CoCalc Public Files2016-01-07-140550.sagews
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Compute Environment: Ubuntu 18.04 (Deprecated)

︠049792a0-27d4-40f3-b768-a2608818aa7f︠
# make a graph
g = graphs.BrouwerHaemersGraph()


g.automorphism_group()

Permutation Group with generators [(27,54)(28,55)(29,56)(30,57)(31,58)(32,59)(33,60)(34,61)(35,62)(36,63)(37,64)(38,65)(39,66)(40,67)(41,68)(42,69)(43,70)(44,71)(45,72)(46,73)(47,74)(48,75)(49,76)(50,77)(51,78)(52,79)(53,80), (3,6)(4,7)(5,8)(12,15)(13,16)(14,17)(21,24)(22,25)(23,26)(30,33)(31,34)(32,35)(39,42)(40,43)(41,44)(48,51)(49,52)(50,53)(57,60)(58,61)(59,62)(66,69)(67,70)(68,71)(75,78)(76,79)(77,80), (3,27)(4,28)(5,29)(6,54)(7,55)(8,56)(12,36)(13,37)(14,38)(15,63)(16,64)(17,65)(21,45)(22,46)(23,47)(24,72)(25,73)(26,74)(33,57)(34,58)(35,59)(42,66)(43,67)(44,68)(51,75)(52,76)(53,77), (1,2)(4,5)(7,8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)(34,35)(37,38)(40,41)(43,44)(46,47)(49,50)(52,53)(55,56)(58,59)(61,62)(64,65)(67,68)(70,71)(73,74)(76,77)(79,80), (1,5,48,76)(2,7,69,44)(3,53,16,77)(4,46,28,42)(6,67,23,43)(8,65,56,75)(9,17,79,51)(11,12,31,59)(13,33,26,57)(14,29,38,52)(15,72,63,58)(18,22,41,66)(19,24,62,34)(21,36,45,35)(25,55,73,68)(27,40,64,60)(30,54,80,47)(32,61)(37,50,74,70)(39,71)(49,78), (0,1)(3,4)(6,7)(9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)(30,31)(33,34)(36,37)(39,40)(42,43)(45,46)(48,49)(51,52)(54,55)(57,58)(60,61)(63,64)(66,67)(69,70)(72,73)(75,76)(78,79)]

v = [(0,0,0)]
for i in range(1000):
v.append([a+random()-.5 for a in v[-1]])
line3d(v, color='red', thickness=3, spin=3)

3D rendering not yet implemented
@interact
def f(n=(1..5)):
print n


︠4780fe2e-c483-481b-8020-b1d26df026b7︠
show(graphs.FruchtGraph())

d3-based renderer not yet implemented
2 + 8

10

%var x y z
g = golden_ratio; r = 4.77
p = 2 - (cos(x + g*y) + cos(x - g*y) + cos(y + g*z) +
cos(y - g*z) + cos(z - g*x) + cos(z + g*x))
show(implicit_plot3d(p == .5, (x, -r, r), (y, -r, r), (z, -r, r),
plot_points=30, color='red', mesh=1, opacity=.7), spin=1)

3D rendering not yet implemented


m = matrix([[1,2],[3,4]])
m

[1 2] [3 4]
m.eigenvalues()

[-0.3722813232690144?, 5.372281323269015?]
show(m)

$\displaystyle \left(\begin{array}{rr} 1 & 2 \\ 3 & 4 \end{array}\right)$
v = vector([1,2])
v

(1, 2)
v+3

Error in lines 1-1 Traceback (most recent call last): File "/projects/sage/sage-6.10/local/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 905, in execute exec compile(block+'\n', '', 'single') in namespace, locals File "", line 1, in <module> File "sage/structure/element.pyx", line 1316, in sage.structure.element.ModuleElement.__add__ (/projects/sage/sage-6.10/src/build/cythonized/sage/structure/element.c:11242) return coercion_model.bin_op(left, right, add) File "sage/structure/coerce.pyx", line 1069, in sage.structure.coerce.CoercionModel_cache_maps.bin_op (/projects/sage/sage-6.10/src/build/cythonized/sage/structure/coerce.c:9736) raise TypeError(arith_error_message(x,y,op)) TypeError: unsupported operand parent(s) for '+': 'Ambient free module of rank 2 over the principal ideal domain Integer Ring' and 'Integer Ring'
factorial(1000)

402387260077093773543702433923003985719374864210714632543799910429938512398629020592044208486969404800479988610197196058631666872994808558901323829669944590997424504087073759918823627727188732519779505950995276120874975462497043601418278094646496291056393887437886487337119181045825783647849977012476632889835955735432513185323958463075557409114262417474349347553428646576611667797396668820291207379143853719588249808126867838374559731746136085379534524221586593201928090878297308431392844403281231558611036976801357304216168747609675871348312025478589320767169132448426236131412508780208000261683151027341827977704784635868170164365024153691398281264810213092761244896359928705114964975419909342221566832572080821333186116811553615836546984046708975602900950537616475847728421889679646244945160765353408198901385442487984959953319101723355556602139450399736280750137837615307127761926849034352625200015888535147331611702103968175921510907788019393178114194545257223865541461062892187960223838971476088506276862967146674697562911234082439208160153780889893964518263243671616762179168909779911903754031274622289988005195444414282012187361745992642956581746628302955570299024324153181617210465832036786906117260158783520751516284225540265170483304226143974286933061690897968482590125458327168226458066526769958652682272807075781391858178889652208164348344825993266043367660176999612831860788386150279465955131156552036093988180612138558600301435694527224206344631797460594682573103790084024432438465657245014402821885252470935190620929023136493273497565513958720559654228749774011413346962715422845862377387538230483865688976461927383814900140767310446640259899490222221765904339901886018566526485061799702356193897017860040811889729918311021171229845901641921068884387121855646124960798722908519296819372388642614839657382291123125024186649353143970137428531926649875337218940694281434118520158014123344828015051399694290153483077644569099073152433278288269864602789864321139083506217095002597389863554277196742822248757586765752344220207573630569498825087968928162753848863396909959826280956121450994871701244516461260379029309120889086942028510640182154399457156805941872748998094254742173582401063677404595741785160829230135358081840096996372524230560855903700624271243416909004153690105933983835777939410970027753472000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000