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r36/xlog/RESIDUE.LOG
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REDUCE 3.6, 15-Jul-95, patched to 6 Mar 96 ... % test file for residue package residue(x/(x^2-2),x,sqrt(2)); 1 --- 2 poleorder(x/(x^2-2),x,sqrt(2)); 1 residue(sin(x)/(x^2-2),x,sqrt(2)); sqrt(2)*sin(sqrt(2)) ---------------------- 4 poleorder(sin(x)/(x^2-2),x,sqrt(2)); 1 residue(1/(x-1)^m/(x-2)^2,x,2); - m poleorder(1/(x-1)/(x-2)^2,x,2); 2 residue(sin(x)/x^2,x,0); 1 poleorder(sin(x)/x^2,x,0); 1 residue((1+x^2)/(1-x^2),x,1); -1 poleorder((1+x^2)/(1-x^2),x,1); 1 residue((1+x^2)/(1-x^2),x,-1); 1 poleorder((1+x^2)/(1-x^2),x,-1); 1 residue(tan(x),x,pi/2); -1 poleorder(tan(x),x,pi/2); 1 residue((x^n-y^n)/(x-y),x,y); 0 poleorder((x^n-y^n)/(x-y),x,y); 0 residue((x^n-y^n)/(x-y)^2,x,y); n y *n ------ y poleorder((x^n-y^n)/(x-y)^2,x,y); 1 residue(tan(x)/sec(x-pi/2)+1/cos(x),x,pi/2); -2 poleorder(tan(x)/sec(x-pi/2)+1/cos(x),x,pi/2); 1 for k:=1:2 sum residue((a+b*x+c*x^2)/(d+e*x+f*x^2),x, part(part(solve(d+e*x+f*x^2,x),k),2)); b*f - c*e ----------- 2 f residue(sin(x)/x^6,x,0); 1 ----- 120 residue((1-cos(x))/x^5,x,0); - 1 ------ 24 residue(exp(1/x),x,0); ***** taylor fails % not implemented residue((A*x+B*x^2+c)/(D*x+E),x,-E/D); 2 2 - a*d*e + b*e + c*d ------------------------ 3 d residue(tan(x),x,pi/2); -1 residue(sec(x),x,pi/2); -1 residue(factorial(x),x,0); ***** not yet implemented % ***** not yet implemented residue(x^3/sin(1/x)^2,x,infinity); - 1 ------ 15 poleorder(x^3/sin(1/x)^2,x,infinity); 5 residue(x^3*sin(1/x)^2,x,infinity); -1 poleorder(x^3*sin(1/x)^2,x,infinity); 1 end; (TIME: residue 1800 2070)