CODEWITHSUNDEEP
pythonmathtrigonometrysagepi
Terrence J
Terrence J

Reputation: 181

NameError: name 'cos' is not defined, sageMath9.4

I am writing a Python module using SageMath9.4. Basically, I want to import this module into Jupyterlab Notebooks (running a SageMath 9.4 kernel) to do calculations etc.

Here is the start of it:

class Coxeter_System:
'''This class defines the standard root system associated to an abstract Coxeter group.'''

def __init__(self, coxeter_matrix):
    '''Sets up a Coxeter system and root system. At this stage, limited to up to rank 7. 
    '''
    def set_up_coefficient_space(coxeter_matrix):
        '''Sets up a polynomial ring a Free module over a polynomial ring quotiented by the minimal polynomials of the 
        non-rational cos(pi/m_ij) values. 
        
        This is so roots can be compared using an abstract free module rather than over reals'''
        
        A = coxeter_matrix
        k = len(A.rows())

        # Get the cos(pi/m_ij) which are irrational
        non_rational_angles = [x for x in [cos(pi/x) for x in set(A[i,j] for i in range(0,k) for j in range(0,k))] if x not in QQ]

However, when I open another Jupyterlab session, import the Python module and try to create an instance of the object "Coxeter_System", I get the following error (I have tried to do from math import cos both from the notebook where I want to import the module to, and in the module itself, but I still get the same error.

Any help would be greatly appreciated!):

NameError                                 Traceback (most recent call last)
<ipython-input-6-6b542b6cb042> in <module>
----> 1 W = c.Coxeter_System(Matrix([[Integer(1),Integer(3),Integer(4)],[Integer(3),Integer(1),Integer(3)],[Integer(4),Integer(3),Integer(1)]]))

~/coxeter_groups.py in __init__(self, coxeter_matrix)
     60             return matrix(R,k,B)
     61 
---> 62         R = set_up_coefficient_space(coxeter_matrix)
     63         A = coxeter_matrix
     64         k = len(A.rows())

~/coxeter_groups.py in set_up_coefficient_space(coxeter_matrix)
     17 
     18             # Get the cos(pi/m_ij) which are irrational
---> 19             non_rational_angles = [x for x in [cos(pi/x) for x in set(A[i,j] for i in range(0,k) for j in range(0,k))] if x not in QQ]
     20 
     21             # sort the irrational values of cos(pi/m_ij) in ascending order

~/coxeter_groups.py in <listcomp>(.0)
     17 
     18             # Get the cos(pi/m_ij) which are irrational
---> 19             non_rational_angles = [x for x in [cos(pi/x) for x in set(A[i,j] for i in range(0,k) for j in range(0,k))] if x not in QQ]
     20 
     21             # sort the irrational values of cos(pi/m_ij) in ascending order

NameError: name 'cos' is not defined

Upvotes: 1

Views: 5125

Answers (2)

AleBuo
AleBuo

Reputation: 220

For most IDEs you will have to import some of the most popular math packages,

# Example:

import numpy as np
import math as m
import sagemath as sm

numpy and math you will have no problem using it with a simple import numpy in Google Colab or most popular IDEs.

What is SageMath?

SageMath, previously known as Sage, is a computational algebraic system (CAS) that stands out for being built on mathematical and contrasted packages such as NumPy, Sympy, PARI/GP o Máxima.

Install the SageMath package in Jupyter Notebook:

In the case of sagemath, inside jupyter you will have to do some extra steps.

To install the sagemath package we must do a pip:

!pip install sagemath

enter image description here

The image shows the confirmation within Jupyter

Using sagemath

# import and add the alias s
import sagemath as s

Yo use it we place the alias "s" in front of the function

s.cos(s.pi/x)

If sagemath does not always work correctly.

We know the following: "The philosophy of SageMath is to use existing open-source libraries wherever they exist. Therefore, it uses many libraries from other projects."

For these mathematical functions you can use numpy:

import numpy as np
np.cos(np.pi/x)

It will not fail and also in Jupyter you do not need additional installation.

I hope I've been useful.

Upvotes: 0

Daniel
Daniel

Reputation: 109

Just use math.cos instead of using cos after from math import cos

e.g. math.cos(pi/x)

import math
math.cos(pi/x)

Upvotes: 3

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