A Python math package written in pure Python programming language [python_requires >= 3.5]
Project description
PyPyNum
A Python math package written in pure Python programming language ( python_requires >= 3.5)
________ ___ ___ ________ ___ ___ ________ ___ ___ _____ ______
|\ __ \ |\ \ / /||\ __ \ |\ \ / /||\ ___ \ |\ \|\ \ |\ _ \ _ \
\ \ \|\ \\ \ \/ / /\ \ \|\ \\ \ \/ / /\ \ \\ \ \\ \ \\\ \\ \ \\\__\ \ \
\ \ ____\\ \ / / \ \ ____\\ \ / / \ \ \\ \ \\ \ \\\ \\ \ \\|__| \ \
\ \ \___| \/ / / \ \ \___| \/ / / \ \ \\ \ \\ \ \\\ \\ \ \ \ \ \
\ \__\ __/ / / \ \__\ __/ / / \ \__\\ \__\\ \_______\\ \__\ \ \__\
\|__| |\___/ / \|__| |\___/ / \|__| \|__| \|_______| \|__| \|__|
\|___|/ \|___|/
Version -> 1.4.0 | PyPI -> https://pypi.org/project/PyPyNum/ | Gitee -> https://www.gitee.com/PythonSJL/PyPyNum
介绍
Introduction
- DIY数学库，类似于numpy、scipy等，专为PyPy解释器制作
- DIY math library, similar to numpy, scipy, etc., specifically designed for PyPy interpreters
- 不定期更新版本，增加更多实用功能
- Update versions periodically to add more practical features
- 如需联系，QQ 2261748025 （Py𝙿𝚢𝚝𝚑𝚘𝚗-水晶兰）
- If you need to contact, QQ 2261748025 (Py𝙿𝚢𝚝𝚑𝚘𝚗-水晶兰)
PyPyNum的Zen
The Zen of PyPyNum
The Zen of PyPyNum, by Shen Jiayi
This is a math package written purely in Python.
... (Do you want to see the entire content?
Then enter "from pypynum import this" on your
Python interpreter and run it!)
December 27, 2023
与上一个版本相比新增功能
New features compared to the previous version
PyPyNum
★ FourierT [Fourier transform and inverse Fourier transform]
CLASSES
FT1D
★ probability [Probability function]
FUNCTIONS
binomial(sample_size: int, successes: int, success_probability: Union[int, float]) -> float
hypergeometric(total_items: int, success_items: int, sample_size: int, successes_in_sample: int) -> float
★ sequence [Various sequences]
FUNCTIONS
bernoulli(n: int, single: bool = True) -> list
catalan(n: int) -> int
fibonacci(n: int) -> int
[“maths”等模块增加了新功能]
[New features have been added to modules such as "maths"]
☆ 一些模块已经更改了名称，所以请记住以下名字 ☆
☆ Some modules have changed their names, so please remember the following names ☆
PACKAGE CONTENTS
Array
FourierT
Geometry
Group
Logic
Matrix
NeuralN
Quaternion
Symbolics
Tensor
Vector
__temporary
cipher
constants
equations
errors
file
maths
plotting
probability
random
regression
sequence
test
this
tools
types
基本结构
Basic structure
PyPyNum
★ __init__
[Import some features from other modules in this package]
★ errors [Special errors]
CLASSES
LogicError
RandomError
ShapeError
★ file [Reading and saving instance data]
FUNCTIONS
read(file: str) -> list
write(file: str, *cls: object)
★ test
[A code test file]
★ this
[The Zen of PyPyNum]
★ types [Special types]
DATA
arr = typing.Union[list, tuple]
ite = typing.Union[list, tuple, str]
num = typing.Union[int, float, complex]
real = typing.Union[int, float]
★ Array [N-dimensional array]
CLASSES
Array
FUNCTIONS
array(data=None)
fill(shape, sequence=None)
function(_array, _function, args=None)
get_shape(data)
is_valid_array(_array, _shape)
zeros(shape)
zeros_like(_nested_list)
★ FourierT [Fourier transform and inverse Fourier transform]
CLASSES
FT1D
★ Geometry [Planar geometry]
CLASSES
Circle
Line
Point
Polygon
Quadrilateral
