Mô-đun toán học có được tích hợp trong python không?

Mô-đun toán học trong Python xử lý các phép tính toán học. Nó liên quan đến nhiều phép toán nâng cao, chẳng hạn như hàm mũ, logarit và lượng giác. Vì vậy, đối với các dự án liên quan đến tài chính, khoa học hoặc toán học, mô-đun

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

6 sẽ rất hữu ích

Về cơ bản, mô-đun Python

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

6 sử dụng các hàm toán học được xác định bởi tiêu chuẩn C giúp nó hoạt động hiệu quả và nhanh chóng. Nó đi kèm với bản phát hành Python tiêu chuẩn. Vì vậy, bạn không cần phải cài đặt nó

Trong bài viết này, chúng ta sẽ đi sâu vào mô-đun Python

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

6 và xem một số trường hợp sử dụng quan trọng nhất của nó

Table of Contents:· Getting Started
· Constants in the math Module
· Pi [π]
· Euler’s Number [e]
· Tau [τ]
· Infinity
· Not a Number [NaN]
· Arithmetic Functions in the math Module
· Factorial
· Greatest Common Divisor [GCD]
· Ceiling and Floor Value
· Absolute Value
· Square Root
· Power Functions
· Natural Exponent
· Logarithmic Functions
· Natural Logarithm
· math.log[] With a Second Argument
· log2[] and log10[]
· Trigonometric Functions
· math vs cmath
· Conclusion
· References

Bắt đầu

Như tôi đã đề cập trước đó, mô-đun

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

6 đi kèm với bản cài đặt Python tiêu chuẩn. Vì vậy, nó là một mô-đun Python tích hợp sẵn và để sử dụng nó, bạn chỉ cần nhập nó

>>> import math

In

>>> import math
>>> math.pi
3.141592653589793

0 của

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

6 sẽ cho bạn biết rằng đó là một mô-đun

________số 8

>>> import math
>>> math.pi
3.141592653589793

2 sẽ cung cấp cho bạn tất cả các thuộc tính và phương thức có sẵn trong

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

6

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

Hình ảnh của tác giảCác hằng số trong Mô-đun toán học

Mô-đun Python

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

6 có một tập hợp các hằng số toán học được xác định trước. Vì vậy, bạn không cần mã hóa cứng các hằng số thường được sử dụng này mỗi khi bạn sử dụng chúng trong mã của mình. Nó đảm bảo tính nhất quán trong mã của bạn và cũng tiết kiệm thời gian. Các hằng số có sẵn trong mô-đun

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

6 là

• Số Pi
• Số Euler
• Tàu
• vô cực
• Không phải là số [NaN]

số Pi [π]

Pi là tỷ lệ giữa chu vi của một vòng tròn và đường kính của nó. Giả sử chu vi của một vòng tròn là c và đường kính là d, thì

Công thức của Pi. Hình ảnh của tác giả

Giá trị không đổi cho tất cả các vòng kết nối và có vô số chữ số thập phân. Giá trị gần đúng của Pi là 22/7 hoặc 3. 141

Bạn có thể truy cập Pi bằng mô-đun

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

6 như sau

>>> import math
>>> math.pi
3.141592653589793

>>> import math
>>> math.pi
3.141592653589793

7 luôn trả về giá trị float

________ 17 Số Euler [e]

Số Euler là một giá trị không đổi là cơ số của logarit tự nhiên. Giá trị của Số Euler cũng có vô số chữ số thập phân, nhưng thường xấp xỉ bằng 2. 718

Bạn có thể truy cập Số của Euler như sau

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

8

Giống như

>>> import math
>>> math.pi
3.141592653589793

7,

>>> import math
>>> math.pi
3.141592653589793

9 cũng trả về giá trị float

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

1Tau [τ]

Tau là tỷ số giữa chu vi và bán kính của hình tròn. Nếu chu vi của một vòng tròn là c và bán kính là r, thì

Công thức Tàu. Hình ảnh của tác giả

Tau, giống như Pi và e, cũng có vô số chữ số thập phân. Giá trị của Tau bằng 2π và có thể xấp xỉ bằng 6. 28

Bạn có thể truy cập Tau từ mô-đun Python

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

6 như sau

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

3

Và như bạn có thể thấy,

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

71 cũng trả về một giá trị float

vô cực

Vô cực không có giá trị số thực tế. Nó được sử dụng trong toán học để đại diện cho một cái gì đó vô tận hoặc không bao giờ kết thúc. Vô cực có thể đi theo một trong hai hướng.

