(1,2,4,5,3,6)(7,8)
13.0500000000000
(1, 2, 4, 5, 3, 6)
6
6
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 957, in execute
exec compile(block+'\n', '', 'single') in namespace, locals
File "<string>", line 1
Integer(4)!
^
SyntaxError: invalid syntax
2
12915302400
12915302400
2471040
This is
39916800
(1,9,11,3,4,10,5,6,2,8,7)
[(1, 9, 11, 3, 4, 10, 5, 6, 2, 8, 7)]
(1, 9, 11, 3, 4, 10, 5, 6, 2, 8, 7)
11
1
[9, 7, 5, 6, 6, 5, 5, 4, 5, 6, 10, 5, 6, 6, 7, 6, 11, 10, 3, 9, 8, 4, 7, 9, 6, 8, 7, 6, 5, 5, 9, 7, 4, 7, 7, 5, 10, 8, 7, 8, 8, 4, 9, 5, 10, 7, 4, 9, 5, 6, 7, 4, 9, 9, 9, 5, 4, 7, 7, 9, 8, 11, 6, 6, 7, 8, 8, 8, 9, 6, 9, 8, 9, 11, 10, 8, 5, 7, 7, 7, 7, 7, 6, 6, 10, 8, 9, 4, 9, 9, 6, 3, 9, 11, 6, 4, 8, 8, 9, 6]
7.21500000000000
Partitions of the integer 7
[[7], [6, 1], [5, 2], [5, 1, 1], [4, 3], [4, 2, 1], [4, 1, 1, 1], [3, 3, 1], [3, 2, 2], [3, 2, 1, 1], [3, 1, 1, 1, 1], [2, 2, 2, 1], [2, 2, 1, 1, 1], [2, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1]]
15
15
[[5, 1, 1], [4, 2, 1], [3, 3, 1], [3, 2, 2]]
[[5, 2], [3, 2, 2]]
31
5005
451276
21618.8176101031
2.63901582154579
500 0.608924
100000 0.60902
1235
40
0
0.6079319118542257
0.6079271018540267
350
8400
8400
322
16384
2187
150
[0.0, 0.0, 0.5144000000000001, 0.327, 0.25880000000000003, 0.2056, 0.1602, 0.1468, 0.125, 0.11120000000000001, 0.097]
43758
498112057
63
33931087734103828901344268647256476554494850685762924621597342996464801589784605059475133384865164529036252066031994855345871665234356842806888449267093509234359078884875609318110606666510890869142825561053120919076669473956860107412958442850376297067619489373931325071407523822884590872646827517799418402810326100066742600757821843472688026520254916700218626719112742578105903860540314961495111422395630099850083222143586130977336793295286700263670768264758729167200080145039533621666985306881245948901798609310054451638995373023989628953955349320399434346505274696979982991692890568489697253604073901819244160638333613324109911532785670872242460987501092320395090524227584198011767301043501547054296185078440499819172566754617574465833324107891106395177027939832474344870734963502234713429840122131504136395080491920841542292117828585309123698386841431487925884672048097653436060166475057523741982012435447399021924160728572742932223618898581884526373480112488174279669517774268361093607090965758281557376997913620979310983462794465757333445530534099570736670074890569660474796577577674932657399492932328300141091012315884393051563872513896814510314701255767131661167855578818687047645394220003316556048000069638255157070961602769749078334816125790877097187873567471166880211709457699577692105308896649632851452814290230417778177094724367273446957406072684664685873234298355936558262411829413708595972450043859309938603417902840645173173789378852070784862031684579435206835757153121368065547594934047652144429563176654017561008554016628781999832120575525343668137868130684497675977124015549991825613898902813521554470684667215386490392454534482209869698083482450465168175971341558330428500922282511700067447539581778630674297796312467346371250185503892422658227103409485995968206774501698230856662772642424582441087021916747112358759991535113065761776986423267601319525420294876674280089342519455574486023936442553386103432