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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($module, x, i, /) -- Return x * (2**i). This is essentially the inverse of frexp().isqrt($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($module, x, y, /) -- greatest common divisor of x and ygamma($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($module, x, /) -- Find x!. Raise a ValueError if x is negative or non-integral.fabs($module, x, /) -- Return the absolute value of the float x.expm1($module, x, /) -- Return exp(x)-1. This function avoids the loss of precision involved in the direct evaluation of exp(x)-1 for small x.exp($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.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($module, x, /) -- Return the arc cosine (measured in radians) of x.This module provides access to the mathematical functions defined by the C standard.x_7a(s(;LXww0uw~Cs+|g!??@@8@^@@@@&AKAAA2A(;L4BuwsBuwB7Bs6Ch0{CZAC Ƶ;(DlYaRwNDAiAApqAAqqiA{DAA@@P@?CQBWLup#B2 B&"B补A?tA*_{ A]v}ALPEA뇇BAX@R;{`Zj@' @intermediate overflow in fsummath.fsum partials-inf + inf in fsumcomb(dd)gcd(di)math domain errormath range errorpowfmodldexpatan2distpermk must not exceed %lldOO:logremaindercopysignpitauacosacoshasinasinhatanatanhceildegreeserferfcexpm1fabsfactorialfloorfrexphypotiscloseisfiniteisinfisnanisqrtlgammalog1plog10log2modfradianstruncprodstartrel_tolabs_tolmath__ceil____floor____trunc__@?9RFߑ?cܥL@@-DT! @??#B ;E@HP?7@i@E@-DT! a@?& .>@@8,6V?0C T꿌(J?iW @-DT!@?-DT!?!3|@-DT!?-DT! @;Lh`Th@Y^!^8(^h4^;^B^^,^M`TabH!b%bb$ bX c c Hch qc c4 c c$ %d+eT?eSe(fXkggDggghXh`ii4Pppr@wx`yz z ~ 0x Ј0Ph D`0(PP L@|0`p0hP< l P  T h |  | @ ` H 08 X `l,@ T@h`| X0lzRx $PFJ w?:*3$"DU\plD ctYH o E zRx  ZPhg ^ E LYF̴D  E |Y 0H0U A L0dH h E T A ldli ` E XYF@mH p E /YFH@ A LdtFEB B(A0A8G 8A0A(B BBBA $zRx ,XHtjBA A(S0(D ABBME0zRx 0$X4H(l:FBB B(A0A8Gp 8A0A(B BBBA zRx p(BXSx  DFAA Jp  AABA xXBBIpzRx p$X`FHB B(A0A8Dn 8A0A(B BBBA UBBI$zRx ,Y$o8H0 E ^ J nzRx 0Y Z A pHn E y L zRx YC(`pqEAG0N AAA zRx 0 )YqH0 G YV A  |D } A lY8 \xEAG` EAE  CAA zRx ` 4Y @pEAG0 CAA I FAE E EAE 4ADD0x EAE Y CAA 4@0LDX0XDpFAD D@/  AABN zRx @$ X=(4EG  EE P CA zRx   W)H0FBE B(D0A8G 8A0A(B BBBA $zRx ,yW(4@<cQ]W ,PFAD F ABA zRx  $WL` qxFBB B(A0A8JJ 8A0A(B BBBD $zRx ,Vl H h E m A  pH h E g A |, vFEB B(A0A8D`q 8D0A(B BBBA R 8H0A(B BBBE | 8C0A(B BBBE zRx `(V zH0q G  A (V( {HEG j AI z CC LVL\ |UFBB B(A0A8G 8A0A(B BBBJ 0SVH FBE B(A0D8Gp^ 8A0A(B BBBA VCL BED D(D@t (D ABBB v (C ABBA zRx @$W       0 D X l   0 $lEKE j AAA cAAzRx   3V( 0,ADG@V AAA zRx @ U0hDFDA DP  AABA zRx P$}U:@FAA Q0  AABJ   DABA <H ^ E U\H ^ E U,|`mEG0K AH  CA zRx 0 T,pEG  FE  CA "UE EGNU` 5j?/pxUfp `-   o`    8(&x oo0ooTo -------.. .0.@.P.`.p.........// /0/@/P/`/p/////////00 000@0P0`0p00000000011 101@1P1`1p11111111122 202@2P2 `@q@@``БwW`mpc @  d@fp 0S'B`;Ч 6R@`P (R.B@4P]kT: AGM`RPbWp@P 5a@_ eP| |@,K` !@ e` GA$3a1`-math.cpython-38-x86_64-linux-gnu.so-3.8.17-2.module_el8.9.0+3633+e453b53a.x86_64.debugL+7zXZִF!t/]?Eh=ڊ2N4R }FFB%2({t_bt[J=4DHaK[9.BA*Cb&ϙһkF^pb>:ӭ֊|F18"tFٜڐ35`hJ$WH S܋rYո %QNbЎ6v>v sl'J^{t,\yXp6( /wcCuyZ1UH5:͡tZXEZ"m3>D|1zS-8|(9dri_!f' ÕY813ٖ-b_jj">"w]!B1MJL`?Y "5sO5Ċ׎?lOtoPWDSSٞ!Ǻ} #z2ؖ0#B^ox*:Uf]lyÕ5?Z^1b-&FE5>o?p Mz(s#CQu6gUa;o[k0̃G)UFعhwi!G@&͵Yuwv\KmNǪ(@bS@=0)wkp@k. uIGbܼD%n-`@Ң,t~%CX|dq: "%S:ߜm^ iiLˌ! 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