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H5H:@UHSHH(dH%(HD$1HGt1ff.Hf(0fT 1f.rff/v1Hk|f.zf/0wy!0HD$yD$f!f.z0tfDH=%\ yHHpitaunextafterintermediate overflow in fsummath.fsum partials-inf + inf in fsum(dd)(di)math domain errormath range errorpowfmodcopysignatan2ldexpdistOO:logremaindercombpermk must not exceed %lldacosacoshasinasinhatanatanhcbrtceildegreeserferfcexp2expm1fabsfactorialfloorfrexpgcdhypotiscloseisfiniteisinfisnanisqrtlcmlgammalog1plog10log2modfradianstruncprodulpstartrel_tolabs_tolmath__ceil____trunc____floor__ .ulp($module, x, /) -- Return the value of the least significant bit of the float x.nextafter($module, x, y, /) -- Return the next floating-point value after x towards y.comb($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.trunc($module, x, /) -- Truncates the Real x to the nearest Integral toward 0. Uses the __trunc__ magic method.tanh($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($module, x, y, /) -- Difference between x and the closest integer multiple of y. Return x - n*y where n*y is the closest integer multiple of y. In the case where x is exactly halfway between two multiples of y, the nearest even value of n is used. The result is always exact.radians($module, x, /) -- Convert angle x from degrees to radians.pow($module, x, y, /) -- Return x**y (x to the power of y).modf($module, x, /) -- Return the fractional and integer parts of x. Both results carry the sign of x and are floats.log2($module, x, /) -- Return the base 2 logarithm of x.log10($module, x, /) -- Return the base 10 logarithm of x.log1p($module, x, /) -- Return the natural logarithm of 1+x (base e). The result is computed in a way which is accurate for x near zero.log(x, [base=math.e]) Return the logarithm of x to the given base. If the base not specified, returns the natural logarithm (base e) of x.lgamma($module, x, /) -- Natural logarithm of absolute value of Gamma function at x.ldexp($module, x, i, /) -- Return x * (2**i). This is essentially the inverse of frexp().lcm($module, *integers) -- Least Common Multiple.isqrt($module, n, /) -- Return the integer part of the square root of the input.isnan($module, x, /) -- Return True if x is a NaN (not a number), and False otherwise.isinf($module, x, /) -- Return True if x is a positive or negative infinity, and False otherwise.isfinite($module, x, /) -- Return True if x is neither an infinity nor a NaN, and False otherwise.isclose($module, /, a, b, *, rel_tol=1e-09, abs_tol=0.0) -- Determine whether two floating point numbers are close in value. rel_tol maximum difference for being considered "close", relative to the magnitude of the input values abs_tol maximum difference for being considered "close", regardless of the magnitude of the input values Return True if a is close in value to b, and False otherwise. For the values to be considered close, the difference between them must be smaller than at least one of the tolerances. -inf, inf and NaN behave similarly to the IEEE 754 Standard. That is, NaN is not close to anything, even itself. inf and -inf are only close to themselves.hypot(*coordinates) -> value Multidimensional Euclidean distance from the origin to a point. Roughly equivalent to: sqrt(sum(x**2 for x in coordinates)) For a two dimensional point (x, y), gives the hypotenuse using the Pythagorean theorem: sqrt(x*x + y*y). For example, the hypotenuse of a 3/4/5 right triangle is: >>> hypot(3.0, 4.0) 5.0 gcd($module, *integers) -- Greatest Common Divisor.gamma($module, x, /) -- Gamma function at x.fsum($module, seq, /) -- Return an accurate floating point sum of values in the iterable seq. Assumes IEEE-754 floating point arithmetic.frexp($module, x, /) -- Return the mantissa and exponent of x, as pair (m, e). m is a float and e is an int, such that x = m * 2.**e. If x is 0, m and e are both 0. Else 0.5 <= abs(m) < 1.0.fmod($module, x, y, /) -- Return fmod(x, y), according to platform C. x % y may differ.floor($module, x, /) -- Return the floor of x as an Integral. This is the largest integer <= x.factorial($module, n, /) -- Find n!. Raise a ValueError if x is negative or non-integral.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.exp2($module, x, /) -- Return 2 raised to the power of x.exp($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.dist($module, p, q, /) -- Return the Euclidean distance between two points p and q. The points should be specified as sequences (or iterables) of coordinates. Both inputs must have the same dimension. Roughly equivalent to: sqrt(sum((px - qx) ** 2.0 for px, qx in zip(p, q)))degrees($module, x, /) -- Convert angle x from radians to degrees.cosh($module, x, /) -- Return the hyperbolic cosine of x.cos($module, x, /) -- Return the cosine of x (measured in radians).copysign($module, x, y, /) -- Return a float with the magnitude (absolute value) of x but the sign of y. On platforms that support signed zeros, copysign(1.0, -0.0) returns -1.0. ceil($module, x, /) -- Return the ceiling of x as an Integral. This is the smallest integer >= x.cbrt($module, x, /) -- Return the cube root of x.atanh($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. The result is between -pi/2 and pi/2.asinh($module, x, /) -- Return the inverse hyperbolic sine of x.asin($module, x, /) -- Return the arc sine (measured in radians) of x. The result is between -pi/2 and pi/2.acosh($module, x, /) -- Return the inverse hyperbolic cosine of x.acos($module, x, /) -- Return the arc cosine (measured in radians) of x. 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