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Xwdf苒S!0!1T$f(9H H8豒1f(qf(H H5H81nff.SH=1 HHr赓H5HHc薓H5HHDwH5wHH%1YH5HH1;H5\HHH[@f.zufےHHd:radiansd:degreesd:isnand:isinfd:isfiniteintermediate overflow in fsummath.fsum partials-inf + inf in fsumd:modf(dd)gcdd:frexp(di)math domain errormath range errordO:ldexpdd:fmoddd:powatan2remaindercopysigndd:hypotOO:logpitau__ceil____floor__brel_tolabs_toldd|$dd:isclose__trunc__mathacosacoshasinasinhatanatanhceilerferfcexpm1fabsfactorialfloorlgammalog1plog10log2sqrttruncxPx_7a(s(;LXww0uw~Cs+|g!??@@8@^@@@@&AKAAA2A(;L4BuwsBuwB7Bs6Ch0{CZAC Ƶ;(DlYaRwNDfactorial() only accepts integral valuesfactorial() argument should not exceed %ldfactorial() not defined for negative valuestype %.100s doesn't define __trunc__ methodtolerances must be non-negativeExpected an int as second argument to ldexp.math.log requires 1 to 2 arguments9RFߑ?cܥL@@-DT! @???& .>#B ;@' @R;{`Zj@P@X@@뇇BA@LPEAA]v}A{DA*_{ AqqiA?tAA补ApqA&"BA2 BiAWLup#BCQBAE@HP?7@i@E@-DT! a@?yPD?9B.?iW @-DT!@?-DT!?!3|@-DT!?-DT! @;=8PPh0pИ 0Оx`P0У(P0x0H@h е@p0p`(PX p( h ` ( pH h P ( X x p P  `@ p  `` zRx $FJ w?;*3$"DЍ7D r\7D rt D0 M 7D rȏ7D r7D rLBEB B(A0A8G 8A0A(B BBBA \,"BND A(G@u (D ABBF  (A ABBJ X (A ABBB |xBBB B(A0A8G`[ 8A0A(B BBBA n 8A0A(B BBBA Z 8C0A(B BBBJ  $D<ؙBAD F AEE K AEG Q DEF ,PAQ AC D CI $D@ D G A $xD@ A g I ,0H z F c E H H Y$4H V B ~ B H$\(H V B ~ B HTBYD DP_  DABG J  DAED _  DABB 8AP@AtD  D 4HPq G [ E D D ] K T_D J J F,tЦAG i CD D AK 4RAG@f AI T CA  CJ 4EAPF`  DAG ` GAH 4ASP AD c AD F AA ,L8@AS` AG  AC ,|HfH@ G U K Z F $H z F R F q G ,AG l AK _ CF ,pAZP CI e AJ ,40AZP CI e AJ ,dAZP CA _ AH <ASP AK _ AH M AJ w AH \PLBED D(D@ (C ABBE ] (A AEBB J (C ABBF <4@AND0n AAE X AAF aAF<tAND0n AAE X AAF aAFD  F J,$AG  CG ] AJ ,$AG  CG ] AJ 4D  F JT D  F J,t$AG  CG ] AJ ,+AG  CC ] AJ ,+AG  CC ] AJ , $AG  CG ] AJ ,4 $AG  CG ] AJ d D  F J @D  F J D  G J, `+AG  CC ] AJ  `D  F J4 QAG  CC ] AJ R CC ,L +AG  CC ] AJ T| mAAG@ AAA w AAG # AAK \ AAB < 0 BEA A(Dpw (D ABBC T UAAG@ AAD w AAG  AAH x AAF l A  -,-H :DYi H'   o    PH oPoooP v'''''''''((&(6(F(V(f(v((((((((())&)6)F)V)f)v)))))))))**&*6*F*V*f*v*********++&+6+F+V+f+v+++++++++,,&,6,F,This module is always available. It provides access to the mathematical functions defined by the C standard.tanh($module, x, /) -- Return the hyperbolic tangent of x.tan($module, x, /) -- Return the tangent of x (measured in radians).sqrt($module, x, /) -- Return the square root of x.sinh($module, x, /) -- Return the hyperbolic sine of x.sin($module, x, /) -- Return the sine of x (measured in radians).remainder($module, x, y, /) -- Difference between x and the closest integer multiple of y. Return x - n*y where n*y is the closest integer multiple of y. In the case where x is exactly halfway between two multiples of y, the nearest even value of n is used. The result is always exact.log1p($module, x, /) -- Return the natural logarithm of 1+x (base e). The result is computed in a way which is accurate for x near zero.lgamma($module, x, /) -- Natural logarithm of absolute value of Gamma function at x.gamma($module, x, /) -- Gamma function at x.fabs($module, x, /) -- Return the absolute value of the float x.expm1($module, x, /) -- Return exp(x)-1. This function avoids the loss of precision involved in the direct evaluation of exp(x)-1 for small x.exp($module, x, /) -- Return e raised to the power of x.erfc($module, x, /) -- Complementary error