SymPy 연산,함수,그래프

SymPy 연습하자.¶

따라하기

In [22]:

from sympy import *
import math
from numpy import linspace
import matplotlib.pyplot as pl 

In [3]:

x = symbols('x')

$f(x) = \frac{x^2 +1}{x-1}$

In [5]:

f = (x**2 +1)/(x-1)

In [6]:

f.subs(x,1)

Out[6]:

$\displaystyle \tilde{\infty}$

In [7]:

f.subs(x,2)

Out[7]:

$\displaystyle 5$

Basic Operations¶

In [8]:

sqrt(2)

Out[8]:

$\displaystyle \sqrt{2}$

In [10]:

N(sqrt(2))

Out[10]:

$\displaystyle 1.4142135623731$

In [12]:

math.sqrt(2)

Out[12]:

1.4142135623730951

In [13]:

N(sqrt(2)+1)

Out[13]:

$\displaystyle 2.41421356237309$

In [14]:

2**3

Out[14]:

8

In [15]:

N(2**3)

Out[15]:

$\displaystyle 8.0$

Fucntions & Plotting¶

In [30]:

f = sin(x)
g = cos(x)

In [31]:

fx = lambdify(x,f,modules=['numpy'])
gx = lambdify(x,g,modules=['numpy'])

In [36]:

xVals = linspace(-math.pi,math.pi,100)

In [21]:

import numpy

In [37]:

pl.plot(xVals,fx(xVals),label = 'f(x)=sin(x)')
pl.plot(xVals,gx(xVals),label = 'g(x)=cos(x)')
pl.xlabel('x')
pl.ylabel('f(x) = sin(x), g(x) = cos(x)')
pl.title('f(x) = sin(x), g(x) = cos(x)')
pl.legend()
pl.show()

In [38]:

f = asin(x)
g = acos(x)

In [39]:

fx = lambdify(x,f,modules=['numpy'])
gx = lambdify(x,g,modules=['numpy'])

In [41]:

xVals = linspace(-1,1,100)
pl.plot(xVals,fx(xVals),label = 'f(x)=sin(x)')
pl.plot(xVals,gx(xVals),label = 'g(x)=cos(x)')
pl.xlabel('x')
pl.ylabel('f(x) = sin(x), g(x) = cos(x)')
pl.title('f(x) = arcsin(x), g(x) = arccos(x)')
pl.legend()
pl.show()

In [42]:

f = sinh(x)
g = cosh(x)

In [43]:

fx = lambdify(x,f,modules=['numpy'])
gx = lambdify(x,g,modules=['numpy'])

In [45]:

xVals = linspace(-10,10,100)
pl.plot(xVals,fx(xVals),label = 'f(x)=sinh(x)')
pl.plot(xVals,gx(xVals),label = 'g(x)=cosh(x)')
pl.xlabel('x')
pl.ylabel('f(x) = sinh(x), g(x) = cosh(x)')
pl.title('f(x) = sinh(x), g(x) = cosh(x)')
pl.legend()
pl.show()

In [46]:

f = asinh(x)
g = acosh(x)

In [47]:

fx = lambdify(x,f,modules=['numpy'])
gx = lambdify(x,g,modules=['numpy'])

In [48]:

xVals = linspace(1,10,100)
pl.plot(xVals,fx(xVals),label = 'f(x)=arcsinh(x)')
pl.plot(xVals,gx(xVals),label = 'g(x)=arccosh(x)')
pl.xlabel('x')
pl.ylabel('f(x) = arcsinh(x), g(x) = arccosh(x)')
pl.title('f(x) = arcsinh(x), g(x) = arccosh(x)')
pl.legend()
pl.show()

$\displaystyle f(x)= \left\lceil{x}\right\rceil, g(x) = \left\lfloor{x}\right\rfloor, h(x) = x- \left\lfloor{x}\right\rfloor$¶

In [57]:

f = ceiling(x)
g = floor(x)
h = frac(x)

In [58]:

fx = lambdify(x,f,modules=['numpy'])
gx = lambdify(x,g,modules=['numpy'])
hx = lambdify(x,h,modules=['numpy'])

In [59]:

xVals = linspace(-10,10,100)
pl.plot(xVals,fx(xVals),label = 'f(x)=ceiling(x)')
pl.plot(xVals,gx(xVals),label = 'g(x)=floor(x)')
pl.plot(xVals,hx(xVals),label = 'h(x)=frac(x)')
pl.xlabel('x')
pl.ylabel('f(x), g(x), h(x)')
pl.title('f(x) = ceiling(x), g(x) = floor(x), h(x)=frac(x)')
pl.legend()
pl.show()

---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
<ipython-input-59-627b385d076d> in <module>
      2 pl.plot(xVals,fx(xVals),label = 'f(x)=ceiling(x)')
      3 pl.plot(xVals,gx(xVals),label = 'g(x)=floor(x)')
----> 4 pl.plot(xVals,hx(xVals),label = 'h(x)=frac(x)')
      5 pl.xlabel('x')
      6 pl.ylabel('f(x), g(x), h(x)')

<lambdifygenerated-19> in _lambdifygenerated(x)
      1 def _lambdifygenerated(x):
----> 2     return (frac(x))

NameError: name 'frac' is not defined

In [52]:

g

Out[52]:

$\displaystyle \left\lfloor{x}\right\rfloor$

In [ ]: