24.sagews

# sage eh Python -- podemos definir uma funcao, por exemplo:
def hello(n):
    print 'Hello world!\n' * n
hello(2)

Hello world! Hello world!

# (eh *quase* Python, na verdade...)
print 2**3, 2^3, eval("2^3")

8 8 1

# vem com varios modulos prontos para serem importados
import numpy
import scipy
import pylab

x = numpy.linspace(0, 10*3.14, 1000)
y = numpy.sin(x)
pylab.close()
pylab.plot(x, y)
pylab.show()
pylab.savefig('sin.png')

# e tem autocomplete/ajuda
#pylab.<tab>

# plots 2D usando comandos nativos do Sage
f = lambda x,y: cos(x*y)
C = contour_plot(f, (-4, 4), (-4, 4))
show(C)

def slow_logistic(n,a,lamb = 3.82):
    """
    A slow logistic map.
    """
    q = a
    for i in range(n):
        q = lamb*q*(1-q)
    return q
 
time a = slow_logistic(10^6,.5)

Time: CPU 4.91 s, Wall: 4.93 s

%cython 
def cython_logistic(int n, float a, float lamb = 3.82):
    cdef float q
    q = a
    for i in range(n):
        q = lamb*q*(1-q)
    return q

time a = cython_logistic(10^6,.5)

Traceback (most recent call last): cdef float q File "/home/server2/sage/local/lib/python2.5/site-packages/sage/server/support.py", line 362, in cython_import_all create_local_c_file=create_local_c_file) File "/home/server2/sage/local/lib/python2.5/site-packages/sage/server/support.py", line 343, in cython_import create_local_c_file=create_local_c_file) File "/home/server2/sage/local/lib/python2.5/site-packages/sage/misc/cython.py", line 344, in cython raise RuntimeError, "Error converting %s to C:\n%s\n%s"%(filename, log, err) RuntimeError: Error converting /home/server2/sage_notebook/worksheets/roberto/0/code/sage39.spyx to C: Error converting Pyrex file to C: ------------------------------------------------------------ ... q = a for i in range(n): q = lamb*q*(1-q) return q time a = cython_logistic(10^6,.5) ^ ------------------------------------------------------------ /home/sage13/.sage/temp/sage/22788/spyx/_home_server2_sage_notebook_worksheets_roberto_0_code_sage39_spyx/_home_server2_sage_notebook_worksheets_roberto_0_code_sage39_spyx_0.pyx:13:5: Syntax error in simple statement list

# resolvendo equacoes diferenciais via Maxima
t = var('t')    # define a variable t
x = function('x',t)   # define x to be a function of that variable
DE = lambda y: diff(y,t) + y - 1
resposta = desolve(DE(x(t)), [x,t])
print resposta

%e^-t*(%e^t+%c)

# plots parametricos interativos
u, v = var('u,v')
fx = u*v
fy = u
fz = v^2
P = parametric_plot3d([fx, fy, fz], (u, -1, 1), (v, -1, 1), frame=False, color="yellow")
show(P)

@interact
def rwalk3d(n=(50,1000), frame=True):
    pnt = [0,0,0]
    v = [copy(pnt)]
    for i in range(int(n)):
        pnt[0] += random()-0.5
        pnt[1] += random()-0.5
        pnt[2] += random()-0.5
        v.append(copy(pnt))
    show(line3d(v,color='black'),aspect_ratio=[1,1,1],frame=frame)

n  frame  [removed] [removed] [removed] [removed]

CPU time: 0.01 s, Wall time: 0.01 s

var('x')
x0  = 0
f   = sin(x)*e^(-x)
p   = plot(f,-1,5, thickness=2)
dot = point((x0,f(x0)),pointsize=80,rgbcolor=(1,0,0))
@interact
def _(order=(1..12)):
  ft = f.taylor(x,x0,order)
  pt = plot(ft,-1, 5, color='green', thickness=2)
  html('$f(x)\;=\;%s$'%latex(f))
  html('$\hat{f}(x;%s)\;=\;%s+\mathcal{O}(x^{%s})$'%(x0,latex(ft),order+1))
  show(dot + p + pt, ymin = -.5, ymax = 1)

order  [removed] [removed] [removed] [removed]

CPU time: 0.12 s, Wall time: 0.34 s