A multivariate polynomial class

ndpoly.py

import numpy as np
from copy import deepcopy

def list_dim(a):
    if not type(a) == list:
        return []
    return [len(a)] + list_dim(a[0])

class Monomial:
    def __init__(self, coefficient, powers):
        if isinstance(coefficient, float):
            self.coefficient = coefficient
        else:
            raise Exception('the first input, coefficient, must be a float')
        
        if isinstance(powers, list):
            powers=np.asarray(powers)
#            if all(isinstance(power, int) and power>=0 for power in powers) and len(list_dim(powers))==1:
#                powers = np.asarray(powers)
#            else:
#                raise Exception('the elements of the second input, one dimensional list of powers, must be non-negative integers')
        if isinstance(powers, np.ndarray):
            if not powers.ndim == 1:
                raise Exception('the second input, powers, must be a one dimensional numpy ndarray or python list')
            if (powers.dtype == np.dtype('int64') and np.all(powers>=0)):
                self.powers = powers
            else:
                raise Exception('the elements of the second input, ndarray of powers, must be non-negative integers')
        else:
            raise Exception('the second input, powers, must be a numpy ndarray or a python list')
            
    def check_dim(monomial1,monomial2):
        if not (isinstance(monomial1, Monomial) and isinstance(monomial2, Monomial) and monomial1.powers.shape==monomial2.powers.shape):
            raise Exception('elements of the function must be of instances of Monomial class of the same size')
        return
        
    def multiply(monomial1,monomial2):
        Monomial.check_dim(monomial1,monomial2)
        return Monomial(monomial1.coefficient*monomial2.coefficient,monomial1.powers+monomial2.powers)
    
    def add(monomial1,monomial2):
        Monomial.check_dim(monomial1,monomial2)
        if not np.array_equal(monomial1.powers,monomial2.powers):
            raise Exception('elements of the add function must have the same powers')
        return Monomial(monomial1.coefficient+monomial2.coefficient,monomial1.powers)
    
    def diff(monomial,axis, der=1):
        if isinstance(monomial,Monomial) and isinstance(axis, int):
            if axis<=monomial.powers.shape[0] and axis>=1 :
                if (not isinstance(der,int)) and der >monomial.powers[axis-1]+1 and der < 0:
                    raise Exception('der must be a non-negative integer smaller than variables degree in the monomial')
                if der ==0:
                    return monomial
                else:
                    tmpmon=Monomial.diff(monomial,axis, der-1)
                    tmp=deepcopy(tmpmon.powers)
                    tmp[axis-1]-=1
                    return Monomial(tmpmon.coefficient*tmpmon.powers[axis-1],tmp)
            else:
                raise Exception('the diffrential variable is byound the number of variables')
        else:
            raise Exception('the inputs must be a Monomial and a positive integer')
            
  
  
  

  
from collections.abc import Sequence

class NDPoly(Sequence):
    def __init__(self, monomials):
        if isinstance(monomials, list):
            monomials=np.asarray(monomials)
#            if all(isinstance(monomial, Monomial) and monomial.powers.shape==monomials[0].powers.shape for monomial in monomials) and len(list_dim(monomials))==1:
#                self.monomials=monomials
#                super().__init__()
#            else:
#                raise Exception('the inputs must be a one dimentional list of equal dimention Monomials')
        if isinstance(monomials, np.ndarray):
            if (not monomials.ndim == 1) and monomials[:].powers.shape==monomials[0].powers.shape:
                raise Exception('the input, monomials, must be a one dimensional numpy ndarray or python list')
            if (type(monomials[0]) == Monomial):
                self.monomials = NDPoly.collect(monomials)
                super().__init__()
            else:
                raise Exception('the elements of the second input, ndarray of monomials, must be of class Monomial')
        else:
            raise Exception('the second input, powers, must be a numpy ndarray or a python list')
        self.coefficients=np.array([p.coefficient for p in monomials])
        self.powers_list=np.array([p.powers for p in monomials])
    
    def __getitem__(self, i):
        return self.monomials[i]
    
    def __len__(self):
        return len(self.monomials)
    
    def collect(monomials):
        tmpmonos=deepcopy(monomials)
        for i in range(len(monomials)):
            for j in range(i+1,len(monomials)):
                if np.array_equal(monomials[i].powers,monomials[j].powers):
                    np.append(tmpmonos,Monomial.add(monomials[i],monomials[j]))
        return tmpmonos

There are also other attempts: POLYNOMIAL, LibPoly and berlin seidler and matthewhr