︠9b7f24c6-cc5a-406b-a3d2-9d623182a481︠
2+3
︡78e74d40-dc88-4084-b974-bfcd9f57e0ba︡︡{"stdout":"5\n","done":false}︡{"done":true}
︠b1da93ed-3870-4faa-99bd-fe6dc6a5cbbc︠
pi.n()
︡43d5c47a-c74f-4794-81e8-15704707af69︡︡{"stdout":"3.14159265358979\n","done":false}︡{"done":true}
︠022a89ef-559d-449d-a3b8-519576710de9︠
2**3
2^3
︡2ee783e0-666f-4d5c-9b92-a4f173c50560︡︡{"stdout":"8\n","done":false}︡{"stdout":"8\n","done":false}︡{"done":true}
︠09691180-c314-4e09-b1ed-c207d4290b71︠
2<3
︡de639ecc-10e8-41a7-ba52-0e83d9584af1︡︡{"stdout":"True\n","done":false}︡{"done":true}
︠39486c6a-40ee-4c45-8798-9b781a264384︠
10/4
10//4
10%4
︡b88bcca3-5e73-44f9-ba01-a4b7b665cd80︡︡{"stdout":"5/2\n","done":false}︡{"stdout":"2\n","done":false}︡{"stdout":"2\n","done":false}︡{"done":true}
︠a8f59fca-ec0b-4c04-9072-d137b710fb34s︠
9e9
︡782b4c49-ba0f-428e-8de0-1ec2fa5c432a︡︡{"stdout":"9.00000000000000e9\n","done":false}︡{"done":true}
︠a7b20eb2-e6ac-4d2a-9b78-4ad384071ed0︠
sin(pi/3)
sin(pi/3).n()
sin(pi/3).n(digits=4)
︡629bb175-d2e0-419b-8581-bc720ca2d9e2︡︡{"stdout":"1/2*sqrt(3)\n","done":false}︡{"stdout":"0.866025403784439\n","done":false}︡{"stdout":"0.8660\n","done":false}︡{"done":true}
︠a0d3cb9b-d6d4-47d4-8397-d8fe8e73863a︠
a=-5
type(a)
a=5/3
type(a)
a='kocka'
type(a)
︡92881cac-66e4-4def-8a9d-80c2dd2f5c72︡︡{"stdout":"<type 'sage.rings.integer.Integer'>\n","done":false}︡{"stdout":"<type 'sage.rings.rational.Rational'>\n","done":false}︡{"stdout":"<type 'str'>\n","done":false}︡{"done":true}
︠2993226a-015e-4b42-82d0-387a35a733ab︠
tan?
︡0593c159-5433-4e02-ab91-a260a5df8518︡︡{"code":{"source":"File: /projects/sage/sage-6.10/local/lib/python2.7/site-packages/sage/functions/trig.py\nSignature : tan(*args, **kwds)\nDocstring :\nThe tangent function.\n\nEXAMPLES:\n\n   sage: tan(pi)\n   0\n   sage: tan(3.1415)\n   -0.0000926535900581913\n   sage: tan(3.1415/4)\n   0.999953674278156\n   sage: tan(pi/4)\n   1\n   sage: tan(1/2)\n   tan(1/2)\n   sage: RR(tan(1/2))\n   0.546302489843790\n\nWe can prevent evaluation using the \"hold\" parameter:\n\n   sage: tan(pi/4,hold=True)\n   tan(1/4*pi)\n\nTo then evaluate again, we currently must use Maxima via\n\"sage.symbolic.expression.Expression.simplify()\":\n\n   sage: a = tan(pi/4,hold=True); a.simplify()\n   1","mode":"text/x-rst","lineno":-1,"filename":null},"done":false}︡{"done":true}
︠332f5d48-9c63-4869-a997-e975b05f6203︠
def is_divisible_by(number, divisor):
    return number%divisor == 0
is_divisible_by(9,3)
is_divisible_by(7,4)
︡0f1e5c06-392a-4eea-8fbd-a6ec4955b897︡︡{"stdout":"True\n","done":false}︡{"stdout":"False\n","done":false}︡{"done":true}
︠041901e4-d8cd-4672-839a-d3a1e2dc792es︠
var('x')
f(x) = x^2
f(5)
︡081e9fa1-fc9e-43ae-9d83-0ea8bd8a92f0︡︡{"stdout":"x\n","done":false}︡{"stdout":"25\n","done":false}︡{"done":true}
︠875827e0-84f7-432a-a8ce-4036771eac96s︠
var('a,b')
sin(a + b).simplify_trig().show()
︡a687477a-afc0-4cb2-ae85-c04b5a0083f1︡︡{"stdout":"(a, b)\n","done":false}︡{"html":"<div align='center'>$\\displaystyle \\cos\\left(b\\right) \\sin\\left(a\\right) + \\cos\\left(a\\right) \\sin\\left(b\\right)$</div>","done":false}︡{"done":true}
︠d1ace0cc-9a1a-4333-a271-e32b166dab9b︠
for i in srange(0,5):
    print i
for i in srange(1,5,2):
    print i
︡037315ca-830e-40fb-ba9a-9800d565ed04︡︡{"stdout":"0\n1\n2\n3\n4\n","done":false}︡{"stdout":"1\n3\n","done":false}︡{"done":true}
︠41b646e7-66eb-4773-bc95-9e25c6c52917︠
list1 = [1,3,4,7]
list1[2]
len(list1)
