€csage.server.notebook.notebook
Notebook
q)q}q(U_Notebook__ulimitqU Usecureq‰U_Notebook__log_serverq‰U_Notebook__filenameqU2/home/was/talks/20070817-ccr/sage_notebook/nb.sobjqU_Notebook__confq (csage.server.notebook.server_conf
ServerConfiguration
q
oq }q Uconfsq
}q(Unumber_of_backupsqKUword_wrap_colsqKHU idle_timeoutqKxU
save_intervalqK Uidle_check_intervalqK usbU_Notebook__server_logq]qU_Notebook__accountsq‰U_Notebook__systemqNUportqM@ U_Notebook__worksheetsq}qUadmin/0q(csage.server.notebook.worksheet
Worksheet
q oq }q (U_Worksheet__filenameq hU_Worksheet__ownerq Uadminq!U_Worksheet__cellsq"]q#((csage.server.notebook.cell
Cell
q$oq%}q&(U _Cell__inq'U2 + 3q(U_Cell__introspect_htmlq)U!q*U_Cell__worksheetq+h U_Cell__completionsq,‰U_Cell__introspectq-‰U_Cell__out_htmlq.U U _Cell__idq/K U_Cell__is_htmlq0‰U_before_preparseq1UWos.chdir("/home/was/talks/20070817-ccr/sage_notebook/worksheets/admin/0/cells/0")
2 + 3q2U
_Cell__outq3U5Uhas_new_outputq4‰U _Cell__sageq5NU_Cell__versionq6KU _Cell__typeq7Uwrapq8U _Cell__timeq9‰U_Cell__interruptedq:‰ub(h$oq;}q<(h'U h+h h,‰h.U h/Kh3U h4‰h6K h7h8h:‰ub(h$oq=}q>(h'Ushow(plot(sin(x^2), 0, pi))q?h)U!q@h+h h,‰h-‰h.U-
qAh/Kh0‰h1Umos.chdir("/home/was/talks/20070817-ccr/sage_notebook/worksheets/admin/0/cells/1")
show(plot(sin(x^2), 0, pi))qBh3U h4‰h5Nh6Kh7h8U_Cell__url_to_selfqCU/home/admin/0/cells/1qDh9‰h:‰ub(h$oqE}qF(h'U h+h h,‰h.U h/Kh3U h4‰h6K h7h8h:‰ub(h$oqG}qH(h'U a = integrate(sin(x^2),x); aqIh)U!qJh+h h,‰h-‰h.U h/Kh0‰h1Unos.chdir("/home/was/talks/20070817-ccr/sage_notebook/worksheets/admin/0/cells/2")
a = integrate(sin(x^2),x); aqKh3Uz
sqrt(pi)*((sqrt(2)*I + sqrt(2))*erf((sqrt(2)*I + sqrt(2))*x/2) + (sqrt(2)*I - sqrt(2))*erf((sqrt(2)*I - sqrt(2))*x/2))/8
qLh4‰h5csage.interfaces.sage0
reduce_load_Sage
qM)RqNh6Kh7UwrapqOh9‰h:‰ub(h$oqP}qQ(h'Ushow(a)qRh)U!qSh+h h,‰h-‰h.U h/Kh0‰h1UYos.chdir("/home/was/talks/20070817-ccr/sage_notebook/worksheets/admin/0/cells/3")
show(a)qTh3T¥
\frac{{\sqrt{ \pi } \cdot \left( {\left( {\sqrt{ 2 } \cdot i} + \sqrt{ 2 } \right) \cdot \left( \text{erf} \left( \frac{{\left( {\sqrt{ 2 } \cdot i} + \sqrt{ 2 } \right) \cdot x}}{2} \right) \right)} + {\left( {\sqrt{ 2 } \cdot i} - \sqrt{ 2 } \right) \cdot \left( \text{erf} \left( \frac{{\left( {\sqrt{ 2 } \cdot i} - \sqrt{ 2 } \right) \cdot x}}{2} \right) \right)} \right)}}{8}
qUh4‰h5hNh6Kh7h8hCU/home/admin/0/cells/3qVh9‰h:‰ub(h$oqW}qX(h'U h+h h,‰h.U h/Kh3U h4‰h6K h7h8h:‰ub(h$oqY}qZ(h'U m = random_matrix(QQ,5)^(-1); mq[h)U!q\h+h h,‰h-‰h.U h/K
h0‰h1Uros.chdir("/home/was/talks/20070817-ccr/sage_notebook/worksheets/admin/0/cells/10")
m = random_matrix(QQ,5)^(-1); mq]h3Uˆ
[ -3 -2 -3 -2 1]
[ -5 -4 -6 -4 2]
[-3/2 -1 -1 -1 1/2]
[ 0 -1/2 -1/2 0 0]
[ 1 1 1 1 0]
q^h4‰h5hNh6Kh7h8hCU/home/admin/0/cells/10q_h9‰h:‰ub(h$oq`}qa(h'U#m.[tab]qbh)U!qch+h h,‰h-‰h.U h/Kh0‰h1U[os.chdir("/home/was/talks/20070817-ccr/sage_notebook/worksheets/admin/0/cells/20")
#m.[tab]qdh3U
h4‰h5hNh6Kh7Uwrapqeh9‰h:‰ub(h$oqf}qg(h'Ulatex(m)qhh)U!qih+h h,‰h-‰h.U h/K h0‰h1U[os.chdir("/home/was/talks/20070817-ccr/sage_notebook/worksheets/admin/0/cells/11")
latex(m)qjh3UŸ
\left(\begin{array}{rrrrr}
-3&-2&-3&-2&1\\
-5&-4&-6&-4&2\\
-\frac{3}{2}&-1&-1&-1&\frac{1}{2}\\
0&-\frac{1}{2}&-\frac{1}{2}&0&0\\
1&1&1&1&0
\end{array}\right)
qkh4‰h5hNh6Kh7h8h9‰h:‰ub(h$oql}qm(h'Ushow(m)qnh)U!qoh+h h,‰h-‰h.U h/K h0‰h1UZos.chdir("/home/was/talks/20070817-ccr/sage_notebook/worksheets/admin/0/cells/12")
show(m)qph3UÄ
\left(\begin{array}{rrrrr}
-3&-2&-3&-2&1\\
-5&-4&-6&-4&2\\
-\frac{3}{2}&-1&-1&-1&\frac{1}{2}\\
0&-\frac{1}{2}&-\frac{1}{2}&0&0\\
1&1&1&1&0
\end{array}\right)