Triangle
FUNCTIONS
distance(g1, g2, error: int | float = 0) -> float
★ Group [Group theory]
CLASSES
Group
FUNCTIONS
add(x, y)
divide(x, y)
group(data)
multiply(x, y)
subtract(x, y)
★ Logic [Logic circuit simulation]
CLASSES
Basic
Binary
AND
COMP
HalfAdder
HalfSuber
JKFF
NAND
NOR
OR
XNOR
XOR
Quaternary
TwoBDiver
TwoBMuler
Ternary
FullAdder
FullSuber
Unary
DFF
NOT
TFF
★ Matrix [Matrix calculation]
CLASSES
Matrix
FUNCTIONS
eig(matrix)
identity(n)
lu(matrix)
mat(data)
qr(matrix)
same(rows, cols, value=0)
svd(matrix)
tril_indices(n, k=0, m=None)
zeros(_dimensions)
zeros_like(_nested_list)
★ NeuralN [A simple neural network model]
CLASSES
NeuralNetwork
FUNCTIONS
neuraln(_input, _hidden, _output)
★ Quaternion [Quaternion calculation]
CLASSES
Euler
Quaternion
FUNCTIONS
change(data: Union[pypynum.Quaternion.Euler, pypynum.Quaternion.Quaternion]) -> Union[pypynum.Quaternion.Euler, pypynum.Quaternion.Quaternion]
euler(yaw: Union[int, float] = 0, pitch: Union[int, float] = 0, roll: Union[int, float] = 0) -> pypynum.Quaternion.Euler
quat(w: Union[int, float] = 0, x: Union[int, float] = 0, y: Union[int, float] = 0, z: Union[int, float] = 0) -> pypynum.Quaternion.Quaternion
★ Symbolics [Symbol calculation]
FUNCTIONS
interpreter(expr: str) -> list
DATA
basic = '%()*+-./0123456789'
english = 'ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz'
greek = 'ΑΒΓΔΕΖΗΘΙΚΛΜΝΞΟ∏ΡΣΤΥΦΧΨΩβγδεζηθικλμνξοπρστυφχψω'
operators = ['**', '*', '//', '/', '%', '+', '-']
valid = '%()*+-./0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcd...yzΑΒΓΔΕΖΗΘ...'
★ Tensor [Tensor calculation]
CLASSES
Tensor
FUNCTIONS
ten(data)
tensor_and_number(tensor, operator, number)
tolist(_nested_list)
zeros(_dimensions)
zeros_like(_nested_list)
★ Vector [Vector calculation]
CLASSES
Vector
FUNCTIONS
same(length, value=0)
vec(data)
zeros(_dimensions)
zeros_like(_nested_list)
★ cipher [String encryption and decryption algorithms]
FUNCTIONS
dna(string: str, decrypt: bool = False) -> str
★ constants [Constants in mathematics and science]
DATA
AMU = 1.6605402e-27
EB = 1152921504606846976
G = 6.6743e-11
GB = 1073741824
KB = 1024
MB = 1048576
NA = 6.02214076e+23
PB = 1125899906842624
TB = 1099511627776
YB = 1208925819614629174706176
ZB = 1180591620717411303424
atto = 1e-18
c = 299792458
centi = 0.01
deci = 0.1
deka = 10.0
e = 2.718281828459045
exa = 1e+18
femto = 1e-15
gamma = 0.5772156649015329
giga = 1000000000.0
h = 6.62607015e-34
hecto = 100.0
inf = inf
kilo = 1000.0
mega = 1000000.0
micro = 1e-06
milli = 0.001
nan = nan
nano = 1e-09
peta = 1000000000000000.0
phi = 1.618033988749895
pi = 3.141592653589793
pico = 1e-12
qe = 1.60217733e-19
tera = 1000000000000.0
yocto = 1e-24
yotta = 1e+24
zepto = 1e-21
zetta = 1e+21
★ equations [Solving specific forms of equations]
FUNCTIONS
linear_equation(left: list, right: list) -> list
polynomial_equation(coefficients: list) -> list
★ maths [Mathematical functions]
FUNCTIONS
A = arrangement(n: int, r: int) -> int
C = combination(n: int, r: int) -> int
acos(x: Union[int, float]) -> Union[int, float]
acosh(x: Union[int, float]) -> Union[int, float]
acot(x: Union[int, float]) -> Union[int, float]
acoth(x: Union[int, float]) -> Union[int, float]
