Python3 - Sympy:扩展trig函数的产品

Question

我找不到让SymPy将产品扩展cos(a)*cos(b)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)或者trigsimp(c)也不提供任何替代形式.

我想cos(a)*cos(b)扩展到1/2*(cos(a+b) + cos(a-b)) ...任何提示？

Answer 1

根据文档字符串help(sympy.fu),

fu将尽量减少目标函数measure.默认情况下,这首先最小化trig项的数量,然后最小化总操作的数量.

但是,如果你通过

measure=lambda x: -x.count_ops()

然后fu 将尝试最大化操作计数.

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,您可以直接调用Fu转换TR8:

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

产生相同的结果.docstring help(sys.modules['sympy.simplify.fu'])解释了可用的转换.这是摘要; 检查docstring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