qqh4‰h5hNh6Kh7h8hCU/home/admin/0/cells/12qrh9‰h:‰ub(h$oqs}qt(h'U h+h h,‰h.U h/Kh3U h4‰h6K h7h8h:‰ub(h$oqu}qv(h'U#time n = number_of_partitions(10^8)qwh)U!qxh+h h,‰h-‰h.U h/Kh0‰h1U›os.chdir("/home/was/talks/20070817-ccr/sage_notebook/worksheets/admin/0/cells/4")
__SAGE_t__=cputime()
__SAGE_w__=walltime()
n = number_of_partitions(10^8)qyh3U$CPU time: 6.01 s, Wall time: 8.28 sqzh4‰h5Nh6Kh7Uwrapq{h9ˆh:‰ub(h$oq|}q}(h'U/%mathematica
Timing[N[Log[PartitionsP[10^8]]]]q~h)U!qh+h h,‰h-‰h.U h/Kh0‰h1U€os.chdir("/home/was/talks/20070817-ccr/sage_notebook/worksheets/admin/0/cells/6")
%mathematica
Timing[N[Log[PartitionsP[10^8]]]]q€h3U {13.6169, 25630.640277658734642}qh4‰h5Nh6Kh7h8hCU/home/admin/0/cells/6q‚h9‰h:‰ub(h$oqƒ}q„(h'U h+h h,‰h.U h/Kh3U h4‰h6K h7h8h:‰ub(h$oq…}q†(h'UIe = EllipticCurve([1,2,3,4,5])
print e.aplist(20)
time n = e.aplist(10^6)q‡h)U!qˆh+h h,‰h-‰h.U h/K
h0‰h1Uœos.chdir("/home/was/talks/20070817-ccr/sage_notebook/worksheets/admin/0/cells/13")
e = EllipticCurve([1,2,3,4,5])
print e.aplist(20)
time n = e.aplist(10^6)q‰h3U<
[1, 0, -3, -1, -1, 1, 5, 4]
Time: CPU 3.68 s, Wall: 5.30 s
qŠh4‰h5hNh6Kh7Uwrapq‹h9‰h:‰ub(h$oqŒ}q(h'U€%magma
print GetVersion();
E := EllipticCurve([1,2,3,4,5]);
print TracesOfFrobenius(E, 20);
time n := TracesOfFrobenius(E,10^6);qŽh)U!qh+h h,‰h-‰h.U h/Kh0‰h1UÒos.chdir("/home/was/talks/20070817-ccr/sage_notebook/worksheets/admin/0/cells/5")
%magma
print GetVersion();
E := EllipticCurve([1,2,3,4,5]);
print TracesOfFrobenius(E, 20);
time n := TracesOfFrobenius(E,10^6);qh3U4
2 13 10
[ 1, 0, -3, -1, -1, 1, 5, 4 ]
Time: 8.570
q‘h4‰h5hNh6Kh7h8hCU/home/admin/0/cells/5q’h9‰h:‰ub(h$oq“}q”(h'U h+h h,‰h.U h/Kh3U h4‰h6K h7h8h:‰ub(h$oq•}q–(h'U>var('a,b,c,X')
s = solve(a*X^2 + b*X + c == 0, X)
show(s[0])q—h)U!q˜h+h h,‰h-‰h.U h/K h0‰h1UŽos.chdir("/home/was/talks/20070817-ccr/sage_notebook/worksheets/admin/0/cells/9")
var('a,b,c,X')
s = solve(a*X^2 + b*X + c == 0, X)
show(s[0])q™h3UmX = \frac{-\sqrt{ {b}^{2} - {{4 \cdot a} \cdot c} } - b}{{2 \cdot a}}
qšh4‰h5Nh6Kh7h8hCU/home/admin/0/cells/9q›h9‰h:‰ub(h$oqœ}q(h'U+%mathematica
Solve[a*X^2 + b*X +c == 0, X]qžh)U!qŸh+h h,‰h-‰h.U h/Kh0‰h1U|os.chdir("/home/was/talks/20070817-ccr/sage_notebook/worksheets/admin/0/cells/8")
%mathematica
Solve[a*X^2 + b*X +c == 0, X]q h3Uá2 2
-b - Sqrt[b - 4 a c] -b + Sqrt[b - 4 a c]
{{X -> ---------------------}, {X -> ---------------------}}
2 a 2 aq¡h4‰h5Nh6Kh7h8h9‰h:‰ub(h$oq¢}q£(h'U]# In SAGE
a = random_matrix(ZZ,300, x=-9, y=9)
time f = a.charpoly()
print log(abs(f[0])*1.0)q¤h)U!q¥h+h h,‰h-‰h.U h/Kh9‰h0‰h1U¯os.chdir("/home/was/talks/20070817-ccr/sage_notebook/worksheets/admin/0/cells/7")
# In SAGE
a = random_matrix(ZZ,300, x=-9, y=9)
time f = a.charpoly()
print log(abs(f[0])*1.0)q¦h3U3
Time: CPU 10.04 s, Wall: 13.03 s
1200.38548128654
q§h4‰h6K h7h8h5hM)Rq¨h:‰ub(h$oq©}qª(h'U«%magma
n := 300;
a := MatrixAlgebra(IntegerRing(), n)![Random(-9,9) : i in [1..n^2]];
time f := CharacteristicPolynomial(a);
print Log(AbsoluteValue(Coefficient(f,0))*1.0)q«h)U!q¬h+h h,‰h-‰h.U h/Kh0‰h1Uþos.chdir("/home/was/talks/20070817-ccr/sage_notebook/worksheets/admin/0/cells/14")
%magma
n := 300;
a := MatrixAlgebra(IntegerRing(), n)![Random(-9,9) : i in [1..n^2]];
time f := CharacteristicPolynomial(a);
print Log(AbsoluteValue(Coefficient(f,0))*1.0)qh3U/
Time: 7.640
1214.76576501968242382405874440
q®h4‰h5h¨h6Kh7h8h9‰h:‰ub(h$oq¯}q°(h'U`# In SAGE
n = 100
a = random_matrix(QQ,n, n+1, num_bound=2^64, den_bound=1)
time a.echelonize()
q±h)U!q²h+h h,‰h-‰h.U h/Kh0‰h1U²os.chdir("/home/was/talks/20070817-ccr/sage_notebook/worksheets/admin/0/cells/15")
# In SAGE
n = 100
