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Question: How to simplify long expressions

Question:How to simplify long expressions

mostibra 20 Maple
simplification
November 17 2015
0
> 

phi := sin((1/4)*Pi*x)*(c__1*cosh((1/4)*Pi*y)+c__2*sinh((1/4)*pi*y)+c__3*y*cosh((1/4)*Pi*y)+c__4*y*sinh((1/4)*Pi*y))

sin((1/4)*Pi*x)*(c__1*cosh((1/4)*Pi*y)+c__2*sinh((1/4)*pi*y)+c__3*y*cosh((1/4)*Pi*y)+c__4*y*sinh((1/4)*Pi*y))

 (1)
> 

phi

sin((1/4)*Pi*x)*(c__1*cosh((1/4)*Pi*y)+c__2*sinh((1/4)*pi*y)+c__3*y*cosh((1/4)*Pi*y)+c__4*y*sinh((1/4)*Pi*y))

 (2)
> 

diff((2), y);

sin((1/4)*Pi*x)*((1/4)*c__1*sinh((1/4)*Pi*y)*Pi+(1/4)*c__2*cosh((1/4)*pi*y)*pi+c__3*cosh((1/4)*Pi*y)+(1/4)*c__3*y*sinh((1/4)*Pi*y)*Pi+c__4*sinh((1/4)*Pi*y)+(1/4)*c__4*y*cosh((1/4)*Pi*y)*Pi)

 (3)
> 

diff((3), y);

sin((1/4)*Pi*x)*((1/16)*c__1*cosh((1/4)*Pi*y)*Pi^2+(1/16)*c__2*sinh((1/4)*pi*y)*pi^2+(1/2)*c__3*sinh((1/4)*Pi*y)*Pi+(1/16)*c__3*y*cosh((1/4)*Pi*y)*Pi^2+(1/2)*c__4*cosh((1/4)*Pi*y)*Pi+(1/16)*c__4*y*sinh((1/4)*Pi*y)*Pi^2)

 (4)
> 

phi

sin((1/4)*Pi*x)*(c__1*cosh((1/4)*Pi*y)+c__2*sinh((1/4)*pi*y)+c__3*y*cosh((1/4)*Pi*y)+c__4*y*sinh((1/4)*Pi*y))

 (5)
> 

diff((5), x);

(1/4)*cos((1/4)*Pi*x)*Pi*(c__1*cosh((1/4)*Pi*y)+c__2*sinh((1/4)*pi*y)+c__3*y*cosh((1/4)*Pi*y)+c__4*y*sinh((1/4)*Pi*y))

 (6)
> 

diff((6), x);

-(1/16)*sin((1/4)*Pi*x)*Pi^2*(c__1*cosh((1/4)*Pi*y)+c__2*sinh((1/4)*pi*y)+c__3*y*cosh((1/4)*Pi*y)+c__4*y*sinh((1/4)*Pi*y))

 (7)
> 

phi

sin((1/4)*Pi*x)*(c__1*cosh((1/4)*Pi*y)+c__2*sinh((1/4)*pi*y)+c__3*y*cosh((1/4)*Pi*y)+c__4*y*sinh((1/4)*Pi*y))

 (8)
> 

diff((8), x);

(1/4)*cos((1/4)*Pi*x)*Pi*(c__1*cosh((1/4)*Pi*y)+c__2*sinh((1/4)*pi*y)+c__3*y*cosh((1/4)*Pi*y)+c__4*y*sinh((1/4)*Pi*y))

 (9)
> 

diff((9), y);

(1/4)*cos((1/4)*Pi*x)*Pi*((1/4)*c__1*sinh((1/4)*Pi*y)*Pi+(1/4)*c__2*cosh((1/4)*pi*y)*pi+c__3*cosh((1/4)*Pi*y)+(1/4)*c__3*y*sinh((1/4)*Pi*y)*Pi+c__4*sinh((1/4)*Pi*y)+(1/4)*c__4*y*cosh((1/4)*Pi*y)*Pi)

 (10)

``

 (11)
> 

(4);

sin((1/4)*Pi*x)*((1/16)*c__1*cosh((1/4)*Pi*y)*Pi^2+(1/16)*c__2*sinh((1/4)*pi*y)*pi^2+(1/2)*c__3*sinh((1/4)*Pi*y)*Pi+(1/16)*c__3*y*cosh((1/4)*Pi*y)*Pi^2+(1/2)*c__4*cosh((1/4)*Pi*y)*Pi+(1/16)*c__4*y*sinh((1/4)*Pi*y)*Pi^2)

 (12)
> 

eval( (12), [x = 0]);

