks,|ddkr3tjSt|ƒ}||ƒt|ƒ||SdS(Niÿÿÿÿ(teuleriii(t%sympy.functions.combinatorial.numbersR™RR"RR (RHRDRIR™((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRJNs  cK s#tjt|tjtjdƒS(Ni(RRR+R(R.R$Rb((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRyXscC s|jdjrtSdS(Ni(R-ROR(R.((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRs[scC s)ddlj}|j|jdjƒƒS(Niÿÿÿÿi(R”R•R˜R-R–(R.R—((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyR–_s(RRRR,R‰RR‡R0RxRRJRyRsR–(((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyR˜9s    tInverseHyperbolicFunctioncB seZdZRS(s,Base class for inverse hyperbolic functions.(RRR(((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyR›isR1cB s\eZdZdd„Zed„ƒZeed„ƒƒZd„Z d„Z dd„Z RS(sž The inverse hyperbolic sine function. * asinh(x) -> Returns the inverse hyperbolic sine of x See Also ======== acosh, atanh, sinh icC s<|dkr)dt|jdddƒSt||ƒ‚dS(Niii(R R-R(R.R/((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyR0{s cC s<ddlm}t|ƒ}|jrÛ|tjkr;tjS|tjkrQtjS|tjkrgtjS|tjkr}tjS|tj kr t t dƒdƒS|tj krÃt t dƒdƒS|j r8|| ƒ Sn]|tjkrñtjS|jtjƒ}|dk r tj||ƒSt|ƒr8|| ƒ SdS(Niÿÿÿÿ(tasinii(R4RœRR5RR6R7R8R"RR R R{R9R:R;RR<R(RBR$RœRC((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRFs0     cG sÈ|dks|ddkr#tjSt|ƒ}t|ƒdkr||dkr||d}| |dd||d|dS|dd}ttj|ƒ}t|ƒ}d||||||SdS(Niiiþÿÿÿiiÿÿÿÿ(RR"RRGR R#R (RHRDRIR'tktRR((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRJ¡s  % cC sbddlm}|jdj|ƒ}||jkrQ|d|ƒj|ƒrQ|S|j|ƒSdS(Niÿÿÿÿ(Rlii(R4RlR-RmRnRoR>(R.RDRlR$((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRp±s 'cK st|t|ddƒƒS(Nii(R R (R.RDRb((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyt_eval_rewrite_as_logºscC stS(s7 Returns the inverse of this function. (R+(R.R/((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyR2½s( RRRR0RwRFRxRRJRpRŸR2(((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyR1os    R?cB s\eZdZdd„Zed„ƒZeed„ƒƒZd„Z d„Z dd„Z RS(s¢ The inverse hyperbolic cosine function. * acosh(x) -> Returns the inverse hyperbolic cosine of x See Also ======== asinh, atanh, cosh icC s<|dkr)dt|jdddƒSt||ƒ‚dS(Niii(R R-R(R.R/((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyR0Ðs cC sßt|ƒ}|jr®|tjkr+tjS|tjkrAtjS|tjkrWtjS|tjkrxtjtjdS|tj krŽtjS|tj kr®tjtjSn|j rfit tjdt dƒƒtj6t tj dt dƒƒtj 6tjdtj6dtjdtj 6tjdt dƒd6dtjdt dƒ d6tjddt dƒ6dtjddt dƒ6tjdt dƒd6dtjdt dƒ d6dtjdt dƒdt d ƒ6d tjdt dƒd t d ƒ6tjd t dt dƒƒd6d tjd t dt dƒƒ d6dtjd t dt dƒƒd6dtjd t dt dƒƒ d6tjddt dƒdt dƒ6d tjddt dƒ dt dƒ6tjdt dƒdd6dtjdt dƒd d6}||krf|jr[||tjS||Sn|tjkr|tjS|tjtjkr«tjtjtjdS|tj tjkrÛtjtjtjdSdS(Niiiiiÿÿÿÿiii iii ii(RR5RR6R7R8R"RRRR{t is_numberR R R#ROR:(RBR$t cst_table((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRFÖs\   !