a = random_matrix(QQ,n, n+1, num_bound=2^64, den_bound=1)
time a.echelonize()q³h3U
Time: CPU 0.31 s, Wall: 0.41 s
q´h4‰h5h¨h6K h7h8hCU/home/admin/0/cells/15qµh9‰h:‰ub(h$oq¶}q·(h'Uy%magma
n := 100;
a := RMatrixSpace(RationalField(), n,n+1)![Random(1,2^64): i in [1..n*(n+1)]];
time e := EchelonForm(a);q¸h)U!q¹h+h h,‰h-‰h.U h/Kh0‰h1UÌos.chdir("/home/was/talks/20070817-ccr/sage_notebook/worksheets/admin/0/cells/26")
%magma
n := 100;
a := RMatrixSpace(RationalField(), n,n+1)![Random(1,2^64): i in [1..n*(n+1)]];
time e := EchelonForm(a);qºh3U
Time: 6.390
q»h4‰h5h¨h6Kh7h8hCU/home/admin/0/cells/26q¼h9‰h:‰ub(h$oq½}q¾(h'U`# In SAGE
n = 200
a = random_matrix(QQ,n, n+1, num_bound=2^64, den_bound=1)
time a.echelonize()
q¿h)U!qÀh+h h,‰h-‰h.U h/Kh0‰h1U²os.chdir("/home/was/talks/20070817-ccr/sage_notebook/worksheets/admin/0/cells/27")
# In SAGE
n = 200
a = random_matrix(QQ,n, n+1, num_bound=2^64, den_bound=1)
time a.echelonize()qÁh3U
Time: CPU 1.96 s, Wall: 3.22 s
qÂh4‰h5h¨h6Kh7h8h9‰h:‰ub(h$oqÃ}qÄ(h'Uy%magma
n := 200;
a := RMatrixSpace(RationalField(), n,n+1)![Random(1,2^64): i in [1..n*(n+1)]];
time e := EchelonForm(a);qÅh)U!qÆh+h h,‰h-‰h.U h/K h0‰h1UÌos.chdir("/home/was/talks/20070817-ccr/sage_notebook/worksheets/admin/0/cells/29")
%magma
n := 200;
a := RMatrixSpace(RationalField(), n,n+1)![Random(1,2^64): i in [1..n*(n+1)]];
time e := EchelonForm(a);qÇh3U
Time: 159.920
qÈh4‰h5h¨h6Kh7h8h9‰h:‰ub(h$oqÉ}qÊ(h'U159.920 / 3.22qËh)U!qÌh+h h,‰h-‰h.U h/K h0‰h1Uaos.chdir("/home/was/talks/20070817-ccr/sage_notebook/worksheets/admin/0/cells/30")
159.920 / 3.22qÍh3U
49.6645962732919
qÎh4‰h5h¨h6Kh7h8h9‰h:‰ub(h$oqÏ}qÐ(h'U h+h h,‰h.U h/K h3U h4‰h6K h7h8h:‰ubeU_Worksheet__synchroqÑKZU_Worksheet__comp_is_runningqÒ‰U_Worksheet__dirqÓU=/home/was/talks/20070817-ccr/sage_notebook/worksheets/admin/0qÔU_Worksheet__last_autosaveqÕGAѱn½·}åU_Worksheet__attachedqÖ}q×U/home/was/.sage/init.sageqØGAÑ¢m€ sU_Worksheet__sageqÙh¨U_Worksheet__user_viewqÚ}qÛh!KsU_Worksheet__queueqÜ]qÝU_Worksheet__next_idqÞK U_Worksheet__docbrowserq߉U_Worksheet__viewersqà]qáU!_Worksheet__last_compute_walltimeqâGAѱo£äæâU_Worksheet__nameqãU
Quick DemoqäU_Worksheet__next_block_idqåK]U_Worksheet__systemqæUsageqçU_Worksheet__collaboratorsqè]qéU_Worksheet__saved_by_infoqê}që(U
1187361716qìh!U
1187361888qíh!U
1187362291qîh!U
1187362485qïh!U
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1187363574qôh!U
1187361901qõh!uU_Worksheet__last_editedqöGAѱn½·}[h!†q÷ubsU_default_filenameqøU2/home/was/talks/20070817-ccr/sage_notebook/nb.sobjqùU_Notebook__history_countqúK U_Notebook__server_poolqû]qüU_Notebook__object_dirqýU2/home/was/talks/20070817-ccr/sage_notebook/objectsqþU_Notebook__show_debugqÿ‰U_Notebook__backup_dirr Usage_notebook/backups/r U_Notebook__historyr ]r U_Notebook__worksheet_dirr U5/home/was/talks/20070817-ccr/sage_notebook/worksheetsr U_Notebook__adminsr ]r U_Notebook__usersr }r h!(csage.server.notebook.user
User
r
or }r (U _User__emailr
U U _User__confr (csage.server.notebook.user_conf
UserConfiguration
r or }r Uconfsr }r (Udefault_systemr Usager Umax_history_lengthr MôUautosave_intervalr K´usbU_User__account_typer Uuserr U_User__passwordr U
aaQSqAReePlq6r U_User__usernamer h!Uhistoryr ]r (UEWorksheet 'Quick Demo' (2007-08-17 at 07:38)
{{{id=0|
2 + 3
///
5
}}}r U‰Worksheet 'Quick Demo' (2007-08-17 at 07:39)
{{{id=1|
show(plot(sin(x^2), 0, pi)))
///
Syntax Error:
show(plot(sin(x^2), 0, pi)))
}}}r UUWorksheet 'Quick Demo' (2007-08-17 at 07:39)
{{{id=1|
show(plot(sin(x^2), 0, pi))
}}}r! UÌWorksheet 'Quick Demo' (2007-08-17 at 07:39)
{{{id=2|
integrate(sin(x^2),x)
///
