142-6-6.sagews

6

x,y=var('x,y')
f=sin(x)*sin(y)
a=1/integral(integral(f,x,0,pi),y,0,pi)
contour_plot(f,(0,pi),(0,pi))
latex??

Syntax Error: $a=$

a

1/4

2

mu=3
f1=mu*exp(-mu*x)
f2=1-exp(-mu*x)
p=f1.plot(0,2,rgbcolor='#003153',thickness=6)
p+=f2.plot(0,2,rgbcolor='#4bb530',thickness=6)
p

M=integral(x*f1,x,0,oo);M

1/3

D=integral((x-M)^2*f1,x,0,infinity);D

1/9

sigM=sqrt(D);sigM

1/3

Me=solve(f2==0.5,x);Me

[x == log(sqrt(3)*I/2^(2/3) - 1/2^(2/3)), x == log(-sqrt(3)*I/2^(2/3) - 1/2^(2/3)), x == log(2)/3]

Mo=f1.find_maximum_on_interval(0,oo);Mo

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "/home/sage/sagenb/sage_notebook/worksheets/LENIN/1/code/4.py", line 7, in <module> exec compile(ur'Mo=f1.find_maximum_on_interval(_sage_const_0 ,oo);Mo' + '\n', '', 'single') File "/home/sage/sage/local/lib/python2.5/site-packages/SQLAlchemy-0.4.6-py2.5.egg/", line 1, in <module> File "/home/sage/sage/local/lib/python2.5/site-packages/sage/calculus/calculus.py", line 3315, in find_maximum_on_interval minval, x = (-self).find_minimum_on_interval(a, b, var=var, tol=tol, maxfun=maxfun) File "/home/sage/sage/local/lib/python2.5/site-packages/sage/calculus/calculus.py", line 3355, in find_minimum_on_interval a = float(a); b = float(b) TypeError: float() argument must be a string or a number

is

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "/home/sage/sagenb/sage_notebook/worksheets/LENIN/1/code/3.py", line 6, in <module> exec compile(ur'oo.is_unit()' + '\n', '', 'single') File "/home/sage/sage/local/lib/python2.5/site-packages/SQLAlchemy-0.4.6-py2.5.egg/", line 1, in <module> File "element.pyx", line 1246, in sage.structure.element.RingElement.is_unit (sage/structure/element.c:9765) NotImplementedError

%latex
        The equation $y^2 = x^3 + x$ defines an elliptic curve.
        We have $2006 = \sage{factor(2006)}$.

Syntax Error: The equation $y^2 = x^3 + x$ defines an elliptic curve.