ComplexityFunction failure in Simplify

• To: mathgroup at smc.vnet.net
• Subject: [mg43556] ComplexityFunction failure in Simplify
• From: Artūras Acus <acus at itpa.lt>
• Date: Sat, 20 Sep 2003 06:39:25 -0400 (EDT)
• Organization: Institute of Theoretical Physics and Astronomy
• Sender: owner-wri-mathgroup at wolfram.com

```Dear Group,
Why complexity function in Simplify and FullSimplify
dont work properly in this case. Thanks in advice for any ideas to
improve it in order to get the first rezult.

In[1]:=
test=-j*(j+1)+2 Cos[2* F]* j *(j+1)+(4/3)*Sin[F]^2 *j*(j+1)-
Cos[2*F]^2* j *(j+1)-4*Sin[F]^4* (1/(4*3*5))*(12*j
*(j+1)-4)-4*Cos[2*F]*
Sin[F]^2*(1/3)*j *(j+1)-(1/3)*Sin[2*F]^2;

In[2]:=
rez1 = Simplify[test] /. Cos[2 F] -> 1 - 2 Sin[F]^2 //
Expand // Factor // InputForm

Out[2]//InputForm=
(-4*Sin[F]^2*(5 - 6*Sin[F]^2 + 8*j*Sin[F]^2 + 8*j^2*Sin[F]^2))/15

In[3]:=
LeafCount[%]

Out[3]=
32

In[4]:=
rez2=FullSimplify[test,
ComplexityFunction -> (Count[ExpToTrig[#],Cos[_],Infinity])&]//
InputForm

Out[4]//InputForm=
(4*(-2*(1 + 2*j*(1 + j)) + (-3 + 4*j*(1 + j))*Cos[2*F])*Sin[F]^2)/15

In[5]:=
LeafCount[%]
Out[5]=
32

Sincerely, Arturas Acus

```

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