function at x.erf($module, x, /) -- Error function at x.cosh($module, x, /) -- Return the hyperbolic cosine of x.cos($module, x, /) -- Return the cosine of x (measured in radians).copysign($module, x, y, /) -- Return a float with the magnitude (absolute value) of x but the sign of y. On platforms that support signed zeros, copysign(1.0, -0.0) returns -1.0. atanh($module, x, /) -- Return the inverse hyperbolic tangent of x.atan2($module, y, x, /) -- Return the arc tangent (measured in radians) of y/x. Unlike atan(y/x), the signs of both x and y are considered.atan($module, x, /) -- Return the arc tangent (measured in radians) of x.asinh($module, x, /) -- Return the inverse hyperbolic sine of x.asin($module, x, /) -- Return the arc sine (measured in radians) of x.acosh($module, x, /) -- Return the inverse hyperbolic cosine of x.acos($module, x, /) -- Return the arc cosine (measured in radians) of x.isclose($module, /, a, b, *, rel_tol=1e-09, abs_tol=0.0) -- Determine whether two floating point numbers are close in value. rel_tol maximum difference for being considered "close", relative to the magnitude of the input values abs_tol maximum difference for being considered "close", regardless of the magnitude of the input values Return True if a is close in value to b, and False otherwise. For the values to be considered close, the difference between them must be smaller than at least one of the tolerances. -inf, inf and NaN behave similarly to the IEEE 754 Standard. That is, NaN is not close to anything, even itself. inf and -inf are only close to themselves.isinf($module, x, /) -- Return True if x is a positive or negative infinity, and False otherwise.isnan($module, x, /) -- Return True if x is a NaN (not a number), and False otherwise.isfinite($module, x, /) -- Return True if x is neither an infinity nor a NaN, and False otherwise.radians($module, x, /) -- Convert angle x from degrees to radians.degrees($module, x, /) -- Convert angle x from radians to degrees.pow($module, x, y, /) -- Return x**y (x to the power of y).hypot($module, x, y, /) -- Return the Euclidean distance, sqrt(x*x + y*y).fmod($module, x, y, /) -- Return fmod(x, y), according to platform C. x % y may differ.log10($module, x, /) -- Return the base 10 logarithm of x.log2($module, x, /) -- Return the base 2 logarithm of x.log(x, [base=math.e]) Return the logarithm of x to the given base. If the base not specified, returns the natural logarithm (base e) of x.modf($module, x, /) -- Return the fractional and integer parts of x. Both results carry the sign of x and are floats.ldexp($module, x, i, /) -- Return x * (2**i). This is essentially the inverse of frexp().frexp($module, x, /) -- Return the mantissa and exponent of x, as pair (m, e). m is a float and e is an int, such that x = m * 2.**e. If x is 0, m and e are both 0. Else 0.5 <= abs(m) < 1.0.trunc($module, x, /) -- Truncates the Real x to the nearest Integral toward 0. Uses the __trunc__ magic method.factorial($module, x, /) -- Find x!. Raise a ValueError if x is negative or non-integral.fsum($module, seq, /) -- Return an accurate floating point sum of values in the iterable seq. Assumes IEEE-754 floating point arithmetic.floor($module, x, /) -- Return the floor of x as an Integral. This is the largest integer <= x.ceil($module, x, /) -- Return the ceiling of x as an Integral. 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