ZS's code

GenF.rb

@@ -0,0 +1,105 @@
+#!/usr/bin/env ruby
+# encoding: UTF-8
+=begin
+Created on Nov 22 2021
+
+Output a string for Mathematica to calculate the Fourier series of a certain hkl index.
+
+@author: ZSun
+=end
+
+puts "h = 1\nk = 1\nl = 3" # change hkl here
+gets
+
+def out(lx, ly, lz, func='Cos')
+  str = ''
+  for i in 0...lx.size
+    str += "#{func}[2 Pi (h (#{lx[i]}) + k (#{ly[i]}) + l (#{lz[i]}))] +"
+  end
+  print("FullSimplify["+str.chop+"]")
+  # these strings should be pasted to and executed in Mathematica to obtain the math expressions.
+  gets
+end
+
+# O70 Fddd; obtained from ITC
+lx = ["x","-x","-x","x","1/4-x","1/4+x","1/4+x","1/4-x",
+"x","-x","-x","x","1/4-x","1/4+x","1/4+x","1/4-x",
+"x+1/2","-x+1/2","-x+1/2","x+1/2","1/4-x+1/2","1/4+x+1/2","1/4+x+1/2","1/4-x+1/2",
+"x+1/2","-x+1/2","-x+1/2","x+1/2","1/4-x+1/2","1/4+x+1/2","1/4+x+1/2","1/4-x+1/2"]
+
+ly=["y","-y","y","-y","1/4-y","1/4+y","1/4-y","1/4+y",
+"y+1/2","-y+1/2","y+1/2","-y+1/2","1/4-y+1/2","1/4+y+1/2","1/4-y+1/2","1/4+y+1/2",
+"y","-y","y","-y","1/4-y","1/4+y","1/4-y","1/4+y",
+"y+1/2","-y+1/2","y+1/2","-y+1/2","1/4-y+1/2","1/4+y+1/2","1/4-y+1/2","1/4+y+1/2"]
+
+lz=["z","z","-z","-z","1/4-z","1/4-z","1/4+z","1/4+z",
+"z+1/2","z+1/2","-z+1/2","-z+1/2","1/4-z+1/2","1/4-z+1/2","1/4+z+1/2","1/4+z+1/2",
+"z+1/2","z+1/2","-z+1/2","-z+1/2","1/4-z+1/2","1/4-z+1/2","1/4+z+1/2","1/4+z+1/2",
+"z","z","-z","-z","1/4-z","1/4-z","1/4+z","1/4+z"]
+
+out(lx, ly, lz)
+out(lx, ly, lz, 'Sin')
+
+=begin
+(111): a=16 (Cos[2 Pi x] Cos[2 Pi y] Cos[2 Pi z] + Sin[2 Pi x] Sin[2 Pi y] Sin[2 Pi z])
+    -16 I (Cos[2 Pi x] Cos[2 Pi y] Cos[2 Pi z] + Sin[2 Pi x] Sin[2 Pi y] Sin[2 Pi z])
+(022): b=16 (Cos[4 Pi (y - z)] + Cos[4 Pi (y + z)])
+(202): c=16 (Cos[4 Pi (z - x)] + Cos[4 Pi (z + x)])
+(220): d=16 (Cos[4 Pi (x - y)] + Cos[4 Pi (x + y)])
+(004): e=32 Cos[8 Pi z]
+(113): f=16 (Cos[2 Pi x] Cos[2 Pi y] Cos[2 Pi 3 z] - Sin[2 Pi x] Sin[2 Pi y] Sin[2 Pi 3 z])
+    +16 I (Cos[2 Pi x] Cos[2 Pi y] Cos[2 Pi 3 z] - Sin[2 Pi x] Sin[2 Pi y] Sin[2 Pi 3 z])
+(222): g=-32 I Sin[4 Pi x] Sin[4 Pi y] Sin[4 Pi z]
+
+x = u
+y = v/2
+z = w/(2 Sqrt[3])
+=end
+
+# M15 C2/c; obtained from ITC
+lx = ["x","-x","-x","x",
+"1/2+x","1/2-x","1/2-x","1/2+x"]
+
+ly = ["y","y","-y","-y",
+"1/2+y","1/2+y","1/2-y","1/2-y"]
+
+lz = ["z","1/2-z","-z","1/2+z",
+"z","1/2-z","-z","1/2+z"]
+
+out(lx, ly, lz)
+out(lx, ly, lz, 'Sin')
+
+=begin
+(110): a=8 Cos[2 Pi x] Cos[2 Pi y]
+(002): b=8 Cos[4 Pi z]
+(021): c=-8 Sin[4 Pi y] Sin[2 Pi z] 
+(111): d=-8 Sin[2 Pi y] Sin[2 Pi (x+z)] 
+(112): e=8 Cos[2 Pi y] Cos[2 Pi (x+2 z)] 
+=end
+
+# T131 P4_2/mmc
+lx = ["x","-x","-y","y",
+"-x","x","y","-y",
+"-x","x","y","-y",
+"x","-x","-y","y",]
+
+ly = ["y","-y","x","-x",
+"y","-y","x","-x",
+"-y","y","-x","x",
+"-y","y","-x","x"]
+
+lz = ["z","z","1/2+z","1/2+z",
+"-z","-z","1/2-z","1/2-z",
+"-z","-z","1/2-z","1/2-z",
+"z","z","1/2+z","1/2+z"]
+
+out(lx, ly, lz)
+out(lx, ly, lz, 'Sin')
+
+=begin
+(110): a=8(Cos[2 Pi (x-y)]+Cos[2 Pi (x+y)])
+(100): b=8(Cos[2 Pi x]+Cos[2 Pi y])
+(101): c=8 (Cos[2 Pi x]-Cos[2 Pi y]) Cos[2 Pi z]
+(002): d=16Cos[4 Pi z]
+(112): e=16 Cos[2 Pi x] Cos[2 Pi y] Cos[4 Pi z] 
+=end