Python3 - Sympy：展开三角函数的乘积

我找不到让 SymPy 扩展产品的方法，例如cos(a)*cos(b)转化为角度和的三角函数之和。

from sympy import *
init_printing()
wrf,wlo,t = symbols('\omega_RF \omega_LO t')
c = cos(wrf*t)*cos(wlo*t)
expand_trig(c)

保持产品完好无损。simplify(c) or trigsimp(c)也不给出任何替代形式。

我想拥有cos(a)*cos(b)扩大到1/2*(cos(a+b) + cos(a-b))...有什么提示吗？

根据文档字符串，help(sympy.fu),

fu将尝试最小化目标函数measure。默认情况下这个 首先最小化三角项的数量，然后最小化总三角项的数量 运营。

但是，如果您通过

measure=lambda x: -x.count_ops()

then fu 会尝试maximize操作数 https://groups.google.com/forum/#!topic/sympy/wTXXjQg9Zyk.

import sympy as sy
sy.init_printing()
wrf, wlo, t = sy.symbols('\omega_RF \omega_LO t')
c = sy.cos(wrf*t)*sy.cos(wlo*t)
print(sy.fu(c, measure=lambda x: -x.count_ops()))

yields

cos(\omega_LO*t - \omega_RF*t)/2 + cos(\omega_LO*t + \omega_RF*t)/2

或者，你可以直接调用Fu变换TR8 https://stackoverflow.com/a/25395386/190597:

from sympy.simplify.fu import TR8
print(TR8(c))

产生相同的结果。文档字符串，help(sys.modules['sympy.simplify.fu'])解释了可用的转换。这是摘要；检查文档字符串以获取更多信息：

TR0 - simplify expression
TR1 - sec-csc to cos-sin
TR2 - tan-cot to sin-cos ratio
TR2i - sin-cos ratio to tan
TR3 - angle canonicalization
TR4 - functions at special angles
TR5 - powers of sin to powers of cos
TR6 - powers of cos to powers of sin
TR7 - reduce cos power (increase angle)
TR8 - expand products of sin-cos to sums
TR9 - contract sums of sin-cos to products
TR10 - separate sin-cos arguments
TR10i - collect sin-cos arguments
TR11 - reduce double angles
TR12 - separate tan arguments
TR12i - collect tan arguments
TR13 - expand product of tan-cot
TRmorrie - prod(cos(x*2**i), (i, 0, k - 1)) -> sin(2**k*x)/(2**k*sin(x))
TR14 - factored powers of sin or cos to cos or sin power
TR15 - negative powers of sin to cot power
TR16 - negative powers of cos to tan power
TR22 - tan-cot powers to negative powers of sec-csc functions
TR111 - negative sin-cos-tan powers to csc-sec-cot