From 4c037f6f20c6dbe1d7c337d820f51e79573091f4 Mon Sep 17 00:00:00 2001 From: QuantumNovice <43876848+QuantumNovice@users.noreply.github.com> Date: Sat, 20 Jul 2019 14:19:56 +0500 Subject: [PATCH 01/21] Create README.md --- Maths/images/README.md | 1 + 1 file changed, 1 insertion(+) create mode 100644 Maths/images/README.md diff --git a/Maths/images/README.md b/Maths/images/README.md new file mode 100644 index 000000000000..532ab8cb3f0d --- /dev/null +++ b/Maths/images/README.md @@ -0,0 +1 @@ +# Place Images Here From c24e855bb51c63e1a8907f1c0f09d255060ad3e7 Mon Sep 17 00:00:00 2001 From: QuantumNovice <43876848+QuantumNovice@users.noreply.github.com> Date: Sat, 20 Jul 2019 14:20:17 +0500 Subject: [PATCH 02/21] Add files via upload --- Maths/images/gaussian.png | Bin 0 -> 53511 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 Maths/images/gaussian.png diff --git a/Maths/images/gaussian.png b/Maths/images/gaussian.png new file mode 100644 index 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z>s8G3(2Td!o1DFIGga@0xhq)*dVNVsjz3jJV%XNvc%8*A0S793SDr=&+Ti%jGhW^y znW@vF_^5G6LJt>(FR%{UGY&>+vCFsIG28SOts7PsGZ`W15H-wF-s{=l0lDIY`2JA4 z9I-OYS~_}2vQ`_YRFwn@owdpiF5|I-dnsmZ8prrd{~MQj1zTkyQg6yK>ls<2$v^^k#NPoOI{iCC?(fv{uVHh*fR0_Mmzo zoakeE9*4&`V`=D@C{&K`8Zmg2cKSN4JTLy%k(cmZ^C~BN;jyFnoR c|G*9_Xra@hu!OYn0~{O?VNu8VM-vPG0{QMTvj6}9 literal 0 HcmV?d00001 From 2179f668af2f6f7ed3ca950850a6ca1ab4e75dc6 Mon Sep 17 00:00:00 2001 From: QuantumNovice <43876848+QuantumNovice@users.noreply.github.com> Date: Sat, 20 Jul 2019 14:21:30 +0500 Subject: [PATCH 03/21] Create README.md --- Maths/README.md | 4 ++++ 1 file changed, 4 insertions(+) create mode 100644 Maths/README.md diff --git a/Maths/README.md b/Maths/README.md new file mode 100644 index 000000000000..1d1302094b61 --- /dev/null +++ b/Maths/README.md @@ -0,0 +1,4 @@ +# Algorithm Output: + +# Gaussian: +!(https://raw.githubusercontent.com/QuantumNovice/Python-1/master/Maths/images/gaussian.png)[] From 6ed611514639db06091a06f706ea0eff40becb03 Mon Sep 17 00:00:00 2001 From: QuantumNovice <43876848+QuantumNovice@users.noreply.github.com> Date: Sat, 20 Jul 2019 14:21:55 +0500 Subject: [PATCH 04/21] Update README.md --- Maths/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Maths/README.md b/Maths/README.md index 1d1302094b61..7a5d4c6026a8 100644 --- a/Maths/README.md +++ b/Maths/README.md @@ -1,4 +1,4 @@ # Algorithm Output: # Gaussian: -!(https://raw.githubusercontent.com/QuantumNovice/Python-1/master/Maths/images/gaussian.png)[] +![](https://raw.githubusercontent.com/QuantumNovice/Python-1/master/Maths/images/gaussian.png) From 40affb9fab87ec5878ca609c04c591bc87d5ce1e Mon Sep 17 00:00:00 2001 From: QuantumNovice <43876848+QuantumNovice@users.noreply.github.com> Date: Sat, 20 Jul 2019 14:30:38 +0500 Subject: [PATCH 05/21] Create Gaussian.py --- Maths/Gaussian.py | 11 +++++++++++ 1 file changed, 11 insertions(+) create mode 100644 Maths/Gaussian.py diff --git a/Maths/Gaussian.py b/Maths/Gaussian.py new file mode 100644 index 000000000000..2fae009d1c03 --- /dev/null +++ b/Maths/Gaussian.py @@ -0,0 +1,11 @@ +""" +Reference: https://en.wikipedia.org/wiki/Gaussian_function +""" +from math import