Python polynomial.Polynomial類代碼示例

    def test_scale_1(self):
        one = Polynomial([2,4,7,3])
        scalar = 12

        r = one.scale(12)

        self.assertEqual(list(r.coefficients), [24, 48, 84, 36])

    def test_scale(self):
        one = Polynomial(map(GF2int, [2,14,7,3]))
        scalar = 12

        r = one.scale(12)

        self.assertEqual(list(r.coefficients), [24, 72, 36, 20])

    def test_mul_at(self):
        one = Polynomial(map(GF2int, [2,4,7,3]))
        two = Polynomial(map(GF2int, [5,2,4,2]))
        k = 3

        r1 = one * two
        r2 = one.mul_at(two, k)

        self.assertEqual(r1.get_coefficient(k), r2)

def polynomialbasin(coeffs, vw, auto=False, n=10, dots=True, mode=1, filename=None, save=True):
    p = Polynomial(*coeffs)
    rootlist = list(p.roots())
    rootlist.sort(cmp=argcmp)
    if auto:
        vw.autocomplex(*rootlist)
    if filename is None:
        filename = "polynomialbasin {poly} {n} {dots} {time}".format(poly=p, n=n, dots=dots, time=str(int(time())))
    return globals()["basin" + str(mode) * (mode in (2, 3))](p, rootlist, Color.colors(len(rootlist)), vw, p.deriv(), n,
                                                             dots, filename, save)

    def test_div_fast(self):
        one = Polynomial(map(GF2int,     [8,3,5,1]))
        two = Polynomial(map(GF2int, [5,3,1,1,6,8]))

        q, r = two._fastdivmod(one)
        self.assertEqual(list(q.coefficients), [101, 152, 11])
        self.assertEqual(list(r.coefficients), [183, 185, 3])

        # Make sure they multiply back out okay
        self.assertEqual(q*one + r, two)

    def test_div_fast_1(self):
        # no remander
        one = Polynomial([1,0,0,2,2,0,1,-2,-4])
        two = Polynomial([1,0,-1])

        q, r = one._fastdivmod(two)
        self.assertEqual(q, one._fastfloordiv(two))
        self.assertEqual(r, one._fastmod(two))

        self.assertEqual(list(q.coefficients), [1,0,1,2,3,2,4])
        self.assertEqual(list(r.coefficients), [0])

def main(argv):
    inputfile = ''
    outputfile = ''
    try:
        opts, args = getopt.getopt(argv,"hi:o:",["ifile=","ofile="])
    except getopt.GetoptError:
        print 'single.py -i <inputfile> -o <outputfile>'
        sys.exit(2)
    for opt, arg in opts:
        if opt == '-h':
            print 'single.py -i <inputfile> -o <outputfile> '
            sys.exit()
        elif opt in ("-i", "--ifile"):
            inputfile = arg
        elif opt in ("-o", "--ofile"):
            outputfile = arg
    
    try:
        fi = open(inputfile,"r")
        fl = open(outputfile,"a")
    except IOError:
        print 'main.py -i <inputfile> -o <outputfile>'
        sys.exit(2)
    l = []
    for i in fi:
        p = Polynomial(i)
        l.append(p)

    name = outputfile
    name = name + ".xlsx"
    name = "" + name
    workbook = xlsxwriter.Workbook(name)
    worksheet = workbook.add_worksheet("irredutiveis")
    worksheet.write(0,0, "Polynomials")
    worksheet.write(0,1, "m")
    worksheet.write(0,2, "a")
    worksheet.write(0,3, "b")
    worksheet.write(0,4, "c")
    worksheet.write(0,5, "d")
    row = 1
    colum = 0
   
    for p in l:
    	colum = 0
    	worksheet.write(row,colum, str(p.coefs()))
    	colum = 1
    	j = sorted(p.coefs(), reverse=True)
    	for num in j:
    		worksheet.write(row,colum, num)
    		colum = colum+1
    	row = row + 1

    workbook.close()

def main(argv):
    inputfile = ''
    outputfile = ''
    debug = False
    try:
        opts, args = getopt.getopt(argv,"hi:o:d",["ifile=","ofile="])
    except getopt.GetoptError:
        print 'single.py -i <inputfile> -o <outputfile>'
        sys.exit(2)
    for opt, arg in opts:
        if opt == '-h':
            print 'single.py -i <inputfile> -o <outputfile> -d for debug'
            sys.exit()
        elif opt in ("-d", "--debug"):
            debug = True
        elif opt in ("-i", "--ifile"):
            inputfile = arg
        elif opt in ("-o", "--ofile"):
            outputfile = arg
        

    try:
        fi = open(inputfile,"r")
        fl = open(outputfile,"a")
    except IOError:
        print 'main.py -i <inputfile> -o <outputfile>'
        sys.exit(2)
    l = []
    pols = []
    files = [inputfile]
    for fileName in files:
        save = outputfile
        f = open(fileName,'r')

