Ejemplo n.º 1
0
#
#  Using Heron's formula from Lubomir Markov's extension of Goehl's Method
#
M = []
from time import time
st = time()
for m in xrange(1, 1001):
    #print "m:",m,
    psum = 0
    #u = 2*m
    fd0 = divisors(2 * m)  # Factoring u = 2m
    for u in fd0:
        ul = u * 3**.5  # choosing factors up to u*sqrt(3)
        mxul = int(ul) + 1
        for v in xrange(1, mxul):
            if gcd(u, v) != 1: continue  # choosing v coprime to u
            f = 4 * m * m * (u * u + v * v)  # = delta1 * delta2
            fd = divisors(f)  # obtaining factors for d1,d2
            ul2 = int(
                2 * m *
                ((u * u + v * v)**.5))  # obtaining sqrt to avoid repetitions
            #print "!",m,u,v             # showing m,u,v for curiosity's sake
            for d1 in fd:
                if ((2 * m) * (v**2 - u**2) / u
                    ) <= d1 <= ul2:  #choosing range of delta1 to ensure A=mP
                    if (d1 + 2 * m * u) % v: continue
                    d2 = f / d1
                    if (d2 + 2 * m * u) % v:
                        print "oooooooooooooops:", m, d1, d2, P
                        continue
                    a = (d1 + 2 * m * u) / v + (2 * m * v) / u
Ejemplo n.º 2
0
def notcoprime(cp, Y):
    for yy in Y:
        if gcd(yy, cp) != 1:
            return yy
    return -1
Ejemplo n.º 3
0
def notcoprime(cp,Y):
  for yy in Y:
    if gcd(yy,cp)!=1:
      return yy
  return -1
Ejemplo n.º 4
0
summ = 0

#
#  Using Heron's formula from Lubomir Markov's extension of Goehl's Method
#
M = []
for m in xrange(1, 1001):
    print "m:", m,
    psum = 0
    # u = 2*m
    fd0 = divisors(2 * m)  # Factoring u = 2m
    for u in fd0:
        ul = u * 3 ** 0.5  # choosing factors up to u*sqrt(3)
        mxul = int(ul) + 1
        for v in xrange(1, mxul):
            if gcd(u, v) != 1:
                continue  # choosing v coprime to u
            f = 4 * m * m * (u * u + v * v)  # = delta1 * delta2
            fd = divisors(f)  # obtaining factors for d1,d2
            ul2 = 2 * m * ((u * u + v * v) ** 0.5)  # obtaining sqrt to avoid repetitions
            # print "!",m,u,v             # showing m,u,v for curiosity's sake
            for d1 in fd:
                if ((2 * m) * (v ** 2 - u ** 2) / u) <= d1 <= ul2:  # choosing range of delta1 to ensure A=mP
                    d2 = f / d1
                    a = (d1 + 2 * m * u) / v + (2 * m * v) / u
                    b = (d2 + 2 * m * u) / v + (2 * m * v) / u
                    c = (d1 + d2 + 4 * m * u) / v
                    A = ta(a, b, c)
                    P = a + b + c
                    R = A / float(P)  # paranoid check to ensure ratios match
                    if R == int(R):  # Making sure Ratio is integer,probably not necessary
Ejemplo n.º 5
0
#
#
#  Euler Problem 283
#
#
from Functions3 import GCD,gcd
summ = 0
ctr,ctr1 = 0,0
for m in xrange(2, 4000):
  for n in xrange(1, m):
    if gcd(m,n)!=1 or (m-n)%2==0: continue
    a = (m*m - n*n)
    b = 2*m*n
    c = (m*m + n*n)
    #if GCD((a,b,c))>1:continue
    #print m,n,":",a,b,c 
    
    #if a**2 +b**2 == c**2:
    A0=a*b/2;P0=a+b+c;R=float(A0)/P0
    ctr+=1
    #print m,n,":",a,b,c,":",A0,P0,R
    if R < 1001: 
      #print a,b,c,":",A0,P0,R
      #summ += P0

      i=1

      while 1:
        A = A0*i**2
        P = P0*i
        R = float(A)/P
Ejemplo n.º 6
0
#
#
#  Euler Problem 283
#
#
from Functions3 import GCD, gcd
summ = 0
ctr, ctr1 = 0, 0
for m in xrange(2, 4000):
    for n in xrange(1, m):
        if gcd(m, n) != 1 or (m - n) % 2 == 0: continue
        a = (m * m - n * n)
        b = 2 * m * n
        c = (m * m + n * n)
        #if GCD((a,b,c))>1:continue
        #print m,n,":",a,b,c

        #if a**2 +b**2 == c**2:
        A0 = a * b / 2
        P0 = a + b + c
        R = float(A0) / P0
        ctr += 1
        #print m,n,":",a,b,c,":",A0,P0,R
        if R < 1001:
            #print a,b,c,":",A0,P0,R
            #summ += P0

            i = 1

            while 1:
                A = A0 * i**2
Ejemplo n.º 7
0
#
#  Using Heron's formula from Lubomir Markov's extension of Goehl's Method
#
#M=[]
from time import time
st = time()
for m in xrange(1,1001):
  print "m:",m,
  psum = 0       # used to determine P sums for each m
  #u = 2*m
  fd0 = divisors(2*m)   # Factoring u = 2m
  for u in fd0:
    ul = u*3**.5         # choosing factors up to u*sqrt(3)
    mxul = int(ul)+1
    for v in xrange(1,mxul):
      if gcd(u,v)!=1:continue     # choosing v coprime to u
      f = 4*m*m*(u*u +v*v)        # = delta1 * delta2
      fd = divisors(f)            # obtaining factors for d1,d2
      ul2 = int(2*m*((u*u+v*v)**.5))   # obtaining sqrt to avoid repetitions
      #print "!",m,u,v             # showing m,u,v for curiosity's sake
      for d1 in fd:
        if ((2*m)*(v**2-u**2)/u)<= d1 <=ul2:  #choosing range of delta1 to ensure A=mP
          if (d1+2*m*u)%v:continue
          d2 = f/d1
          if (d2+2*m*u)%v:continue          
          a = (d1+2*m*u)/v + (2*m*v)/u
          b = (d2+2*m*u)/v + (2*m*v)/u
          c = (d1+d2+4*m*u)/v
          #A = ta(a,b,c)
          P = a+b+c