pi, sqrt, exp + +def gaussian(x, mu=0,sigma=1): + """ + >>> gaussian(1) + 0.24197072451914337 + """ + return (1/sqrt(2*pi*sigma**2))*exp(-((x-mu)**2)/(2*sigma**2)) From 04dab8f6d42511b2cbaaf749adc830559d45ae24 Mon Sep 17 00:00:00 2001 From: QuantumNovice <43876848+QuantumNovice@users.noreply.github.com> Date: Sat, 20 Jul 2019 14:36:41 +0500 Subject: [PATCH 06/21] Create README.md --- Physics/README.md | 1 + 1 file changed, 1 insertion(+) create mode 100644 Physics/README.md diff --git a/Physics/README.md b/Physics/README.md new file mode 100644 index 000000000000..5f7114c279ea --- /dev/null +++ b/Physics/README.md @@ -0,0 +1 @@ +# Physics Code goes here From 7dc3f04946ccd7892fd197c1812ec3dd4ee4cc67 Mon Sep 17 00:00:00 2001 From: QuantumNovice <43876848+QuantumNovice@users.noreply.github.com> Date: Sat, 20 Jul 2019 14:47:39 +0500 Subject: [PATCH 07/21] Create HarmonOscillator.py --- Physics/HarmonOscillator.py | 78 +++++++++++++++++++++++++++++++++++++ 1 file changed, 78 insertions(+) create mode 100644 Physics/HarmonOscillator.py diff --git a/Physics/HarmonOscillator.py b/Physics/HarmonOscillator.py new file mode 100644 index 000000000000..d0f53dcbec74 --- /dev/null +++ b/Physics/HarmonOscillator.py @@ -0,0 +1,78 @@ +''' +Class to return properties of harmonic motion at x displacement. +This object can be used in game physics too. +''' +__authors__ = ['n0vice'] +__created__ = '2-14-2019' +__last_modified__ = '7-20-2019' + +from numpy import * +import matplotlib.pyplot as plt + +class HarmonicOscillator: + """ + Harmonic Oscillator object. + Parameters: + mass + k ==> stifness of the oscillator + angular_frequency ==> + A ==> Amplitude + """ + def __init__(self): + self.mass = 1 + self.k = 1 + self.angular_frequency = sqrt(self.k/self.mass) + self.AMPLITUDE = 6 + self.E = 0.5*self.k*self.AMPLITUDE**2 + + def force(self,x): + return -self.k*x + + def position(self, t, A, phase): + return A*cos(self.angular_frequency*t + phase) + + def kinetic_energy(self, x): + return (0.5*self.mass*self.angular_frequency**2)*(self.AMPLITUDE**2-x**2) + + def potential_energy(self, x): + return self.E - self.kinetic_energy(x) + + def hamiltonian(self,x): + return self.potential_energy(x)+self.kinetic_energy(x) + + def lagrangian(self,x): + return self.kinetic_energy(x)-self.potential_energy(x) + + +if __name__ == '__main__': + oscillator = HarmonicOscillator() + # Displacement of oscillator + x = linspace(-6,6,100) + + plt.title('Properties of Harmonic Oscillator') + + plt.subplot(2,2,1) + plt.plot(oscillator.force(x), oscillator.potential_energy(x)) + plt.xlabel('Applied Force') + plt.ylabel('Potential') + + plt.subplot(2,2,2) + plt.plot(oscillator.force(x),oscillator.position(x,1,1)) + plt.xlabel('Applied Force') + plt.ylabel('Position') + + + plt.subplot(2,2,3) + plt.plot(oscillator.potential_energy(x), label='Potential Energy') + plt.plot(oscillator.kinetic_energy(x), label='Kinetic Energy') + plt.xlabel('Displacement') + plt.ylabel('Energy') + plt.legend() + + plt.subplot(2,2,4) + plt.plot(oscillator.hamiltonian(x), label='Hamiltonian') + plt.plot(oscillator.lagrangian(x), label='Lagrangian') + plt.xlabel('Displacement') + plt.ylabel('Energy') + plt.legend() + plt.show() From