sqrt(pi)*((sqrt(2)*I + sqrt(2))*erf((sqrt(2)*I + sqrt(2))*x/2) + (sqrt(2)*I - sqrt(2))*erf((sqrt(2)*I - sqrt(2))*x/2))/8
}}}r" Tü Worksheet 'Quick Demo' (2007-08-17 at 07:39)
{{{id=3|
show(integrate(sin(x^2),x))
///
\frac{{\sqrt{ \pi } \cdot \left( {\left( {\sqrt{ 2 } \cdot i} + \sqrt{ 2 } \right) \cdot \left( \text{erf} \left( \frac{{\left( {\sqrt{ 2 } \cdot i} + \sqrt{ 2 } \right) \cdot x}}{2} \right) \right)} + {\left( {\sqrt{ 2 } \cdot i} - \sqrt{ 2 } \right) \cdot \left( \text{erf} \left( \frac{{\left( {\sqrt{ 2 } \cdot i} - \sqrt{ 2 } \right) \cdot x}}{2} \right) \right)} \right)}}{8}
}}}r# U†Worksheet 'Quick Demo' (2007-08-17 at 07:40)
{{{id=4|
time n = number_of_partitions(10^8)
///
CPU time: 6.01 s, Wall time: 8.28 s
}}}r$ UWorksheet 'Quick Demo' (2007-08-17 at 07:41)
{{{id=5|
%magma
E := EllipticCurve([1,2,3,4,5]);
TracesOfFrobenius(E, 20)
///
[ 1, 0, -3, -1, -1, 1, 5, 4 ]
}}}r% U¹Worksheet 'Quick Demo' (2007-08-17 at 07:41)
{{{id=5|
%magma
print GetVersion();
E := EllipticCurve([1,2,3,4,5]);
TracesOfFrobenius(E, 20)
///
2 13 10
[ 1, 0, -3, -1, -1, 1, 5, 4 ]
}}}r& U¹Worksheet 'Quick Demo' (2007-08-17 at 07:41)
{{{id=5|
%magma
print GetVersion();
E := EllipticCurve([1,2,3,4,5]);
TracesOfFrobenius(E, 20)
///
2 13 10
[ 1, 0, -3, -1, -1, 1, 5, 4 ]
}}}r' UÏWorksheet 'Quick Demo' (2007-08-17 at 07:41)
{{{id=6|
%mathematics
NumberOfPartitions[10^3]
///
Traceback (most recent call last): NumberOfPartitions[10^3]
NameError: name 'mathematics' is not defined
}}}r( U„Worksheet 'Quick Demo' (2007-08-17 at 07:42)
{{{id=6|
%mathematica
NumberOfPartitions[10^3]
///
NumberOfPartitions[1000]
}}}r) U€Worksheet 'Quick Demo' (2007-08-17 at 07:42)
{{{id=6|
%mathematica
NumberPartitions[10^3]
///
NumberPartitions[1000]
}}}r* UvWorksheet 'Quick Demo' (2007-08-17 at 07:42)
{{{id=6|
%mathematica
NPartitions[10^3]
///
NPartitions[1000]
}}}r+ UxWorksheet 'Quick Demo' (2007-08-17 at 07:42)
{{{id=6|
%mathematica
NPartitionsP[10^3]
///
NPartitionsP[1000]
}}}r, U…Worksheet 'Quick Demo' (2007-08-17 at 07:42)
{{{id=6|
%mathematica
PartitionsP[10^3]
///
24061467864032622473692149727991
}}}r- U…Worksheet 'Quick Demo' (2007-08-17 at 07:42)
{{{id=6|
%mathematica
PartitionsP[10^3]
///
24061467864032622473692149727991
}}}r. U“Worksheet 'Quick Demo' (2007-08-17 at 07:42)
{{{id=6|
%mathematica
Timing[PartitionsP[10^3]]
///
{0., 24061467864032622473692149727991}
}}}r/ Tü Worksheet 'Quick Demo' (2007-08-17 at 07:42)
{{{id=6|
%mathematica
Timing[PartitionsP[10^5]]
///
{0.432027, 2749351056977569651267751632098635268817342931598005475820
> 31259843021473281149641730550507416607366215901578447742962489404930630
> 70200461792764493033510116079342457190155718943509725312466108452006369
> 55893446424871682878983218234500926285383140459702130713067451062441922
> 73112389997022844086093709355316296978515695698921961084801586005694210
> 98519}
}}}r0 U}Worksheet 'Quick Demo' (2007-08-17 at 07:43)
{{{id=6|
%mathematica
Timing[n := PartitionsP[10^6];]
///
{0., Null}
}}}r1 U}Worksheet 'Quick Demo' (2007-08-17 at 07:43)
{{{id=6|
%mathematica
Timing[n := PartitionsP[10^6]]
///
{0., Null}
}}}r2 T0 Worksheet 'Quick Demo' (2007-08-17 at 07:43)
{{{id=6|
%mathematica
Timing[PartitionsP[10^6]]
///
{0.896056, 147168498635822339863100476060989594348403048443914212533
> 46127473516661174189186182763301488739835975558420153741306002880959293
> 87347128232270327849578001932784396072064228659048713020170971840761025
> 67647986084690814282935670692978599129051989944549067221999782345287498
> 29740222882298501367675662947818874946878790038246999881977292006320686
> 6873599666227381679826621348241720844663102742800191813...
}}}r3 U³Worksheet 'Quick Demo' (2007-08-17 at 07:43)
{{{id=6|
%mathematica
Timing[N[Log[PartitionsP[10^6]]]]
///
-17
{1.01915 10 , 2549.348105937980440}
}}}r4 U•Worksheet 'Quick Demo' (2007-08-17 at 07:43)
{{{id=6|
%mathematica
Timing[N[Log[PartitionsP[10^6]]]]
///
{0.704044, 2549.348105937980440}
}}}r5 U•Worksheet 'Quick Demo' (2007-08-17 at 07:43)
{{{id=6|
%mathematica
Timing[N[Log[PartitionsP[10^8]]]]
///
{13.6169, 25630.640277658734642}
}}}r6 Td Worksheet 'Quick Demo' (2007-08-17 at 07:44)
{{{id=8|
%mathematica
Solve[a*X^2 + b*X +c == 0, X]
///
2 2
-b - Sqrt[b - 4 a c] -b + Sqrt[b - 4 a c]
{{X -> ---------------------}, {X -> ---------------------}}
2 a 2 a
}}}r7 UµWorksheet 'Quick Demo' (2007-08-17 at 07:44)
{{{id=9|
var('a,b,c,X')
solve(a*X^2 + b*X + c == 0, X)
///
[X == (-sqrt(b^2 - 4*a*c) - b)/(2*a), X == (sqrt(b^2 - 4*a*c) - b)/(2*a)]
}}}r8 UèWorksheet 'Quick Demo' (2007-08-17 at 07:44)
{{{id=9|
var('a,b,c,X')
s = solve(a*X^2 + b*X + c == 0, X)
show(s[0])
///
X = \frac{-\sqrt{ {b}^{2} - {{4 \cdot a} \cdot c} } - b}{{2 \cdot a}}
}}}r9 UÓWorksheet 'Quick Demo' (2007-08-17 at 07:45)
{{{id=2|
a = integrate(sin(x^2),x); a
///
sqrt(pi)*((sqrt(2)*I + sqrt(2))*erf((sqrt(2)*I + sqrt(2))*x/2) + (sqrt(2)*I - sqrt(2))*erf((sqrt(2)*I - sqrt(2))*x/2))/8
}}}r: Tè Worksheet 'Quick Demo' (2007-08-17 at 07:45)
{{{id=3|
show(a)
///
\frac{{\sqrt{ \pi } \cdot \left( {\left( {\sqrt{ 2 } \cdot i} + \sqrt{ 2 } \right) \cdot \left( \text{erf} \left( \frac{{\left( {\sqrt{ 2 } \cdot i} + \sqrt{ 2 } \right) \cdot x}}{2} \right) \right)} + {\left( {\sqrt{ 2 } \cdot i} - \sqrt{ 2 } \right) \cdot \left( \text{erf} \left( \frac{{\left( {\sqrt{ 2 } \cdot i} - \sqrt{ 2 } \right) \cdot x}}{2} \right) \right)} \right)}}{8}
}}}r; TÅ Worksheet 'Quick Demo' (2007-08-17 at 07:45)
{{{id=10|
latex(a)
///
\frac{{\sqrt{ \pi } \cdot \left( {\left( {\sqrt{ 2 } \cdot i} + \sqrt{ 2 } \right) \cdot \left( \text{erf} \left( \frac{{\left( {\sqrt{ 2 } \cdot i} + \sqrt{ 2 } \right) \cdot x}}{2} \right) \right)} + {\left( {\sqrt{ 2 } \cdot i} - \sqrt{ 2 } \right) \cdot \left( \text{erf} \left( \frac{{\left( {\sqrt{ 2 } \cdot i} - \sqrt{ 2 } \right) \cdot x}}{2} \right) \right)} \right)}}{8}
}}}r< U±Worksheet 'Quick Demo' (2007-08-17 at 07:45)
{{{id=10|
m = random_matrix(QQ,4); m
///
[ 0 0 1/2 0]
[ 2 1 -2 1]
[ 1/2 0 -1 -1/2]
[ 0 -2 1 -1]
}}}r= U½Worksheet 'Quick Demo' (2007-08-17 at 07:45)
{{{id=11|
latex(m)
///
\left(\begin{array}{rrrr}
0&0&\frac{1}{2}&0\\
2&1&-2&1\\
\frac{1}{2}&0&-1&-\frac{1}{2}\\
0&-2&1&-1
\end{array}\right)
}}}r> UáWorksheet 'Quick Demo' (2007-08-17 at 07:45)
{{{id=12|
show(m)
///
\left(\begin{array}{rrrr}
0&0&\frac{1}{2}&0\\
2&1&-2&1\\
\frac{1}{2}&0&-1&-\frac{1}{2}\\
0&-2&1&-1
\end{array}\right)
}}}r? U¶Worksheet 'Quick Demo' (2007-08-17 at 07:45)
{{{id=10|
m = random_matrix(QQ,4)^(-1); m
///
[ 1/2 1/4 0 2]
[ -1 -1/2 0 -2]
[-1/2 -1/4 -1/2 -1]
[ 1/2 -3/4 1/2 1]
}}}r@ T* Worksheet 'Quick Demo' (2007-08-17 at 07:45)
{{{id=10|
m = random_matrix(QQ,4)^(-1); m
///
Traceback (most recent call last):
File "", line 1, in
File "/home/was/talks/20070817-ccr/sage_notebook/worksheets/admin/0/code/34.py", line 4, in
exec compile(ur'm = random_matrix(QQ,Integer(4))**(-Integer(1)); m' + '\n', '', 'single')
File "/home/was/s/local/lib/python2.5/site-packages/zope.interface-3.3.0-py2.5-linux-i686.egg/", line 1, in
File "matrix0.pyx", line 2195, in matrix0.Matrix.__pow__
F...
