qNh6‰h7Kh!h#h8hAh&‰h9‰ub(h oqO}qP(h*UE.name()qQhU!qRh-hh.‰h‰h/U h0Mh‰hUaos.chdir("/Volumes/HOME/talks/2006-12-waterloo/sage/sage_notebook/worksheets/_/cells/5")
E.name()qSh2U"sage_notebook/worksheets/_/cells/5qTh4U
'_sage_[7]'
qUh6‰h7Kh!h#h8hAh&‰h9‰ub(h oqV}qW(h*UE.Rank()qXhU!qYh-hh.‰h‰h/U h0Mh‰hUaos.chdir("/Volumes/HOME/talks/2006-12-waterloo/sage/sage_notebook/worksheets/_/cells/6")
E.Rank()qZh2U"sage_notebook/worksheets/_/cells/6q[h4U
1
q\h6‰h7Kh!h#h8hAh&‰h9‰ub(h oq]}q^(h*Ua = maple('2007')q_hU!q`h-hh.‰h‰h/U h0Mh‰hUjos.chdir("/Volumes/HOME/talks/2006-12-waterloo/sage/sage_notebook/worksheets/_/cells/7")
a = maple('2007')qah2U"sage_notebook/worksheets/_/cells/7qbh4U
qch6‰h7Kh!h#h8hAh&‰h9‰ub(h oqd}qe(h*UahU!qfh-hh.‰h‰h/U h0Mh‰hUZos.chdir("/Volumes/HOME/talks/2006-12-waterloo/sage/sage_notebook/worksheets/_/cells/8")
aqgh2U"sage_notebook/worksheets/_/cells/8qhh4U
2007
qih6‰h7Kh!h#h8hAh&‰h9‰ub(h oqj}qk(h*U a.ifactor()qlhU!qmh-hh.‰h‰h/U h0M h‰hUdos.chdir("/Volumes/HOME/talks/2006-12-waterloo/sage/sage_notebook/worksheets/_/cells/9")
a.ifactor()qnh2U"sage_notebook/worksheets/_/cells/9qoh4U
``(3)^2*``(223)
qph6‰h7Kh!h#h8hAh&‰h9‰ub(h oqq}qr(h*Ua.name()qshU!qth-hh.‰h‰h/U h‰h0M
U_word_being_completedquUa.ifacqvhUbos.chdir("/Volumes/HOME/talks/2006-12-waterloo/sage/sage_notebook/worksheets/_/cells/10")
a.name()qwh2U#sage_notebook/worksheets/_/cells/10qxh4U
'sage1'
qyh6‰h7Kh!h#h8hAh&‰h9‰ub(h oqz}q{(h*U for i in range(5):
print iq|hU!q}h-hh.‰h‰h/U h0M h‰hUxos.chdir("/Volumes/HOME/talks/2006-12-waterloo/sage/sage_notebook/worksheets/_/cells/11")
for i in range(5):
print iq~h2U#sage_notebook/worksheets/_/cells/11qh4U
0
1
2
3
4
q€h6‰h7Kh!h#h8hAh&‰h9‰ub(h oq}q‚(h*U h-hh.‰h/U h0M h2U#sage_notebook/worksheets/_/cells/12qƒh4U h6‰h7K h8hAh9‰ubeU_Worksheet__synchroq„KU_Worksheet__comp_is_runningq…‰U_Worksheet__dirq†Usage_notebook/worksheets/_q‡U_Worksheet__attachedqˆ}q‰U_Worksheet__queueqŠ]q‹U_Worksheet__next_idqŒM
U_Worksheet__passcryptqˆU_Worksheet__nameqŽU U_Worksheet__saltqU1165187731.576083qU_Worksheet__notebookq‘hU_Worksheet__idq’KU_Worksheet__next_block_idq“KU_Worksheet__systemq”NU_Worksheet__passcodeq•U
11G3BJNEUV/Pkq–ubUqsieveq—(hoq˜}q™(U_Worksheet__filenameqšUqsieveq›U_Worksheet__cellsqœ]q((h oqž}qŸ(U _Cell__inq U/n = next_prime(10^32)*next_prime(10^33)
print nq¡U_Cell__introspect_htmlq¢U!q£U_Cell__worksheetq¤h˜U_Cell__completionsq¥‰U_Cell__introspectq¦‰U_Cell__out_htmlq§U U
_Cell__outq¨UE
100000000000000000000000000000055100000000000000000000000000002989
q©U _Cell__idqªM `U_Cell__is_htmlq«‰U_before_preparseq¬Uƒos.chdir("/Users/was/talks/2007-01-05-msr/sage_notebook/worksheets/qsieve/cells/0")
n = next_prime(10^32)*next_prime(10^33)
print nqU
_Cell__dirq®U'sage_notebook/worksheets/qsieve/cells/0q¯U_word_being_completedq°Uqsiq±Uhas_new_outputq²‰U_Cell__versionq³K U _Cell__sageq´h#U _Cell__typeqµh%U _Cell__timeq¶‰U_Cell__interruptedq·‰ub(h oq¸}q¹(h Utime factor(n) qºh¢U!q»h¤h˜h¥‰h¦‰h§U hªM`h«‰h¬Uˆos.chdir("/Users/was/talks/2007-01-05-msr/sage_notebook/worksheets/qsieve/cells/1")
__SAGE_t__=cputime()
__SAGE_w__=walltime()
factor(n)q¼h®U'sage_notebook/worksheets/qsieve/cells/1q½h¨Up
100000000000000000000000000000049 * 1000000000000000000000000000000061
CPU time: 64.23 s, Wall time: 87.90 s
q¾h²‰h³Kh´h#hµh%h¶ˆh·‰ub(h oq¿}qÀ(h U+F, t = qsieve(n, time=True)
print F
print tqÁh¢U!qÂh¤h˜h¥‰h¦‰h§U h¨Ux
[100000000000000000000000000000049, 1000000000000000000000000000000061]
80.95 real 45.56 user 0.49 sys
qÃhªM`h«‰h¬Uos.chdir("/Users/was/talks/2007-01-05-msr/sage_notebook/worksheets/qsieve/cells/2")
F, t = qsieve(n, time=True)
print F
print tqÄh®U'sage_notebook/worksheets/qsieve/cells/2qÅh°UqsiqÆh²‰h³K h´h#hµh%h¶‰h·‰ub(h oqÇ}qÈ(h U%q = qsieve(n, time=True, block=False)qÉh¢U!qÊh¤h˜h¥‰h¦‰h§U hªM`h«‰h¬Uyos.chdir("/Users/was/talks/2007-01-05-msr/sage_notebook/worksheets/qsieve/cells/3")
q = qsieve(n, time=True, block=False)qËh®U'sage_notebook/worksheets/qsieve/cells/3qÌh¨U
qÍh²‰h³Kh´h#hµh%h¶‰h·‰ub(h oqÎ}qÏ(h Uqh¢U!qÐh¤h˜h¥‰h¦‰h§U h¨U
([], '')
qÑhªM`h«‰h¬UUos.chdir("/Users/was/talks/2007-01-05-msr/sage_notebook/worksheets/qsieve/cells/4")
qqÒh®U'sage_notebook/worksheets/qsieve/cells/4qÓh°Uq.cpuqÔh²‰h³Kh´h#hµh%h¶‰h·‰ub(h oqÕ}qÖ(h U2+2q×h¢U!qØh¤h˜h¥‰h¦‰h§U hªM`h«‰h¬UWos.chdir("/Users/was/talks/2007-01-05-msr/sage_notebook/worksheets/qsieve/cells/5")
2+2qÙh®U'sage_notebook/worksheets/qsieve/cells/5qÚh¨U
4
qÛh²‰h³Kh´h#hµh%h¶‰h·‰ub(h oqÜ}qÝ(h U
print q.log()qÞh¢U!qßh¤h˜h¥‰h¦‰h§U h¨T”
Input number to factor [ >=40 decimal digits]: 100000000000000000000000000000055100000000000000000000000000002989
100 relations, 9 partials.
