Goulib.expr

In [1]:

    

from Goulib.notebook import *
from Goulib.expr import *
from Goulib.table import Table
from math import pi,sin
from Goulib.math2 import sqrt


    

In [2]:

    

Expr(3**5) # is evaluated before Expr is created


    

    
Out[2]:




${243}$

In [3]:

    

e=Expr(3)**Expr(5) # combine Expr essions
h('as LaTeX (default) :',e)
print('as math formula :',e)
print('as python code :',repr(e))
print('evaluated :',e())


    

    





as LaTeX (default) : ${3^5}$






    




as math formula : 3^5
as python code : 3**5
evaluated : 243

In [4]:

    

e=Expr('5**3+(-3^2)') # ^ and ** are both considered as power operator for clarity+compatibility
h('as LaTeX (default) :',e)
print('as math formula :',e)
print('as python code :',repr(e))
print('evaluated :',e())


    

    





as LaTeX (default) : ${5^3-3^2}$






    




as math formula : 5^3-3^2
as python code : 5**3-3**2
evaluated : 116

In [5]:

    

e=Expr('x^2')
h('an Expr may contain variables :',e)
h('and be evaluated as a function : for x=2, ',e,'=',e(x=2))


    

    





an Expr may contain variables : ${x^2}$






    





and be evaluated as a function : for x=2,  ${x^2}$ = 4

In [6]:

    

functions=default_context.functions # functions known by default to Expr
t=Table()
for n in functions:
    f=functions[n][0] # get the function itself
    try:
        e=Expr(f)
        t.append([n,repr(e),str(e),e])
    except Exception as e:
        t.append([n,e])
t


    

    
Out[6]:




abs
abs(x)
abs(x)
${\lvert{x}\rvert}$
acos
acos(x)
acos(x)
${\arccos\left(x\right)}$
acosh
acosh(x)
acosh(x)
${\cosh^{-1}\left(x\right)}$
asin
asin(x)
asin(x)
${\arcsin\left(x\right)}$
asinh
asinh(x)
asinh(x)
${\sinh^{-1}\left(x\right)}$
atan
atan(x)
atan(x)
${\arctan\left(x\right)}$
atan2
atan2(x)
atan2(x)
${\atan2\left(x\right)}$
atanh
atanh(x)
atanh(x)
${\tanh^{-1}\left(x\right)}$
ceil
ceil(x)
ceil(x)
${\left\lceil{x}\right\rceil}$
copysign
copysign(x)
copysign(x)
${\copysign\left(x\right)}$
cos
cos(x)
cos(x)
${\cos\left(x\right)}$
cosh
cosh(x)
cosh(x)
${\cosh\left(x\right)}$
degrees
degrees(x)
degrees(x)
${x\cdot\frac{360}{2\pi}}$
erf
erf(x)
erf(x)
${\erf\left(x\right)}$
erfc
erfc(x)
erfc(x)
${\erfc\left(x\right)}$
exp
exp(x)
exp(x)
${e^{x}}$
expm1
expm1(x)
expm1(x)
${e^{x}-1}$
fabs
fabs(x)
fabs(x)
${\lvert{x}\rvert}$
factorial
fact(x)
x!
${x!}$
factorial2
'factorialk'
floor
floor(x)
floor(x)
${\left\lfloor{x}\right\rfloor}$
fmod
fmod(x)
fmod(x)
${\fmod\left(x\right)}$
frexp
frexp(x)
frexp(x)
${\frexp\left(x\right)}$
fsum
fsum(x)
fsum(x)
${\fsum\left(x\right)}$
gamma
gamma(x)
gamma(x)
${\Gamma\left(x\right)}$
gcd
gcd(x)
gcd(x)
${\gcd\left(x\right)}$
hypot
hypot(x)
hypot(x)
${\hypot\left(x\right)}$
isclose
isclose(x)
isclose(x)
${\isclose\left(x\right)}$
isfinite
isfinite(x)
isfinite(x)
${\isfinite\left(x\right)}$
isinf
isinf(x)
isinf(x)
${\isinf\left(x\right)}$
isnan
isnan(x)
isnan(x)
${\isnan\left(x\right)}$
ldexp
ldexp(x)
ldexp(x)
${\ldexp\left(x\right)}$
lgamma
log(abs(gamma(x)))
log(abs(gamma(x)))
${\ln\lvert\Gamma\left({x}\rvert)\right)}$
log
log(x)
log(x)
${\ln\left(x\right)}$
log10
log10(x)
log10(x)
${\log_{10}\left(x\right)}$
log1p
log1p(x)
log1p(x)
${\ln\left(1-{x}\rvert)}$
log2
log2(x)
log2(x)
${\log_2\left(x\right)}$
modf
modf(x)
modf(x)
${\modf\left(x\right)}$
pow
pow(x)
pow(x)
${\pow\left(x\right)}$
radians
radians(x)
radians(x)
${x\cdot\frac{2\pi}{360}}$
remainder
remainder(x)
remainder(x)
${\remainder\left(x\right)}$
sin
sin(x)
sin(x)
${\sin\left(x\right)}$
sinh
sinh(x)
sinh(x)
${\sinh\left(x\right)}$
sqrt
sqrt(x)
sqrt(x)
${\sqrt{x}}$
tan
tan(x)
tan(x)
${\tan\left(x\right)}$
tanh
tanh(x)
tanh(x)
${\tanh\left(x\right)}$
trunc
trunc(x)
trunc(x)
${\left\lfloor{x}\right\rfloor}$

In [7]:

    

e=Expr(sqrt) #(Expr(pi))+Expr(1/5)
h('as LaTeX (default) :',e)
print('as math formula :',e)
print('as python code :',repr(e))
print('evaluated :',e())


    

    





as LaTeX (default) : ${\sqrt{x}}$






    




as math formula : sqrt(x)
as python code : sqrt(x)
evaluated : sqrt(x)

In [8]:

    

e1=Expr('3*x+2') #a very simple expression defined from text
e1


    

    
Out[8]:




${3x+2}$

In [9]:

    

e1=Expr(lambda x:3*x+2) #the same expression defined from a lambda function
e1


    

    
Out[9]:




${3x+2}$

In [10]:

    

def f(x):
    return 3*x+2
Expr(f) #the same expression defined from a regular (simple...) function


    

    
Out[10]:




${3x+2}$

In [11]:

    

e3=Expr(sqrt)(e1) #Expr can be composed
e3


    

    
Out[11]:




${\sqrt{3x+2}}$

In [12]:

    

print(e3(x=1)) # Expr can be evaluated as a function
print(e3((pi-4)/6)) #the x variable is implicit


    

    




2.23606797749979
1.2533141373155001

In [13]:

    

e1([-2,1,0,1,2]) # Expr can be evaluated at different x values at once


    

    
Out[13]:





[-4, 5, 2, 5, 8]

In [14]:

    

e3.plot()  # Expr can be also plotted. Note the X axis is automatically restricted to the definition domain


    

    
Out[14]:

In [15]:

    

Expr('1/x').plot(x=range(-100,100))


    

    
Out[15]:

In [16]:

    

e=Expr('(-b+sqrt(b^2-4*a*c))/(2*a)') #laTex is rendered with some simple simplifications
e


    

    
Out[16]:




${\frac{-b+\sqrt{b^2-4ac}}{2a}}$

In [17]:

    

e(a=1) # substitution doesn't work yet ...


    

    
Out[17]:




${\frac{-b+\sqrt{b^2-4ac}}{2a}}$

In [18]:

    

e=Expr("e**(i*pi)")
e


    

    
Out[18]:




${e^{ipi}}$

In [19]:

    

e() # should be -1 one day...


    

    
Out[19]:




${e^ipi}$