︡3c583927-5c40-451f-97fc-39bdda83531d︡︡{"stdout":"4\n","done":false}︡{"stdout":"4\n","done":false}︡{"done":true}
︠daccdb8d-5621-47cf-ba0b-fbaf9a045dc6︠
list2 = [[0,5],[1,3],[3,4]]
list2[0]
list2[0][1]
︡8b873c76-4057-4c84-b980-0c189875207d︡︡{"stdout":"[0, 5]\n","done":false}︡{"stdout":"5\n","done":false}︡{"done":true}
︠e36f3fb6-45f3-4aef-9d4e-8891aee3b9af︠
point(list2,size=30,color='red')
︡e6a26b4e-1191-41e1-ab79-4487faf74102︡︡{"once":false,"done":false,"file":{"show":true,"uuid":"3fb04c01-ee96-437a-a055-1ce52289c120","filename":"/projects/deb543f0-64c7-4e12-a8c6-32e4785eaa9f/.sage/temp/compute1-us/13269/tmp_y0C9O4.svg"}}︡{"html":"<div align='center'></div>","done":false}︡{"done":true}
︠4d2068d0-f34c-4c65-a9fa-7bb9d3f0d77b︠
var('x')
solve(x^2-3*x+2,x)
︡508f7842-576c-443d-a0bc-594b9ff39693︡︡{"stdout":"x\n","done":false}︡{"stdout":"[x == 1, x == 2]","done":false}︡{"stdout":"\n","done":false}︡{"done":true}
︠aad357ea-f4ef-4519-9bab-2e158f0a93ac︠
var('x,y')
solve([x+y==6, x-y==4], x, y)
︡28c867a8-cdbf-4531-89ae-eeec2e9ac771︡︡{"stdout":"(x, y)\n","done":false}︡{"stdout":"[[x == 5, y == 1]]\n","done":false}︡{"done":true}
︠48b3d312-a61a-429f-abcf-7d85e07c65ae︠
diff(sin(x^2),x)
diff(sin(x^2),x,4)
︡1769cd7b-296b-4919-8b5b-1ed4b3c44b43︡︡{"stdout":"2*x*cos(x^2)\n","done":false}︡{"stdout":"16*x^4*sin(x^2) - 48*x^2*cos(x^2) - 12*sin(x^2)\n","done":false}︡{"done":true}
︠bd6d0062-b364-454f-9d22-683629a4d891s︠
limit((x ^ 2 + 1) / (2 + x + 3 * x ^ 2), x=Infinity)
︡75dbaf84-1939-47f9-8e8d-2298d504ad34︡︡{"stdout":"1/3","done":false}︡{"stdout":"\n","done":false}︡{"done":true}
︠2c1f702b-33cb-41b8-abf1-e37d9a009b97︠
var('x,y')
f = x^2+3*y^2
f.diff(x)
f.diff(y)
︡c9b6ba78-14de-43a5-bedf-9e7ff36d0fdd︡︡{"stdout":"(x, y)\n","done":false}︡{"stdout":"2*x\n","done":false}︡{"stdout":"6*y\n","done":false}︡{"done":true}
︠37de9e36-554e-4a00-8a66-1df15aae43abs︠
integral(x*sin(x^2),x).show()
︡5effca6e-2bad-4e4d-8206-fd7babcd13d9︡︡{"html":"<div align='center'>$\\displaystyle -\\frac{1}{2} \\, \\cos\\left(x^{2}\\right)$</div>","done":false}︡{"done":true}
︠596b4106-b83c-4b51-9cd1-daf36bbb46c2︠
integral(sin(x),x,pi,2*pi)
sin(x).integral(x,pi,2*pi)
︡29f68e3f-ce24-4c50-93a5-3ec07da038b3︡︡{"stdout":"-2\n","done":false}︡{"stdout":"-2\n","done":false}︡{"done":true}
︠c307fab2-2071-4a58-b410-edc14fb31bf6s︠
numerical_integral(exp(-x^2),-infinity,infinity)
︡7936749d-811c-4857-956b-b5194c02cfbd︡︡{"stdout":"(1.7724538509055137, 3.429548872025538e-08)\n","done":false}︡{"done":true}
︠eab67fc5-5a75-43e3-9509-9f6108680104︠
t = var('t')
x = function('x')(t)
DE = diff(x, t) + x - 1
desolve(DE, [x,t])
︡5d72c25a-c09c-4fed-85fc-c36566505bea︡︡{"stdout":"(_C + e^t)*e^(-t)\n","done":false}︡{"done":true}
︠8fea84b8-5770-4b43-bc06-9341cfe6b034︠
var('phi')
find_root(cos(phi)==sin(phi),0,pi/2)
︡2baa6bbf-b13e-48da-ae69-22d5afca2f08︡︡{"stdout":"phi\n","done":false}︡{"stdout":"0.7853981633974484\n","done":false}︡{"done":true}
︠afad46af-5eef-49fe-b342-f6498f426237︠
var('x')
plot(cos(x),x,-2*pi,4*pi,ticks=pi,tick_formatter=pi)
︡5c49486a-f3f9-4b7d-8171-046ee940a9a8︡︡{"stdout":"x\n","done":false}︡{"once":false,"done":false,"file":{"show":true,"uuid":"21021871-bcce-47a5-bfe9-5007d6bf5cae","filename":"/projects/deb543f0-64c7-4e12-a8c6-32e4785eaa9f/.sage/temp/compute1-us/13269/tmp_eNr5JN.svg"}}︡{"html":"<div align='center'></div>","done":false}︡{"done":true}
︠f6b5a5cb-9334-4df8-8ffd-2b69e5a4af70︠
c=circle((0,0), 1, rgbcolor=(1,1,0), fill=True)
c.show()
#c.save('kruh.pdf')
︡0545bc7a-19fd-4b52-a13a-e1854a3dd781︡︡{"once":false,"done":false,"file":{"show":true,"uuid":"104713f5-19c1-47eb-9d07-63868a5324de","filename":"/projects/deb543f0-64c7-4e12-a8c6-32e4785eaa9f/.sage/temp/compute1-us/13269/tmp_RI6liT.svg"}}︡{"html":"<div align='center'></div>","done":false}︡{"done":true}
︠e4d11f84-3a83-46c2-8530-7140b1375077︠
var('x')
plot(cos(x),x,0,2*pi)+plot(sin(x),x,0,2*pi,color='red')
︡a9706c6c-9464-48e0-925f-0e8a5d0ecee5︡︡{"stdout":"x\n","done":false}︡{"once":false,"done":false,"file":{"show":true,"uuid":"81a5b2d0-313a-4e0a-8fbb-3e74d043f551","filename":"/projects/deb543f0-64c7-4e12-a8c6-32e4785eaa9f/.sage/temp/compute1-us/13269/tmp_RoMbQW.svg"}}︡{"html":"<div align='center'></div>","done":false}︡{"done":true}
︠145ccccb-9932-4fba-a5ba-fab612192b33︠
var('x')
plot(cos(x),x,0,2*pi)+line([(1,0),(1,cos(1))],linestyle='dashed')
︡19a284e2-bc3a-47e8-b7d3-bd0ed20b6c87︡︡{"stdout":"x\n","done":false}︡{"once":false,"done":false,"file":{"show":true,"uuid":"5822c4ac-c03e-447c-83df-c7f7c5893677","filename":"/projects/deb543f0-64c7-4e12-a8c6-32e4785eaa9f/.sage/temp/compute1-us/13269/tmp_dwkb9g.svg"}}︡{"html":"<div align='center'></div>","done":false}︡{"done":true}
︠ee9673d6-d924-4859-b1cc-96bd878ddb82︠
var('x,y')
contour_plot(x^2-y^3+10*sin(x*y), (x, -4, 4), (y, -4, 4),plot_points=121,cmap='hsv')
︡f4c9791d-a54d-4826-bbe4-dd9c324abb4d︡︡{"stdout":"(x, y)\n","done":false}︡{"once":false,"done":false,"file":{"show":true,"uuid":"15c9a519-9d47-4886-a729-6699141a04e4","filename":"/projects/deb543f0-64c7-4e12-a8c6-32e4785eaa9f/.sage/temp/compute1-us/13269/tmp_WKkRbJ.svg"}}︡{"html":"<div align='center'></div>","done":false}︡{"done":true}
︠e2fafe33-1328-4720-b0a1-0d3b0d0faf09︠
var('x,y')
plot3d(x^2 + y^2, (x,-2,2), (y,-2,2))
︡b4294227-c54b-48a6-8208-b635fc6b407e︡︡{"stdout":"(x, y)\n","done":false}︡{"done":false,"file":{"uuid":"e9d1d0be-9f12-4b16-874e-36fa648ea5cb","filename":"e9d1d0be-9f12-4b16-874e-36fa648ea5cb.sage3d"}}︡{"html":"<div align='center'></div>","done":false}︡{"done":true}
︠b6474c33-ddaa-4c00-8269-0ad42e4c6c67︠
A = matrix([[1,2,3],[3,2,1],[1,1,1]])
w = vector([1,1,-4])
A*w
w*A
A.eigenvalues()
A.eigenvectors_right()
︡02811fb3-89b6-4a8d-b8b1-f19f6536fad6︡︡{"stdout":"(-9, 1, -2)\n","done":false}︡{"stdout":"(0, 0, 0)\n","done":false}︡{"stdout":"[5, 0, -1]\n","done":false}︡{"stdout":"[(5, [\n(1, 13/11, 6/11)\n], 1), (0, [\n(1, -2, 1)\n], 1), (-1, [\n(1, -1, 0)\n], 1)]\n","done":false}︡{"done":true}
︠ad8c7e14-18e1-4de2-bc83-50f8e87f0279s︠
B = matrix([[1,2],[3,4]])
B.det()
v = vector([0,1])
B.solve_right(v)
B.inverse()
︡ca913f30-8f1f-4cec-85ef-1fb1f4ce69de︡︡{"stdout":"-2\n","done":false}︡{"stdout":"(1, -1/2)\n","done":false}︡{"stdout":"[  -2    1]\n[ 3/2 -1/2]\n","done":false}︡{"done":true}
︠547b92eb-95ce-41ee-851b-141982c55dde︠
a = Sudoku('5...8..49...5...3..673....115..........2.8..........187....415..3...2...49..5...3')
a
next(a.solve())
︡3ca099fe-45a1-4016-a55b-701a5051ab2c︡︡{"stdout":"+-----+-----+-----+\n|5    |  8  |  4 9|\n|     |5    |  3  |\n|  6 7|3    |    1|\n+-----+-----+-----+\n|1 5  |     |     |\n|     |2   8|     |\n|     |     |  1 8|\n+-----+-----+-----+\n|7    |    4|1 5  |\n|  3  |    2|     |\n|4 9  |  5  |    3|\n+-----+-----+-----+\n","done":false}︡{"stdout":"+-----+-----+-----+\n|5 1 3|6 8 7|2 4 9|\n|8 4 9|5 2 1|6 3 7|\n|2 6 7|3 4 9|5 8 1|\n+-----+-----+-----+\n|1 5 8|4 6 3|9 7 2|\n|9 7 4|2 1 8|3 6 5|\n|3 2 6|7 9 5|4 1 8|\n+-----+-----+-----+\n|7 8 2|9 3 4|1 5 6|\n|6 3 5|1 7 2|8 9 4|\n|4 9 1|8 5 6|7 2 3|\n+-----+-----+-----+\n","done":false}︡{"done":true}
