wehub-resource-sync
107 lines
2.4 KiB
Python
107 lines
2.4 KiB
Python
"""
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This script calculates solutions to some of the problems from the
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"Many Digits" competition:
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http://www.cs.ru.nl/~milad/manydigits/problems.php
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Run with:
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python manydigits.py
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"""
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from mpmath import (asin, asinh, atan, atanh, catalan, cos, e, exp, findroot,
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mp, mpf, pi, quadts, sin, sqrt, tan, tanh, zeta)
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from mpmath.libmp.libintmath import bin_to_radix
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from mpmath.libmp.libmpf import to_fixed
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dps = 100
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mp.dps = dps + 10
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def pr(x):
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"""Return the first dps digits after the decimal point"""
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x = x._mpf_
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p = int(dps*3.33 + 10)
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t = to_fixed(x, p)
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d = bin_to_radix(t, p, 10, dps)
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s = str(d).zfill(dps)[-dps:]
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return s[:dps//2] + "\n" + s[dps//2:]
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print("""
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This script prints answers to a selection of the "Many Digits"
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competition problems: http://www.cs.ru.nl/~milad/manydigits/problems.php
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The output for each problem is the first 100 digits after the
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decimal point in the result.
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""")
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print("C01: sin(tan(cos(1)))")
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print(pr(sin(tan(cos(1)))))
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print()
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print("C02: sqrt(e/pi)")
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print(pr(sqrt(e/pi)))
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print()
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print("C03: sin((e+1)^3)")
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print(pr(sin((e+1)**3)))
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print()
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print("C04: exp(pi*sqrt(2011))")
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mp.dps += 65
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print(pr(exp(pi*sqrt(2011))))
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mp.dps -= 65
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print()
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print("C05: exp(exp(exp(1/2)))")
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print(pr(exp(exp(exp(0.5)))))
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print()
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print("C06: arctanh(1-arctanh(1-arctanh(1-arctanh(1/pi))))")
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print(pr(atanh(1-atanh(1-atanh(1-atanh(1/pi))))))
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print()
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print("C07: pi^1000")
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mp.dps += 505
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print(pr(pi**1000))
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mp.dps -= 505
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print()
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print("C08: sin(6^(6^6))")
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print(pr(sin(6**(6**6))))
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print()
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print("C09: sin(10*arctan(tanh(pi*(2011^(1/2))/3)))")
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mp.dps += 150
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print(pr(sin(10*atan(tanh(pi*sqrt(2011)/3)))))
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mp.dps -= 150
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print()
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print("C10: (7+2^(1/5)-5*(8^(1/5)))^(1/3) + 4^(1/5)-2^(1/5)")
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a = mpf(1)/5
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print(pr(((7 + 2**a - 5*(8**a))**(mpf(1)/3) + 4**a - 2**a)))
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print()
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print("C11: tan(2^(1/2))+arctanh(sin(1))")
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print(pr((tan(sqrt(2)) + atanh(sin(1)))))
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print()
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print("C12: arcsin(1/e^2) + arcsinh(e^2)")
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print(pr(asin(1/exp(2)) + asinh(exp(2))))
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print()
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print("C17: S= -4*Zeta(2) - 2*Zeta(3) + 4*Zeta(2)*Zeta(3) + 2*Zeta(5)")
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print(pr(-4*zeta(2) - 2*zeta(3) + 4*zeta(2)*zeta(3) + 2*zeta(5)))
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print()
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print(r"C18: Catalan G = Sum{i=0}{\infty}(-1)^i/(2i+1)^2")
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print(pr(catalan))
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print()
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print("C21: Equation exp(cos(x)) = x")
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print(pr(findroot(lambda x: exp(cos(x))-x, 1)))
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print()
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print("C22: J = integral(sin(sin(sin(x)))), x=0..1")
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print(pr(quadts(lambda x: sin(sin(sin(x))), [0, 1])))
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print()
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