Texas Instruments TI-89 User Manual - Page 800

Simultaneous polynomial equations can have extra variables that have no values, but represent given numeric values that could be substituted later. cSolve(u_ùv_ìu_=c_ùv_ and v_^2=ëu_,{u_,v_}) ¸ u_= ë( 1ì4øc_+1)2 4 and v_= 1ì4øc_+1 2 or u_= and v_= ë( 1ì4øc_ì1) 2 or u_=0 and v_=0 You can also include solution variables that do not appear in the equations. These solutions show how families of solutions might contain arbitrary constants of the form @k, where k is an integer suffix from 1 through 255. The suffix resets to 1 when you use ClrHome or ƒ 8:Clear Home. For polynomial systems, computation time or memory exhaustion may depend strongly on the order in which you list solution variables. If your initial choice exhausts memory or your patience, try rearranging the variables in the equations and/or varOrGuess list. cSolve(u_ùv_ìu_=v_ and v_^2=ëu_,{u_,v_,w_}) ¸ u_=1/2 + 23øi and v_=1/2 ì 23øi and w_=@1 or u_=1/2 ì 23øi and v_=1/2 + 23øi and w_=@1 or u_=0 and v_=0 and w_=@1 If you do not include any guesses and if any equation is non-polynomial in any variable but all equations are linear in all solution variables, cSolve() uses Gaussian elimination to attempt to determine all solutions. cSolve(u_+v_=e^(w_) and u_ìv_= i, {u_,v_}) ¸ u_= e w_ 2 +1/2øi and v_= ew_ì i 2 If a system is neither polynomial in all of its variables nor linear in its solution variables, cSolve() determines at most one solution using an approximate iterative method. To do so, the number of solution variables must equal the number of equations, and all other variables in the equations must simplify to numbers. cSolve(e^(z_)=w_ and w_=z_^2, {w_,z_}) ¸ w_=.494... and z_=ë.703... A non-real guess is often necessary to determine a non-real solution. For convergence, a guess might have to be rather close to a solution. cSolve(e^(z_)=w_ and w_=z_^2, {w_,z_=1+ i}) ¸ w_=.149... + 4.891...øi and z_=1.588... + 1.540...øi 800 Appendix A: Functions and Instructions