916629919668048219224864951111272699130893906353027159740738835823517199856842410474351493420074365266969587584629623246170925954814760916633251108183367047829039642772329603065432062881303171326473274784088864711175502725522891692976325286289960874148287795332021019170175743912385323139721110937345954228970698098814088780032960736716127543386784085410250453102855226979009140947483110598671549236302405980242835053724646921600516023954682356191143023647945836544213782337196393383035101150902925967111001304312561534088860639031598058785817836265690855929443081305806085774999206906102199749512038292462521597332925432940093993451970313676982765732305448371997449528447367439213093823699213224857906816915506680824065402571625875013869166514632665730219518789150281073973527353790917415227277239925729920311755321764104602590582257364606165141999378702412830424318748754721986601241465067971885822122610210203460316734017436524225768072047627756306030304078713
[[11], [10, 1], [9, 2], [9, 1, 1], [8, 3], [8, 2, 1], [8, 1, 1, 1], [7, 4], [7, 3, 1], [7, 2, 2], [7, 2, 1, 1], [7, 1, 1, 1, 1], [6, 5], [6, 4, 1], [6, 3, 2], [6, 3, 1, 1], [6, 2, 2, 1], [6, 2, 1, 1, 1], [6, 1, 1, 1, 1, 1], [5, 5, 1], [5, 4, 2], [5, 4, 1, 1], [5, 3, 3], [5, 3, 2, 1], [5, 3, 1, 1, 1], [5, 2, 2, 2], [5, 2, 2, 1, 1], [5, 2, 1, 1, 1, 1], [5, 1, 1, 1, 1, 1, 1], [4, 4, 3], [4, 4, 2, 1], [4, 4, 1, 1, 1], [4, 3, 3, 1], [4, 3, 2, 2], [4, 3, 2, 1, 1], [4, 3, 1, 1, 1, 1], [4, 2, 2, 2, 1], [4, 2, 2, 1, 1, 1], [4, 2, 1, 1, 1, 1, 1], [4, 1, 1, 1, 1, 1, 1, 1], [3, 3, 3, 2], [3, 3, 3, 1, 1], [3, 3, 2, 2, 1], [3, 3, 2, 1, 1, 1], [3, 3, 1, 1, 1, 1, 1], [3, 2, 2, 2, 2], [3, 2, 2, 2, 1, 1], [3, 2, 2, 1, 1, 1, 1], [3, 2, 1, 1, 1, 1, 1, 1], [3, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2, 1], [2, 2, 2, 2, 1, 1, 1], [2, 2, 2, 1, 1, 1, 1, 1], [2, 2, 1, 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, 1, 1]]
[7, 3, 1]
3
1/1728000*(x^5 + 5*x^4 + 20*x^3 + 60*x^2 + 120*x)^3
1/1728000*x^15 + 1/115200*x^14 + 1/12800*x^13 + 181/345600*x^12 + 9/3200*x^11 + 71/5760*x^10 + 391/8640*x^9 + 67/480*x^8 + 43/120*x^7 + 3/4*x^6 + 5/4*x^5 + 3/2*x^4 + x^3
[[1, 3], [3/2, 4], [5/4, 5], [3/4, 6], [43/120, 7], [67/480, 8], [391/8640, 9], [71/5760, 10], [9/3200, 11], [181/345600, 12], [1/12800, 13], [1/115200, 14], [1/1728000, 15]]
9330
[1/12800, 13]
44730
x^28 + 4*x^27 + 10*x^26 + 20*x^25 + 35*x^24 + 56*x^23 + 80*x^22 + 104*x^21 + 125*x^20 + 140*x^19 + 146*x^18 + 140*x^17 + 125*x^16 + 104*x^15 + 80*x^14 + 56*x^13 + 35*x^12 + 20*x^11 + 10*x^10 + 4*x^9 + x^8
146
[[1, 8], [4, 9], [10, 10], [20, 11], [35, 12], [56, 13], [80, 14], [104, 15], [125, 16], [140, 17], [146, 18], [140, 19], [125, 20], [104, 21], [80, 22], [56, 23], [35, 24], [20, 25], [10, 26], [4, 27], [1, 28]]
-x^88 + x^73 + x^72 + x^62 - x^57 - x^47 - x^46 + x^31
11152843844517873604890
[11152843844517873604890, 40]
* a b c d e f g h
+----------------
a| a b c d e f g h
b| b a f h g c e d
c| c e d g h b a f
d| d h g a f e c b
e| e c b f a d h g
f| f g h e d a b c
g| g f a c b h d e
h| h d e b c g f a
