Sympy how to define variable for functions, integrals and polynomials
Sympy how to define variable for functions, integrals and polynomials
Define variables before :-)
from sympy import *
x,y,z,t,a,b,c,n,m,p,k = symbols('x y z t a b c n m p k')
Check if variable is well defined
sin(x)*exp(x)
$\displaystyle e^{x} \sin{\left(x \right)}$
v is not defined
sin(v)*exp(v)
Since v is not defined, we got an error:
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-3-e79911d4ea2b> in <module>
----> 1 sin(v)*exp(v)
NameError: name 'v' is not defined
Define polynomial use ** and not symbol ^
x**4-3*x**2 +15*x -1
$\displaystyle x^{4} - 3 x^{2} + 15 x - 1$
x^^2
Oups … You got an error …
File "<ipython-input-5-5d18a81177b2>", line 1
x^^2
^
SyntaxError: invalid syntax
Remember that ^ is a logic binary operator:
alpha,beta=1,10;
print(bin(alpha),bin(beta))
print(alpha^beta == (0b1)^(0b1010));
print(alpha^beta, bin(alpha^beta))
0b1 0b1010 True 11 0b1011
First way to define an function
def f(x):
return x**2 + 1
Check f(3) value:
f(3)
10
Second way to define a function
g = x**2+1
Check g(3) value:
g.subs(x,3)
10
Calculate an integral
integrate(x**2 + x + 1, x)
$\displaystyle \frac{x^{3}}{3} + \frac{x^{2}}{2} + x$
integrate(t**2 * exp(t) * cos(t))
$\displaystyle \frac{t^{2} e^{t} \sin{\left(t \right)}}{2} + \frac{t^{2} e^{t} \cos{\left(t \right)}}{2} - t e^{t} \sin{\left(t \right)} + \frac{e^{t} \sin{\left(t \right)}}{2} - \frac{e^{t} \cos{\left(t \right)}}{2}$
integrate(f(x))
$\displaystyle \frac{x^{3}}{3} + x$
integrate(g(t))
Remember how g was defined !!!!
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
<ipython-input-14-3849471c42ec> in <module>
----> 1 integrate(g(t))
TypeError: 'Add' object is not callable
Here is the good way to integrate it:
integrate(g)
$\displaystyle \frac{x^{3}}{3} + x$
That’s all folks !!! Below , jupyter’s notebook.
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