f7dec1c74c323fa456c96adfa22ae1aeac165cc0 Mon Sep 17 00:00:00 2001 From: QuantumNovice <43876848+QuantumNovice@users.noreply.github.com> Date: Sat, 20 Jul 2019 14:48:58 +0500 Subject: [PATCH 08/21] Create README.md --- Physics/images/README.md | 1 + 1 file changed, 1 insertion(+) create mode 100644 Physics/images/README.md diff --git a/Physics/images/README.md b/Physics/images/README.md new file mode 100644 index 000000000000..8b137891791f --- /dev/null +++ b/Physics/images/README.md @@ -0,0 +1 @@ + From 694e66afe4750720f06dd665fc1bf4b0de8ce079 Mon Sep 17 00:00:00 2001 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zvXbkDhF0m~E6bvGzbqOY_RAj?{(E#eUP0xYGY28U#6n1cYP#r+bei}N$2tN_YLad$kypaU)#jO$1)6DS5u zSI$~nTOq*K>cIo8d}*!wD~^qz34!R@RW2S`zK5`OV1KEF^88mSNZ+9FfIzl+c;n8~ zO^CN{5aJn%L&TtiI`s5=sfV z*As3KkB8JgV3dL4CO{SH()8341_7L197 z1f?KKPJsBWU|}IWL0nv%$5Wm<<5KuQK}g3eB0>(E2V_PSJYG{Gj)5XFnx*qAPiLqK5-Yt@01s@1#x|!M8mDi%_klX+yA{B>#d}euB5e`hKbOdfq zi;UGh=0t|YcE90=!KjfC#tP|K;BYsom8LK&_J%8jtkuCHBSF|$?}Lt|)|v!cjlU{!ic4|Nri` i{;!X&|Eu=xoE}p+Bu->@A0Gq$Q@*b*Uvkef Date: Sat, 20 Jul 2019 14:53:07 +0500 Subject: [PATCH 10/21] Delete README.md --- Physics/README.md | 1 - 1 file changed, 1 deletion(-) delete mode 100644 Physics/README.md diff --git a/Physics/README.md b/Physics/README.md deleted file mode 100644 index 5f7114c279ea..000000000000 --- a/Physics/README.md +++ /dev/null @@ -1 +0,0 @@ -# Physics Code goes here From 7a4d9f148b9d86615a8959cfbdfb93f68552502b Mon Sep 17 00:00:00 2001 From: QuantumNovice <43876848+QuantumNovice@users.noreply.github.com> Date: Sat, 20 Jul 2019 14:54:15 +0500 Subject: [PATCH 11/21] Delete README.md --- Maths/README.md | 4 ---- 1 file changed, 4 deletions(-) delete mode 100644 Maths/README.md diff --git a/Maths/README.md b/Maths/README.md deleted file mode 100644 index 7a5d4c6026a8..000000000000 --- a/Maths/README.md +++ /dev/null @@ -1,4 +0,0 @@ -# Algorithm Output: - -# Gaussian: -![](https://raw.githubusercontent.com/QuantumNovice/Python-1/master/Maths/images/gaussian.png) From 6e751755d01272f3faa2ce9e158c6a759884c58e Mon Sep 17 00:00:00 2001 From: QuantumNovice <43876848+QuantumNovice@users.noreply.github.com> Date: Sat, 20 Jul 2019 14:54:31 +0500 Subject: [PATCH 12/21] Delete README.md --- Maths/images/README.md | 1 - 1 file changed, 1 deletion(-) delete mode 100644 Maths/images/README.md diff --git a/Maths/images/README.md b/Maths/images/README.md deleted file mode 100644 index 532ab8cb3f0d..000000000000 --- a/Maths/images/README.md +++ /dev/null @@ -1 +0,0 @@ -# Place Images Here From 9cfd86608f129333cf68e9606b7ef3947ca6af60 Mon Sep 17 00:00:00 2001 From: QuantumNovice <43876848+QuantumNovice@users.noreply.github.com> Date: Sat, 20 Jul 2019 15:34:46 +0500 Subject: [PATCH 13/21] Update Gaussian.py --- Maths/Gaussian.py | 59 ++++++++++++++++++++++++++++++++++++++++++----- 1 file changed, 53 insertions(+), 6 deletions(-) diff --git a/Maths/Gaussian.py b/Maths/Gaussian.py index 2fae009d1c03..b23b97d0ed76 100644 --- a/Maths/Gaussian.py +++ b/Maths/Gaussian.py @@ -1,11 +1,58 @@ """ Reference: https://en.wikipedia.org/wiki/Gaussian_function + +python/black : True + + """ -from math import pi, sqrt, exp +from numpy import pi, sqrt, exp +from typing import Dict -def gaussian(x, mu=0,sigma=1): - """ - >>> gaussian(1) - 0.24197072451914337 +def gaussian(x, mu:float=0.0, sigma:float=1.0) -> int: + """ + >>> gaussian(1) + 0.24197072451914337 + + >>> gaussian(24) + 3.342714441794458e-126 + + # Supports NumPy Arrays + # Use numpy.meshgrid with this to generate gaussian blur on images. + >>> import numpy as np + >>> x = np.arange(15) + >>> gaussian(x) + array([3.98942280e-01, 2.41970725e-01, 5.39909665e-02, 4.43184841e-03, + 1.33830226e-04, 1.48671951e-06, 6.07588285e-09, 9.13472041e-12, + 5.05227108e-15, 1.02797736e-18, 7.69459863e-23, 2.11881925e-27, + 2.14638374e-32, 7.99882776e-38, 1.09660656e-43]) + + >>> gaussian(15) + 5.530709549844416e-50 + + >>> gaussian([1,2, 'string']) + Traceback (most recent call last): + ... + TypeError: unsupported operand type(s) for -: 'list' and 'float' + + >>> gaussian('hello world') + Traceback (most recent call last): + ... + TypeError: unsupported operand type(s) for -: 'str' and 'float' + + >>> gaussian(10**234) + Traceback (most recent call last): + ... + OverflowError: (34, 'Result too large') + + >>> gaussian(10**-326) + 0.3989422804014327 + + >>> gaussian(2523, mu=234234, sigma=3425) + 0.0 """ - return (1/sqrt(2*pi*sigma**2))*exp(-((x-mu)**2)/(2*sigma**2)) + return 1 / sqrt(2 * pi * sigma ** 2) * exp(-(x - mu) ** 2 / 2 * sigma ** 2) + +if __name__ == '__main__': + import doctest + doctest.testmod() + From dbfb93c09a5f3c33eeb703c014ac7b04cf9c79f7 Mon Sep 17 00:00:00 2001 From: QuantumNovice <43876848+QuantumNovice@users.noreply.github.com> Date: Sat, 20 Jul 2019 15:35:32 +0500 Subject: [PATCH 14/21] Update Gaussian.py --- Maths/Gaussian.py | 8 +++++--- 1 file changed, 5 insertions(+), 3 deletions(-) diff --git a/Maths/Gaussian.py b/Maths/Gaussian.py index b23b97d0ed76..dfef9f2aa356 100644 --- a/Maths/Gaussian.py +++ b/Maths/Gaussian.py @@ -8,7 +8,8 @@ from numpy import pi, sqrt, exp from typing import Dict -def gaussian(x, mu:float=0.0, sigma:float=1.0) -> int: + +def gaussian(x, mu: float = 0.0, sigma: float = 1.0) -> int: """ >>> gaussian(1) 0.24197072451914337 @@ -52,7 +53,8 @@ def gaussian(x, mu:float=0.0, sigma:float=1.0) -> int: """ return 1 / sqrt(2 * pi * sigma ** 2) * exp(-(x - mu) ** 2 / 2 * sigma ** 2) -if __name__ == '__main__': + +if __name__ == "__main__": import doctest + doctest.testmod() - From 72e13537bf1ac79fdcfb7ebda172379807a91ab9 Mon Sep 17 00:00:00 2001 From: QuantumNovice <43876848+QuantumNovice@users.noreply.github.com> Date: Sat, 20 Jul 2019 15:36:31 +0500 Subject: [PATCH 15/21] Update Gaussian.py --- Maths/Gaussian.py | 1 - 1 file changed, 1 deletion(-) diff --git a/Maths/Gaussian.py b/Maths/Gaussian.py index dfef9f2aa356..7907eb2633ec 100644 --- a/Maths/Gaussian.py +++ b/Maths/Gaussian.py @@ -6,7 +6,6 @@ """ from numpy import pi, sqrt, exp -from typing import Dict def gaussian(x, mu: float = 0.0, sigma: float = 1.0) -> int: From 958118a4ae197d57facd03e0c143dea243e4b1e6 Mon Sep 17 00:00:00 2001 From: QuantumNovice <43876848+QuantumNovice@users.noreply.github.com> Date: Sat, 20 Jul 2019 15:43:06 +0500 Subject: [PATCH 