︠d988c6f7-2f5b-4be0-b63b-85839fe3785cs︠
var('a,b')
matrix([[a,b],[b,a]]).det()
︡c8b00d05-ee2f-4af9-8798-4bc3f3537775︡︡{"stdout":"(a, b)\n","done":false}︡{"stdout":"a^2 - b^2\n","done":false}︡{"done":true}
︠60ed9dc8-e530-4f84-a570-a38e0ca9091d︠
import scipy
from scipy import optimize
var('l,alpha,y,j,jj');
l = 1; alpha=1
def fun(x):
    return [4*pi*alpha*l+x[1]+exp(-x[1])*cos(x[0]),
             -x[0]+exp(-x[1])*sin(x[0])]
def fun2(x):
    return [4*pi*alpha*l+x[1]-exp(-x[1])*cos(x[0]),
             -x[0]-exp(-x[1])*sin(x[0])]
def fun0(x):
    return [x[1]+exp(-x[1])*cos(x[0]),
             -x[0]+exp(-x[1])*sin(x[0])]
def fun02(x):
    return [x[1]-exp(-x[1])*cos(x[0]),
             -x[0]-exp(-x[1])*sin(x[0])]
list1 = [];
list2 = [];
for j in srange(0,40):
    for jj in srange(-5,-1,0.5):
        sol = optimize.root(fun, [j, jj])
        if sol.success: list1 = list1+[[sol.x[0],sol.x[1]]]
        sol2 = optimize.root(fun2, [j, jj])
        if sol2.success: list1 = list1+[[sol2.x[0],sol2.x[1]]]
        sol3 = optimize.root(fun0, [j, jj])
        if sol3.success: list2 = list2+[[sol3.x[0],sol3.x[1]]]
        sol4 = optimize.root(fun02, [j, jj])
        if sol4.success: list2 = list2+[[sol4.x[0],sol4.x[1]]]
(point(list1,size=40)+point(list2,size=40,color='red',axes_labels=['Re $k$','Im $k$'],axes_labels_size=1.3, xmin=0))
list1
list2
︡f02fd1c4-6446-43c2-98e1-043ee8f3b9be︡︡{"stdout":"(l, alpha, y, j, jj)\n","done":false}︡{"done":false,"stderr":"/projects/sage/sage-6.10/local/lib/python2.7/site-packages/scipy/optimize/minpack.py:236: RuntimeWarning: The iteration is not making good progress, as measured by the \n  improvement from the last ten iterations.\n  warnings.warn(msg, RuntimeWarning)\n/projects/sage/sage-6.10/local/lib/python2.7/site-packages/scipy/optimize/minpack.py:236: RuntimeWarning: The iteration is not making good progress, as measured by the \n  improvement from the last five Jacobian evaluations.\n  warnings.warn(msg, RuntimeWarning)\n"}︡{"once":false,"done":false,"file":{"show":true,"uuid":"8a9ea564-e248-4258-a672-ab4e0579ac5c","filename":"/projects/deb543f0-64c7-4e12-a8c6-32e4785eaa9f/.sage/temp/compute1-us/13562/tmp_4jtdUq.svg"}}︡{"html":"<div align='center'></div>","done":false}︡{"stdout":"[[8.3178266735179471e-18, -2.3263077579169575], [1.1316755983480576e-17, -2.3263077579169691], [1.5521633432800781e-18, -2.3263077579169575], [-8.7445520472860571e-19, -2.3263077579169575], [4.237563305315237e-20, -2.3263077579169575], [1.7998217588381106e-21, -2.3263077579169651], [-8.7620170937011011e-21, -2.3263077579169571], [2.015314828388391e-17, -2.326307757917065], [2.8676631247954121, -2.3609195178131968], [-1.5507644140317223e-13, -2.3263077579168798], [2.867663124782263, -2.3609195178329836], [2.62546846920002e-14, -2.3263077579169651], [2.8676631247835811, -2.3609195178338798], [6.3299265786873251e-12, -2.32630775790114], [2.8676631247674096, -2.3609195178690379], [-1.2423917017809147e-12, -2.3263077579225082], [2.8676631247811453, -2.360919517832996], [7.5935347028065185e-12, -2.3263077579252802], [2.8676631247812856, -2.3609195178163365], [2.3877627489599913e-11, -2.3263077579118678], [2.867663124782486, -2.3609195178329849], [-4.2017793240153008e-15, -2.3263077579169722], [2.8676631247676405, -2.3609195178438624], [2.2636085979479938e-12, -2.3263077579155831], 