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H?uDT$%T$Y?!f(AH!jH8AH01]fL$HuL$ŊL$f?YE?!f.{ f.f(<f(fT%>;f{fHmT$ST$Y>!f(>fD _fD!W"V>f/H5iH5:H817f(HD$\$L$螉L$\$HD$f(@ff/w@T$L$腉L$T$f. ! c=^f(-f(L@ATHUHHHFHD$0Ht3H HBhH5H831HH]A\f1HT$(H5#:MHl$(Ld$0HEjH}HG-:f.,$z:f(fT <f.f.zff/L$fDKMHH ЄID$I|$tL謋f.$HeH&gH8~LAHt$8L$f.$f(躊H蜇f!*<YfDfH*D$8Y;Xf[IHHHHmAI,$-LH$貇H$f1HL$0HT$(H5=8h1HH]A\fDHH fH8ct*Ht$8H f.$f(裉Hu艆f!;YfH*D$8Yx:XH訉58D$f.4$z$T$8f(fT%4:f.2f.Yff(f/f.w f.r f(of.rHdH56H8̆HH1]A\fLf.$$zq$7f(fT%9f.f.ff(f/Lf.wvf.r f(Dx7f(fT $9f.f.ff/r̈́f!Y[9VfDf.rf.HcH5o5H8躅HmH1{T$HlT$QT$f%8!Y 8f.{ f.of(6f(fT98&@!ff/蝅x!" 8f/HbH54H8Ƅ1胃f!Y 8f(ff/}f(HD$d$$HD$d$f(f.{ f.zf(5f(fT27DHH$|H$ff/vv葄|@ff/f(HD$d$fT$HD$d$f([@胂L$!Y 7f(fDL$D$OD$L$!f.zu56f!f.!f.5)$H;$軁$f%5!Y <6mH3f(fT5f.of.ff/L$?L$!fDL$$$L$!f.~4f.!1f.!!f.4 3f(fT4f.f.ff/ef!Y4fD!" ~4f/H]_H51H8>H*_H8J1ff/vf(蠁f(dL$T$T$L$!f.+%3$f(H^H8ff/vf('f(L$$N$L$!f.-3f(ATH=BbIHy3H5$0LH貂2ŀH550LH蓂2覀H5/LHt1M舀H5}0LHV1jH5e0LH8LA\ff.2zuHHUnreachable C code path reachedfactorial() only accepts integral valuesfactorial() argument should not exceed %ldfactorial() not defined for negative valuesn must be a non-negative integerk must be a non-negative integermin(n - k, k) must not exceed %lldtolerances must be non-negativeboth points must have the same number of dimensionstype %.100s doesn't define __trunc__ methodisqrt() argument must be nonnegativeExpected an int as second argument to ldexp.math.log requires 1 to 2 argumentsuuu vuThis module provides access to the mathematical functions defined by the C standard.hypot(*coordinates) -> value Multidimensional Euclidean distance from the origin to a point. Roughly equivalent to: sqrt(sum(x**2 for x in coordinates)) For a two dimensional point (x, y), gives the hypotenuse using the Pythagorean theorem: sqrt(x*x + y*y). For example, the hypotenuse of a 3/4/5 right triangle is: >>> hypot(3.0, 4.0) 5.0 x_7a(s(;LXww0uw~Cs+|g!tanh($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($module, x, /) -- Return the arc cosine (measured in radians) of x.??@@8@^@@@@&AKAAA2A(;L4BuwsBuwB7Bs6Ch0{CZAC Ƶ;(DlYaRwNDcomb($module, n, k, /) -- Number of ways to choose k items from n items without repetition and without order. Evaluates to n! / (k! * (n - k)!) when k <= n and evaluates to zero when k > n. Also called the binomial coefficient because it is equivalent to the coefficient of k-th term in polynomial expansion of the expression (1 + x)**n. Raises TypeError if either of the arguments are not integers. Raises ValueError if either of the arguments are negative.perm($module, n, k=None, /) -- Number of ways to choose k items from n items without repetition and with order. Evaluates to n! / (n - k)! when k <= n and evaluates to zero when k > n. If k is not specified or is None, then k defaults to n and the function returns n!. Raises TypeError if either of the arguments are not integers. Raises ValueError if either of the arguments are negative.prod($module, iterable, /, *, start=1) -- Calculate the product of all the elements in the input iterable. The default start value for the product is 1. When the iterable is empty, return the start value. This function is intended specifically for use with numeric values and may reject non-numeric types.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($module, x, y, /) -- Return x**y (x to the power of y).dist($module, p, q, /) -- Return the Euclidean distance between two points p and q. The points should be specified as sequences (or iterables) of coordinates. Both inputs must have the same dimension. Roughly equivalent to: sqrt(sum((px - qx) ** 2.0 for px, qx in zip(p, q)))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.isqrt($module, n, /) -- Return the integer part of the square root of the input.fsum($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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