        #read, pols = recoverfile(save, f)
        if True:
            for line in f:
                try:
                    pol = Polynomial(line)
                    pols.append(pol)
                except Exception as e:
                    print line
                    sys.exit(2)
    result = defaultdict(list)
    print len(pols)
    for pol in pols:
        if len(pol.coefs()) > 1:
            red = Reduction(debug)
            count = red.reduction(pol.coefs())
            result =  str(pol.coefs()) + ":" + str(count)
            print result
            fl.write(result + "\n")

	def test_simple_operations(self):
		"""tests with some specific polynomials"""
		p1 = Polynomial([2.,0,3.,0]) # 2 + 3x^2
		self.assertEqual(str(p1), '2.0 + 3.0X^2')
		self.assertEqual(repr(p1), 'Polynomial([2.0, 0.0, 3.0])')
		p2 = Polynomial([3.,2.]) #3 + 2x
		self.assertEqual(str(p2), '3.0 + 2.0X')
		self.assertEqual(p1.degree(), 2)
		self.assertEqual(p1[4], 0, "Index out of range should return zero")
		self.assertEqual(p1[0], 2)
		self.assertEqual(p1+p2, Polynomial([5,2,3]))
		self.assertEqual(p1.differentiate(), Polynomial([0,6]))
		self.assertEqual(p1(2), 14)
		self.assertEqual(p1*p2, Polynomial([6., 4., 9., 6.]))

def recover(shares, pword=""):
    #Intial Stuff
    intmod.set_base(59)
    #Construct key, If no password is provided, default password of "" is used
    seclen=len(shares[0])-1
    if pword:
        key=genpad(seclen,pword)
    else:
        key=[intmod(0) for c in xrange(seclen)]
       
     
    #Catch errors Two keys for the same point
    lsh=len(shares)
    xs=[intmod(b58conv(shares[i][-1])) for i in xrange(lsh)]
    todel=[]
    for i in xrange(lsh-1):
        for j in xrange(i+1,lsh):
            if xs[i]==xs[j]:
                if j not in todel:
                    todel.append(j)
    d=0
    todel=sorted(todel,reverse=True)
    for  i in todel:
        del xs[i]
        del shares[i]
        d=d+1
    lsh=lsh-d
      
    #Construct the Lagrange Polynomials (These are the same for all elements)
    l=[]
    for i in xrange(lsh):
        lt=Polynomial(x0=intmod(1))
        for j in xrange(lsh):
            if i != j:
                if (xs[i]-xs[j])==intmod(0):
                    raise ValueError("Two of your keys are for identical points please remedy this")
                lt=lt*(Polynomial(x1=intmod(1),x0=-xs[j]))
                lt=lt//Polynomial(x0=(xs[i]-xs[j]))
        l.append(lt)
    #Reconstruct Secret (To best knowledge), Completes Lagrange integration for each character
    #Evaluates at 0 and converts into a base 58 character
    
    rect=[]
    for i in xrange(seclen):
        p=Polynomial(x0=intmod(0))
        for j in xrange(lsh):
            p=p+Polynomial(x0=(b58conv(shares[j][i])))*l[j]
        rect.append(r58conv(p.evaluate(intmod(0))-key[i%64]))
    return "".join(rect)

    def test_div_gffast(self):
        one = Polynomial(map(GF2int,     [1,3,5,1])) # must be monic! (because the function is optimized for monic divisor polynomial)
        two = Polynomial(map(GF2int, [5,3,1,1,6,8]))
        
        q, r = two._gffastdivmod(one) # optimized for monic divisor polynomial

        q2, r2 = two._fastdivmod(one)
        self.assertEqual(q, q2)
        self.assertEqual(r, r2)

        self.assertEqual(list(q.coefficients), [5, 12, 4])
        self.assertEqual(list(r.coefficients), [52, 30, 12])

        # Make sure they multiply back out okay
        self.assertEqual(q*one + r, two)

    def test_orientation_reprojection(self):
        true_s = np.array([.1, .2, -.3])
        true_r = utils.cayley(true_s)
        true_k = 1. / (1. + np.dot(true_s, true_s))
        true_vars = np.r_[true_s, true_k]

        xs = np.random.rand(8, 3)
        true_ys = np.dot(xs, true_r.T)

        sym_vars = Polynomial.coordinates(4, ctype=float)
        x, y, z, w = sym_vars
        sym_s = sym_vars[:3]
        sym_k = sym_vars[3]
        sym_r = utils.cayley_mat(sym_s)
        sym_rd = utils.cayley_denom(sym_s)

        residuals = (np.dot(xs, sym_r.T) - true_ys * sym_rd).flatten()
        cost = sum(r**2 for r in residuals)
        gradients = cost.partial_derivatives()
        constraint = sym_k * (1 + np.dot(sym_s, sym_s)) - 1