acsc(x: Union[int, float]) -> Union[int, float]
acsch(x: Union[int, float]) -> Union[int, float]
arrangement(n: int, r: int) -> int
asec(x: Union[int, float]) -> Union[int, float]
asech(x: Union[int, float]) -> Union[int, float]
asin(x: Union[int, float]) -> Union[int, float]
asinh(x: Union[int, float]) -> Union[int, float]
atan(x: Union[int, float]) -> Union[int, float]
atanh(x: Union[int, float]) -> Union[int, float]
beta(p: Union[int, float], q: Union[int, float]) -> Union[int, float]
combination(n: int, r: int) -> int
cos(x: Union[int, float]) -> Union[int, float]
cosh(x: Union[int, float]) -> Union[int, float]
cot(x: Union[int, float]) -> Union[int, float]
coth(x: Union[int, float]) -> Union[int, float]
csc(x: Union[int, float]) -> Union[int, float]
csch(x: Union[int, float]) -> Union[int, float]
definite_integral(f, x_start: Union[int, float], x_end: Union[int, float], n: int = 10000000) -> float
derivative(f, x: Union[int, float], h: Union[int, float] = 1e-07) -> float
erf(x: Union[int, float]) -> float
exp(x: Union[int, float]) -> Union[int, float]
factorial(n: int) -> int
freq(data: Union[list, tuple]) -> dict
gamma(alpha: Union[int, float]) -> float
gaussian(x: Union[int, float], _mu: Union[int, float] = 0, _sigma: Union[int, float] = 1) -> float
gcd(*args: int) -> int
lcm(*args: int) -> int
ln(x: Union[int, float]) -> Union[int, float]
mean(numbers: Union[list, tuple]) -> Union[int, float, complex]
median(numbers: Union[list, tuple]) -> Union[int, float, complex]
mode(data: Union[list, tuple])
parity(x: int) -> int
pi(i: int, n: int, f) -> Union[int, float, complex]
poisson(x: int, _lambda: Union[int, float]) -> float
product(numbers: Union[list, tuple]) -> Union[int, float, complex]
ptp(numbers: Union[list, tuple]) -> Union[int, float, complex]
root(x: Union[int, float, complex], y: Union[int, float, complex]) -> Union[int, float, complex]
sec(x: Union[int, float]) -> Union[int, float]
sech(x: Union[int, float]) -> Union[int, float]
sigma(i: int, n: int, f) -> Union[int, float, complex]
sigmoid(x: Union[int, float]) -> float
sign(x: Union[int, float]) -> int
sin(x: Union[int, float]) -> Union[int, float]
sinh(x: Union[int, float]) -> Union[int, float]
std(numbers: Union[list, tuple]) -> Union[int, float, complex]
tan(x: Union[int, float]) -> Union[int, float]
tanh(x: Union[int, float]) -> Union[int, float]
var(numbers: Union[list, tuple]) -> Union[int, float, complex]
zeta(alpha: Union[int, float]) -> float
★ plotting [Draw a graph of equations using characters]
FUNCTIONS
background(right: int | float = 5, left: int | float = -5, top: int | float = 5, bottom: int | float = -5, complexity: int | float = 5, ratio: int | float = 3, merge: bool = False) -> list | str
binary(function, right: int | float = 5, left: int | float = -5, top: int | float = 5, bottom: int | float = -5, complexity: int | float = 5, ratio: int | float = 3, error=0, compare='==', merge: bool = True, basic: list = None, character: str = '.', data: bool = False) -> list | str
c_unary(function, start: int | float, end: int | float, interval: int | float = 5, projection: str = 'ri', right: int | float = 5, left: int | float = -5, top: int | float = 5, bottom: int | float = -5, complexity: int | float = 5, ratio: int | float = 3, merge: bool = True, basic: list = None, character: str = '.', data: bool = False) -> list | str