0

 (13)
> 

sin((1/4)*Pi*x)*((1/16)*c__1*cosh((1/4)*Pi*y)*Pi^2+(1/16)*c__2*sinh((1/4)*pi*y)*pi^2+(1/2)*c__3*sinh((1/4)*Pi*y)*Pi+(1/16)*c__3*y*cosh((1/4)*Pi*y)*Pi^2+(1/2)*c__4*cosh((1/4)*Pi*y)*Pi+(1/16)*c__4*y*sinh((1/4)*Pi*y)*Pi^2)

sin((1/4)*Pi*x)*((1/16)*c__1*cosh((1/4)*Pi*y)*Pi^2+(1/16)*c__2*sinh((1/4)*pi*y)*pi^2+(1/2)*c__3*sinh((1/4)*Pi*y)*Pi+(1/16)*c__3*y*cosh((1/4)*Pi*y)*Pi^2+(1/2)*c__4*cosh((1/4)*Pi*y)*Pi+(1/16)*c__4*y*sinh((1/4)*Pi*y)*Pi^2)

 (14)
> 

eval( (14), [x = 20]);

0

 (15)
> 

-(1/16)*sin((1/4)*Pi*x)*Pi^2*(c__1*cosh((1/4)*Pi*y)+c__2*sinh((1/4)*pi*y)+c__3*y*cosh((1/4)*Pi*y)+c__4*y*sinh((1/4)*Pi*y)) = 0;

-(1/16)*sin((1/4)*Pi*x)*Pi^2*(c__1*cosh((1/4)*Pi*y)+c__2*sinh((1/4)*pi*y)+c__3*y*cosh((1/4)*Pi*y)+c__4*y*sinh((1/4)*Pi*y)) = 0

 (16)
> 

eval( (16), [y = 9]);

-(1/16)*sin((1/4)*Pi*x)*Pi^2*(c__1*cosh((9/4)*Pi)+c__2*sinh((9/4)*pi)+9*c__3*cosh((9/4)*Pi)+9*c__4*sinh((9/4)*Pi)) = 0

 (17)
> 

evalf[5]( (17) );

-.61686*sin(.78540*x)*(587.25*c__1+c__2*sinh(2.2500*pi)+5285.2*c__3+5285.2*c__4) = 0.

 (18)
> 

-(1/16)*sin((1/4)*Pi*x)*Pi^2*(c__1*cosh((1/4)*Pi*y)+c__2*sinh((1/4)*pi*y)+c__3*y*cosh((1/4)*Pi*y)+c__4*y*sinh((1/4)*Pi*y)) = -sin((1/4)*pi*x);

-(1/16)*sin((1/4)*Pi*x)*Pi^2*(c__1*cosh((1/4)*Pi*y)+c__2*sinh((1/4)*pi*y)+c__3*y*cosh((1/4)*Pi*y)+c__4*y*sinh((1/4)*Pi*y)) = -sin((1/4)*pi*x)

 (19)
> 

eval( (19), [y = -9]);

-(1/16)*sin((1/4)*Pi*x)*Pi^2*(c__1*cosh((9/4)*Pi)-c__2*sinh((9/4)*pi)-9*c__3*cosh((9/4)*Pi)+9*c__4*sinh((9/4)*Pi)) = -sin((1/4)*pi*x)

 (20)
> 

evalf[5]( (20) );

-.61686*sin(.78540*x)*(587.25*c__1-1.*c__2*sinh(2.2500*pi)-5285.2*c__3+5285.2*c__4) = -1.*sin(.25000*pi*x)

 (21)
> 

-(1/4)*cos((1/4)*Pi*x)*Pi*((1/4)*c__1*sinh((1/4)*Pi*y)*Pi+(1/4)*c__2*cosh((1/4)*pi*y)*pi+c__3*cosh((1/4)*Pi*y)+(1/4)*c__3*y*sinh((1/4)*Pi*y)*Pi+c__4*sinh((1/4)*Pi*y)+(1/4)*c__4*y*cosh((1/4)*Pi*y)*Pi) = 0;

-(1/4)*cos((1/4)*Pi*x)*Pi*((1/4)*c__1*sinh((1/4)*Pi*y)*Pi+(1/4)*c__2*cosh((1/4)*pi*y)*pi+c__3*cosh((1/4)*Pi*y)+(1/4)*c__3*y*sinh((1/4)*Pi*y)*Pi+c__4*sinh((1/4)*Pi*y)+(1/4)*c__4*y*cosh((1/4)*Pi*y)*Pi) = 0

 (22)
> 

eval( (22), [y = 9]);

-(1/4)*cos((1/4)*Pi*x)*Pi*((1/4)*c__1*sinh((9/4)*Pi)*Pi+(1/4)*c__2*cosh((9/4)*pi)*pi+c__3*cosh((9/4)*Pi)+(9/4)*c__3*sinh((9/4)*Pi)*Pi+c__4*sinh((9/4)*Pi)+(9/4)*c__4*cosh((9/4)*Pi)*Pi) = 0

 (23)
> 

evalf[5]( (23) );

-.78540*cos(.78540*x)*(461.22*c__1+.25000*c__2*cosh(2.2500*pi)*pi+4738.2*c__3+4738.2*c__4) = 0.

