CODEWITHSUNDEEP
pythonsympy
gus
gus

Reputation: 407

Getting an indefinite integral from sympy

I'm trying to get an indefinite integral from sympy, but it is not actually solving it. I just get the input expression repeated. Here is the setup:

rt = sympy.Matrix([t**2, sympy.cos(t)+t*sympy.sin(t),sympy.sin(t)-t*sympy.cos(t)])
vt = sympy.diff(rt)
vt_norm = vt.norm()
vt_int = sympy.integrate(vt_norm, t)

print("position function:")
display(rt)
print("velocity function:")
display(vt)
print("velocity norm")
display(vt_norm)
print("vt_integrate")
display(vt_int)
print("vt_integrate , do_it")
display(vt_int.doit())

Here is the output:

Output

Any suggestions?

Upvotes: 2

Views: 315

Answers (1)

Oscar Benjamin
Oscar Benjamin

Reputation: 14480

I presume t is real and if you explain that to sympy then it can give you a simpler result. The result can simplify further if t is positive:

In [11]: t = Symbol('t', real=True)

In [12]: rt = sympy.Matrix([t**2, sympy.cos(t)+t*sympy.sin(t),sympy.sin(t)-t*sympy.cos(t)])
    ...: vt = sympy.diff(rt)
    ...: vt_norm = vt.norm()

In [13]: vt_norm
Out[13]: 
   ________________________________
  ╱  2    2       2    2         2 
╲╱  t ⋅sin (t) + t ⋅cos (t) + 4⋅t  

In [14]: vt_norm.simplify()
Out[14]: √5⋅│t│

In [15]: vt_norm.simplify().integrate(t)
Out[15]: 
⎧     2            
⎪-√5⋅t             
⎪───────  for t ≤ 0
⎪   2              
⎨                  
⎪     2            
⎪ √5⋅t             
⎪ ─────   otherwise
⎩   2

Upvotes: 4

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