}}}rA UÆWorksheet 'Quick Demo' (2007-08-17 at 07:46)
{{{id=10|
m = random_matrix(QQ,4)^(-1); m
///
[ 2 4 2 0]
[ 0 2 1 0]
[ 2/3 -1/3 0 1/3]
[ -4/3 -10/3 -2 1/3]
}}}rB UåWorksheet 'Quick Demo' (2007-08-17 at 07:46)
{{{id=10|
m = random_matrix(QQ,5)^(-1); m
///
[ -3 -2 -3 -2 1]
[ -5 -4 -6 -4 2]
[-3/2 -1 -1 -1 1/2]
[ 0 -1/2 -1/2 0 0]
[ 1 1 1 1 0]
}}}rC UåWorksheet 'Quick Demo' (2007-08-17 at 07:46)
{{{id=11|
latex(m)
///
\left(\begin{array}{rrrrr}
-3&-2&-3&-2&1\\
-5&-4&-6&-4&2\\
-\frac{3}{2}&-1&-1&-1&\frac{1}{2}\\
0&-\frac{1}{2}&-\frac{1}{2}&0&0\\
1&1&1&1&0
\end{array}\right)
}}}rD T Worksheet 'Quick Demo' (2007-08-17 at 07:46)
{{{id=12|
show(m)
///
\left(\begin{array}{rrrrr}
-3&-2&-3&-2&1\\
-5&-4&-6&-4&2\\
-\frac{3}{2}&-1&-1&-1&\frac{1}{2}\\
0&-\frac{1}{2}&-\frac{1}{2}&0&0\\
1&1&1&1&0
\end{array}\right)
}}}rE U†Worksheet 'Quick Demo' (2007-08-17 at 07:47)
{{{id=13|
e = EllipticCurve([1,2,3,4,5])
e.aplist(20)
///
[1, 0, -3, -1, -1, 1, 5, 4]
}}}rF T‰ Worksheet 'Quick Demo' (2007-08-17 at 07:47)
{{{id=5|
%magma
print GetVersion();
E := EllipticCurve([1,2,3,4,5]);
print TracesOfFrobenius(E, 20);
time n := TraceOfFrobenius(E,10^6);
///
Traceback (most recent call last): time n := TraceOfFrobenius(E,10^6);
File "/home/was/s/local/lib/python2.5/site-packages/sage/server/support.py", line 255, in syseval
return system.eval(cmd)
File "/home/was/s/local/lib/python2.5/site-packages/sage/interfaces/magma.py", line 264, in eval
raise RuntimeError, "Error evaluation Magma code.\nIN:%s\nOUT:%s"%(x, ans)
RuntimeError: Error evaluation Magma code.
IN:print GetVersion();
E := Ellip...
}}}rG UñWorksheet 'Quick Demo' (2007-08-17 at 07:47)
{{{id=5|
%magma
print GetVersion();
E := EllipticCurve([1,2,3,4,5]);
print TracesOfFrobenius(E, 20);
time n := TracesOfFrobenius(E,10^6);
///
2 13 10
[ 1, 0, -3, -1, -1, 1, 5, 4 ]
Time: 8.570
}}}rH UÃWorksheet 'Quick Demo' (2007-08-17 at 07:47)
{{{id=13|
e = EllipticCurve([1,2,3,4,5])
print e.aplist(20)
time n = e.aplist(10^6)
///
[1, 0, -3, -1, -1, 1, 5, 4]
Time: CPU 3.68 s, Wall: 5.30 s
}}}rI UŒWorksheet 'Quick Demo' (2007-08-17 at 07:48)
{{{id=7|
a = random_matrix(ZZ,200)
time f = a.charpoly()
///
Time: CPU 4.48 s, Wall: 5.93 s
}}}rJ U—Worksheet 'Quick Demo' (2007-08-17 at 07:48)
{{{id=7|
a = random_matrix(ZZ,200, x=-9, y=9)
time f = a.charpoly()
///
Time: CPU 3.46 s, Wall: 4.58 s
}}}rK UÇWorksheet 'Quick Demo' (2007-08-17 at 07:49)
{{{id=14|
%magma
n := 200;
a := MatrixAlgebra(IntegerRing(), n)![Random(-9,9) : i in [1..n^2]];
time f := CharacteristicPolynomial(a);
///
Time: 1.740
}}}rL U™Worksheet 'Quick Demo' (2007-08-17 at 07:49)
{{{id=7|
a = random_matrix(ZZ,300, x=-9, y=9)
time f = a.charpoly()
///
Time: CPU 10.57 s, Wall: 13.73 s
}}}rM UÇWorksheet 'Quick Demo' (2007-08-17 at 07:49)
{{{id=14|
%magma
n := 300;
a := MatrixAlgebra(IntegerRing(), n)![Random(-9,9) : i in [1..n^2]];
time f := CharacteristicPolynomial(a);
///
Time: 6.760
}}}rN U£Worksheet 'Quick Demo' (2007-08-17 at 07:49)
{{{id=7|
# In SAGE
a = random_matrix(ZZ,300, x=-9, y=9)
time f = a.charpoly()
///
Time: CPU 10.88 s, Wall: 14.80 s
}}}rO UÇWorksheet 'Quick Demo' (2007-08-17 at 07:50)
{{{id=14|
%magma
n := 300;
a := MatrixAlgebra(IntegerRing(), n)![Random(-9,9) : i in [1..n^2]];
time f := CharacteristicPolynomial(a);
///
Time: 7.320
}}}rP UCWorksheet 'Quick Demo' (2007-08-17 at 07:51)
{{{id=20|
#m.[tab]
}}}rQ UMWorksheet 'Quick Demo' (2007-08-17 at 07:51)
{{{id=19|
show(plot(a,0,pi))
}}}rR UÓWorksheet 'Quick Demo' (2007-08-17 at 07:51)
{{{id=2|
a = integrate(sin(x^2),x); a
///
sqrt(pi)*((sqrt(2)*I + sqrt(2))*erf((sqrt(2)*I + sqrt(2))*x/2) + (sqrt(2)*I - sqrt(2))*erf((sqrt(2)*I - sqrt(2))*x/2))/8
}}}rS U«Worksheet 'Quick Demo' (2007-08-17 at 07:51)
{{{id=19|
show(plot(a,0,pi))
///
WARNING: When plotting, failed to evaluate function at 201 points.
Last error message: ''
}}}rT U½Worksheet 'Quick Demo' (2007-08-17 at 07:52)
{{{id=19|
show(plot(lambda x: abs(a(x)),0,pi))
///
WARNING: When plotting, failed to evaluate function at 201 points.
Last error message: ''
}}}rU UfWorksheet 'Quick Demo' (2007-08-17 at 07:52)
{{{id=19|
show(plot(lambda x: abs(a(x)).real(),0,pi))
}}}rV UŽWorksheet 'Quick Demo' (2007-08-17 at 07:53)
{{{id=7|
# In SAGE
a = random_matrix(ZZ,300, x=-9, y=9)
time f = a.charpoly()
print len(f[0])
}}}rW U¼Worksheet 'Quick Demo' (2007-08-17 at 07:53)
{{{id=7|
# In SAGE
a = random_matrix(ZZ,300, x=-9, y=9)
time f = a.charpoly()
print len(str(f[0]))
///
Time: CPU 10.50 s, Wall: 13.84 s
521
}}}rX Tf Worksheet 'Quick Demo' (2007-08-17 at 07:54)
{{{id=7|
# In SAGE
a = random_matrix(ZZ,300, x=-9, y=9)
time f = a.charpoly()
print N(log(str(f[0])))
///
Time: CPU 10.76 s, Wall: 14.10 s
Traceback (most recent call last):
File "", line 1, in
File "/home/was/talks/20070817-ccr/sage_notebook/worksheets/admin/0/code/58.py", line 7, in
exec compile(ur'print N(log(str(f[Integer(0)])))' + '\n', '', 'single')
File "/home/was/s/local/lib/python2.5/site-packages/zope.interface-3.3.0-py2.5-linux-i686.egg/", line 1, in
File "/home/was/s/local/lib/python2.5/site-pa...