change(data: list | str) -> list | str
unary(function, right: int | float = 5, left: int | float = -5, top: int | float = 5, bottom: int | float = -5, complexity: int | float = 5, ratio: int | float = 3, merge: bool = True, basic: list = None, character: str = '.', data: bool = False) -> list | str
★ probability [Probability function]
FUNCTIONS
binomial(sample_size: int, successes: int, success_probability: Union[int, float]) -> float
hypergeometric(total_items: int, success_items: int, sample_size: int, successes_in_sample: int) -> float
★ random [Generate random numbers or random arrays]
FUNCTIONS
choice(seq: Union[list, tuple, str], shape: Union[list, tuple] = None)
gauss(mu: Union[int, float] = 0, sigma: Union[int, float] = 1, shape: Union[list, tuple] = None) -> Union[float, list]
gauss_error(original: Union[list, tuple], mu: Union[int, float] = 0, sigma: Union[int, float] = 1) -> list
rand(shape: Union[list, tuple] = None) -> Union[float, list]
randint(a: int, b: int, shape: Union[list, tuple] = None) -> Union[int, list]
uniform(a: Union[int, float], b: Union[int, float], shape: Union[list, tuple] = None) -> Union[float, list]
★ regression [Formula based polynomial regression]
FUNCTIONS
linear_regression(x: Union[list, tuple], y: Union[list, tuple]) -> list
parabolic_regression(x: Union[list, tuple], y: Union[list, tuple]) -> list
polynomial_regression(x: Union[list, tuple], y: Union[list, tuple], n: int = None) -> list
★ sequence [Various sequences]
FUNCTIONS
bernoulli(n: int, single: bool = True) -> list
catalan(n: int) -> int
fibonacci(n: int) -> int
★ tools [Other useful tools]
FUNCTIONS
classify(array: Union[list, tuple]) -> dict
deduplicate(iterable: Union[list, tuple, str]) -> Union[list, tuple, str]
frange(start: Union[int, float], stop: Union[int, float], step: float = 1.0) -> list
linspace(start: Union[int, float], stop: Union[int, float], number: int) -> list
split(iterable: Union[list, tuple, str], key: Union[list, tuple], retain: bool = False) -> list
代码测试
Code testing
>>> from pypynum import (Array, Geometry, Matrix, Quaternion, Symbolics, Tensor, Vector,
cipher, constants, equations, mathematics, plotting, random, regression, tools)
...
>>> print(Array.array())
>>> print(Array.array([1, 2, 3, 4, 5, 6, 7, 8]))
>>> print(Array.array([[1, 2, 3, 4], [5, 6, 7, 8]]))
>>> print(Array.array([[[1, 2], [3, 4]], [[5, 6], [7, 8]]]))
[]
[1 2 3 4 5 6 7 8]
[[1 2 3 4]
[5 6 7 8]]
[[[1 2]
[3 4]]
[[5 6]
[7 8]]]
>>> triangle = Geometry.Triangle((0, 0), (2, 2), (3, 0))
>>> print(triangle.perimeter())
>>> print(triangle.area())
>>> print(triangle.centroid())
8.06449510224598
3.0
(1.6666666666666667, 0.6666666666666666)
>>> m0 = Matrix.mat([[1, 2], [3, 4]])
>>> m1 = Matrix.mat([[5, 6], [7, 8]])
>>> print(m0)
>>> print(m1)
>>> print(m0 + m1)
>>> print(m0 @ m1)
>>> print(m0.inv())
>>> print(m1.rank())
[[1 2]
[3 4]]
[[5 6]
[7 8]]
[[ 6 8]
[10 12]]
[[19 22]
[43 50]]
[[-2.0 1.0]
[ 1.5 -0.5]]
2
>>> q0 = Quaternion.quat(1, 2, 3, 4)
>>> q1 = Quaternion.quat(5, 6, 7, 8)
