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Kernel: SageMath 7.6

Un premier contact avec SageMath

On essaye les maths avec $\pi$ , ...

In [1]:

i*i

Out[1]:

-1

e^(i*pi)

In [2]:

e^(i*pi)

Out[2]:

-1

In [3]:

preparse("e^(i*pi)")

Out[3]:

'e**(i*pi)'

In [4]:

%display latex

In [5]:

e^(i*pi)

Out[5]:

In [6]:

n(pi)

Out[6]:

In [7]:

n(e)

Out[7]:

In [0]:

numerical_approx?

In [8]:

print(n(pi, digits=1000))

Out[8]:

3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609433057270365759591953092186117381932611793105118548074462379962749567351885752724891227938183011949129833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132000568127145263560827785771342757789609173637178721468440901224953430146549585371050792279689258923542019956112129021960864034418159813629774771309960518707211349999998372978049951059731732816096318595024459455346908302642522308253344685035261931188171010003137838752886587533208381420617177669147303598253490428755468731159562863882353787593751957781857780532171226806613001927876611195909216420199

In [9]:

a=e^(pi*sqrt(163))
a
n(a, digits=50)

Out[9]:

In [10]:

f(x)=sin(x^2)
f

Out[10]:

In [11]:

f(2)

Out[11]:

In [12]:

n(f(2))

Out[12]:

In [13]:

g=diff(f(x), x)

In [14]:

u=var('u')

In [15]:

g(u)

Out[15]:

/projects/sage/sage-7.6/local/lib/python2.7/site-packages/IPython/core/interactiveshell.py:2881: DeprecationWarning: Substitution using function-call syntax and unnamed arguments is deprecated and will be removed from a future release of Sage; you can use named arguments instead, like EXPR(x=..., y=...)
See http://trac.sagemath.org/5930 for details.
  exec(code_obj, self.user_global_ns, self.user_ns)

In [16]:

diff(f(x), x, 4)

Out[16]:

In [17]:

n(integrate(f(x), (x, 0, sqrt(pi))), digits=100)

Out[17]:

plot(f(x))

In [18]:

g1=plot(f(x), (x, 0, 4), color='red', thickness=1, axes_labels=[r"$x$", r"$y$"])

In [19]:

g2=plot(f(x)^2, (x, 0, 4), color='blue', thickness=1, axes_labels=[r"$x$", r"$y$"])

In [20]:

g1+g2

Out[20]:

In [21]:

show(g1+g2, gridlines=True, aspect_ratio=1, title='A beatiful graphic')

Out[21]:

In [22]:

(g1+g2).save("plot_first_graphic.pdf")

In [23]:

g=Graphics()
for i in range(10):
    g+=plot(chebyshev_T(i,x), (x,-1,1), color=hue(i/10),
           legend_label=r"$T_{}(x)$".format(i))
show(g, axes_labels=[r"$x$", r"$y$"], legend_loc='upper right')

Out[23]:

In [24]:

restore('i')

In [25]:

def f1(x):
    if x<2:
        return sin(x)
    return cos(x)

In [26]:

f1(3)

Out[26]:

In [27]:

f1(1)

Out[27]:

In [28]:

plot(f1, (0,4))

Out[28]:

In [56]:

trace("f1(x)")

In [31]:

fi=open("data.d", 'r')
fi.readline()
data=[]
for line in fi:
    xs, ys = line.split(' ')
    data.append((float(xs), float(ys)))
list
fi.close()
data

Out[31]:

In [32]:

list_plot(data)

Out[32]:

In [0]:

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