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0.56714329040978062], [26.580471499342703, -3.2877686115613587], [-3.3694206439415712e-16, 0.56714329040978462], [26.580471499457076, -3.2877686112363249], [-1.8987129603096397e-12, 0.56714329040821077], [26.580471499357692, -3.2877686115421945], [1.8179296872279278e-17, 0.56714329040978384], [26.580471499553731, -3.2877686114830658], [3.0142765548919974e-16, 0.56714329040978395], [26.580471499699851, -3.2877686116440343], [2.0944319801998443e-12, 0.56714329041129607], [26.580471499356754, -3.2877686118287488], [-7.4418919540337372e-12, 0.56714329040852507], [26.580471499966308, -3.2877686119615483], [4.1038680705649565e-14, 0.56714329040982125], [26.580471498665954, -3.2877686113679316], [29.731310707815744, -3.3986921967654862], [26.580471499281302, -3.2877686115260691], [29.731310708014355, -3.3986921971703805], [26.580471499379538, -3.2877686115547511], [29.731310707836244, -3.3986921967696464], [26.580471499703105, -3.2877686114653439], [29.73131070782501, -3.3986921967699257], [26.58047149950783, -3.2877686117132865], [29.731310707767275, -3.3986921967809245], [26.580471499336689, -3.2877686115595814], [29.731310707665351, -3.3986921966771346], [26.580471499436939, -3.2877686115068756], [29.731310708840304, -3.3986921983222014], [20.272457641614398, -3.0202397081649637], [23.427747503756002, -3.1629527388056347], [1.3372357014307039, -0.31813150520478151], [29.731310708093421, -3.3986921972191726], [29.731310707828424, -3.3986921967643893], [1.3372357013673211, -0.31813150520044714], [29.731310707828527, -3.3986921967647379], [1.3372357014307128, -0.31813150520481714], [29.731310707828705, -3.3986921967646206], [-1.337235701430268, -0.31813150520552486], [29.73131070870463, -3.3986921975815161], [-1.3372357014307059, -0.31813150520473749], [29.731310707828527, -3.398692196764721], [-1.3372357014307037, -0.31813150520472977], [29.731310707738484, -3.398692196729427], [-1.3372357014306755, -0.31813150520477101], [29.731310707828236, -3.3986921967650114], [1.3372357014307019, -0.3181315052047563], [29.731310707436709, -3.3986921969401513], [-1.3372357014306875, -0.31813150520476657], [29.731310707815137, -3.3986921967739079], [-1.3372357014306893, -0.3181315052047658], [29.731310707496981, -3.3986921973168855], [-1.3372357014308651, -0.31813150520444688], [29.731310708958983, -3.398692197058959], [1.3372357014302894, -0.31813150520451955], [29.731310708757974, -3.3986922073772767], [-1.3372357014305654, -0.31813150520489858], [29.731310707831966, -3.3986921967831729], [-1.3372357014329233, -0.3181315052042627], [29.731310707334096, -3.3986921979177835], [-1.3372357014306044, -0.31813150520994055], [29.731310707826839, -3.3986921967702695], [32.880721480071259, -3.4985152121570624], [29.731310708732565, -3.3986921966112056], [32.880721480069738, -3.498515212153773], [29.731310707252412, -3.3986921966248849], [32.880721480068772, -3.4985152121542686], [29.731310707835959, -3.398692196762596], [32.880721480060359, -3.498515212095147], [29.731310707551035, -3.3986921968132675], [32.880721480068914, -3.4985152121541043], [29.731310706416295, -3.3986921969915267], [32.880721480010195, -3.4985152121380878], [29.731310708801391, -3.3986921975889381], [32.880721480085001, -3.4985152121204282], [29.731310707769168, -3.3986921967391019], [-1.337235701432788, -0.31813150520992539], [29.731310707827983, -3.3986921967651087], [32.880721480099325, -3.4985152122291749], [10.776299516101892, -2.401585104874731], [32.880721480068601, -3.4985152121529843], [1.8628662420527128e-11, 