Question

我想定义任意函数f。我知道f总是会返回一个正数。我希望能够在运行简化时（尤其是简化文档中提到的三个电源规则）使用这些知识。有没有办法做到这一点？我正在寻找类似下面的内容：

f = Function("f", positive = True)
g = Function("g", positive = True)
x = symbols("x")
y = symbols("y")
n = symbols("n", real = True)

test = ( f(x) * g(y) ) ** n
# This should work but doesn't
expand_power_base(test)

Answer 1

这是一种不那么好的方式：

alphabet = list(string.ascii_lowercase)

def assert_positive(value, args):
    result = value
    for i in range( len(args) ):
        a_symbol = symbols( alphabet[i], positive = True)
        result = result.subs(args[i], a_symbol)

    result = simplify(result)

    for i in range( len(args) ):
        a_symbol = symbols( alphabet[i], positive = True)
        result = result.subs(a_symbol, args[i])

    return(result)

Answer 2

一种解决方法是使用expand_power_base选项调用force=True。这迫使sympy执行功率简化，而不考虑假设。

import sympy as sp

f = sp.Function("f")
g = sp.Function("g")
x, y, n = sp.symbols("x, y, n")

test = ( f(x) * g(y) ) ** n
sp.expand_power_base(test, force=True)

f(x)**n*g(y)**n

Answer 3

定义为Function('f')的函数目前不支持假设。您需要显式创建子类，如

class f(Function):
    is_positive = True

同意任意功能范围

3 个答案: