Newtonmathsolver

python
t - 1
print('t - 1', t)


t - 1 9.999999999177334e-07

python
t * 2
print('t * 2', t)


t * 2 1.9999999998354667e-06

python
t / 2
print('t / 2', t)


t / 2 9.999999999177334e-07

python
t ** 2
print('t ** 2', t)


t ** 2 9.999999998354668e-13

python
t ** (1 / 2)
print('t ** (1 / 2)', t)


t ** (1 / 2) 9.999999999177334e-07

python
t.more()
print('more', t)


more 9.999999999177333e-08

python
t.less()
print('less', t)


less 9.999999999177334e-07

逻辑运算

python
print(t == 0)
print(t > 0)
print(t >= 0)
print(t < 1)
print(t <= 1e-7)


False

True

True

True

False

NewtonMathSolver

> 使用牛顿法无限迭代求任意方程近似解

基础调用

python
from NewtonMathSolver import Tolerance, NewtonMathSolver

n = NewtonMathSolver('x - 1 = 10', 'x', 2, Tolerance(level=6))
print(n.iterate(10))
print(n.result)



与之等效的是

python
from NewtonMathSolver import Tolerance, NewtonMathSolver

n = NewtonMathSolver('x - 1 = 10', 'x', 2, 1e-6)
print(n.iterate(10))
print(n.result)



进一步探究

这样可以看到计算步骤

python
from NewtonMathSolver import Tolerance, NewtonMathSolver

n = NewtonMathSolver('x - 1 = 10', 'x', 2, Tolerance(level=6))

while 1 + 1 == 2:
n.iterate()
print(n.result)
if n.result.result:
break



容忍与误差

使用牛顿法通常会有误差，于是我们会将误差与设定的容忍度进行对比，容忍度即误差允许的最大值

这样可以设定一个可操作的误差

python
[NewtonMathSolver-0.1.0.tar.gz](https://github.com/MoYeRanqianzhi/NewtonMathSolver/files/12750527/NewtonMathSolver-0.1.0.tar.gz)

from NewtonMathSolver import Tolerance

t = Tolerance(1e-6)



与之等价的是

python
from NewtonMathSolver import Tolerance

t = Tolerance(level=6)



以及

python
from NewtonMathSolver import Tolerance

t = Tolerance(1e-6, 666)
若是同时存在两个参数，则tolerance优先



其可以进行多种操作

自增

python
from NewtonMathSolver import Tolerance

t = Tolerance(level=6)


以下操作均允许

python
t + 1
print('t + 1', t)