#&'"'&'&+$   cG så|dkrtjtjdS|dks:|ddkrAtjSt|ƒ}t|ƒdkr™|dkr™|d}||dd||d|dS|dd}ttj|ƒ}t|ƒ}| |tj|||SdS(Niiiþÿÿÿi( RRRR"RRGR R#R (RHRDRIR'RRžR((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRJ s   $ cC spddlm}|jdj|ƒ}||jkr_|d|ƒj|ƒr_tjtjdS|j |ƒSdS(Niÿÿÿÿ(Rliii( R4RlR-RmRnRoRRRR>(R.RDRlR$((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRps 'cK s&t|t|dƒt|dƒƒS(Ni(R R (R.RDRb((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRŸ'scC stS(s7 Returns the inverse of this function. (R,(R.R/((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyR2*s( RRRR0RwRFRxRRJRpRŸR2(((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyR?Äs  6 R@cB s\eZdZdd„Zed„ƒZeed„ƒƒZd„Z d„Z dd„Z RS(s¤ The inverse hyperbolic tangent function. * atanh(x) -> Returns the inverse hyperbolic tangent of x See Also ======== asinh, acosh, tanh icC s6|dkr#dd|jddSt||ƒ‚dS(Niii(R-R(R.R/((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyR0=s cC sdddlm}t|ƒ}|jr×|tjkr;tjS|tjkrQtjS|tjkrgtjS|tj kr}tj S|tjkržtj ||ƒS|tj kr¿tj || ƒS|j r`|| ƒ Sn‰|tj krddlm}tj |tj dtjdƒS|jtj ƒ}|dk rHtj ||ƒSt|ƒr`|| ƒ SdS(Niÿÿÿÿ(tatan(t AccumBoundsi(R4R¢RR5RR6R"RR7R{R8RR9R:tsympy.calculus.utilR£RR;R<R(RBR$R¢R£RC((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRFCs2   #  cG s?|dks|ddkr#tjSt|ƒ}|||SdS(Nii(RR"R(RHRDRI((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRJds cC sbddlm}|jdj|ƒ}||jkrQ|d|ƒj|ƒrQ|S|j|ƒSdS(Niÿÿÿÿ(Rlii(R4RlR-RmRnRoR>(R.RDRlR$((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRpms 'cK s td|ƒtd|ƒdS(Nii(R (R.RDRb((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRŸvscC stS(s7 Returns the inverse of this function. (Rf(R.R/((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyR2ys( RRRR0RwRFRxRRJRpRŸR2(((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyR@1s  ! RAcB s\eZdZdd„Zed„ƒZeed„ƒƒZd„Z d„Z dd„Z RS(su The inverse hyperbolic cotangent function. * acoth(x) -> Returns the inverse hyperbolic cotangent of x icC s6|dkr#dd|jddSt||ƒ‚dS(Niii(R-R(R.R/((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyR0‡s cC s.ddlm}t|ƒ}|jrÌ|tjkr;tjS|tjkrQtjS|tjkrgtjS|tjkrˆtj tj dS|tj kržtjS|tj kr´tjS|j r*|| ƒ Sn^|tjkrâtjS|jtj ƒ}|dk rtj ||ƒSt|ƒr*|| ƒ SdS(Niÿÿÿÿ(tacoti(R4R¥RR5RR6R7R"R8RRRR{R9R:R;R<R(RBR$R¥RC((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRFs0     cG s]|dkrtjtjdS|dks:|ddkrAtjSt|ƒ}|||SdS(Nii(RRRR"R(RHRDRI((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRJ­s   cC spddlm}|jdj|ƒ}||jkr_|d|ƒj|ƒr_tjtjdS|j |ƒSdS(Niÿÿÿÿ(Rliii( R4RlR-RmRnRoRRRR>(R.RDRlR$((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRp¸s 'cK s(tdd|ƒtdd|ƒdS(Nii(R (R.RDRb((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRŸÁscC stS(s7 Returns the inverse of this function. (Ri(R.R/((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyR2Äs( RRRR0RwRFRxRRJRpRŸR2(((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRA€s   tasechcB sSeZdZdd„Zed„ƒZeed„ƒƒZdd„Z d„Z RS(s² The inverse hyperbolic secant function. * asech(x) -> Returns the inverse hyperbolic secant of x Examples ======== >>> from sympy import asech, sqrt, S >>> from sympy.abc import x >>> asech(x).diff(x) -1/(x*sqrt(1 - x**2)) >>> asech(1).diff(x) 0 >>> asech(1) 0 >>> asech(S(2)) I*pi/3 >>> asech(-sqrt(2)) 3*I*pi/4 >>> asech((sqrt(6) - sqrt(2))) I*pi/12 See Also ======== asinh, atanh, cosh, acoth References ========== .. [1] https://en.wikipedia.org/wiki/Hyperbolic_function .. [2] http://dlmf.nist.gov/4.37 .. [3] http://functions.wolfram.com/ElementaryFunctions/ArcSech/ icC sF|dkr3|jd}d|td|dƒSt||ƒ‚dS(Niiiÿÿÿÿi(R-R R(R.R/tz((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyR0ñs  cC sAt|ƒ}|jr¹|tjkr+tjS|tjkrLtjtjdS|tjkrmtjtjdS|tjkrƒtjS|tj kr™tjS|tj kr¹tjtjSn|j rûitjtjd t dt dƒƒtj6tjtjdt dt dƒƒtj 6tjdt dƒt dƒ6dtjdt dƒt dƒ6tjdt ddt dƒƒ6dtjdt ddt dƒƒ 6tjd dt dt dƒƒ6d tjd d t dt dƒƒ6tjddt d ƒ6dtjdd t d ƒ6tjdt dƒd6d tjddt dƒ6tjd t dƒ6d tjd t dƒ 6d tjdt ddt dƒƒ6d tjdt ddt dƒƒ 6tjd tdƒ6dtjd tdƒ 6d tjd t ddt dƒƒ6dtjd t ddt dƒƒ 6dtjddt dƒ6d tjddt dƒ6dtjdt dƒt dƒ6d tjdt dƒ t dƒ6}||krû|jrð||tjS||Sn|tjkr=ddlm}tj|tj dtjdƒSdS(Niii ii i ii iiiþÿÿÿiiiÿÿÿÿ(R£(RR5RR6R7RRR8R"RR{R R R ROR:R¤R£(RBR$R¡R£((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRFøs^   --""'"&&'&'"&   cG sñ|dkrtd|ƒS|dks6|ddkr=tjSt|ƒ}t|ƒdkr™|dkr™|d}||dd|dd|ddS|d}ttj|ƒ|}t|ƒ|d|d}d||||dSdS(Niiiiþÿÿÿiiÿÿÿÿ(R RR"RRGR R#R (RHRDRIR'RRžR((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pytexpansion_term/s   ( cC stS(s7 Returns the inverse of this function. (R˜(R.R/((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyR2AscK s2td|td|dƒtd|dƒƒS(Ni(R R (R.R$Rb((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRŸGs( RRRR0RwRFRxRR¨R2RŸ(((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyR¦Ës$ 7 tacschcB s>eZdZdd„Zed„ƒZdd„Zd„ZRS(s¸ The inverse hyperbolic cosecant function. * acsch(x) -> Returns the inverse hyperbolic cosecant of x Examples ======== >>> from sympy import acsch, sqrt, S >>> from sympy.abc import x >>> acsch(x).diff(x) -1/(x**2*sqrt(1 + x**(-2))) >>> acsch(1).diff(x) 0 >>> acsch(1) log(1 + sqrt(2)) >>> acsch(S.ImaginaryUnit) -I*pi/2 >>> acsch(-2*S.ImaginaryUnit) I*pi/6 >>> acsch(S.ImaginaryUnit*(sqrt(6) - sqrt(2))) -5*I*pi/12 References ========== .. [1] https://en.wikipedia.org/wiki/Hyperbolic_function .. [2] http://dlmf.nist.gov/4.37 .. [3] http://functions.wolfram.com/ElementaryFunctions/ArcCsch/ icC sN|dkr;|jd}d|dtdd|dƒSt||ƒ‚dS(Niiiÿÿÿÿi(R-R R(R.R/R§((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyR0ls  "cC sãt|ƒ}|jr·|tjkr+tjS|tjkrAtjS|tjkrWtjS|tjkrmtjS|tjkrt dt dƒƒS|tj kr·t dt dƒƒ Sn|j r±i tj dtj6tj dtjt dƒt dƒ6tj dtjdt dƒ6tj dtjdt dt dƒƒ6tj dtjd6tj dtjt ddt dƒƒ6tj dtjt dƒ6d tj dtjt dƒd6tj d tjdt d ƒ6d tj dtjdt dt dƒƒ6d tj dtjt ddt dƒƒ6d tj dtjt dƒt dƒ6tj t dt dƒdƒtdƒ6}||kr±||tjSn|tjkrÇtjSt|ƒrß|| ƒ SdS( Niii ii iiiiýÿÿÿiiþÿÿÿiûÿÿÿ(RR5RR6R7R"R8R:RR R R{R RRR(RBR$R¡((sDlib/python2.7/site-packages/sympy/functions/elementary/hyperbolic.pyRFssF   & **# --),  cC stS(s7 Returns the inverse of this function. 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