16/21] Update HarmonOscillator.py --- Physics/HarmonOscillator.py | 113 +++++++++++++++++++----------------- 1 file changed, 61 insertions(+), 52 deletions(-) diff --git a/Physics/HarmonOscillator.py b/Physics/HarmonOscillator.py index d0f53dcbec74..3bbe07ce1879 100644 --- a/Physics/HarmonOscillator.py +++ b/Physics/HarmonOscillator.py @@ -1,13 +1,15 @@ -''' +""" Class to return properties of harmonic motion at x displacement. This object can be used in game physics too. -''' -__authors__ = ['n0vice'] -__created__ = '2-14-2019' -__last_modified__ = '7-20-2019' -from numpy import * -import matplotlib.pyplot as plt +python/black: True +""" +__authors__ = ["n0vice"] +__created__ = "2-14-2019" +__last_modified__ = "7-20-2019" + +from numpy import sqrt, linspace, cos + class HarmonicOscillator: """ @@ -18,61 +20,68 @@ class HarmonicOscillator: angular_frequency ==> A ==> Amplitude """ + def __init__(self): self.mass = 1 self.k = 1 - self.angular_frequency = sqrt(self.k/self.mass) + self.angular_frequency = sqrt(self.k / self.mass) self.AMPLITUDE = 6 - self.E = 0.5*self.k*self.AMPLITUDE**2 + self.E = 0.5 * self.k * self.AMPLITUDE ** 2 - def force(self,x): - return -self.k*x + def force(self, x): + return -self.k * x def position(self, t, A, phase): - return A*cos(self.angular_frequency*t + phase) + return A * cos(self.angular_frequency * t + phase) def kinetic_energy(self, x): - return (0.5*self.mass*self.angular_frequency**2)*(self.AMPLITUDE**2-x**2) + return (0.5 * self.mass * self.angular_frequency ** 2) * ( + self.AMPLITUDE ** 2 - x ** 2 + ) def potential_energy(self, x): return self.E - self.kinetic_energy(x) - def hamiltonian(self,x): - return self.potential_energy(x)+self.kinetic_energy(x) - - def lagrangian(self,x): - return self.kinetic_energy(x)-self.potential_energy(x) - - -if __name__ == '__main__': - oscillator = HarmonicOscillator() - # Displacement of oscillator - x = linspace(-6,6,100) - - plt.title('Properties of Harmonic Oscillator') - - plt.subplot(2,2,1) - plt.plot(oscillator.force(x), oscillator.potential_energy(x)) - plt.xlabel('Applied Force') - plt.ylabel('Potential') - - plt.subplot(2,2,2) - plt.plot(oscillator.force(x),oscillator.position(x,1,1)) - plt.xlabel('Applied Force') - plt.ylabel('Position') - - - plt.subplot(2,2,3) - plt.plot(oscillator.potential_energy(x), label='Potential Energy') - plt.plot(oscillator.kinetic_energy(x), label='Kinetic Energy') - plt.xlabel('Displacement') - plt.ylabel('Energy') - plt.legend() - - plt.subplot(2,2,4) - plt.plot(oscillator.hamiltonian(x), label='Hamiltonian') - plt.plot(oscillator.lagrangian(x), label='Lagrangian') - plt.xlabel('Displacement') - plt.ylabel('Energy') - plt.legend() - plt.show() + def hamiltonian(self, x): + return self.potential_energy(x) + self.kinetic_energy(x) + + def lagrangian(self, x): + return self.kinetic_energy(x) - self.potential_energy(x) + + def demo(self): + import matplotlib.pyplot as plt + + oscillator = self + # Displacement of oscillator + x = linspace(-6, 6, 100) + + plt.title("Properties of Harmonic Oscillator") + + plt.subplot(2, 2, 1) + plt.plot(oscillator.force(x), oscillator.potential_energy(x)) + plt.xlabel("Applied