import sympy
sympy.E**(sympy.I*sympy.pi) + 1
0
x = sympy.symbols("x", real=True)y = sympy.expand(sympy.exp(sympy.I*x), complex=True)y
I*sin(x) + cos(x)
tmp1 = sympy.series(sympy.cos(x), x, 0, 10)tmp1
1 - x**2/2 + x**4/24 - x**6/720 + x**8/40320 + O(x**10)
tmp2 = sympy.series(sympy.sin(x), x, 0, 10)tmp2
x - x**3/6 + x**5/120 - x**7/5040 + x**9/362880 + O(x**10)
tmp3 = sympy.integrate(x*sympy.sin(x), x)tmp3
-x*cos(x) + sin(x)
tmp4 = sympy.integrate(x*sympy.sin(x), (x, 0, 2*sympy.pi))tmp4
-2*pi
x, y = sympy.symbols("x, y")r = sympy.symbols("r", positive=True)circle_area = 2*sympy.integrate(sympy.sqrt(r**2 - x**2), (x, -r, r))circle_area
pi*r**2
expression.subs(x, y): 将计算式中的x替换成y
expression.subs({x:y, u:v}): 使用字典进行多个替换
expression.subs([(x,y), (u,v)]): 使用列表进行替换
circle_area = circle_area.subs(r, sympy.sqrt(r**2 - x**2))circle_area
pi*(r**2 - x**2)
tmp4 = sympy.integrate(circle_area, (x, -r, r))tmp4
4*pi*r**3/3
x = sympy.symbols("x", real=True)h = sympy.symbols("h", positive=True)f = sympy.symbols("f", cls=sympy.Function)
f_diff = f(x).diff(x, 1)f_diff
Derivative(f(x), x)
调用as_finite_diff(),将一阶倒数转换为使用f(x), f(x-h), f(x-2h), f(x-3h)表达的四点公式:
expr_diff = sympy.Derivative.as_finite_difference(f_diff, [x, x-h, x-2*h, x-3*h])expr_diff
11*f(x)/(6*h) - f(-3*h + x)/(3*h) + 3*f(-2*h + x)/(2*h) - 3*f(-h + x)/h
sym_dexpr = f_diff.subs(f(x), x*sympy.exp(-x**2)).doit()sym_dexpr
-2*x**2*exp(-x**2) + exp(-x**2)
数学符号用Symbol对象表示,符号对象的name属性是符号名,符号名在显示由此符号构成的表达式时使用。如下面的例子
x = sympy.symbols("我是X", real=True)x.name
'我是X'
m, n = sympy.symbols("m, n", integer=True)x = sympy.symbols("x", positive=True)
每个符号都有很多is_*属性,用来判断符号的各种假设条件。
[attr for attr in dir(x) if attr.startswith("is_") and attr.lower() == attr]
['is_algebraic', 'is_algebraic_expr', 'is_antihermitian', 'is_commutative', 'is_comparable', 'is_complex', 'is_composite', 'is_constant', 'is_even', 'is_finite', 'is_hermitian', 'is_hypergeometric', 'is_imaginary', 'is_infinite', 'is_integer', 'is_irrational', 'is_negative', 'is_noninteger', 'is_nonnegative', 'is_nonpositive', 'is_nonzero', 'is_number', 'is_odd', 'is_polar', 'is_polynomial', 'is_positive', 'is_prime', 'is_rational', 'is_rational_function', 'is_real', 'is_symbol', 'is_transcendental', 'is_zero']
1/2 + 1/3
0.8333333333333333
sympy.S(1)/2 + 1/sympy.S(3)
5/6
print(sympy.N(sympy.pi, 50))
3.1415926535897932384626433832795028841971693993751
x, y = sympy.symbols("x, y")expr = sympy.expand((x+y)**3)expr
x**3 + 3*x**2*y + 3*x*y**2 + y**3
**S**ympy重新定义了所有的数学运算符和数学函数。
- Add类表示加法
- Mul表示乘法
- Pow表示指数
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