0.56714329041501255], [32.880721480049594, -3.4985152122328667], [6.0403035315281668e-14, 0.56714329040972711], [32.880721481101943, -3.4985152117984462], [9.0830384283320527e-17, 0.56714329040978395], [32.880721480069994, -3.4985152121535004], [-1.3231674673626047e-15, 0.56714329040978284], [32.880721479893346, -3.4985152119277059], [7.4797602877406439e-13, 0.56714329041104605], [32.880721480068047, -3.4985152121530638], [-7.5410281165527754e-16, 0.56714329040978761], [32.880721480035277, -3.4985152121701746], [3.1796425567512004e-12, 0.56714329041118894], [32.880721479703709, -3.4985152122266401], [1.6448091482075893e-11, 0.56714329039728351], [32.880721480068942, -3.4985152121540941], [1.5692155684036744e-17, 0.56714329040978384], [32.880721479824601, -3.4985152123129728], [-7.2101547010529838e-13, 0.56714329041035538], [32.880721480072737, -3.4985152121484382], [5.8342583488442268e-13, 0.567143290409721], [32.880721481387418, -3.4985152128845991], [-1.4311452433492335e-11, 0.56714329041416978], [32.880721480701332, -3.4985152113116427], [1.6486795662903665e-16, 0.56714329040978384], [32.880721480059471, -3.4985152121840537], [4.1644435088479677e-16, 0.56714329040978617], [-7.0904725170426183e-12, 0.56714329039352818], [32.88072148004467, -3.4985152122413656], [36.02902170342734, -3.589262524529047], [32.880721480121196, -3.4985152121547198], [36.029021704184927, -3.5892625243973226], [32.880721480071081, -3.4985152121483987], [36.029021706977083, -3.5892625327736964], [32.880721480067109, -3.4985152121540097], [36.029021703416987, -3.5892625245224927], [32.880721477522805, -3.4985152121880585], [36.029021703442872, -3.5892625244888579], [32.880721480069184, -3.4985152121547824], [36.029021703468047, -3.5892625246717338], [32.880721480171502, -3.4985152120856511], [-4.1150101536095944e-14, 0.56714329040979528], [32.880721480064331, -3.4985152121626681], [32.880721480082599, -3.4985152121390626], [36.029021703424412, -3.5892625245204779], [32.880721480069695, -3.498515212159663], [36.029021703504235, -3.5892625257127766], [32.880721480077568, -3.4985152121569718], [36.029021701754196, -3.5892625240806444], [32.880721479769392, -3.4985152127457515], [36.029021701819701, -3.5892625242145502], [32.88072148006809, -3.4985152121590248], [36.029021703221694, -3.5892625248514993], [1.3372357014300877, -0.3181315052063115], [36.029021703379975, -3.589262524482423], [1.3372357014306917, 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-3.5892625245255534], [39.176440021717987, -3.6724500686560404], [36.029021703513834, -3.5892625245144609], [39.176440021952288, -3.6724500688787862], [36.029021696372126, -3.5892625114015462], [39.176440021577505, -3.672450068704836], [36.029021698499122, -3.5892625270897134], [39.176440021708075, -3.6724500686350146], [36.029021703451747, -3.5892625245304801], [-1.3372357014328198, -0.31813150520320332], [36.029021703428057, -3.5892625245293739], [39.176440021735338, -3.6724500687098685], [36.029021703387038, -3.5892625244876295], [39.176440021774141, -3.6724500687112869], [36.02902170581465, -3.5892625207894477], [39.176440021731054, -3.6724500687089749], [36.029021703388757, -3.5892625244779919], [39.176440021925345, -3.6724500687198729], [36.029021703422096, -3.5892625245452505], [39.176440017894741, -3.6724500691485966], [36.029021703427631, -3.5892625245293774], [39.176440021781296, -3.6724500685568828], [36.029021703427297, -3.5892625245295506], [39.176440021892319, -3.6724500695155307], [-1.1209990033937295e-11, 