如何在Python中定义等同于多项式的函数

我用Python编写了一个函数，它接受列表多项式并忽略末尾的所有零多项式

我现在的任务是定义一个函数

eq_poly（p，q）

，它在列表中取两个多项式，如果它们相等，则输出

True

，如果它们不相等，则输出

False

请注意，应该保留end属性处的零。所以

p = [1,2,3,0]
q = [1,2,3] 

仍应输出

True

谁能告诉我怎么做？代码写在下面

def drop_zeroes(list):
    while list and list[-1] == 0: #drops zeroes at the end, all else equal
        list.pop()

    terms = []
    degree = 0

    # Collect a list of terms
    for coeff in list:
        if degree == 0:
            terms.append(str(coeff))
        elif degree == 1:
            terms.append(str(coeff) + 'x')
        else:
            term = str(coeff) + 'x^' + str(degree)
            terms.append(term)
        degree += 1

    final_string = ' + '.join(terms) # The string ' + ' is used as "glue" between the elements in the string
    return final_string

b = [1,2,0,3,2,0,0] #example of list with zeroes at the end

drop_zeroes(b)

预期产出：

1 + 2x + 0x^2 + 3x^3 + 2x^4

---

对字符串使用格式化字符串而不是

+

操作，并按如下方式比较两个列表：

def drop_0s_and_compare(p, q):
    results = []
    for lst in [p, q]:
        while lst[-1] == 0:
            lst.pop()
        final_string = ''
        for i, coeff in enumerate(lst):
            if not i:
                final_string += f'{coeff}'
            elif i == 1:
                final_string += f' + {coeff}x'
            else:
                final_string += f' + {coeff}x^{i}'
        results.append(final_string)
        
    return results[0] == results[1]
        

p = [1,2,3,0]
q = [1,2,3] 

print(drop_0s_and_compare(p, q))

输出：

True

True

以下是一个较短的方法：

def drop_0s_and_compare(p, q):
    results = []
    for lst in [p, q]:
        while lst[-1] == 0:
            lst.pop()
        final_string = ''.join([f' + {coeff}x^{i}' if i else str(coeff) for i, coeff in enumerate(lst)]).replace('^1', '')
        results.append(final_string)
    return results[0] == results[1]

p = [1, 2, 3]
q = [1, 2, 3, 0]

print(drop_0s_and_compare(p, q))

输出：

True

True

---

有很多方法可以做到这一点。这里有一个：

def remove_zeros(p):
    
    # this just creates a copy of p so we don't mutate it:
    p = [j for j in p]
    while True:
        if p[-1] == 0:
            p.pop()
        else:
            break
    return p

def eq_poly(p, q):
    q = remove_zeros(q)
    p = remove_zeros(p)
    if len(p) != len(q):
        return False
    for j, k in zip(p,q):
        if j != k:
             return False
    return True

# examples:
p = [1,2,3,0] 
q = [1,2,3] 
eq_poly(p,q) # True
eq_poly([2,1,2], [2,1,2]) # True
eq_poly([2,1,0], [2,1]) # True
eq_poly([2,1,0,1], [2,1]) # False

---

只需使用现有函数删除两个列表中的所有最后零，然后测试剩余的是否相等。