from sage.all_cmdline import *
_sage_const_3 = Integer(3); _sage_const_2 = Integer(2); _sage_const_1 = Integer(1); _sage_const_0 = Integer(0); _sage_const_7 = Integer(7); _sage_const_6 = Integer(6); _sage_const_5 = Integer(5); _sage_const_4 = Integer(4); _sage_const_22 = Integer(22); _sage_const_20 = Integer(20); _sage_const_67 = Integer(67); _sage_const_18 = Integer(18); _sage_const_44 = Integer(44); _sage_const_2017 = Integer(2017); _sage_const_41 = Integer(41); _sage_const_38 = Integer(38); _sage_const_10 = Integer(10); _sage_const_57 = Integer(57); _sage_const_30 = Integer(30); _sage_const_55 = Integer(55); _sage_const_32 = Integer(32); _sage_const_52 = Integer(52); _sage_const_37 = Integer(37); _sage_const_74 = Integer(74); _sage_const_p5 = RealNumber('.5'); _sage_const_4p5 = RealNumber('4.5')
import sagetex
_st_ = sagetex.SageTeXProcessor('SageTex', version='2015/08/26 v3.0-92d9f7a', version_check=True)
_st_.current_tex_line = _sage_const_18
_st_.blockbegin()
try:
n=_sage_const_2017
except:
_st_.goboom(_sage_const_20 )
_st_.blockend()
try:
_st_.current_tex_line = _sage_const_22
_st_.inline(_sage_const_0 , latex(n))
except:
_st_.goboom(_sage_const_22 )
try:
_st_.current_tex_line = _sage_const_22
_st_.inline(_sage_const_1 , latex(n))
except:
_st_.goboom(_sage_const_22 )
try:
_st_.current_tex_line = _sage_const_22
_st_.inline(_sage_const_2 , latex(number_of_partitions(n)))
except:
_st_.goboom(_sage_const_22 )
try:
_st_.current_tex_line = _sage_const_22
_st_.inline(_sage_const_3 , latex(factor(number_of_partitions(n))))
except:
_st_.goboom(_sage_const_22 )
_st_.current_tex_line = _sage_const_30
_st_.blockbegin()
try:
__tmp__=var("x"); f = symbolic_expression(exp(x) * sin(_sage_const_2 *x)).function(x)
except:
_st_.goboom(_sage_const_32 )
_st_.blockend()
try:
_st_.current_tex_line = _sage_const_37
_st_.inline(_sage_const_4 , latex(f(x)))
except:
_st_.goboom(_sage_const_37 )
try:
_st_.current_tex_line = _sage_const_38
_st_.inline(_sage_const_5 , latex(diff(f, x, _sage_const_2 )(x)))
except:
_st_.goboom(_sage_const_38 )
try:
_st_.current_tex_line = _sage_const_41
_st_.inline(_sage_const_6 , latex(f(x)))
except:
_st_.goboom(_sage_const_41 )
try:
_st_.current_tex_line = _sage_const_44
_st_.plot(_sage_const_0 , format='notprovided', _p_=plot(f, -pi/_sage_const_2 , pi/_sage_const_2 , figsize = _sage_const_4 , axes_labels=['$x$','$y$'], axes_labels_size = _sage_const_1 , tick_formatter = [pi,_sage_const_2 ]))
except:
_st_.goboom(_sage_const_44 )
_st_.current_tex_line = _sage_const_52
_st_.blockbegin()
try:
y=function('y')(x)
eq = diff(y,x)==-tan(x)/y
except:
_st_.goboom(_sage_const_55 )
_st_.blockend()
try:
_st_.current_tex_line = _sage_const_57
_st_.inline(_sage_const_7 , latex(desolve(eq,y,show_method=True)))
except:
_st_.goboom(_sage_const_57 )
_st_.current_tex_line = _sage_const_67
_st_.blockbegin()
try:
var('c,x,y')
F1=[plot(c*sin(x),(x,-_sage_const_2 *pi,_sage_const_2 *pi),color='darkgreen', aspect_ratio=_sage_const_1 ) for c in sxrange(-_sage_const_4 ,_sage_const_4p5 ,_sage_const_p5 )]
F2=[implicit_plot(y**_sage_const_2 +_sage_const_2 *log(abs(sec(x)))-c,(x,-_sage_const_2 *pi,_sage_const_2 *pi),(y,-_sage_const_5 ,_sage_const_5 ),color='red',aspect_ratio=_sage_const_1 ) for c in sxrange(-_sage_const_10 ,_sage_const_10 ,_sage_const_1 )]
Fig = sum(F2)+sum(F1)
Fig.save("Figure.png")
except:
_st_.goboom(_sage_const_74 )
_st_.blockend()
_st_.endofdoc()