}}}rY T Worksheet 'Quick Demo' (2007-08-17 at 07:54)
{{{id=14|
%magma
n := 300;
a := MatrixAlgebra(IntegerRing(), n)![Random(-9,9) : i in [1..n^2]];
time f := CharacteristicPolynomial(a);
print Log(Coefficient(f,0)*1.0)
///
Time: 7.060
1215.18267407038834444713323203
}}}rZ UºWorksheet 'Quick Demo' (2007-08-17 at 07:54)
{{{id=7|
# In SAGE
a = random_matrix(ZZ,300, x=-9, y=9)
time f = a.charpoly()
print N(log(f[0]))
///
Time: CPU 10.66 s, Wall: 12.79 s
NaN
}}}r[ U»Worksheet 'Quick Demo' (2007-08-17 at 07:55)
{{{id=7|
# In SAGE
a = random_matrix(ZZ,300, x=-9, y=9)
time f = a.charpoly()
print log(f[0]*1.0)
///
Time: CPU 10.57 s, Wall: 13.74 s
NaN
}}}r\ T Worksheet 'Quick Demo' (2007-08-17 at 07:55)
{{{id=24|
f[0]
///
-37593830494800648913243409398750485667240561164695466932680860259948608390189874098670105715211835060505310843528629875372231507811662344683464485690882283103679173548106698771152989084100908282338920120040135211462287296520076076724560920267726277330398726445700704177874189003472665540647826252839912833742003053053248734464557136015312396694778940681793482821613481401227265984580676641950729274115132958889276839010612254436660740468278283971671810063...
}}}r] Tÿ Worksheet 'Quick Demo' (2007-08-17 at 07:55)
{{{id=24|
f[0].log()
///
Traceback (most recent call last):
File "", line 1, in
File "/home/was/talks/20070817-ccr/sage_notebook/worksheets/admin/0/code/63.py", line 4, in
exec compile(ur'f[Integer(0)].log()' + '\n', '', 'single')
File "/home/was/s/local/lib/python2.5/site-packages/zope.interface-3.3.0-py2.5-linux-i686.egg/", line 1, in
AttributeError: 'sage.rings.integer.Integer' object has no attribute 'log'
}}}r^ UOWorksheet 'Quick Demo' (2007-08-17 at 07:55)
{{{id=24|
N(log(f[0]))
///
NaN
}}}r_ UQWorksheet 'Quick Demo' (2007-08-17 at 07:56)
{{{id=24|
RDF(log(f[0]))
///
nan
}}}r` USWorksheet 'Quick Demo' (2007-08-17 at 07:56)
{{{id=24|
N(log(f[0]),200)
///
NaN
}}}ra UTWorksheet 'Quick Demo' (2007-08-17 at 07:56)
{{{id=24|
N(log(f[0]),2000)
///
NaN
}}}rb UCWorksheet 'Quick Demo' (2007-08-17 at 07:56)
{{{id=24|
a = f[0]
}}}rc U>Worksheet 'Quick Demo' (2007-08-17 at 07:56)
{{{id=25|
a.l
}}}rd UFWorksheet 'Quick Demo' (2007-08-17 at 07:56)
{{{id=25|
a.exact_log
}}}re Tè Worksheet 'Quick Demo' (2007-08-17 at 07:56)
{{{id=25|
a.exact_log()
///
Traceback (most recent call last):
File "", line 1, in
File "/home/was/talks/20070817-ccr/sage_notebook/worksheets/admin/0/code/71.py", line 4, in
exec compile(ur'a.exact_log()' + '\n', '', 'single')
File "/home/was/s/local/lib/python2.5/site-packages/zope.interface-3.3.0-py2.5-linux-i686.egg/", line 1, in
TypeError: function takes exactly 1 argument (0 given)
}}}rf Tè Worksheet 'Quick Demo' (2007-08-17 at 07:56)
{{{id=25|
a.exact_log()
///
Traceback (most recent call last):
File "", line 1, in
File "/home/was/talks/20070817-ccr/sage_notebook/worksheets/admin/0/code/71.py", line 4, in
exec compile(ur'a.exact_log()' + '\n', '', 'single')
File "/home/was/s/local/lib/python2.5/site-packages/zope.interface-3.3.0-py2.5-linux-i686.egg/", line 1, in
TypeError: function takes exactly 1 argument (0 given)
}}}rg T Worksheet 'Quick Demo' (2007-08-17 at 07:56)
{{{id=25|
a.exact_log(10)
///
Traceback (most recent call last):
File "", line 1, in
File "/home/was/talks/20070817-ccr/sage_notebook/worksheets/admin/0/code/73.py", line 4, in
exec compile(ur'a.exact_log(Integer(10))' + '\n', '', 'single')
File "/home/was/s/local/lib/python2.5/site-packages/zope.interface-3.3.0-py2.5-linux-i686.egg/", line 1, in
File "integer.pyx", line 970, in integer.Integer.exact_log
ValueError: self must be po...
