Sympy to numpy causes the AttributeError: 'Symbol' object has no attribute 'cos'
Question: I am trying to do partial derivatives using sympy and I want to convert it to
a function so that I can substitute values and estimate the derivatives at
some values of t_1, t_2. The code I am using is as follows:

    
    
    import sympy as sp
    import numpy as np
    from sympy import init_printing
    init_printing()
    t_1,t_2,X_1,X_2,Y_1,Y_2,X_c1,X_c2,Y_c1,Y_c2,a_1,a_2,psi_1,psi_2,b_1,b_2= sp.symbols('t_1 t_2 X_1 X_2 Y_1 Y_2 X_c1 X_c2 Y_c1 Y_c2 a_1 a_2 psi_1 psi_2 b_1 b_2')
    
    X_1=X_c1 + (a_1 * sp.cos(t_1) * sp.cos(psi_1)) - ((b_1) * sp.sin(t_1)* sp.sin(psi_1))
    
    X_2=X_c2 + (a_2 * sp.cos(t_2) * sp.cos(psi_2)) - ((b_2) * sp.sin(t_2)* sp.sin(psi_2))
    
    Y_1=Y_c1 + (a_1 * sp.cos(t_1) * sp.sin(psi_1)) + ((b_1) * sp.sin(t_1)* sp.cos(psi_1))
    
    Y_2=Y_c2 + (a_2 * sp.cos(t_2) * sp.sin(psi_2)) + ((b_2) * sp.sin(t_2)* sp.sin(psi_2))
    
    D=(((X_2-X_1)**2) + ((Y_2-Y_1)**2))**0.5
    
    y_1=sp.diff(D,t_1)
    
    y_2=sp.diff(D,t_2)
    
    f=sp.lambdify(t_1, y_1, "numpy")
    
    g=sp.lambdify(t_2, y_2, "numpy")
    

When I try to substitute a value for t_1 using,

    
    
    f(np.pi/2)
    

I get the following error:

    
    
    AttributeError   Traceback (most recent call last)
    <ipython-input-26-f37892b21c8b> in <module>()
    ----> 1 f(np.pi/2)
    
    /users/vishnu/anaconda3/lib/python3.5/site-packages/numpy    /__init__.py in <lambda>(_Dummy_23)
    
    AttributeError: 'Symbol' object has no attribute 'cos'
    

I referred to the following links:

[What causes this error (AttributeError: 'Mul' object has no attribute 'cos')
in Python?](http://stackoverflow.com/questions/32640759/what-causes-this-
error-attributeerror-mul-object-has-no-attribute-cos-in)

[Python
AttributeError:cos](http://stackoverflow.com/questions/13336048/python-
attributeerrorcos)

but I think my imports of numpy and sympy are not clashing unlike the cases
mentioned in those links. Any help is appreciated.


Answer: This type of error occurs when you call `np.cos(a_symbol)`, which apparently
translates under-the-hood in numpy to `a_symbol.cos()`.

`lambdify` is for numeric calculations - it replaces all `sp` calls with `np`
calls. But what you're doing is symbolic. This is enough for your problem:

    
    
    f1 = lambda t: y_1.subs({t_1: t})
    f2 = lambda t: y_2.subs({t_2: t})
    