1260 curves.
200 relations, 15 partials.
2520 curves.
300 relations, 25 partials.
400 relations, 38 partials.
3780 curves.
500 relations, 46 partials.
600 relations, 55 partials.
5040 curves.
700 relations, 61 partials.
6300 curves.
800 relations, 70 partials.
900 relations, 81 partials.
7560 curves.
1000 relations, 90 partials.
8820 curves.
1100 relations, 96 partials.
1200 relations, 106 partials.
10080 curves.
1300 relations, 109 partials.
11340 curves.
1400 relations, 121 partials.
1500 relations, 135 partials.
12600 curves.
1600 relations, 151 partials.
13860 curves.
1700 relations, 162 partials.
15120 curves.
1800 relations, 172 partials.
1900 relations, 181 partials.
16380 curves.
2000 relations, 194 partials.
17640 curves.
2100 relations, 203 partials.
2200 relations, 213 partials.
18900 curves.
2300 relations, 225 partials.
20160 curves.
2400 relations, 237 partials.
2500 relations, 247 partials.
21420 curves.
2600 relations, 255 partials.
22680 curves.
2700 relations, 273 partials.
2800 relations, 280 partials.
23940 curves.
2900 relations, 298 partials.
25200 curves.
3000 relations, 307 partials.
3100 relations, 318 partials.
26460 curves.
3200 relations, 324 partials.
27720 curves.
3300 relations, 334 partials.
3400 relations, 340 partials.
28980 curves.
3500 relations, 350 partials.
3600 relations, 363 partials.
30240 curves.
3700 relations, 374 partials.
31500 curves.
3800 relations, 389 partials.
32760 curves.
3900 relations, 398 partials.
4000 relations, 415 partials.
34020 curves.
4100 relations, 429 partials.
4200 relations, 438 partials.
35280 curves.
4300 relations, 453 partials.
36540 curves.
4400 relations, 461 partials.
4500 relations, 473 partials.
37800 curves.
4600 relations, 486 partials.
39060 curves.
4700 relations, 498 partials.
40320 curves.
4800 relations, 507 partials.
4900 relations, 526 partials.
41580 curves.
5000 relations, 540 partials.
42840 curves.
5100 relations, 555 partials.
5200 relations, 565 partials.
44100 curves.
5300 relations, 574 partials.
45360 curves.
5400 relations, 587 partials.
5500 relations, 597 partials.
46620 curves.
5600 relations, 604 partials.
47880 curves.
5700 relations, 614 partials.
5800 relations, 623 partials.
49140 curves.
5900 relations, 634 partials.
50400 curves.
6000 relations, 645 partials.
qàhªM`h«‰h¬Uaos.chdir("/Users/was/talks/2007-01-05-msr/sage_notebook/worksheets/qsieve/cells/6")
print q.log()qáh®U'sage_notebook/worksheets/qsieve/cells/6qâh°Uq.qãh²‰h³Kh´h#hµh%h¶‰h·‰ub(h oqä}qå(h Uq.quit()qæh¢U!qçh¤h˜h¥‰h¦‰h§U hªM`h«‰h¬U\os.chdir("/Users/was/talks/2007-01-05-msr/sage_notebook/worksheets/qsieve/cells/7")
q.quit()qèh®U'sage_notebook/worksheets/qsieve/cells/7qéh¨U
qêh²‰h³Kh´h#hµh%h¶‰h·‰ub(h oqë}qì(h U h¤h˜h¥‰h§U hªM`h®U'sage_notebook/worksheets/qsieve/cells/8qíh¨U h²‰h³K hµh%h·‰ubeU_Worksheet__synchroqîK1U_Worksheet__nameqïUqsieveqðU_Worksheet__attachedqñ}qòU_Worksheet__saltqóU1168019690.935546qôU_Worksheet__dirqõU sage_notebook/worksheets/qsieveqöU_Worksheet__queueq÷]qøU_Worksheet__next_idqùM `U_Worksheet__passcryptqúˆU_Worksheet__comp_is_runningqû‰U_Worksheet__passcodeqüU
11G3BJNEUV/PkqýU_Worksheet__notebookqþhU_Worksheet__idqÿKU_Worksheet__next_block_idr KU_Worksheet__systemr NubUgraphr (hor }r (h Ugraphr h
]r ((h or }r (U _Cell__inr U*time b = bernoulli(10000, algorithm='gap')r
U_Cell__introspect_htmlr U!r U_Cell__worksheetr
j U_Cell__completionsr ‰U_Cell__introspectr ‰U_Cell__out_htmlr U U _Cell__idr M0U_Cell__is_htmlr ‰U_before_preparser U®os.chdir("/Volumes/HOME/talks/2006-12-waterloo/sage/sage_notebook/worksheets/graph/cells/14")
__SAGE_t__=cputime()
__SAGE_w__=walltime()
b = bernoulli(10000, algorithm='gap')r U
_Cell__dirr U'sage_notebook/worksheets/graph/cells/14r U_word_being_completedr Ubernr Uhas_new_outputr ‰U_Cell__versionr KU _Cell__sager NU_Cell__interruptedr ˆU _Cell__typer Uwrapr U _Cell__timer ˆU
_Cell__outr U ub(h or! }r" (j U+time b = bernoulli(10000, algorithm='pari')r# j U!r$ j
j j ‰j ‰j U j M0j ‰j U¯os.chdir("/Volumes/HOME/talks/2006-12-waterloo/sage/sage_notebook/worksheets/graph/cells/15")
__SAGE_t__=cputime()
__SAGE_w__=walltime()
b = bernoulli(10000, algorithm='pari')r% j U'sage_notebook/worksheets/graph/cells/15r& j U'
CPU time: 0.24 s, Wall time: 0.26 s
r' j ‰j Kj h#j j j ˆj ‰ub(h or( }r) (j UE = EllipticCurve('389a')r* j U!r+ j
j j ‰j ‰j U j M
0j ‰j Uwos.chdir("/Volumes/HOME/talks/2006-12-waterloo/sage/sage_notebook/worksheets/graph/cells/10")
E = EllipticCurve('389a')r, j U'sage_notebook/worksheets/graph/cells/10r- j UEllr. j ‰j Kj h#j ‰j j j ‰j U
r/ ub(h or0 }r1 (j UL = E.Lseries_zeros(5)r2 j U!r3 j
j j ‰j ‰j U j M 0j ‰j Utos.chdir("/Volumes/HOME/talks/2006-12-waterloo/sage/sage_notebook/worksheets/graph/cells/11")
L = E.Lseries_zeros(5)r4 j U'sage_notebook/worksheets/graph/cells/11r5 j U
E.Lseries_zerr6 j ‰j Kj h#j ‰j j j ‰j U
r7 ub(h or8 }r9 (j ULj U!r: j
j j ‰j ‰j U j M 0j ‰j U_os.chdir("/Volumes/HOME/talks/2006-12-waterloo/sage/sage_notebook/worksheets/graph/cells/12")
Lr; j U'sage_notebook/worksheets/graph/cells/12r< j UA
[0.000000000, 0.000000000, 2.87609907, 4.41689608, 5.79340263]
r= j ‰j Kj h#j j j ‰j ‰ub(h or> }r? (hUg = graphs.PetersenGraph()r@ U_Cell__introspect_htmlrA U!rB hj h‰U_Cell__introspectrC ‰hU hM 0U_Cell__is_htmlrD ‰U_before_preparserE Uwos.chdir("/Volumes/HOME/talks/2006-12-waterloo/sage/sage_notebook/worksheets/graph/cells/0")
g = graphs.PetersenGraph()rF hU&sage_notebook/worksheets/graph/cells/0rG U_word_being_completedrH U
graphs.PetrI h ‰h KU _Cell__sagerJ h#h'‰h$UwraprK U _Cell__timerL ‰h U
rM ub(h orN }rO (hUshow(g)rP jA U!rQ hj h‰jC ‰hU>
rR hM0jD ‰jE Udos.chdir("/Volumes/HOME/talks/2006-12-waterloo/sage/sage_notebook/worksheets/graph/cells/1")
show(g)rS hU&sage_notebook/worksheets/graph/cells/1rT h U
rU h ‰h KjJ h#h$jK jL ‰h'‰ub(h orV }rW (hU(g = graphs.CompleteBipartiteGraph(5,100)rX hU!rY hj h‰h‰hU h‰hM0huUgraphs.CompleteBirZ hU…os.chdir("/Volumes/HOME/talks/2006-12-waterloo/sage/sage_notebook/worksheets/graph/cells/2")
g = graphs.CompleteBipartiteGraph(5,100)r[ hU&sage_notebook/worksheets/graph/cells/2r\ h U
r] h ‰h Kh!h#h$j h&‰h'‰ub(h or^ }r_ (h*U graphs.CompleteBipartiteGraphr` hT? File: /Volumes/HOME/s/local/lib/python2.5/site-packages/sage/graphs/graph_database.py
Source Code (starting at line 566):
def CompleteBipartiteGraph(self, n1, n2):
"""
Returns a Complete Bipartite Graph sized n1+n2, with each of the
nodes [0,(n1-1)] connected to each of the nodes [n1,(n2-1)] and
vice versa.