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

72 đại diện cho một điều gì đó không bao giờ kết thúc theo hướng tích cực. Mặt khác,

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

73 đại diện cho một thứ không bao giờ kết thúc theo hướng tiêu cực

Bạn có thể truy cập vô cực bằng cách sử dụng mô-đun

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

6 như sau

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

8

Để biểu thị vô cực âm, bạn chỉ cần đặt dấu trừ [-] trước

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

75

>>> import math

0

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

76 lớn hơn bất kỳ giá trị số dương nào và

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

77 nhỏ hơn bất kỳ giá trị số âm nào

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

75 đã được giới thiệu trong Python 3. 5 tương đương với

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

79

>>> import math

1Không phải là số [NaN]

NaN được sử dụng trong Khoa học máy tính để biểu thị rằng đó không phải là giá trị số hợp pháp. NaN có thể dẫn đến một giá trị không hợp lệ hoặc bị hỏng

Giá trị của NaN được truy xuất từ ​​module

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

6 như sau

>>> import math

2

Giống như

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

75,

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

82 cũng được giới thiệu trong Python 3. 5 tương đương với

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

83. Chúng đại diện cho cùng một thứ, nhưng câu lệnh sau sẽ trả về

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

84

>>> import math

3

Thậm chí

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

85 trả về

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

84

Hình ảnh của tác giả Hàm số học trong Học phần toán học

Mô-đun Python

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

6 có phần lớn các hàm số học tích hợp được sử dụng rộng rãi trong các phép tính toán học và lý thuyết số. Các chức năng này cho phép chúng tôi tạo ra các giá trị quan trọng như

• Tìm giai thừa của một số
• Tìm ước chung lớn nhất [GCD] của hai số
• Tìm giá trần và giá trị sàn
• Tìm giá trị tuyệt đối của một số
• Tìm căn bậc hai của một số

yếu tố

Giai thừa của một số là phép nhân của tất cả các số từ nó xuống 1. Giai thừa được thể hiện bằng ký hiệu. Vậy giai thừa của 5 là

5. = 5 * 4 * 3 * 2 * 1 = 120

Để tìm giai thừa của một số bằng mô-đun

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

6, bạn cần làm như sau

>>> import math

4

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

89 luôn trả về một giá trị số nguyên. Bạn chỉ có thể tìm giai thừa của một số nguyên dương. Vì vậy, áp dụng

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

89 cho giá trị float hoặc giá trị âm sẽ cho

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

11

>>> import math

5

Bạn có thể viết thuật toán của riêng mình để tìm giai thừa của một số, nhưng rất có thể mã của bạn sẽ chậm hơn và kém hiệu quả hơn so với

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

89

Ước chung lớn nhất [GCD]

ƯCLN của hai số là ước chung lớn nhất của hai số đó chia hết cho chúng không dư

Bạn có thể tìm GCD của hai số bằng cách sử dụng

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

13.

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

13 nhận hai đối số, hai số bạn muốn tìm GCD của

>>> import math

6

Một lần nữa,

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

13 giống như

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

89 trả về một giá trị số nguyên

Giá trị trần và sàn

Giá trị trần của một số là giá trị nguyên nhỏ nhất lớn hơn hoặc bằng số đó. Mặt khác Giá trị sàn của một số là giá trị nguyên lớn nhất nhỏ hơn hoặc bằng số đó

Bạn có thể tìm thấy giá trị trần và sàn của một số lần lượt là

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

17 và

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

18

>>> import math

7

Lưu ý rằng giá trị trần và sàn của một số nguyên là chính số đó

>>> import math

8Giá trị tuyệt đối

Giá trị tuyệt đối của một số là giá trị không âm của số đó không phụ thuộc vào dấu của nó. Trong toán học, giá trị tuyệt đối của một số x được ký hiệu là. x

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

19 sẽ trả về giá trị tuyệt đối của một số

>>> import math

9

Và vâng,

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

19 luôn trả về giá trị float

Căn bậc hai

Sử dụng

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

31 bạn có thể tìm căn bậc hai của một số. Hàm

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

32 nhận một đối số, một giá trị số không âm. Hàm luôn trả về giá trị float

>>> type[math]

0

Cố gắng tìm căn bậc hai của một số âm sẽ cho kết quả là

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

11

>>> type[math]

1

Hình ảnh của tác giảPower Functions

Hàm lũy thừa nhận một giá trị và trả về một giá trị được nâng lên một số lũy thừa. Biểu thức là x^n, trong đó x lũy thừa n

Bạn có thể tính lũy thừa của một số bằng cách sử dụng

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

34. Cú pháp diễn ra như sau

>>> type[math]

2

Biểu thức

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

35 tương đương với biểu thức toán học 2⁴. Biểu thức

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

34 hợp lệ luôn trả về giá trị float

Hàm

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

37 và hàm

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

38 cũng sẽ tính công suất

>>> type[math]

3

Nhưng chúng chậm hơn

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

34

số mũ tự nhiên

Hàm mũ tự nhiên có thể được coi là một hàm lũy thừa đặc biệt. Một hàm lũy thừa trong toán học trông như thế này

Chức năng nguồn chung. Hình ảnh của tác giả

Nhưng một hàm số mũ tự nhiên trông như thế này

Hàm số mũ tự nhiên. Hình ảnh của tác giả

Trong phần Hằng số, chúng ta đã thảo luận về số e của Euler. Số mũ tự nhiên của một số là e lũy thừa của số đó. Hàm số mũ tự nhiên thường được sử dụng để biểu diễn sự tăng trưởng theo cấp số nhân của nhiều trường hợp thực tế