[Subgroup of (Dihedral group of order 8 as a permutation group) generated by [()], Subgroup of (Dihedral group of order 8 as a permutation group) generated by [(1,3)(2,4)], Subgroup of (Dihedral group of order 8 as a permutation group) generated by [(2,4)], Subgroup of (Dihedral group of order 8 as a permutation group) generated by [(1,3)], Subgroup of (Dihedral group of order 8 as a permutation group) generated by [(1,2)(3,4)], Subgroup of (Dihedral group of order 8 as a permutation group) generated by [(1,4)(2,3)], Subgroup of (Dihedral group of order 8 as a permutation group) generated by [(2,4), (1,3)(2,4)], Subgroup of (Dihedral group of order 8 as a permutation group) generated by [(1,2,3,4), (1,3)(2,4)], Subgroup of (Dihedral group of order 8 as a permutation group) generated by [(1,2)(3,4), (1,3)(2,4)], Subgroup of (Dihedral group of order 8 as a permutation group) generated by [(2,4), (1,2,3,4), (1,3)(2,4)]]
57 333
1/12*(a + b + c)^6 + 1/4*(a^2 + b^2 + c^2)^2*(a + b + c)^2 + 2/3*(a^3 + b^3 + c^3)^2
a^6 + a^5*b + 2*a^4*b^2 + 4*a^3*b^3 + 2*a^2*b^4 + a*b^5 + b^6 + a^5*c + 3*a^4*b*c + 6*a^3*b^2*c + 6*a^2*b^3*c + 3*a*b^4*c + b^5*c + 2*a^4*c^2 + 6*a^3*b*c^2 + 9*a^2*b^2*c^2 + 6*a*b^3*c^2 + 2*b^4*c^2 + 4*a^3*c^3 + 6*a^2*b*c^3 + 6*a*b^2*c^3 + 4*b^3*c^3 + 2*a^2*c^4 + 3*a*b*c^4 + 2*b^2*c^4 + a*c^5 + b*c^5 + c^6
[210.519044010060]
3.30403021361001
625
500
(1, 5)
(2, 25)
(3, 125)
(4, 625)
(5, 1108)
(6, 1506)
(7, 1479)
(8, 1344)
(9, 669)
(10, 1328)
(11, 589)
(12, 928)
(13, 606)
(14, 1013)
(15, 1031)
(16, 1121)
(17, 1571)
(18, 1804)
(19, 952)
(20, 726)
52441
2016
Defined N, mandel_cython, x0, x1, y0, y1
Auto-generated code...Error in lines 2-2
Traceback (most recent call last):
File "/projects/sage/sage-7.3/local/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 976, in execute
exec compile(block+'\n', '', 'single') in namespace, locals
File "", line 1, in <module>
File "/projects/sage/sage-7.3/local/lib/python2.7/site-packages/matplotlib-1.5.1-py2.7-linux-x86_64.egg/matplotlib/pyplot.py", line 3022, in imshow
**kwargs)
File "/projects/sage/sage-7.3/local/lib/python2.7/site-packages/matplotlib-1.5.1-py2.7-linux-x86_64.egg/matplotlib/__init__.py", line 1812, in inner
return func(ax, *args, **kwargs)
File "/projects/sage/sage-7.3/local/lib/python2.7/site-packages/matplotlib-1.5.1-py2.7-linux-x86_64.egg/matplotlib/axes/_axes.py", line 4945, in imshow
resample=resample, **kwargs)
File "/projects/sage/sage-7.3/local/lib/python2.7/site-packages/matplotlib-1.5.1-py2.7-linux-x86_64.egg/matplotlib/image.py", line 597, in __init__
**kwargs
File "/projects/sage/sage-7.3/local/lib/python2.7/site-packages/matplotlib-1.5.1-py2.7-linux-x86_64.egg/matplotlib/image.py", line 130, in __init__
self.update(kwargs)
File "/projects/sage/sage-7.3/local/lib/python2.7/site-packages/matplotlib-1.5.1-py2.7-linux-x86_64.egg/matplotlib/artist.py", line 856, in update
raise AttributeError('Unknown property %s' % k)
AttributeError: Unknown property aspectratio
'Produce custom labelling for a colorbar.\n\nContributed by Scott Sinclair\n'
<matplotlib.text.Text object at 0x7f733f7bc450>
[<matplotlib.text.Text object at 0x7f733f732990>, <matplotlib.text.Text object at 0x7f733f71e490>, <matplotlib.text.Text object at 0x7f733f683950>]
<matplotlib.text.Text object at 0x7f733f7c2cd0>
[<matplotlib.text.Text object at 0x7f733f967ed0>, <matplotlib.text.Text object at 0x7f733f91ce10>, <matplotlib.text.Text object at 0x7f733fa21f90>]
(-1, 1)
25
[0, 1, 4, 9, 16, 25]