A Complete Bipartite Graph is a graph with its vertices partitioned
into two groups, V1 and V2. Each v in V1 is connected to every v
in V2, and vice versa.
PLOTTING:
Upon construction, the position dictionary is filled to override
the spring-layout algorithm. By convention, each complete bipartite
graph will be displayed with the first n1 nodes on the top row (at
y=1) from left to right. The remaining n2 nodes appear at y=0,
also from left to right. The shorter row (partition with fewer
nodes) is stretched to the same length as the longer row, unless
the shorter row has 1 node; in which case it is centered. The x
values in the plot are in domain [0,max{n1,n2}].
In the Complete Bipartite graph, there is a visual difference in
using the spring-layout algorithm vs. the position dictionary used
in this constructor. The position dictionary flattens the graph
and separates the partitioned nodes, making it clear which nodes
an edge is connected to. The Complete Bipartite graph plotted with
the spring-layout algorithm tends to center the nodes in n1 (see
spring_med in examples below), thus overlapping its nodes and edges,
making it typically hard to decipher.
Filling the position dictionary in advance adds O(n) to the
constructor. Feel free to race the constructors below in the
examples section. The much larger difference is the time added by
the spring-layout algorithm when plotting. (Also shown in the
example below). The spring model is typically described as O(n^3),
as appears to be the case in the NetworkX source code.
EXAMPLES:
# The following examples require NetworkX (to use default)
sage: import networkx as NX
# Compare the constructors (results will vary)
sage.: time n = NX.complete_bipartite_graph(389,157); spring_big = Graph(n)
# CPU time: 9.28 s, Wall time: 11.02 s
sage.: time posdict_big = graphs.CompleteBipartiteGraph(389,157)
# CPU time: 10.72 s, Wall time: 13.84 s
# Compare the plotting speeds (results will vary)
sage: n = NX.complete_bipartite_graph(11,17)
sage: spring_med = Graph(n)
sage: posdict_med = graphs.CompleteBipartiteGraph(11,17)
# Notice here how the spring-layout tends to center the nodes of n1
sage.: time spring_med.show()
# CPU time: 3.84 s, Wall time: 4.49 s
sage.: time posdict_med.show()
# CPU time: 0.96 s, Wall time: 1.14 s
# View many Complete Bipartite graphs with a SAGE Graphics Array
# With this constructor (i.e., the position dictionary filled)
sage: g = []
sage: j = []
sage: for i in range(9):
... k = graphs.CompleteBipartiteGraph(i+1,4)
... g.append(k)
...
sage: for i in range(3):
... n = []
... for m in range(3):
... n.append(g[3*i + m].plot(node_size=50, with_labels=False))
... j.append(n)
...
sage: G = sage.plot.plot.GraphicsArray(j)
sage.: G.show()
# Compared to plotting with the spring-layout algorithm
sage: g = []
sage: j = []
sage: for i in range(9):
... spr = NX.complete_bipartite_graph(i+1,4)
... k = Graph(spr)
... g.append(k)
...
sage: for i in range(3):
... n = []
... for m in range(3):
... n.append(g[3*i + m].plot(node_size=50, with_labels=False))
... j.append(n)
...
sage: G = sage.plot.plot.GraphicsArray(j)
sage.: G.show()
"""
pos_dict = {}
c1 = 1 # scaling factor for top row
c2 = 1 # scaling factor for bottom row
c3 = 0 # pad to center if top row has 1 node
c4 = 0 # pad to center if bottom row has 1 node
if n1 > n2:
if n2 == 1:
c4 = (n1-1)/2
else:
c2 = ((n1-1)/(n2-1))
elif n2 > n1:
if n1 == 1:
c3 = (n2-1)/2
else:
c1 = ((n2-1)/(n1-1))
for i in range(n1):
x = c1*i + c3
y = 1
pos_dict[i] = [x,y]
for i in range(n1+n2)[n1:]:
x = c2*(i-n1) + c4
y = 0
pos_dict[i] = [x,y]
G = NX.complete_bipartite_graph(n1,n2)
return graph.Graph(G, pos=pos_dict, name="Complete bipartite graph on %d vertices"%(n1+n2))ra h-j h.‰h]rb (U graphs.CompleteBipartiteGraph??rc U eh/U>
rd h‰h0M0huUgraphs.CompleteBire hU|os.chdir("/Volumes/HOME/talks/2006-12-waterloo/sage/sage_notebook/worksheets/graph/cells/3")
graphs.CompleteBipartiteGraph??rf h2U&sage_notebook/worksheets/graph/cells/3rg h4U
rh h6‰h7Kh!h#h8hAh&‰h9‰ub(h ori }rj (j Ugj U!rk j
j j ‰j ‰j U j M0j ‰j U^os.chdir("/Volumes/HOME/talks/2006-12-waterloo/sage/sage_notebook/worksheets/graph/cells/5")
grl j U&sage_notebook/worksheets/graph/cells/5rm j UK
Complete bipartite graph on 105 vertices: a simple graph on 105 vertices
rn j ‰j Kj h#j j j ‰j ‰ub(h oro }rp (h*Ug.save('mygraph')rq j U!rr h-j h.‰j ‰h/U h0M0j ‰j Unos.chdir("/Volumes/HOME/talks/2006-12-waterloo/sage/sage_notebook/worksheets/graph/cells/4")