Mô-đun toán Python cung cấp hàm

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

80 để tính số mũ tự nhiên của một số. Bạn có thể tìm số mũ tự nhiên của một số như sau

>>> type[math]

4

Giống như trước đây

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

81 và

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

82 cũng sẽ hoạt động. Nhưng

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

80 hiệu quả và chính xác hơn

Hàm logarit

Hàm logarit ngược lại với hàm lũy thừa trong toán học. Biểu thức toán học cho các hàm logarit là

Hàm logarit. Hình ảnh của tác giả

Trong đó a là cơ số của logarit

Logarit tự nhiên

Logarit tự nhiên sử dụng số e của Euler làm cơ số. Trong toán học logarit tự nhiên được ký hiệu là ln[] thay vì log[]. Nhưng mô-đun Python

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

6 sử dụng cùng một

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

85 cho logarit tổng quát và logarit tự nhiên. Hãy xem làm thế nào

Hàm

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

85 nhận hai đối số. Đối số đầu tiên là bắt buộc. Nó là số đầu vào. Đối số thứ hai là tùy chọn. Bạn cần để trống đối số thứ hai để tìm logarit tự nhiên của một số

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

85 không có đối số thứ hai sẽ tính logarit tự nhiên của một số đã cho

>>> type[math]

5

Cố gắng tìm logarit tự nhiên của một số không dương sẽ cho kết quả là

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

11

>>> type[math]

6toán học. log[] Với đối số thứ hai

Đối số thứ hai của

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

85 sẽ đóng vai trò là cơ sở.

>>> import math

00 sẽ cung cấp cho bạn giá trị logarit là 2 với cơ số là 10

>>> type[math]

7log2[] và log10[]

Lôgarit cơ số 2 và lôgarit cơ số 10 là những kiểu tính lôgarit phổ biến mà bạn sẽ gặp phải. Vì vậy, mô-đun Python

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

6 cung cấp các chức năng riêng cho chúng

>>> type[math]

8

Hàm lượng giác

Trong toán học, lượng giác là nghiên cứu về tam giác. Nó đề cập đến mối quan hệ giữa các thiên thần

Bạn có thể tính sin[], cosin[], tang[] của một góc bằng cách sử dụng mô-đun

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

6

>>> type[math]

9

Bạn cũng có thể chuyển đổi một giá trị góc từ độ sang radian và ngược lại

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

0

toán vs cmath

Mô-đun

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

6 xử lý các số dấu phẩy động. Mặt khác,

>>> import math

04 xử lý các số phức. Số phức là sự kết hợp của một số thực và một số ảo

Một số thực theo nghĩa đen là bất kỳ số nào bạn có thể nghĩ ra. Nếu bạn bình phương một số thực, bạn sẽ luôn nhận được một giá trị dương. Nhưng một số ảo sẽ cho giá trị âm khi bình phương

Một ví dụ về số phức có thể là 4+7i. Trong đó 4 là phần thực và 7i là phần ảo. Ở đây tôi đại diện cho trí tưởng tượng. Đôi khi j cũng được sử dụng để biểu diễn các số ảo

Giống như

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

6,

>>> import math

04 cũng có tiêu chuẩn với Python. Vì vậy, bạn không cần phải cài đặt nó. Chỉ cần nhập

>>> import math

04 để sử dụng

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

1

Có hai cách bạn có thể viết một số phức trong Python

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

2

Và cũng với chức năng

>>> import math

08

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

3

Sau khi tạo xong số phức, bạn có thể sử dụng

>>> import math

04 để tính các hàm toán học của số phức. Một số ví dụ được đưa ra dưới đây

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

4

Có nhiều chức năng cụ thể về số phức có sẵn trong mô-đun

>>> import math

04.

>>> import math

11 sẽ tiết lộ các chức năng và thuộc tính có sẵn trong

>>> import math

04

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

5

Sự kết luận

Mô-đun Python

>>> dir[math]
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘
asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘comb’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘di
st’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fs
um’, ‘gamma’, ‘gcd’, ‘hypot’, ‘inf’, ‘isclose’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘isqrt’, ‘lcm
‘, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘nan’, ‘nextafter’, ‘perm’, 
‘pi’, ‘pow’, ‘prod’, ‘radians’, ‘remainder’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘tau’, ‘
trunc’, ‘ulp’]

6 cung cấp nhiều chức năng để thực hiện các phép toán hữu ích. Bài viết này cung cấp cho bạn cái nhìn tổng quan chuyên sâu về mô-đun mạnh mẽ này có sẵn trong Python. Tôi hy vọng bạn tìm thấy nó hữu ích. Cảm ơn vì đã đọc

Mô-đun toán học nằm ở đâu trong Python?

Toán học là một mô-đun hay thư viện?

toán học được xây dựng là gì