Python3 - Sympy：扩展三角函数的产品

Question

我找不到让 SymPy 将 cos(a)*cos(b) 之类的产品扩展为角度和的三角函数之和的方法。

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) 或 trigsimp(c) 也不提供任何替代形式。

我想将cos(a)*cos(b) 扩展为1/2*(cos(a+b) + cos(a-b)) ...有什么提示吗？

Answer 1

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 首先最小化触发项的数量，然后最小化总的数量 操作。

但是，如果你通过了

measure=lambda x: -x.count_ops()

然后fuwill try to maximize the op count。

---

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()))

产量

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

---

或者，你可以call the Fu transformation TR8 directly:

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