g.save('mygraph')rs h2U&sage_notebook/worksheets/graph/cells/4rt h4U
ru h6‰h7Kj h#h8j j ‰h9‰ub(h orv }rw (j U5P = plot(sin, 0, 10, rgbcolor=(0,0.5,0), thickness=5)rx j U!ry j
j j ‰j ‰j U j M0j ‰j U’os.chdir("/Volumes/HOME/talks/2006-12-waterloo/sage/sage_notebook/worksheets/graph/cells/6")
P = plot(sin, 0, 10, rgbcolor=(0,0.5,0), thickness=5)rz j U&sage_notebook/worksheets/graph/cells/6r{ j U
r| j ‰j Kj h#j j j ‰j ‰ub(h or} }r~ (j UPj U!r j
j j ‰j ‰j U j M0j ‰j U^os.chdir("/Volumes/HOME/talks/2006-12-waterloo/sage/sage_notebook/worksheets/graph/cells/7")
Pr€ j U&sage_notebook/worksheets/graph/cells/7r j U5
Graphics object consisting of 1 graphics primitive
r‚ j ‰j Kj h#j j j ‰j ‰ub(h orƒ }r„ (j UP.show()r… j U!r† j
j j ‰j ‰j U>
r‡ j M0j ‰j Ueos.chdir("/Volumes/HOME/talks/2006-12-waterloo/sage/sage_notebook/worksheets/graph/cells/8")
P.show()rˆ j U&sage_notebook/worksheets/graph/cells/8r‰ j U
rŠ j ‰j Kj h#j j j ‰j ‰ub(h or‹ }rŒ (j U j
j j ‰j U j M 0j U&sage_notebook/worksheets/graph/cells/9r j U j ‰j K j j j ‰ubeU_Worksheet__synchrorŽ Krž hj— h‰jC ‰hU hM jD ‰jE Uwos.chdir("/Volumes/HOME/talks/2006-12-waterloo/sage/sage_notebook/worksheets/bernoull_mod/cells/0")
bernoulli_mod_p(37)rŸ hU-sage_notebook/worksheets/bernoull_mod/cells/0r jH U bernoulli_mor¡ h ‰h KU _Cell__sager¢ h#h'‰h$jK jL ‰h UF
[1, 31, 16, 15, 16, 4, 17, 32, 22, 31, 15, 15, 17, 12, 29, 2, 0, 2]
r£ ub(h or¤ }r¥ (U _Cell__inr¦ U)time v=bernoulli_mod_p(next_prime(50000))r§ U_Cell__introspect_htmlr¨ U!r© U_Cell__worksheetrª j— U_Cell__completionsr« ‰U_Cell__introspectr¬ ‰U_Cell__out_htmlr U U _Cell__idr® M U_Cell__is_htmlr¯ ‰U_before_preparser° U³os.chdir("/Volumes/HOME/talks/2006-12-waterloo/sage/sage_notebook/worksheets/bernoull_mod/cells/1")
__SAGE_t__=cputime()
__SAGE_w__=walltime()
v=bernoulli_mod_p(next_prime(50000))r± U
_Cell__dirr² U-sage_notebook/worksheets/bernoull_mod/cells/1r³ U_word_being_completedr´ U bernoulli_morµ Uhas_new_outputr¶ ‰U_Cell__versionr· Kj¢ h#U_Cell__interruptedr¸ ‰U _Cell__typer¹ jK U _Cell__timerº ˆU
_Cell__outr» U'
CPU time: 0.44 s, Wall time: 0.47 s
r¼ ub(h or½ }r¾ (j¦ Ulen(v)r¿ j¨ U!rÀ jª j— j« ‰j¬ ‰j U j® M j¯ ‰j° Ujos.chdir("/Volumes/HOME/talks/2006-12-waterloo/sage/sage_notebook/worksheets/bernoull_mod/cells/2")
len(v)rÁ j² U-sage_notebook/worksheets/bernoull_mod/cells/2r j» U
25010
rà j¶ ‰j· Kj¢ h#j¹ jK jº ‰j¸ ‰ub(h orÄ }rÅ (j¦ U jª j— j« ‰j U j® M j² U-sage_notebook/worksheets/bernoull_mod/cells/4rÆ j» U j¶ ‰j· K j¹ jK j¸ ‰ubejŽ K
h…‰hˆ}rÇ h†U%sage_notebook/worksheets/bernoull_modrÈ hŠ]rÉ hŒM hˆhŽU bernoull_modrÊ hU1165187752.734722rË h‘hh’Kj” K h”Nh•U
11G3BJNEUV/PkrÌ ubUfactorrÍ (horÎ }rÏ (U_Worksheet__filenamerÐ UfactorrÑ U_Worksheet__cellsrÒ ]rÓ ((csage.server.notebook.cell
TextCell
rÔ orÕ }rÖ (U_TextCell__worksheetr× jÎ U_TextCell__textrØ UúFactor Tree Worksheet
This worksheet uses the SAGE Notebook to illustrate integer factorization as a
product of primes using the ``factor trees'' that students learn about in school.rÙ U
_TextCell__idrÚ M@ub(h orÛ }rÜ (h TÙ %hideall
#auto
# The source code to draw factorization trees...
import random
def factor_tree(n, font=10):
rows = []
v = [(n,None,0)]
ftree(rows, v, 0, factor(n))
return draw_ftree(rows, font)
def ftree(rows, v, i, F):
if len(v) > 0:
# add a row to g at the ith level.
rows.append(v)
w = []
for i in range(len(v)):
k, _,_ = v[i]
if k is None or is_prime(k):
w.append((None,None,None))
else:
d = random.choice(divisors(k)[1:-1])
w.append((d,k,i))
e = k//d
if e == 1:
w.append((None,None))
else:
w.append((e,k,i))
if len(w) > len(v):
ftree(rows, w, i+1, F)
def draw_ftree(rows,font):
g = Graphics()
for i in range(len(rows)):
cur = rows[i]
for j in range(len(cur)):
e, f, k = cur[j]
if not e is None:
if is_prime(e):
c = (1,0,0)
else:
c = (0,0,.4)
g += text(str(e), (j*2-len(cur),-i), fontsize=font, rgbcolor=c)
if not k is None and not f is None:
g += line([(j*2-len(cur),-i), (k*2-len(rows[i-1]),-i+1)], alpha=0.4, thickness=1)
return g
def factor_trees(n, cols=4, rows=3, font=10):
return graphics_array([[factor_tree(n,font) for _ in range(cols)] for _ in range(rows)])rÝ h¢U!rÞ h¤jÎ h¥‰h§U hªM@h«‰h¬TY os.chdir("/Users/was/talks/2007-01-05-msr/sage_notebook/worksheets/factor/cells/21")
__SAGE_t__=cputime()
__SAGE_w__=walltime()
%hideall
#auto
# The source code to draw factorization trees...
import random
def factor_tree(n, font=10):
rows = []
v = [(n,None,0)]
ftree(rows, v, 0, factor(n))
return draw_ftree(rows, font)
def ftree(rows, v, i, F):
if len(v) > 0:
