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Examples of using latex in cocalc

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## -*- encoding: utf-8 -*-

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## This file (sagetex.sagetex.sage) was *autogenerated* from sagetex.tex with sagetex.sty version 2015/08/26 v3.0-92d9f7a.

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import sagetex

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_st_ = sagetex.SageTeXProcessor('sagetex', version='2015/08/26 v3.0-92d9f7a', version_check=True)

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try:

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 _st_.current_tex_line = 35

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 _st_.inline(0, latex(2+2))

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except:

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 _st_.goboom(35)

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try:

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 _st_.current_tex_line = 36

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 _st_.inline(1, latex(mod(2018, 100)))

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except:

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 _st_.goboom(36)

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try:

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 _st_.current_tex_line = 38

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 _st_.inline(2, latex(Integer(mod(2018, 100))^21))

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except:

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 _st_.goboom(38)

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try:

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 _st_.current_tex_line = 39

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 _st_.inline(3, latex(2018%42))

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except:

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 _st_.goboom(39)

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_st_.current_tex_line = 42

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_st_.blockbegin()

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try:

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  1+1

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  var('a,b,c')

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  eqn = [a+b*c==1, b-a*c==0, a+b==5]

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  s = solve(eqn, a,b,c)

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except:

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 _st_.goboom(47)

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_st_.blockend()

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try:

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 _st_.current_tex_line = 49

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 _st_.inline(4, latex(eqn))

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except:

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 _st_.goboom(49)

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try:

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 _st_.current_tex_line = 51

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 _st_.inline(5, latex(s[0]))

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except:

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 _st_.goboom(51)

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try:

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 _st_.current_tex_line = 54

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 _st_.inline(6, latex(s[1]))

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except:

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 _st_.goboom(54)

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_st_.current_tex_line = 58

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_st_.blockbegin()

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try:

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 E = EllipticCurve("37a")

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except:

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 _st_.goboom(60)

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_st_.blockend()

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try:

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 _st_.current_tex_line = 63

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 _st_.inline(7, latex(E))

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except:

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 _st_.goboom(63)

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try:

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 _st_.current_tex_line = 64

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 _st_.inline(8, latex(E.discriminant()))

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except:

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 _st_.goboom(64)

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_st_.current_tex_line = 68

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_st_.blockbegin()

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try:

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 try:

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     E = load('E2')

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 except IOError:

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     E = EllipticCurve([1,2,3,4,5])

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     E.anlist(100000)

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     E.save('E2')

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except:

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 _st_.goboom(75)

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_st_.blockend()

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try:

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 _st_.current_tex_line = 77

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 _st_.inline(9, latex(E))

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except:

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 _st_.goboom(77)

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try:

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 _st_.current_tex_line = 78

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 _st_.inline(10, latex(E.anlist(100000)[9999]))

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except:

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 _st_.goboom(78)

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_st_.current_tex_line = 81

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_st_.blockbegin()

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try:

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   e = 2

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   e = 3*e + 1

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except:

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 _st_.goboom(84)

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_st_.blockend()

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try:

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 _st_.current_tex_line = 85

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 _st_.inline(11, latex(e))

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except:

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 _st_.goboom(85)

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_st_.current_tex_line = 87

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_st_.blockbegin()

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try:

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   var('x')

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   f(x) = log(sin(x)/x)

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except:

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 _st_.goboom(90)

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_st_.blockend()

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try:

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 _st_.current_tex_line = 91

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 _st_.inline(12, latex( f.taylor(x, 0, 10) ))

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except:

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 _st_.goboom(91)

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try:

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 _st_.current_tex_line = 97

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 _st_.plot(0, format='notprovided', _p_=E.plot(-3,3))

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except:

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 _st_.goboom(97)

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_st_.current_tex_line = 99

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_st_.blockbegin()

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try:

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   # the var line is unecessary unless you've defined x to be something

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   # other than a symbolic variable

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   var('x')

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   f(x) = -x^3+3*x^2+7*x-4

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except:

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 _st_.goboom(104)

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_st_.blockend()

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_st_.current_tex_line = 107

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_st_.blockbegin()

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try:

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   p = plot(f, x, -5, 5)

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except:

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 _st_.goboom(109)

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_st_.blockend()

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try:

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 _st_.current_tex_line = 113

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 _st_.plot(1, format='notprovided', _p_=p)

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except:

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 _st_.goboom(113)

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try:

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 _st_.current_tex_line = 118

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 _st_.plot(2, format='notprovided', _p_=p, axes=False)

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except:

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 _st_.goboom(118)

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_st_.current_tex_line = 122

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_st_.blockbegin()

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try:

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 f = maxima('sin(x)^2*exp(x)')

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 g = f.integrate('x')

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except:

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 _st_.goboom(125)

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_st_.blockend()

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_st_.current_tex_line = 127

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_st_.blockbegin()