        print 'Cost:', cost
        print 'Constraint:', constraint
        print 'At ground truth:'
        print '  Cost = ', cost(*true_vars)
        print '  Constraint = ', constraint(*true_vars)
        print '  Gradients = ', [p(*true_vars) for p in gradients]
        expansions = [solvers.all_monomials(sym_vars, 2) for _ in range(cost.num_vars)]
        for a in expansions:
            a.extend([z*z*w, x*x*w, y*y*w, z*z*w*w, z*w*w])
        minima = optimize.minimize_globally(cost,
                                            [constraint],
                                            expansions=expansions,
                                            diagnostic_solutions=[true_vars])
        print 'Minima: ', minima

def test_ntt_mul():
	global w,wInv
	print "test_ntt_mul"

	powers2 = [pow(2,i) for i in range(1,19)]

	for N in powers2:
		print N
		
		k = (P-1)/(2*N)
		assert (P-1)%(2*N) == 0
		wN = pow(7,k,P)
		assert pow(wN,(2*N),P) == 1
		
		w = []
		for j in range(2*N):
			w.append(pow(wN,j,P))
		wInv = []
		for j in range(2*N):
			wInv.append(pow(w[j],P-2,P))

		a = [randint(0,2**16) for _ in xrange(N)]+[0]*N
		b = [randint(0,2**16) for _ in xrange(N)]+[0]*N

		polynomial_a = Polynomial()	
		polynomial_a.coef = a
		polynomial_b = Polynomial()
		polynomial_b.coef = b

		polynomial_c = polynomial_a*polynomial_b

		my_ntt_a = CPU_NTT(a)
		my_ntt_b = CPU_NTT(b)
		my_ntt_c = [x[0]*x[1] % P for x in zip(my_ntt_a,my_ntt_b)]

		ntt_intt_c = CPU_INTT(my_ntt_c)

		# assert len(ntt_intt_c) == len(polynomial_c.coef)
		for i,v in enumerate(polynomial_c.coef):
			v2 = ntt_intt_c[i]/(2*N)
			assert v == v2
	print "We are good"	

 def test_two_vars(self):
     x, y = Polynomial.coordinates(2)
     equations = [x**2 + y**2 - 1,
                  x-y]
     expansion_monomials = [
         [x, y],
         [x, y, x*y, x*x, y*y]
     ]
     result = solvers.solve_via_basis_selection(equations, expansion_monomials, x+y+1)
     expected_solutions = [np.sqrt([.5, .5]), -np.sqrt([.5, .5])]
     self.assert_solutions_found(result, expected_solutions)

    def test_estimate_pose_and_depths(self):
        np.random.seed(0)
        num_landmarks = 5

        # Generate ground truth
        true_cayleys = np.array([.1, .2, -.3])
        true_orientation = utils.cayley(true_cayleys)
        true_position = np.array([2., 3., 10.])

        # Generate observed quantities
        true_landmarks = np.random.randn(num_landmarks, 3)
        true_pfeatures = np.dot(true_landmarks - true_position, true_orientation.T)
        true_depths = np.sqrt(np.sum(np.square(true_pfeatures), axis=1))
        true_features = true_pfeatures / true_depths[:, None]
        true_vars = np.hstack((true_orientation.flatten(), true_position, true_depths))

        # Create symbolic quantities
        sym_vars = Polynomial.coordinates(12 + num_landmarks, ctype=float)
        sym_orientation = np.reshape(sym_vars[:9], (3, 3))
        sym_position = np.array(sym_vars[9:12])
        sym_depths = np.array(sym_vars[12:])

        residuals = []
        for i, (landmark, feature, sym_depth) in enumerate(zip(true_landmarks, true_features, sym_depths)):
            residual = np.dot(sym_orientation, landmark - sym_position) - sym_depth * feature
            residuals.extend(residual)

        constraints = (np.dot(sym_orientation.T, sym_orientation) - np.eye(3)).flatten()

        cost = sum(r**2 for r in residuals)
        gradients = cost.partial_derivatives()

        print 'Cost:', cost
        print 'Constraints:'
        for constraint in constraints:
            print '  ', constraint

        print 'At ground truth:'
        print '  Cost = ', cost(*true_vars)
        print '  Constraints = ', utils.evaluate_array(constraints, *true_vars)
        print '  Gradients = ', [p(*true_vars) for p in gradients]
        expansions = solvers.all_monomials(sym_vars, 2)
        minima = optimize.minimize_globally(cost,
                                            constraints,
                                            expansions=expansions,
                                            #diagnostic_solutions=[true_vars],
                                            )

        estimated_r = np.reshape(minima, (3, 3))
        error = np.linalg.norm(estimated_r - true_orientation)

        print 'Minima:\n', estimated_r
        print 'Ground truth:\n', true_orientation
        print 'Error:', error