# add a row to g at the ith level.
rows.append(v)
w = []
for i in range(len(v)):
k, _,_ = v[i]
if k is None or is_prime(k):
w.append((None,None,None))
else:
d = random.choice(divisors(k)[1:-1])
w.append((d,k,i))
e = k//d
if e == 1:
w.append((None,None))
else:
w.append((e,k,i))
if len(w) > len(v):
ftree(rows, w, i+1, F)
def draw_ftree(rows,font):
g = Graphics()
for i in range(len(rows)):
cur = rows[i]
for j in range(len(cur)):
e, f, k = cur[j]
if not e is None:
if is_prime(e):
c = (1,0,0)
else:
c = (0,0,.4)
g += text(str(e), (j*2-len(cur),-i), fontsize=font, rgbcolor=c)
if not k is None and not f is None:
g += line([(j*2-len(cur),-i), (k*2-len(rows[i-1]),-i+1)], alpha=0.4, thickness=1)
return g
def factor_trees(n, cols=4, rows=3, font=10):
return graphics_array([[factor_tree(n,font) for _ in range(cols)] for _ in range(rows)])rß h®U(sage_notebook/worksheets/factor/cells/21rà h¨U'
CPU time: 0.00 s, Wall time: 0.00 s
rá h²‰h³Kh´h#h·‰ub(jÔ orâ }rã (j× jÎ jØ U
rä jÚ M@ub(h orå }ræ (h UVF = factor_trees(300000000, rows=1, cols=1, font=8)
F.show(axes=False, figsize=[10,6])rç h¢U!rè h¤jÎ h¥‰h¦‰h§U@
ré hªM@h¶‰h«‰h¬U«os.chdir("/Users/was/talks/2007-01-05-msr/sage_notebook/worksheets/factor/cells/23")
F = factor_trees(300000000, rows=1, cols=1, font=8)
F.show(axes=False, figsize=[10,6])rê h®U(sage_notebook/worksheets/factor/cells/23rë h¨U
rì h²‰h³Kh´h#hµh%h·‰ub(h orí }rî (h UbF = factor_tree(prod(primes(40)))
F.show(xmin=-3,xmax=7,ymin=-5,ymax=0.5,figsize=[8,2],axes=False)rï h¢U!rð h¤jÎ h¥‰h¦‰h§U@
rñ hªM@h¶‰h«‰h¬U·os.chdir("/Users/was/talks/2007-01-05-msr/sage_notebook/worksheets/factor/cells/24")
F = factor_tree(prod(primes(40)))
F.show(xmin=-3,xmax=7,ymin=-5,ymax=0.5,figsize=[8,2],axes=False)rò h®U(sage_notebook/worksheets/factor/cells/24ró h¨U
rô h²‰h³Kh´h#hµh%h·‰ub(h orõ }rö (h U9show(factor_trees(1200,cols=3,rows=3),axes=False,dpi=100)r÷ h¢U!rø h¤jÎ h¥‰h¦‰h§U@
rù hªM@h¶‰h«‰h¬UŽos.chdir("/Users/was/talks/2007-01-05-msr/sage_notebook/worksheets/factor/cells/25")
show(factor_trees(1200,cols=3,rows=3),axes=False,dpi=100)rú h®U(sage_notebook/worksheets/factor/cells/25rû h¨U
rü h²‰h³Kh´h#hµh%h·‰ub(h orý }rþ (h U h¤jÎ h¥‰h§U hªM@h®U(sage_notebook/worksheets/factor/cells/26rÿ h¨U h²‰h³K hµh%h·‰ubeU_Worksheet__synchror KU_Worksheet__comp_is_runningr ‰U_Worksheet__attachedr }r U_Worksheet__dirr U sage_notebook/worksheets/factorr U_Worksheet__queuer ]r U_Worksheet__next_idr M@U_Worksheet__passcryptr ˆU_Worksheet__namer
Ufactorr U_Worksheet__saltr U1165225547.833440r
U_Worksheet__notebookr hU_Worksheet__idr KU_Worksheet__next_block_idr KU_Worksheet__systemr NU_Worksheet__passcoder U
11G3BJNEUV/Pkr ubUtestr (hor }r (U_Worksheet__filenamer Utestr U_Worksheet__cellsr ]r (h or }r (j¦ U jª j j« ‰j U j® M Pj² U%sage_notebook/worksheets/test/cells/0r j» U j¶ ‰j· K j¹ jK j¸ ‰ubaU_Worksheet__namer Utestr U_Worksheet__attachedr }r! U_Worksheet__dirr" U sage_notebook/worksheets/testr# U_Worksheet__queuer$ ]r% U_Worksheet__next_idr& MPU_Worksheet__passcryptr' ˆU_Worksheet__comp_is_runningr( ‰U_Worksheet__saltr) U1165250401.859302r* U_Worksheet__notebookr+ hU_Worksheet__idr, KU_Worksheet__systemr- NU_Worksheet__passcoder. U
11G3BJNEUV/Pkr/ ubuU_Notebook__historyr0 ]r1 (U¨# Worksheet 'graph' (2006-12-03 at 15:35)
sage: g = graphs.StarGraph()
Traceback (most recent call last):
...
TypeError: StarGraph() takes exactly 2 arguments (1 given)r2 UK# Worksheet 'graph' (2006-12-03 at 15:35)
sage: g = graphs.PetersenGraph()
r3 U8# Worksheet 'graph' (2006-12-03 at 15:35)
sage: show(g)
r4 T¶ # Worksheet 'factor' (2006-12-04 at 01:46)
sage: %hide
sage: print "CLICK ABOVE FOR THE SOURCE CODE"
sage: # The source code to draw factorization trees...
sage: import random
sage: def factor_tree(n, font=10):
... rows = []
... v = [(n,None,0)]
... ftree(rows, v, 0, factor(n))
... return draw_ftree(rows, font)
...
sage: def ftree(rows, v, i, F):
... if len(v) > 0:
... # add a row to g at the ith level.
... rows.append(v)
... w = []
... for i in range(len(v)):
... k, _,_ = v[i]
... if k is None or is_prime(k):
... w.append((None,None,None))
... else:
... d = random.choice(divisors(k)[1:-1])
... w.append((d,k,i))
... e = k//d
... if e == 1:
... w.append((None,None))
... else:
... w.append((e,k,i))
... if len(w) > len(v):
... ftree(rows, w, i+1, F)
...
sage: def draw_ftree(rows,font):
... g = Graphics()
... for i in range(len(rows)):
... cur = rows[i]
... for j in range(len(cur)):
... e, f, k = cur[j]
... if not e is None:
... if is_prime(e):
... c = (1,0,0)
... else:
... c = (0,0,.4)
... g += text(str(e), (j*2-len(cur),-i), fontsize=font, rgbcolor=c)
... if not k is None and not f is None:
... g += line([(j*2-len(cur),-i), (k*2-len(rows[i-1]),-i+1)], alpha=0.4, thickness=0.4)
... return g
...
sage: def factor_trees(n, cols=4, rows=3, font=10):
... return graphics_array([[factor_tree(n,font) for _ in range(cols)] for _ in range(rows)])
CLICK ABOVE FOR THE SOURCE CODEr5 UŽ# Worksheet 'factor' (2006-12-04 at 01:46)
sage: F = factor_trees(300000000, rows=1, cols=1, font=8)
sage: F.show(axes=False, figsize=[10,6])
r6 Uš# Worksheet 'factor' (2006-12-04 at 01:46)
sage: F = factor_tree(prod(primes(30)))
sage: F.show(xmin=-3,xmax=7,ymin=-5,ymax=0.5,figsize=[8,2],axes=False)
r7 Uk# Worksheet 'factor' (2006-12-04 at 01:46)
sage: show(factor_trees(1200,cols=3,rows=3),axes=False,dpi=100)
r8 U,# Worksheet 'factor' (2006-12-04 at 01:46)
r9 U,# Worksheet 'factor' (2006-12-04 at 01:46)
r: UK# Worksheet 'graph' (2006-12-04 at 08:38)
sage: g = graphs.PetersenGraph()
r; U8# Worksheet 'graph' (2006-12-04 at 08:38)
sage: show(g)
r< UK# Worksheet 'graph' (2006-12-04 at 08:38)
sage: g = graphs.PetersenGraph()
r= U8# Worksheet 'graph' (2006-12-04 at 08:38)
sage: show(g)
r> T´ # Worksheet 'factor' (2006-12-04 at 08:38)
sage: %hide
sage: print "CLICK ABOVE FOR THE SOURCE CODE"
sage: # The source code to draw factorization trees...
sage: import random
sage: def factor_tree(n, font=10):
... rows = []
... v = [(n,None,0)]
... ftree(rows, v, 0, factor(n))
... return draw_ftree(rows, font)
...
sage: def ftree(rows, v, i, F):
... if len(v) > 0:
... # add a row to g at the ith level.
... rows.append(v)
... w = []
... for i in range(len(v)):
... k, _,_ = v[i]
... if k is None or is_prime(k):
... w.append((None,None,None))
... else:
... d = random.choice(divisors(k)[1:-1])
... w.append((d,k,i))
... e = k//d
... if e == 1:
... w.append((None,None))
... else:
... w.append((e,k,i))
... if len(w) > len(v):
... ftree(rows, w, i+1, F)
...
sage: def draw_ftree(rows,font):
... g = Graphics()
... for i in range(len(rows)):
... cur = rows[i]
... for j in range(len(cur)):
... e, f, k = cur[j]
... if not e is None:
... if is_prime(e):
... c = (1,0,0)
... else:
... c = (0,0,.4)
... g += text(str(e), (j*2-len(cur),-i), fontsize=font, rgbcolor=c)
... if not k is None and not f is None:
... g += line([(j*2-len(cur),-i), (k*2-len(rows[i-1]),-i+1)], alpha=0.4, thickness=1)
... return g
...
sage: def factor_trees(n, cols=4, rows=3, font=10):
... return graphics_array([[factor_tree(n,font) for _ in range(cols)] for _ in range(rows)])
CLICK ABOVE FOR THE SOURCE CODEr? UŽ# Worksheet 'factor' (2006-12-04 at 08:38)
sage: F = factor_trees(300000000, rows=1, cols=1, font=8)
sage: F.show(axes=False, figsize=[10,6])
r@ Uš# Worksheet 'factor' (2006-12-04 at 08:38)
sage: F = factor_tree(prod(primes(30)))
sage: F.show(xmin=-3,xmax=7,ymin=-5,ymax=0.5,figsize=[8,2],axes=False)
rA Uš# Worksheet 'factor' (2006-12-04 at 08:39)
sage: F = factor_tree(prod(primes(40)))
sage: F.show(xmin=-3,xmax=7,ymin=-5,ymax=0.5,figsize=[8,2],axes=False)
rB Uš# Worksheet 'factor' (2006-12-04 at 08:39)
sage: F = factor_tree(prod(primes(40)))
sage: F.show(xmin=-3,xmax=7,ymin=-5,ymax=0.5,figsize=[8,2],axes=False)
rC UŽ# Worksheet 'bernoull_mod' (2006-12-04 at 08:43)
sage: bernoulli_mod_p(37)
[1, 31, 16, 15, 16, 4, 17, 32, 22, 31, 15, 15, 17, 12, 29, 2, 0, 2]rD U„# Worksheet 'bernoull_mod' (2006-12-04 at 08:43)
sage: time v=bernoulli_mod_p(next_prime(5000))
CPU time: 0.03 s, Wall time: 0.07 srE UB# Worksheet 'bernoull_mod' (2006-12-04 at 08:44)
sage: len(v)
2501rF T # Worksheet 'bernoull_mod' (2006-12-04 at 08:44)
sage: v
[1, 834, 2835, 2978, 2835, 3108, 2285, 835, 4888, 2243, 4580, 2458, 756, 496, 1317, 2489, 3478, 4680, 3187, 2262, 2324, 4505, 4911, 2558, 4545, 905, 8, 377, 3917, 4639, 3600, 117, 2518, 229, 2505, 1860, 1165, 3868, 1535, 3272, 3541, 2424, 2600, 4612, 4701, 2935, 709, 2363, 2790, 1538, 1367, 1803, 2090, 4292, 3056, 2545, 2590, 1578, 1042, 3748, 1051, 3430, 125, 3684, 1830, 3890, 3630, 2170, 4351, 50, 2361, 3842, 1265, 2985, 3199, 11, 4662, 2269, 833, 2141, ...rG U…# Worksheet 'bernoull_mod' (2006-12-04 at 08:44)
sage: time v=bernoulli_mod_p(next_prime(50000))
CPU time: 0.44 s, Wall time: 0.47 srH UC# Worksheet 'bernoull_mod' (2006-12-04 at 08:44)
sage: len(v)
25010rI UŽ# Worksheet 'bernoull_mod' (2006-12-04 at 08:44)
sage: bernoulli_mod_p(37)
[1, 31, 16, 15, 16, 4, 17, 32, 22, 31, 15, 15, 17, 12, 29, 2, 0, 2]rJ U0# Worksheet '' (2006-12-04 at 13:44)
sage: 2+3
5rK U0# Worksheet '' (2006-12-04 at 13:44)
sage: 2+5
7rL UP# Worksheet '' (2006-12-04 at 13:44)
sage: E = magma.EllipticCurve([1,2,3,4,5])
rM U‚# Worksheet '' (2006-12-04 at 13:44)
sage: E
Elliptic Curve defined by y^2 + x*y + 3*y = x^3 + 2*x^2 + 4*x + 5 over Rational FieldrN U_# Worksheet '' (2006-12-04 at 13:44)
sage: type(E)
rO U?# Worksheet '' (2006-12-04 at 13:45)
sage: E.name()
'_sage_[7]'rP U5# Worksheet '' (2006-12-04 at 13:45)
sage: E.Rank()
1rQ U<# Worksheet '' (2006-12-04 at 13:45)
sage: a = maple('2+3')
rR U.# Worksheet '' (2006-12-04 at 13:45)
sage: a
5rS U=# Worksheet '' (2006-12-04 at 13:46)
sage: a = maple('2007')
rT U1# Worksheet '' (2006-12-04 at 13:46)
sage: a
2007rU UF# Worksheet '' (2006-12-04 at 13:46)
sage: a.ifactor()
``(3)^2*``(223)rV U;# Worksheet '' (2006-12-04 at 13:46)
sage: a.name()
'sage1'rW UV# Worksheet '' (2006-12-04 at 13:47)
sage: for i in range(5):
... print i
0
1
2
3
4rX UY# Worksheet 'graph' (2006-12-04 at 14:09)
sage: g = graphs.CompleteBipartiteGraph(5,100)
rY U8# Worksheet 'graph' (2006-12-04 at 14:09)
sage: show(g)
rZ U{# Worksheet 'graph' (2006-12-04 at 14:16)
sage: g
Traceback (most recent call last):
...
