Trig Functions with arguments = Integer * Pi

*To*: mathgroup at christensen.cybernetics.net*Subject*: Trig Functions with arguments = Integer * Pi*From*: olness at phyvms.physics.smu.edu (Fredrick Olness (214) 768-2500 or -2495, Fax -4095)*Date*: Wed, 26 Oct 1994 12:36:57 -0500

> Fedor G. Pikus WRITES: > I need to declare some variables as integer, so that the trig functions > would be simplified. I have Declare package from MathSource, > but it does not help: I declare n to be integer, and Sin[n Pi] stays > as it is. ================================================================= Fedor, I have attached a solution below. I have also included the case of the Cos[n Pi] which may be of interest. You may wish to practice on a sample function like sin[] or cos[] (lowercase) before you start redefining system functions. Fred Olness ================================================================= IntegerQ[n] ^= True; ?n Global`n IntegerQ[n] ^= True Unprotect[Sin]; Sin[n_?IntegerQ Pi] := 0; Protect[Sin]; {Sin[ n Pi],Sin[ 2 n Pi],Sin[ 2 Pi],Sin[ j Pi]} {0, Sin[2 n Pi], 0, Sin[j Pi]} (*Note, the 2nd did not simplify*) Unprotect[Cos]; Cos[n_?IntegerQ Pi] := (-1)^n; Protect[Cos]; {Cos[ n Pi],Cos[ 2 n Pi],Cos[ 2 Pi],Cos[ 3 Pi]} n {(-1) , Cos[2 n Pi], 1, -1} ================================================================= Fredrick I. Olness SMU Mail: Department of Physics Fondren Science Bldg. Southern Methodist University Dallas, TX 75275 Phone: (214) 768-2500 (SMU Office) (214) 768-2495 (SMU Secretary) (214) 768-4095 (SMU FAX) Internet: Olness at phyvms.physics.smu.edu (129.119.200.74) Olness at mail.physics.smu.edu