Untitled
system:sage

{{{id=0|
3 + 5
///
8
}}}

{{{id=1|
57.1 ^ 100
///
4.60904368661396e175
}}}

{{{id=2|
matrix([[1,2], [3,4]])^(-1)
///
[  -2    1]
[ 3/2 -1/2]
}}}

{{{id=3|
integrate(sqrt(x)*sqrt(1+x), x)
///
(-log(sqrt(x + 1)/sqrt(x) + 1))/8 + log(sqrt(x + 1)/sqrt(x) - 1)/8 + ((x + 1)^(3/2)/x^(3/2) + sqrt(x + 1)/sqrt(x))/(4*(x + 1)^2/x^2 - (8*(x + 1)/x) + 4)
}}}

{{{id=4|
var('a x')
S = solve(x^2 + x == a, x); S
///
[x == (-sqrt(4*a + 1) - 1)/2, x == (sqrt(4*a + 1) - 1)/2]
}}}

{{{id=18|
S[0].rhs()
///
(-sqrt(4*a + 1) - 1)/2
}}}

{{{id=19|
S[1].rhs()
///
(sqrt(4*a + 1) - 1)/2
}}}

{{{id=17|
plot(lambda x: sin(x) + sin(1.6*x), 0, 40).save('sin_plot.eps')
}}}

{{{id=5|
show(plot(sin(x) + sin(1.6*x), 0, 40))
}}}

{{{id=6|
m = random_matrix(RDF,500)
}}}

{{{id=7|
time e, v = m.eigen()
///
CPU time: 2.32 s,  Wall time: 2.63 s
}}}

{{{id=8|
w = [(i, abs(e[i])) for i in range(len(e))]
show(points(w))
}}}

{{{id=20|
points(w).save('eigen_plot.eps')
}}}

{{{id=9|
factorial(100)
///
93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000
}}}

{{{id=21|
time n = factorial(1000000)
///
CPU time: 2.33 s,  Wall time: 2.56 s
}}}

{{{id=10|
N(pi, digits=100)
///
3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798
}}}

{{{id=11|
R.<x,y> = QQ[]
F = factor(x^99 + y^99)
F
///
(x + y) * (x^2 - x*y + y^2) * (x^6 - x^3*y^3 + y^6) * (x^10 - x^9*y + x^8*y^2 - x^7*y^3 + x^6*y^4 - x^5*y^5 + x^4*y^6 - x^3*y^7 + x^2*y^8 - x*y^9 + y^10) * (x^20 + x^19*y - x^17*y^3 - x^16*y^4 + x^14*y^6 + x^13*y^7 - x^11*y^9 - x^10*y^10 - x^9*y^11 + x^7*y^13 + x^6*y^14 - x^4*y^16 - x^3*y^17 + x*y^19 + y^20) * (x^60 + x^57*y^3 - x^51*y^9 - x^48*y^12 + x^42*y^18 + x^39*y^21 - x^33*y^27 - x^30*y^30 - x^27*y^33 + x^21*y^39 + x^18*y^42 - x^12*y^48 - x^9*y^51 + x^3*y^57 + y^60)
}}}

{{{id=13|
F.expand()
///
x^99 + y^99
}}}

{{{id=14|
time z = number_of_partitions(10^8, algorithm='pari')
///
CPU time: 88.90 s,  Wall time: 89.74 s
}}}

{{{id=15|
str(z)[:40]
///
'1760517045946249141360373894679135204009'
}}}

{{{id=16|

}}}