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try:

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   # g is a Maxima thingy, it needs to get converted into a Sage object

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   plot1 = plot(g.sage(),x,-1,2*pi)

160
except:

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 _st_.goboom(130)

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_st_.blockend()

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try:

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 _st_.current_tex_line = 136

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 _st_.plot(3, format='png', _p_=plot1)

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except:

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 _st_.goboom(136)

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try:

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 _st_.current_tex_line = 146

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 _st_.plot(4, format='notprovided', _p_=plot1 + plot(f.sage(),x,-1,2*pi,rgbcolor=hue(0.4)), figsize=[1,2])

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except:

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 _st_.goboom(146)

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_st_.current_tex_line = 151

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_st_.blockbegin()

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try:

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   p = plot(x, 0, 1) + circle((0,0), 1)

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   p.set_aspect_ratio(1)

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except:

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 _st_.goboom(154)

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_st_.blockend()

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try:

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 _st_.current_tex_line = 158

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 _st_.plot(5, format='notprovided', _p_=p)

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except:

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 _st_.goboom(158)

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_st_.current_tex_line = 161

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_st_.blockbegin()

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try:

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  s     = 7

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  s2    = 2^s

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  P.<x> = GF(2)[]

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  M     = matrix(parent(x),s2)

193
  for i in range(s2):

194
     p  = (1+x)^i

195
     pc = p.coefficients(sparse=False)

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     a  = pc.count(1)

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     for j in range(a):

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         idx        = pc.index(1)

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         M[i,idx+j] = pc.pop(idx)

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  matrixprogram = matrix_plot(M,cmap='Greys')

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except:

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 _st_.goboom(175)

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_st_.blockend()

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try:

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 _st_.current_tex_line = 178

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 _st_.plot(6, format='notprovided', _p_=matrixprogram)

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except:

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 _st_.goboom(178)

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try:

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 _st_.current_tex_line = 181

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 _st_.inline(13, latex(var('x')))

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except:

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 _st_.goboom(181)

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try:

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 _st_.current_tex_line = 253

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 _st_.inline(14, latex(var('x')))

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except:

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 _st_.goboom(253)

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_st_.current_tex_line = 337

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_st_.blockbegin()

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try:

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   x, y = var('x y')

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except:

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 _st_.goboom(339)

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_st_.blockend()

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try:

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 _st_.current_tex_line = 345

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 _st_.plot(7, format='notprovided', _p_=plot3d(sin(pi*(x^2+y^2))/2,(x,-1,1),(y,-1,1)))

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except:

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 _st_.goboom(345)

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_st_.current_tex_line = 349

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_st_.blockbegin()

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try:

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   G = graphs.CubeGraph(5)

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except:

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 _st_.goboom(351)

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_st_.blockend()

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try:

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 _st_.current_tex_line = 355

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 _st_.plot(8, format='png', _p_=G.plot3d())

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except:

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 _st_.goboom(355)

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print 'SageTeX paused on sagetex.tex line 365'

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"""

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try:

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 _st_.current_tex_line = 367

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 _st_.inline(15, latex(factor(2^325 + 1)))

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except:

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 _st_.goboom(367)

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_st_.current_tex_line = 370

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_st_.blockbegin()

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try:

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   import time

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   time.sleep(15)

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except:

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 _st_.goboom(373)

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_st_.blockend()

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try:

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 _st_.current_tex_line = 375

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 _st_.plot(9, format='notprovided', _p_=plot(2*sin(x^2) + x^2, (x, 0, 5)))

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except:

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 _st_.goboom(375)

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"""

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print 'SageTeX unpaused on sagetex.tex line 377'

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_st_.current_tex_line = 389

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_st_.blockbegin()

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try:

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 def pascals_triangle(n):

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     # start of the table

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     s  = [r"\begin{tabular}{cc|" + "r" * (n+1) + "}"]

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     s.append(r"  & & $k$: & \\")

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     # second row, with k values:

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     s.append(r"  & ")

275
     for k in [0..n]:

276
         s.append("& {0} ".format(k))

277
     s.append(r"\\")

278
     # the n = 0 row:

279
     s.append(r"\hline" + "\n" + r"$n$: & 0 & 1 & \\")

280
     # now the rest of the rows

281
     for r in [1..n]:

282
         s.append(" & {0} ".format(r))

283
         for k in [0..r]:

284
             s.append("& {0} ".format(binomial(r, k)))

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         s.append(r"\\")

286
     # add the last line and return

287
     s.append(r"\end{tabular}")

288
     return ''.join(s)

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290
 # how big should the table be?