Force") + plt.ylabel("Potential") + + plt.subplot(2, 2, 2) + plt.plot(oscillator.force(x), oscillator.position(x, 1, 1)) + plt.xlabel("Applied Force") + plt.ylabel("Position") + + plt.subplot(2, 2, 3) + plt.plot(oscillator.potential_energy(x), label="Potential Energy") + plt.plot(oscillator.kinetic_energy(x), label="Kinetic Energy") + plt.xlabel("Displacement") + plt.ylabel("Energy") + plt.legend() + + plt.subplot(2, 2, 4) + plt.plot(oscillator.hamiltonian(x), label="Hamiltonian") + plt.plot(oscillator.lagrangian(x), label="Lagrangian") + plt.xlabel("Displacement") + plt.ylabel("Energy") + plt.legend() + plt.show() + + +if __name__ == "__main__": + HarmonicOscillator().demo() From 107d77a9aa5c542201fb7df672dd6f76adbb9187 Mon Sep 17 00:00:00 2001 From: QuantumNovice <43876848+QuantumNovice@users.noreply.github.com> Date: Sat, 20 Jul 2019 15:44:09 +0500 Subject: [PATCH 17/21] Rename Maths/Gaussian.py to maths/gaussian.py --- Maths/Gaussian.py => maths/gaussian.py | 0 1 file changed, 0 insertions(+), 0 deletions(-) rename Maths/Gaussian.py => maths/gaussian.py (100%) diff --git a/Maths/Gaussian.py b/maths/gaussian.py similarity index 100% rename from Maths/Gaussian.py rename to maths/gaussian.py From ca79594bf289c191a9807bde4b9edf9f67eb8d97 Mon Sep 17 00:00:00 2001 From: QuantumNovice <43876848+QuantumNovice@users.noreply.github.com> Date: Sat, 20 Jul 2019 15:45:13 +0500 Subject: [PATCH 18/21] Rename Physics/HarmonOscillator.py to physics/harmonic_oscillator.py --- Physics/HarmonOscillator.py => physics/harmonic_oscillator.py | 0 1 file changed, 0 insertions(+), 0 deletions(-) rename Physics/HarmonOscillator.py => physics/harmonic_oscillator.py (100%) diff --git a/Physics/HarmonOscillator.py b/physics/harmonic_oscillator.py similarity index 100% rename from Physics/HarmonOscillator.py rename to physics/harmonic_oscillator.py From 1bef461c762b2bccd6cada6066131f7e21b14c3f Mon Sep 17 00:00:00 2001 From: QuantumNovice <43876848+QuantumNovice@users.noreply.github.com> Date: Sat, 20 Jul 2019 15:46:17 +0500 Subject: [PATCH 19/21] Update harmonic_oscillator.py --- physics/harmonic_oscillator.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/physics/harmonic_oscillator.py b/physics/harmonic_oscillator.py index 3bbe07ce1879..3534a14369af 100644 --- a/physics/harmonic_oscillator.py +++ b/physics/harmonic_oscillator.py @@ -18,7 +18,7 @@ class HarmonicOscillator: mass k ==> stifness of the oscillator angular_frequency ==> - A ==> Amplitude + Amplitude """ def __init__(self): From c907bc10fb58f302f88e7ba0609ddf286e9c4296 Mon Sep 17 00:00:00 2001 From: QuantumNovice <43876848+QuantumNovice@users.noreply.github.com> Date: Sat, 20 Jul 2019 15:49:24 +0500 Subject: [PATCH 20/21] Delete harmonic_oscillator.png --- Physics/images/harmonic_oscillator.png | Bin 52392 -> 0 bytes 1 file changed, 0 insertions(+), 0 deletions(-) delete mode 100644 Physics/images/harmonic_oscillator.png diff --git a/Physics/images/harmonic_oscillator.png b/Physics/images/harmonic_oscillator.png deleted file mode 100644 index 1c42b7debabe75d9e8e02485456a91d70d8f3c82..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 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