}}}rh T Worksheet 'Quick Demo' (2007-08-17 at 07:57)
{{{id=14|
%magma
n := 300;
a := MatrixAlgebra(IntegerRing(), n)![Random(-9,9) : i in [1..n^2]];
time f := CharacteristicPolynomial(a);
print Log(AbsoluteValue(Coefficient(f,0))*1.0)
///
Time: 7.640
1214.76576501968242382405874440
}}}ri UÍWorksheet 'Quick Demo' (2007-08-17 at 07:57)
{{{id=7|
# In SAGE
a = random_matrix(ZZ,300, x=-9, y=9)
time f = a.charpoly()
print log(abs(f[0])*1.0)
///
Time: CPU 10.04 s, Wall: 13.03 s
1200.38548128654
}}}rj UªWorksheet 'Quick Demo' (2007-08-17 at 07:58)
{{{id=15|
# In SAGE
n := 300
a = random_matrix(ZZ,300, 301, x=-9, y=9)
time a.echelonize()
///
Syntax Error:
n := 300
}}}rk U«Worksheet 'Quick Demo' (2007-08-17 at 07:58)
{{{id=15|
# In SAGE
n = 100
a = random_matrix(ZZ,n, n+1, x=-9, y=9)
time a.echelonize()
///
Time: CPU 1.13 s, Wall: 1.89 s
}}}rl T€ Worksheet 'Quick Demo' (2007-08-17 at 07:59)
{{{id=26|
%magma
n := 100;
a := MatrixAlgebra(RationalField(), n,n+1)![Random(-9,9) : i in [1..n^2]];
time e := EchelonForm(a);
///
Traceback (most recent call last): time e := EchelonForm(a);
File "/home/was/s/local/lib/python2.5/site-packages/sage/server/support.py", line 255, in syseval
return system.eval(cmd)
File "/home/was/s/local/lib/python2.5/site-packages/sage/interfaces/magma.py", line 264, in eval
raise RuntimeError, "Error evaluation Magma code.\nIN:%s\nOUT:%s"%(x, ans)
RuntimeError: Error evaluation Magma code.
IN:n := 100;
a := MatrixAlgebra(RationalFie...
}}}rm T Worksheet 'Quick Demo' (2007-08-17 at 07:59)
{{{id=26|
%magma
n := 100;
a := RMatrixSpace(RationalField(), n,n+1)![Random(-9,9) : i in [1..n^2]];
time e := EchelonForm(a);
///
Traceback (most recent call last): time e := EchelonForm(a);
File "/home/was/s/local/lib/python2.5/site-packages/sage/server/support.py", line 255, in syseval
return system.eval(cmd)
File "/home/was/s/local/lib/python2.5/site-packages/sage/interfaces/magma.py", line 264, in eval
raise RuntimeError, "Error evaluation Magma code.\nIN:%s\nOUT:%s"%(x, ans)
RuntimeError: Error evaluation Magma code.
IN:n := 100;
a := RMatrixSpace(RationalFiel...
}}}rn UÃWorksheet 'Quick Demo' (2007-08-17 at 07:59)
{{{id=26|
%magma
n := 100;
a := RMatrixSpace(RationalField(), n,n+1)![Random(-9,9) : i in [1..n*(n+1)]];
time e := EchelonForm(a);
///
Time: 0.140
}}}ro T¤ Worksheet 'Quick Demo' (2007-08-17 at 07:59)
{{{id=15|
# In SAGE
n = 100
a = random_matrix(QQ,n, n+1, x=-9, y=9)
time a.echelonize()
///
Traceback (most recent call last): time a.echelonize()
File "/home/was/s/local/lib/python2.5/site-packages/sage/matrix/constructor.py", line 424, in random_matrix
A.randomize(density=density, *args, **kwds)
TypeError: 'y' is an invalid keyword argument for this function
}}}rp ULWorksheet 'Quick Demo' (2007-08-17 at 07:59)
{{{id=28|
QQ.random_element
}}}rq ULWorksheet 'Quick Demo' (2007-08-17 at 07:59)
{{{id=28|
QQ.random_element
}}}rr U»Worksheet 'Quick Demo' (2007-08-17 at 08:00)
{{{id=15|
# In SAGE
n = 100
a = random_matrix(QQ,n, n+1, num_bound=10, den_bound=1)
time a.echelonize()
///
Time: CPU 0.09 s, Wall: 0.10 s
}}}rs U»Worksheet 'Quick Demo' (2007-08-17 at 08:00)
{{{id=15|
# In SAGE
n = 200
a = random_matrix(QQ,n, n+1, num_bound=10, den_bound=1)
time a.echelonize()
///
Time: CPU 0.31 s, Wall: 0.32 s
}}}rt UÃWorksheet 'Quick Demo' (2007-08-17 at 08:00)
{{{id=26|
%magma
n := 200;
a := RMatrixSpace(RationalField(), n,n+1)![Random(-9,9) : i in [1..n*(n+1)]];
time e := EchelonForm(a);
///
Time: 3.330
}}}ru U½Worksheet 'Quick Demo' (2007-08-17 at 08:00)
{{{id=15|
# In SAGE
n = 200
a = random_matrix(QQ,n, n+1, num_bound=2^64, den_bound=1)
time a.echelonize()
///
Time: CPU 1.84 s, Wall: 2.86 s
}}}rv UÄWorksheet 'Quick Demo' (2007-08-17 at 08:00)
{{{id=26|
%magma
n := 100;
a := RMatrixSpace(RationalField(), n,n+1)![Random(1,2^64): i in [1..n*(n+1)]];
time e := EchelonForm(a);
///
Time: 6.390
}}}rw U½Worksheet 'Quick Demo' (2007-08-17 at 08:00)
{{{id=15|
# In SAGE
n = 100
a = random_matrix(QQ,n, n+1, num_bound=2^64, den_bound=1)
time a.echelonize()
///
Time: CPU 0.31 s, Wall: 0.41 s
}}}rx U½Worksheet 'Quick Demo' (2007-08-17 at 08:01)
{{{id=27|
# In SAGE
n = 200
a = random_matrix(QQ,n, n+1, num_bound=2^64, den_bound=1)
time a.echelonize()
///
Time: CPU 1.96 s, Wall: 3.22 s
}}}ry UÆWorksheet 'Quick Demo' (2007-08-17 at 08:05)
{{{id=29|
%magma
n := 200;
a := RMatrixSpace(RationalField(), n,n+1)![Random(1,2^64): i in [1..n*(n+1)]];
time e := EchelonForm(a);
///
Time: 159.920
}}}rz U^Worksheet 'Quick Demo' (2007-08-17 at 08:12)
{{{id=30|
159.920 / 3.22
///
49.6645962732919
}}}r{ eubsUaddressr| U localhostr} U_Notebook__dirr~ U*/home/was/talks/20070817-ccr/sage_notebookr ub.