0.56714329036658528], [39.176440022915628, -3.6724500686763095], [1.4580402005107972e-17, 0.56714329040978395], [1.3372357014306853, -0.31813150520474665], [1.4551157395675274e-16, 0.56714329040978306], [39.176440021735722, -3.6724500687099924], [7.9283879622203531e-14, 0.56714329040970146], [39.176440022918371, -3.6724500694691975], [3.3365739638924399e-12, 0.56714329040946598], [39.176440021733114, -3.6724500687030504], [-9.9991867776058169e-14, 0.56714329040977929], [39.176440022585275, -3.6724500705419176], [3.8438259687110483e-13, 0.56714329040973877], [39.17644002173467, -3.672450068710039], [3.8944320190926193e-13, 0.56714329040975209], [39.176440021725639, -3.6724500687069606], [-1.9794236901262643e-13, 0.56714329040976563], [39.176440021740639, -3.6724500686938653], [-1.1780931378852428e-11, 0.56714329038203715], [39.176440021726933, -3.6724500687171768], [2.801938781237192e-16, 0.56714329040978362]]","done":false}︡{"stdout":"\n","done":false}︡{"done":true}
︠442beb66-2728-4d49-9381-8fc4de314538︠
var('k,j,st,kold')
st = 0.01 #step
#resonances from the condition with the minus before the exponential, i.e. fun02
k = [0, 0.56714329042655232]
list3 = [k]
for j in srange(0,1,st):
    kold = k
    k = [kold[0]-(4*3.14159265359*exp(-kold[1])*sin(kold[0]))/(1+exp(-2*kold[1])+2*exp(-kold[1])*cos(kold[0]))*st,kold[1]-4*3.14159265359*(1+exp(-kold[1])*cos(kold[0]))/(1+exp(-2*kold[1])+2*exp(-kold[1])*cos(kold[0]))*st]
    list3 = list3+[[k[0],k[1]]]
k = [4.3751851530619321, -1.533913319793369]
list4 = [k]
for j in srange(0,1,st):
    kold = k
    k = [kold[0]-(4*3.14159265359*exp(-kold[1])*sin(kold[0]))/(1+exp(-2*kold[1])+2*exp(-kold[1])*cos(kold[0]))*st,kold[1]-4*3.14159265359*(1+exp(-kold[1])*cos(kold[0]))/(1+exp(-2*kold[1])+2*exp(-kold[1])*cos(kold[0]))*st]
    list4 = list4+[[k[0],k[1]]]
k = [10.776299518376746, -2.4015851038246172]
list5 = [k]
for j in srange(0,1,st):
    kold = k
    k = [kold[0]-(4*3.14159265359*exp(-kold[1])*sin(kold[0]))/(1+exp(-2*kold[1])+2*exp(-kold[1])*cos(kold[0]))*st,kold[1]-4*3.14159265359*(1+exp(-kold[1])*cos(kold[0]))/(1+exp(-2*kold[1])+2*exp(-kold[1])*cos(kold[0]))*st]
    list5 = list5+[[k[0],k[1]]]
#resonances from the condition with plus before the exponential, i.e. fun0
k = [1.3372357014304412, -0.31813150520512345]
list6 = [k]
for j in srange(0,1,st):
    kold = k
    k = [kold[0]+(4*3.14159265359*exp(-kold[1])*sin(kold[0]))/(1+exp(-2*kold[1])-2*exp(-kold[1])*cos(kold[0]))*st,kold[1]-4*3.14159265359*(1-exp(-kold[1])*cos(kold[0]))/(1+exp(-2*kold[1])-2*exp(-kold[1])*cos(kold[0]))*st]
    list6 = list6+[[k[0],k[1]]]
k = [7.5886311784702549, -2.0622777295952646]
list7 = [k]
for j in srange(0,1,st):
    kold = k
    k = [kold[0]+(4*3.14159265359*exp(-kold[1])*sin(kold[0]))/(1+exp(-2*kold[1])-2*exp(-kold[1])*cos(kold[0]))*st,kold[1]-4*3.14159265359*(1-exp(-kold[1])*cos(kold[0]))/(1+exp(-2*kold[1])-2*exp(-kold[1])*cos(kold[0]))*st]
    list7 = list7+[[k[0],k[1]]]
k = [13.949208334511937, -2.6531919740771563]
list8 = [k]
for j in srange(0,1,st):
    kold = k
    k = [kold[0]+(4*3.14159265359*exp(-kold[1])*sin(kold[0]))/(1+exp(-2*kold[1])-2*exp(-kold[1])*cos(kold[0]))*st,kold[1]-4*3.14159265359*(1-exp(-kold[1])*cos(kold[0]))/(1+exp(-2*kold[1])-2*exp(-kold[1])*cos(kold[0]))*st]
    list8 = list8+[[k[0],k[1]]]