NameError: name 'g' is not definedr[ UY# Worksheet 'graph' (2006-12-04 at 14:16)
sage: g = graphs.CompleteBipartiteGraph(5,100)
r\ Uz# Worksheet 'graph' (2006-12-04 at 14:16)
sage: g
Complete bipartite graph on 105 vertices: a simple graph on 105 verticesr] UB# Worksheet 'graph' (2006-12-04 at 14:16)
sage: g.save('mygraph')
r^ UW# Worksheet 'graph' (2006-12-04 at 14:18)
sage: P = plot(sin, 0, 10, rgbcolor=(1,1,0))
r_ Ud# Worksheet 'graph' (2006-12-04 at 14:18)
sage: P
Graphics object consisting of 1 graphics primitiver` U9# Worksheet 'graph' (2006-12-04 at 14:18)
sage: P.show()
ra UY# Worksheet 'graph' (2006-12-04 at 14:18)
sage: P = plot(sin, 0, 10, rgbcolor=(0,0.5,0))
rb Ud# Worksheet 'graph' (2006-12-04 at 14:18)
sage: P
Graphics object consisting of 1 graphics primitiverc U9# Worksheet 'graph' (2006-12-04 at 14:18)
sage: P.show()
rd Uf# Worksheet 'graph' (2006-12-04 at 14:18)
sage: P = plot(sin, 0, 10, rgbcolor=(0,0.5,0), thickness=5)
re Ud# Worksheet 'graph' (2006-12-04 at 14:18)
sage: P
Graphics object consisting of 1 graphics primitiverf U9# Worksheet 'graph' (2006-12-04 at 14:18)
sage: P.show()
rg U™# Worksheet 'graph' (2006-12-04 at 14:25)
sage: bernoulli(100)
-94598037819122125295227433069493721872702841533066936133385696204311395415197247711/33330rh UJ# Worksheet 'graph' (2006-12-04 at 14:25)
sage: E = EllipticCurve('389a')
ri UG# Worksheet 'graph' (2006-12-04 at 14:25)
sage: L = E.Lseries_zeros(2)
rj UL# Worksheet 'graph' (2006-12-04 at 14:25)
sage: L
[0.000000000, 0.000000000]rk UG# Worksheet 'graph' (2006-12-04 at 14:25)
sage: L = E.Lseries_zeros(5)
rl Up# Worksheet 'graph' (2006-12-04 at 14:26)
sage: L
[0.000000000, 0.000000000, 2.87609907, 4.41689608, 5.79340263]rm U~# Worksheet 'graph' (2006-12-04 at 14:27)
sage: time b = bernoulli(1000, algorithm='gap')
CPU time: 0.06 s, Wall time: 4.59 srn U~# Worksheet 'graph' (2006-12-04 at 14:27)
sage: time b = bernoulli(1000, algorithm='gap')
CPU time: 0.01 s, Wall time: 0.01 sro U~# Worksheet 'graph' (2006-12-04 at 14:27)
sage: time b = bernoulli(1002, algorithm='gap')
CPU time: 0.02 s, Wall time: 0.03 srp U€# Worksheet 'graph' (2006-12-04 at 14:28)
sage: time b = bernoulli(10000, algorithm='pari')
CPU time: 0.44 s, Wall time: 0.48 srq U€# Worksheet 'graph' (2006-12-04 at 14:28)
sage: time b = bernoulli(10000, algorithm='pari')
CPU time: 0.24 s, Wall time: 0.27 srr U€# Worksheet 'graph' (2006-12-04 at 14:28)
sage: time b = bernoulli(10000, algorithm='pari')
CPU time: 0.24 s, Wall time: 0.26 srs U€# Worksheet 'graph' (2006-12-04 at 14:28)
sage: time b = bernoulli(10000, algorithm='pari')
CPU time: 0.24 s, Wall time: 0.26 srt U0# Worksheet '' (2007-01-05 at 09:53)
sage: 2+3
5ru U0# Worksheet '' (2007-01-05 at 09:53)
sage: 2+5
7rv Tþ # Worksheet 'factor' (2007-01-05 at 09:54)
sage: %hideall
sage: #auto
sage:
sage: # The source code to draw factorization trees...
sage:
sage: import random
sage:
sage: def factor_tree(n, font=10):
... rows = []
... v = [(n,None,0)]
... ftree(rows, v, 0, factor(n))
... return draw_ftree(rows, font)
...
sage:
sage: def ftree(rows, v, i, F):
... if len(v) > 0:
... # add a row to g at the ith level.
... rows.append(v)
... w = []
... for i in range(len(v)):
... k, _,_ = v[i]
... if k is None or is_prime(k):
... w.append((None,None,None))
... else:
... d = random.choice(divisors(k)[1:-1])
... w.append((d,k,i))
... e = k//d
... if e == 1:
... w.append((None,None))
... else:
... w.append((e,k,i))
... if len(w) > len(v):
... ftree(rows, w, i+1, F)
...
sage:
sage:
sage: def draw_ftree(rows,font):
... g = Graphics()
... for i in range(len(rows)):
... cur = rows[i]
... for j in range(len(cur)):
... e, f, k = cur[j]
... if not e is None:
... if is_prime(e):
... c = (1,0,0)
... else:
... c = (0,0,.4)
... g += text(str(e), (j*2-len(cur),-i), fontsize=font, rgbcolor=c)
... if not k is None and not f is None:
... g += line([(j*2-len(cur),-i), (k*2-len(rows[i-1]),-i+1)], alpha=0.4, thickness=1)
... return g
...
sage:
sage: def factor_trees(n, cols=4, rows=3, font=10):
... return graphics_array([[factor_tree(n,font) for _ in range(cols)] for _ in range(rows)])
CPU time: 0.00 s, Wall time: 0.00 srw UŽ# Worksheet 'factor' (2007-01-05 at 09:54)
sage: F = factor_trees(300000000, rows=1, cols=1, font=8)
sage: F.show(axes=False, figsize=[10,6])
rx Uš# Worksheet 'factor' (2007-01-05 at 09:54)
sage: F = factor_tree(prod(primes(40)))
sage: F.show(xmin=-3,xmax=7,ymin=-5,ymax=0.5,figsize=[8,2],axes=False)
ry Uk# Worksheet 'factor' (2007-01-05 at 09:54)
sage: show(factor_trees(1200,cols=3,rows=3),axes=False,dpi=100)
rz UY# Worksheet 'qsieve' (2007-01-05 at 09:55)
sage: n = next_prime(10^21)*next_prime(10^22)
r{ U•# Worksheet 'qsieve' (2007-01-05 at 09:55)
sage: time factor(n)
1000000000000000000117 * 10000000000000000000009
CPU time: 0.53 s, Wall time: 0.78 sr| Uœ# Worksheet 'qsieve' (2007-01-05 at 09:55)
sage: time qsieve(n)
([1000000000000000000117, 10000000000000000000009], '')
CPU time: 0.00 s, Wall time: 0.53 sr} UY# Worksheet 'qsieve' (2007-01-05 at 09:55)
sage: n = next_prime(10^22)*next_prime(10^24)
r~ U˜# Worksheet 'qsieve' (2007-01-05 at 09:55)
sage: time factor(n)
10000000000000000000009 * 1000000000000000000000007
CPU time: 0.95 s, Wall time: 1.51 sr UŸ# Worksheet 'qsieve' (2007-01-05 at 09:55)
sage: time qsieve(n)
([10000000000000000000009, 1000000000000000000000007], '')
CPU time: 0.01 s, Wall time: 0.81 sr€ UY# Worksheet 'qsieve' (2007-01-05 at 09:55)
sage: n = next_prime(10^24)*next_prime(10^26)
r Uœ# Worksheet 'qsieve' (2007-01-05 at 09:55)
sage: time factor(n)
1000000000000000000000007 * 100000000000000000000000067
CPU time: 2.30 s, Wall time: 3.65 sr‚ U£# Worksheet 'qsieve' (2007-01-05 at 09:55)
sage: time qsieve(n)
([1000000000000000000000007, 100000000000000000000000067], '')
CPU time: 0.01 s, Wall time: 2.08 srƒ U°# Worksheet 'qsieve' (2007-01-05 at 09:55)
sage: qsieve(n, time=True)
([1000000000000000000000007, 100000000000000000000000067], '2.55 real 1.46 user 0.01 sys')r„ UY# Worksheet 'qsieve' (2007-01-05 at 09:56)
sage: n = next_prime(10^25)*next_prime(10^27)
r… Už# Worksheet 'qsieve' (2007-01-05 at 09:56)
sage: time factor(n)
10000000000000000000000013 * 1000000000000000000000000103
CPU time: 3.60 s, Wall time: 5.46 sr† Uœ# Worksheet 'qsieve' (2007-01-05 at 09:56)
sage: n = next_prime(10^25)*next_prime(10^27)
sage: print n
10000000000000000000000014030000000000000000000001339r‡ U²# Worksheet 'qsieve' (2007-01-05 at 09:56)
sage: qsieve(n, time=True)
([10000000000000000000000013, 1000000000000000000000000103], '2.71 real 2.06 user 0.01 sys')rˆ UÐ# Worksheet 'qsieve' (2007-01-05 at 09:56)
sage: F, t = qsieve(n, time=True)
sage: print F
sage: print t
[10000000000000000000000013, 1000000000000000000000000103]
2.73 real 2.06 user 0.01 sysr‰ Už# Worksheet 'qsieve' (2007-01-05 at 09:56)
sage: n = next_prime(10^26)*next_prime(10^28)
sage: print n
1000000000000000000000000703100000000000000000000022177rŠ U # Worksheet 'qsieve' (2007-01-05 at 09:56)
sage: time factor(n)
100000000000000000000000067 * 10000000000000000000000000331
CPU time: 5.33 s, Wall time: 8.05 sr‹ UÒ# Worksheet 'qsieve' (2007-01-05 at 09:56)
sage: F, t = qsieve(n, time=True)
sage: print F
sage: print t
[100000000000000000000000067, 10000000000000000000000000331]
4.96 real 3.46 user 0.02 sysrŒ U¡# Worksheet 'qsieve' (2007-01-05 at 09:58)
sage: n = next_prime(10^27)*next_prime(10^30)
sage: print n
1000000000000000000000000103057000000000000000000000005871r U¥# Worksheet 'qsieve' (2007-01-05 at 09:58)
sage: time factor(n)
1000000000000000000000000103 * 1000000000000000000000000000057
CPU time: 12.82 s, Wall time: 19.37 srŽ UÖ# Worksheet 'qsieve' (2007-01-05 at 09:59)
sage: F, t = qsieve(n, time=True)
sage: print F
sage: print t
[1000000000000000000000000103, 1000000000000000000000000000057]
12.09 real 8.88 user 0.06 sysr U¤# Worksheet 'qsieve' (2007-01-05 at 09:59)
sage: n = next_prime(10^29)*next_prime(10^31)
sage: print n
1000000000000000000000000003193300000000000000000000000010527r U¨# Worksheet 'qsieve' (2007-01-05 at 10:00)
sage: time factor(n)
100000000000000000000000000319 * 10000000000000000000000000000033
CPU time: 27.28 s, Wall time: 41.15 sr‘ UÙ# Worksheet 'qsieve' (2007-01-05 at 10:00)
sage: F, t = qsieve(n, time=True)
sage: print F
sage: print t
[100000000000000000000000000319, 10000000000000000000000000000033]
22.45 real 15.22 user 0.11 sysr’ U¬# Worksheet 'qsieve' (2007-01-05 at 10:19)
sage: n = next_prime(10^33)*next_prime(10^35)
sage: print n
100000000000000000000000000000006169000000000000000000000000000004209r“ U©# Worksheet 'qsieve' (2007-01-05 at 10:21)
sage: n = next_prime(10^32)*next_prime(10^33)
sage: print n
100000000000000000000000000000055100000000000000000000000000002989r” UÞ# Worksheet 'qsieve' (2007-01-05 at 10:22)
sage: F, t = qsieve(n, time=True)
sage: print F
sage: print t
[100000000000000000000000000000049, 1000000000000000000000000000000061]
80.95 real 45.56 user 0.49 sysr• U# Worksheet 'qsieve' (2007-01-05 at 10:24)
sage: time factor(n)
100000000000000000000000000000049 * 1000000000000000000000000000000061
CPU time: 64.23 s, Wall time: 87.90 sr– UW# Worksheet 'qsieve' (2007-01-05 at 10:41)
sage: q = qsieve(n, time=True, block=False)
r— UL# Worksheet 'qsieve' (2007-01-05 at 10:41)
sage: q
Proper factors so far: []r˜ U?# Worksheet 'qsieve' (2007-01-05 at 10:41)
sage: q.done()
Falser™ U6# Worksheet 'qsieve' (2007-01-05 at 10:41)
sage: 2+2
4rš T # Worksheet 'qsieve' (2007-01-05 at 10:41)
sage: q.log()
'Input number to factor [ >=40 decimal digits]: 100000000000000000000000000000055100000000000000000000000000002989\r\n\r\n\r\n\r\n100 relations, 9 partials.\r\n1260 curves.\r\n200 relations, 15 partials.\r\n2520 curves.\r\n300 relations, 25 partials.\r\n400 relations, 38 partials.\r\n3780 curves.\r\n500 relations, 46 partials.\r\n600 relations, 55 partials.\r\n5040 curves.\r\n700 relations, 61 partials.\r\n6300 curves.\r\n800 relations, 70 partials.\r\n900...r› T # Worksheet 'qsieve' (2007-01-05 at 10:41)
sage: print q.log()
Input number to factor [ >=40 decimal digits]: 100000000000000000000000000000055100000000000000000000000000002989
100 relations, 9 partials.
1260 curves.
200 relations, 15 partials.
2520 curves.
300 relations, 25 partials.
400 relations, 38 partials.
3780 curves.
500 relations, 46 partials.
600 relations, 55 partials.
5040 curves.
700 relations, 61 partials.
6300 curves.
800 relations, 70 partials.
900 relations, 81 partials.
7560 curves.
1000 relations...rœ U?# Worksheet 'qsieve' (2007-01-05 at 10:45)
sage: q.done()
Falser U?# Worksheet 'qsieve' (2007-01-05 at 10:45)
sage: q.done()
Falserž UL# Worksheet 'qsieve' (2007-01-05 at 10:45)
sage: q
Proper factors so far: []rŸ T # Worksheet 'qsieve' (2007-01-05 at 10:46)
sage: print q.log()
Input number to factor [ >=40 decimal digits]: 100000000000000000000000000000055100000000000000000000000000002989
100 relations, 9 partials.
1260 curves.
200 relations, 15 partials.
2520 curves.
300 relations, 25 partials.
400 relations, 38 partials.
3780 curves.
500 relations, 46 partials.
600 relations, 55 partials.
5040 curves.
700 relations, 61 partials.
6300 curves.
800 relations, 70 partials.
900 relations, 81 partials.
7560 curves.
1000 relations...r T # Worksheet 'qsieve' (2007-01-05 at 10:46)
sage: print q.log()
Input number to factor [ >=40 decimal digits]: 100000000000000000000000000000055100000000000000000000000000002989
100 relations, 9 partials.
1260 curves.
200 relations, 15 partials.
2520 curves.
300 relations, 25 partials.
400 relations, 38 partials.
3780 curves.
500 relations, 46 partials.
600 relations, 55 partials.
5040 curves.
700 relations, 61 partials.
6300 curves.
800 relations, 70 partials.
900 relations, 81 partials.
7560 curves.
1000 relations...r¡ U¡# Worksheet 'qsieve' (2007-01-05 at 10:46)
sage: q.stop()
Traceback (most recent call last):
...
AttributeError: qsieve_nonblock instance has no attribute 'stop'r¢ U²# Worksheet 'qsieve' (2007-01-05 at 10:46)
sage: q.quit()
Traceback (most recent call last):
...
pexpect.ExceptionPexpect: close() could not terminate the child using terminate()r£ U:# Worksheet 'qsieve' (2007-01-05 at 10:46)
sage: q.quit()
r¤ U;# Worksheet 'qsieve' (2007-01-05 at 10:46)
sage: q
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