>>> print(q0)
>>> print(q1)
>>> print(q0 + q1)
>>> print(q0 * q1)
>>> print(q0.inverse())
>>> print(q1.conjugate())
(1+2i+3j+4k)
(5+6i+7j+8k)
(6+8i+10j+12k)
(-60+12i+30j+24k)
(0.18257418583505536+-0.3651483716701107i+-0.5477225575051661j+-0.7302967433402214k)
(5+-6i+-7j+-8k)
>>> print(Symbolics.basic)
>>> print(Symbolics.english)
>>> print(Symbolics.greek)
>>> print(Symbolics.interpreter("-(10+a-(3.14+b0)*(-5))**(-ζn1-2.718/mΣ99)//9"))
%()*+-./0123456789
ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz
ΑΒΓΔΕΖΗΘΙΚΛΜΝΞΟ∏ΡΣΤΥΦΧΨΩβγδεζηθικλμνξοπρστυφχψω
[['10', '+', 'a', '-', ['3.14', '+', 'b0'], '*', '-5'], '**', ['-ζn1', '-', '2.718', '/', 'mΣ99'], '//', '9']
>>> t0 = Tensor.ten([[[1, 2], [3, 4]], [[5, 6], [7, 8]]])
>>> t1 = Tensor.ten([[[9, 10], [11, 12]], [[13, 14], [15, 16]]])
>>> print(t0)
>>> print(t1)
>>> print(t0 + t1)
>>> print(t0 @ t1)
[[[1 2]
[3 4]]
[[5 6]
[7 8]]]
[[[ 9 10]
[11 12]]
[[13 14]
[15 16]]]
[[[10 12]
[14 16]]
[[18 20]
[22 24]]]
[[[ 31 34]
[ 71 78]]
[[155 166]
[211 226]]]
>>> string = "PyPyNum"
>>> encrypted = cipher.dna(string)
>>> print(string)
>>> print(encrypted)
>>> print(cipher.dna(encrypted, decrypt=True))
PyPyNum
CCCTAGACCCTCGTCCCGCTAAACCCTG
PyPyNum
v0 = Vector.vec([1, 2, 3, 4])
v1 = Vector.vec([5, 6, 7, 8])
print(v0)
print(v1)
print(v0 + v1)
print(v0 @ v1)
print(v0.normalize())
print(v1.angles())
[1 2 3 4]
[5 6 7 8]
[ 5 12 21 32]
70
[0.18257418583505536 0.3651483716701107 0.5477225575051661 0.7302967433402214]
[1.1820279130506308, 1.0985826410133916, 1.0114070854293842, 0.9191723423169716]
>>> print(constants.TB)
>>> print(constants.e)
>>> print(constants.h)
>>> print(constants.phi)
>>> print(constants.pi)
>>> print(constants.tera)
1099511627776
2.718281828459045
6.62607015e-34
1.618033988749895
3.141592653589793
1000000000000.0
>>> p = [1, -2, -3, 4]
>>> m = [
[
[1, 2, 3],
[6, 10, 12],
[7, 16, 9]
],
[-1, -2, -3]
]
>>> print(equations.pe(p))
>>> print(equations.mles(*m))
提示：Matrix模块的eig函数可能存在计算错误
Tip: The eig function of the Matrix module may have calculation errors
[2.561552812809, -1.561552812809, 1.0]
[1.666666666667, -0.666666666667, -0.444444444444]
>>> print(mathematics.cot(constants.pi / 3))
>>> print(mathematics.gamma(1.5))
>>> print(mathematics.pi(1, 10, lambda x: x ** 2))
>>> print(mathematics.product([2, 3, 5, 7, 11, 13, 17, 19, 23, 29]))
>>> print(mathematics.sigma(1, 10, lambda x: x ** 2))
>>> print(mathematics.var([2, 3, 5, 7, 11, 13, 17, 19, 23, 29]))
0.577350269189626
0.886226925452758
13168189440000
6469693230
385
73.29
>>> plt = plotting.unary(lambda x: x ** 2, top=10, bottom=0, character="+")
>>> print(plt)
>>> print(plotting.binary(lambda x, y: x ** 2 + y ** 2 - 10, right=10, left=0, compare="<=", basic=plotting.change(plt)))
>>> print(plotting.c_unary(lambda x: x ** x, start=-10, end=10, interval=100, right=2, left=-2, top=2, bottom=-2, complexity=20, character="-"))
1.00e+01| + +
|
| + +
|
| + +
| + +
|
| + +
5.00e+00|_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
| + +
| + +
| + +
| + +
| + +
| + +
| + +
| +++ +++
0.00e+00|________________________+++________________________
-5.00e+00 0.00e+00 5.00e+00
1.00e+01| + +
|
| + +
|
|......... + +
|............. +
|..............
|................ +
5.00e+00|................_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
|................ +
|................ +
|.............. + +
|............. + +
|......... + +
| + +
| + +
| +++ +++
0.00e+00|________________________+++________________________
-5.00e+00 0.00e+00 5.00e+00
2.00e+00|
|
|
|
|
|
|
|
|
| -------
| ------ -----
| ---- --
| --- --
0.00e+00|_ _ _ _ _ _ _ _ _ _ --_ _ _ _ _ _ _ _ _-- _ _-- _ _ _ ---------------------------
| -- ------- ---
| - --
| - -
| -- -
| -- -
| -- -
| --- ---
| ---- ----
| -------- -------
| ------------
|
|
|
-2.00e+00|_________________________________________________________________________________
-2.00e+00 0.00e+00 2.00e+00
>>> print(random.gauss(0, 1, [2, 3, 4]))
>>> print(random.rand([2, 3, 4]))
>>> print(random.randint(0, 9, [2, 3, 4]))
>>> print(random.uniform(0, 9, [2, 3, 4]))
[[[0.005010042633490881, 1.1160375815053902, 0.6145920379300898, -1.4696487204627253], [-0.20685462876933186, 0.8275330804972041, -0.8377832703632173, -0.8880186869697656], [-0.2653914684173608, -0.5205164919803434, -0.08359499889147641, -0.3006165927585791]], [[-1.1666695379454972, -1.0979019033440636, 0.5647293393684544, 0.23438322147503707], [0.04298318405503412, -0.6059076560822075, 1.600626179545926, 0.5204087192933082], [-0.058768641542423485, -0.4369666543837353, 0.37851158006771385, 2.0777148219436796]]]
[[[0.40140286579987816, 0.07095255870174488, 0.6446608375143889, 0.6279016180497422], [0.804158734480493, 0.38595139889111474, 0.5653398643367361, 0.9106406788835898], [0.8502113481455789, 0.5679511415517262, 0.667955293914048, 0.43668222316158123]], [[0.06619508720421818, 0.09573784118592021, 0.6821744904157657, 0.9052002792268913], [0.30333795786917084, 0.13357618895131063, 0.144258651211569, 0.648655098110358], [0.8474099644680997, 0.8461881711073397, 0.6529621910052777, 0.17709859779327897]]]
[[[1, 3, 9, 9], [0, 8, 0, 6], [5, 0, 0, 3]], [[9, 5, 6, 2], [6, 4, 9, 6], [8, 4, 8, 6]]]
[[[2.3714687054662273, 7.8682431629091605, 3.4889108978334065, 7.8710116452525885], [8.524292784475549, 6.98190581041993, 3.4297944437860264, 6.068508585966597], [5.111615446006805, 7.916996987595166, 3.589747975729174, 1.3794064763997484]], [[3.295260189867274, 5.608688777939621, 8.217536152479274, 5.209074856197099], [4.95611538157316, 3.2743034659238717, 2.7104110034788764, 2.541949514340043], [8.033753127455242, 4.943764676329522, 7.150364785741341, 6.550305532995521]]]
>>> print(regression.linear_regression(range(5), [2, 4, 6, 7, 8]))
>>> print(regression.parabolic_regression(range(5), [2, 4, 6, 7, 8]))
f(x) = 1.5 * x + 2.4
[1.5, 2.4]
f(x) = -0.214285714 * x ** 2 + 2.357142857 * x + 1.971428571
[-0.214285714, 2.357142857, 1.971428571]
>>> print(tools.classify([1, 2.3, 4 + 5j, "string", list, True, 3.14, False, tuple, tools]))
>>> print(tools.deduplicate(["Python", 6, "NumPy", int, "PyPyNum", 9, "pypynum", "NumPy", 6, True]))
>>> print(tools.frange(0, 3, 0.4))
>>> print(tools.linspace(0, 2.8, 8))
{<class 'int'>: [1], <class 'float'>: [2.3, 3.14], <class 'complex'>: [(4+5j)], <class 'str'>: ['string'], <class 'type'>: [<class 'list'>, <class 'tuple'>], <class 'bool'>: [True, False], <class 'module'>: [<module 'pypynum.tools' from 'F:\\PyPyproject\\PyPyproject1\\pypynum\\tools.py'>]}
['Python', 6, 'NumPy', <class 'int'>, 'PyPyNum', 9, 'pypynum', True]
[0.0, 0.4, 0.8, 1.2000000000000002, 1.6, 2.0, 2.4000000000000004, 2.8000000000000003]
[0.0, 0.39999999999999997, 0.7999999999999999, 1.2, 1.5999999999999999, 1.9999999999999998, 2.4, 2.8]
提示：
测试已成功通过并结束。
这些测试只是这个包功能的一部分。
更多的功能需要自己探索和尝试！
Tip:
The test has been successfully passed and ended.
These tests are only part of the functionality of this package.
More features need to be explored and tried by yourself!
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