c3 = animate([point(list3[j],size=40)+point(list4[j],size=40)+point(list5[j],size=40)+point(list6[j],size=40)+point(list7[j],size=40)+point(list8[j],size=40) for j in srange(0,len(list3),2)],xmin=0,xmax=15,ymin=-3,ymax=0.6,axes_labels=['Re $k$','Im $k$'],axes_labels_size=1.3)
c3.show()
︡45bd86ac-6aee-40d1-902c-5e47af5d3aee︡︡{"stdout":"(k, j, st, kold)\n","done":false}︡{"once":false,"done":false,"file":{"url":"/deb543f0-64c7-4e12-a8c6-32e4785eaa9f/raw/.sage/temp/compute1-us/13562/tmp_WhoDYL.webm","show":true,"filename":"/projects/deb543f0-64c7-4e12-a8c6-32e4785eaa9f/.sage/temp/compute1-us/13562/tmp_WhoDYL.webm"}}︡{"html":"<div align='center'></div>","done":false}︡{"done":true}
︠2ef9d47b-9413-465c-b608-3cd46917b76ds︠
list(Partitions(10))
︡54a8f989-c091-4159-abba-a28514803bd7︡︡{"stdout":"[[10], [9, 1], [8, 2], [8, 1, 1], [7, 3], [7, 2, 1], [7, 1, 1, 1], [6, 4], [6, 3, 1], [6, 2, 2], [6, 2, 1, 1], [6, 1, 1, 1, 1], [5, 5], [5, 4, 1], [5, 3, 2], [5, 3, 1, 1], [5, 2, 2, 1], [5, 2, 1, 1, 1], [5, 1, 1, 1, 1, 1], [4, 4, 2], [4, 4, 1, 1], [4, 3, 3], [4, 3, 2, 1], [4, 3, 1, 1, 1], [4, 2, 2, 2], [4, 2, 2, 1, 1], [4, 2, 1, 1, 1, 1], [4, 1, 1, 1, 1, 1, 1], [3, 3, 3, 1], [3, 3, 2, 2], [3, 3, 2, 1, 1], [3, 3, 1, 1, 1, 1], [3, 2, 2, 2, 1], [3, 2, 2, 1, 1, 1], [3, 2, 1, 1, 1, 1, 1], [3, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2], [2, 2, 2, 2, 1, 1], [2, 2, 2, 1, 1, 1, 1], [2, 2, 1, 1, 1, 1, 1, 1], [2, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]\n","done":false}︡{"done":true}
︠f00f0c8a-5be5-40a7-a8cc-b6281fdde6afs︠
@interact
def power_table_plot(p=(7,prime_range(50))):
     P=matrix_plot(matrix(p-1,[mod(a,p)^b for a in range(1,p) for b in srange(p)]),cmap='jet')
     show(P)
︡b407f189-46be-471a-b07c-270fda4cc0df︡︡{"interact":{"style":"None","flicker":false,"layout":[[["p",12,null]],[["",12,null]]],"id":"b639fc85-c3f1-4e40-a198-7f439dcbeb6d","controls":[{"buttons":false,"control_type":"selector","ncols":null,"button_classes":null,"default":3,"lbls":["2","3","5","7","11","13","17","19","23","29","31","37","41","43","47"],"label":"p","nrows":null,"width":null,"var":"p"}]},"done":false}︡{"done":true}
︠fb78694e-cb99-414f-abba-5e45d45c182as︠
data = [(i, 1.2 * sin(0.5*i-0.2) + 0.1 * normalvariate(0, 1)) for i in xsrange(0, 4*pi, 0.2)]
var('a, b, c, x')
model(x) = a * sin(b * x - c)
find_fit(data, model)
︡3689debf-9e6c-48aa-a05a-08e44e3fab91︡︡{"stdout":"(a, b, c, x)\n","done":false}︡{"stdout":"[a == 1.1944541985230013, b == 0.5020324442123956, c == 0.2170655514425861]","done":false}︡{"stdout":"\n","done":false}︡{"done":true}
︠0f13bd87-25f5-40ab-838b-4b3aa9341da5s︠
for i in primes(50):
    print i
︡ed4da5d1-6ad8-4d77-8f67-e9bf002c719c︡︡{"stdout":"2\n3\n5\n7\n11\n13\n17\n19\n23\n29\n31\n37\n41\n43\n47\n","done":false}︡{"done":true}
︠f6e98132-f515-42e2-847a-54a0cb6bde3as︠
2013.is_prime()
︡fa3a9234-18a7-4018-b0e9-39e662bb27c8︡︡{"stdout":"False\n","done":false}︡{"done":true}
︠108b54cb-3c53-4467-af10-bfff83e8d9cfs︠
2013.factor()
︡8594d41f-430e-4867-baf0-9cdb248a743c︡︡{"stdout":"3 * 11 * 61\n","done":false}︡{"done":true}
︠29812b01-b37c-4790-bfd3-3760d75aa5c7s︠
M = random_matrix(RDF,3)
M
︡0f969f61-d293-4384-a27d-225d0265a6e7︡︡{"stdout":"[  0.3188488737301076   0.1528502049690592 0.018806925561862364]\n[  0.5489269518124278 -0.37019418700864004   0.6865308007479909]\n[  -0.697472245544493  0.42472775905086535  -0.9684808204803959]\n","done":false}︡{"done":true}
︠8e3b0de7-9940-4ea1-a23d-3803205e3173︠