reduce-historical/r36/xlog/RESIDUE.LOG

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)