 (24)
> 

-(1/4)*cos((1/4)*Pi*x)*Pi*((1/4)*c__1*sinh((1/4)*Pi*y)*Pi+(1/4)*c__2*cosh((1/4)*pi*y)*pi+c__3*cosh((1/4)*Pi*y)+(1/4)*c__3*y*sinh((1/4)*Pi*y)*Pi+c__4*sinh((1/4)*Pi*y)+(1/4)*c__4*y*cosh((1/4)*Pi*y)*Pi) = 0;

-(1/4)*cos((1/4)*Pi*x)*Pi*((1/4)*c__1*sinh((1/4)*Pi*y)*Pi+(1/4)*c__2*cosh((1/4)*pi*y)*pi+c__3*cosh((1/4)*Pi*y)+(1/4)*c__3*y*sinh((1/4)*Pi*y)*Pi+c__4*sinh((1/4)*Pi*y)+(1/4)*c__4*y*cosh((1/4)*Pi*y)*Pi) = 0

 (25)
> 

eval( (25), [y = -9]);

-(1/4)*cos((1/4)*Pi*x)*Pi*(-(1/4)*c__1*sinh((9/4)*Pi)*Pi+(1/4)*c__2*cosh((9/4)*pi)*pi+c__3*cosh((9/4)*Pi)+(9/4)*c__3*sinh((9/4)*Pi)*Pi-c__4*sinh((9/4)*Pi)-(9/4)*c__4*cosh((9/4)*Pi)*Pi) = 0

 (26)
> 

evalf[5]( (26) );

-.78540*cos(.78540*x)*(-461.22*c__1+.25000*c__2*cosh(2.2500*pi)*pi+4738.2*c__3-4738.2*c__4) = 0.

 (27)
> 

s:=solve({(18),(21),(24),(27)},{c__1,c__2,c__3,c__4});

{c__1 = 0.1113637578e-1*sin(.2500000000*pi*x)/sin(.7854000000*x), c__2 = 38405.79710*sin(.2500000000*pi*x)/(sin(.7854000000*x)*(13213.*cosh(2.250000000*pi)*pi-47382.*sinh(2.250000000*pi))), c__3 = -2.026391726*sin(.2500000000*pi*x)*cosh(2.250000000*pi)*pi/(sin(.7854000000*x)*(13213.*cosh(2.250000000*pi)*pi-47382.*sinh(2.250000000*pi))), c__4 = -0.1084023308e-2*sin(.2500000000*pi*x)/sin(.7854000000*x)}

 (28)
> 

phi1 := subs({c__1 = 0.1113637578e-1*sin(.2500000000*pi*x)/sin(.7854000000*x), c__2 = 38405.79710*sin(.2500000000*pi*x)/(sin(.7854000000*x)*(13213.*cosh(2.250000000*pi)*pi-47382.*sinh(2.250000000*pi))), c__3 = -2.026391726*sin(.2500000000*pi*x)*cosh(2.250000000*pi)*pi/(sin(.7854000000*x)*(13213.*cosh(2.250000000*pi)*pi-47382.*sinh(2.250000000*pi))), c__4 = -0.1084023308e-2*sin(.2500000000*pi*x)/sin(.7854000000*x)}, sin((1/4)*Pi*x)*(c__1*cosh((1/4)*Pi*y)+c__2*sinh((1/4)*pi*y)+c__3*y*cosh((1/4)*Pi*y)+c__4*y*sinh((1/4)*Pi*y)))

sin((1/4)*Pi*x)*(0.1113637578e-1*sin(.2500000000*pi*x)*cosh((1/4)*Pi*y)/sin(.7854000000*x)+38405.79710*sin(.2500000000*pi*x)*sinh((1/4)*pi*y)/(sin(.7854000000*x)*(13213.*cosh(2.250000000*pi)*pi-47382.*sinh(2.250000000*pi)))-2.026391726*sin(.2500000000*pi*x)*cosh(2.250000000*pi)*pi*y*cosh((1/4)*Pi*y)/(sin(.7854000000*x)*(13213.*cosh(2.250000000*pi)*pi-47382.*sinh(2.250000000*pi)))-0.1084023308e-2*sin(.2500000000*pi*x)*y*sinh((1/4)*Pi*y)/sin(.7854000000*x))

 (29)
> 

syy := diff(phi1, x, x);