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 n = 8

292
except:

293
 _st_.goboom(413)

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_st_.blockend()

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try:

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 _st_.current_tex_line = 420

297
 _st_.inline(16, pascals_triangle(n))

298
except:

299
 _st_.goboom(420)

300
try:

301
 _st_.current_tex_line = 426

302
 _st_.doctest(17, r"""

303
  sage: 2+2

304
  4

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  sage: print 'middle'

306
  middle

307
  sage: factor(x^2 + 2*x + 1)

308
  (x + 1)^2

309
""", globals(), locals(), False)

310
except:

311
 _st_.goboom(433)

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try:

313
 _st_.current_tex_line = 448

314
 _st_.doctest(18, r"""

315
  sage: print 'middle'

316
  middle

317
""", globals(), locals(), True)

318
except:

319
 _st_.goboom(451)

320
try:

321
 _st_.current_tex_line = 455

322
 _st_.doctest(19, r"""

323
  sage: is_prime(57)

324
  toothpaste

325
""", globals(), locals(), True)

326
except:

327
 _st_.goboom(458)

328
try:

329
 _st_.current_tex_line = 463

330
 _st_.doctest(20, r"""

331
  sage: gcd([5656565656,

332
  ....:      4747474747,

333
  ....:      123456789])

334
  1

335
  sage: mystr = '''my

336
  ....: string

337
  ....: has

338
  ....: several

339
  ....: lines.'''

340
  sage: len(mystr)

341
  28

342
  sage: def f(a):

343
  ....:     '''This function is really quite nice,

344
  ....:     although perhaps not very useful.'''

345
  ....:     print "f called with a = ", a

346
  ....:     y = integrate(SR(cyclotomic_polynomial(10)) + a, x)

347
  ....:     return y + 1

348
  sage: f(x)

349
  f called with a =  x

350
  1/5*x^5 - 1/4*x^4 + 1/3*x^3 + x + 1

351
""", globals(), locals(), False)

352
except:

353
 _st_.goboom(484)

354
try:

355
 _st_.current_tex_line = 512

356
 _st_.doctest(21, r"""

357
  sage: 1; 2; a=4; 3; a

358
  1

359
  2

360
  3

361
  4

362
""", globals(), locals(), False)

363
except:

364
 _st_.goboom(518)

365
try:

366
 _st_.current_tex_line = 519

367
 _st_.inline(22, latex(a))

368
except:

369
 _st_.goboom(519)

370
try:

371
 _st_.current_tex_line = 521

372
 _st_.doctest(23, r"""

373
  sage: f(a)

374
  f called with a =  4

375
  1/5*x^5 - 1/4*x^4 + 1/3*x^3 - 1/2*x^2 + 5*x + 1

376
""", globals(), locals(), False)

377
except:

378
 _st_.goboom(525)

379
try:

380
 _st_.current_tex_line = 622

381
 _st_.commandline(0, r"""

382
  sage: 1+1

383
  sage: is_prime(57)

384
  sage: if is_prime(57):

385
  ....:     print 'prime'

386
  ....: else:

387
  ....:     print 'composite'

388
""", globals(), locals(), True)

389
except:

390
 _st_.goboom(629)

391
try:

392
 _st_.current_tex_line = 639

393
 _st_.commandline(1, r"""

394
  sage: x = 2010; len(x.divisors())

395
  sage: print 'Hola, mundo!'

396
""", globals(), locals(), True)

397
except:

398
 _st_.goboom(642)

399
try:

400
 _st_.current_tex_line = 651

401
 _st_.commandline(2, r"""

402
  sage: l = matrix([[1,0,0],[3/5,1,0],[-2/5,-2,1]])

403
  sage: d = diagonal_matrix([15, -1, 4]) #@\label{diagonal}

404
  sage: u = matrix([[1,0,1/3],[0,1,2],[0,0,1]]) #@\label{anotherlabel} \# foo

405
  sage: l*d*u   # this is a comment

406
""", globals(), locals(), True)

407
except:

408
 _st_.goboom(656)

409
try:

410
 _st_.current_tex_line = 667

411
 _st_.commandline(3, r"""

412
  sage: l*d*u

413
  sage: x = var('x')

414
  sage: (1-cos(x)^2).trig_simplify()

415
""", globals(), locals(), False)

416
except:

417
 _st_.goboom(671)

418
try:

419
 _st_.current_tex_line = 683

420
 _st_.commandline(4, r"""

421
  sage: pi.n(100)

422
""", globals(), locals(), True)

423
except:

424
 _st_.goboom(685)

425
try:

426
 _st_.current_tex_line = 693

427
 _st_.commandline(5, r"""

428
  sage: plot(sin(x), (x, 0, 2*pi))

429
""", globals(), locals(), True)

430
except:

431
 _st_.goboom(695)

432
try:

433
 _st_.current_tex_line = 709

434
 _st_.commandline(6, r"""

435
  sage: factor(x^2 + 2*x + 1)

436
  (x + 999)^2

437
""", globals(), locals(), True)

438
except:

439
 _st_.goboom(712)

440
_st_.endofdoc()

441


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