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Integer declaration

• To: mathgroup at smc.vnet.net
• Subject: [mg13014] Integer declaration
• From: "Le Van Tri" <lvtri at cs.uwm.edu>
• Date: Tue, 30 Jun 1998 00:26:11 -0400
• Organization: University of Wisconsin - Milwaukee
• Sender: owner-wri-mathgroup at wolfram.com

Dear mathematica gurus,
I have seen several times in this news group someone needs to do
simplification
with integers. The following might help you to do it.

Unprotect[IntegerQ];
IntegerQ[m_+n_]/;IntegerQ[m]&&IntegerQ[n]=True;
IntegerQ[m_*n_]/;IntegerQ[m]&&IntegerQ[n]=True;
IntegerQ[m_^n_]/;IntegerQ[m]&&IntegerQ[n]&&NonNegative[n]=True;

Unprotect[Sin,Cos];
Sin[m_*Pi]/;IntegerQ[m]=0;
Cos[m_*Pi]/;IntegerQ[m]=1;
Sin[m_*Pi+x_]/;IntegerQ[m]=Sin[x];
Cos[m_*Pi+x_]/;IntegerQ[m]=Cos[x];
...

Ofcourse, you could add more simplification rules for your other
functions as well. I think this will work in many situations. How ever,
I dont know if there is a solution for the following situation:
  IntegerQ[m]=True;
  IntegerQ[n*n]=True;
  Should IntegerQ[m*(n-1)*(n+1)*(n^2+1)] be True? Does anyone have some
idea on this?

Regards,
Tri.