-(1/16)*sin((1/4)*Pi*x)*Pi^2*(0.1113637578e-1*sin(.2500000000*pi*x)*cosh((1/4)*Pi*y)/sin(.7854000000*x)+38405.79710*sin(.2500000000*pi*x)*sinh((1/4)*pi*y)/(sin(.7854000000*x)*(13213.*cosh(2.250000000*pi)*pi-47382.*sinh(2.250000000*pi)))-2.026391726*sin(.2500000000*pi*x)*cosh(2.250000000*pi)*pi*y*cosh((1/4)*Pi*y)/(sin(.7854000000*x)*(13213.*cosh(2.250000000*pi)*pi-47382.*sinh(2.250000000*pi)))-0.1084023308e-2*sin(.2500000000*pi*x)*y*sinh((1/4)*Pi*y)/sin(.7854000000*x))+(1/2)*cos((1/4)*Pi*x)*Pi*(0.2784093945e-2*cos(.2500000000*pi*x)*pi*cosh((1/4)*Pi*y)/sin(.7854000000*x)-0.8746509538e-2*sin(.2500000000*pi*x)*cosh((1/4)*Pi*y)*cos(.7854000000*x)/sin(.7854000000*x)^2-30163.91304*sin(.2500000000*pi*x)*sinh((1/4)*pi*y)*cos(.7854000000*x)/(sin(.7854000000*x)^2*(13213.*cosh(2.250000000*pi)*pi-47382.*sinh(2.250000000*pi)))+9601.449275*cos(.2500000000*pi*x)*pi*sinh((1/4)*pi*y)/(sin(.7854000000*x)*(13213.*cosh(2.250000000*pi)*pi-47382.*sinh(2.250000000*pi)))-.5065979315*cos(.2500000000*pi*x)*pi^2*cosh(2.250000000*pi)*y*cosh((1/4)*Pi*y)/(sin(.7854000000*x)*(13213.*cosh(2.250000000*pi)*pi-47382.*sinh(2.250000000*pi)))+1.591528062*sin(.2500000000*pi*x)*cosh(2.250000000*pi)*pi*y*cosh((1/4)*Pi*y)*cos(.7854000000*x)/(sin(.7854000000*x)^2*(13213.*cosh(2.250000000*pi)*pi-47382.*sinh(2.250000000*pi)))-0.2710058270e-3*cos(.2500000000*pi*x)*pi*y*sinh((1/4)*Pi*y)/sin(.7854000000*x)+0.8513919061e-3*sin(.2500000000*pi*x)*y*sinh((1/4)*Pi*y)*cos(.7854000000*x)/sin(.7854000000*x)^2)+sin((1/4)*Pi*x)*(-0.6960234862e-3*sin(.2500000000*pi*x)*pi^2*cosh((1/4)*Pi*y)/sin(.7854000000*x)-0.4373254768e-2*cos(.2500000000*pi*x)*pi*cosh((1/4)*Pi*y)*cos(.7854000000*x)/sin(.7854000000*x)^2+0.1373901718e-1*sin(.2500000000*pi*x)*cosh((1/4)*Pi*y)*cos(.7854000000*x)^2/sin(.7854000000*x)^3+0.6869508591e-2*sin(.2500000000*pi*x)*cosh((1/4)*Pi*y)/sin(.7854000000*x)+47381.47460*sin(.2500000000*pi*x)*sinh((1/4)*pi*y)*cos(.7854000000*x)^2/(sin(.7854000000*x)^3*(13213.*cosh(2.250000000*pi)*pi-47382.*sinh(2.250000000*pi)))-15081.95652*cos(.2500000000*pi*x)*pi*sinh((1/4)*pi*y)*cos(.7854000000*x)/(sin(.7854000000*x)^2*(13213.*cosh(2.250000000*pi)*pi-47382.*sinh(2.250000000*pi)))+23690.73730*sin(.2500000000*pi*x)*sinh((1/4)*pi*y)/(sin(.7854000000*x)*(13213.*cosh(2.250000000*pi)*pi-47382.*sinh(2.250000000*pi)))-2400.362319*sin(.2500000000*pi*x)*pi^2*sinh((1/4)*pi*y)/(sin(.7854000000*x)*(13213.*cosh(2.250000000*pi)*pi-47382.*sinh(2.250000000*pi)))+.1266494829*sin(.2500000000*pi*x)*pi^3*cosh(2.250000000*pi)*y*cosh((1/4)*Pi*y)/(sin(.7854000000*x)*(13213.*cosh(2.250000000*pi)*pi-47382.*sinh(2.250000000*pi)))+.7957640309*cos(.2500000000*pi*x)*pi^2*cosh(2.250000000*pi)*y*cosh((1/4)*Pi*y)*cos(.7854000000*x)/(sin(.7854000000*x)^2*(13213.*cosh(2.250000000*pi)*pi-47382.*sinh(2.250000000*pi)))-2.499972280*sin(.2500000000*pi*x)*cosh(2.250000000*pi)*pi*y*cosh((1/4)*Pi*y)*cos(.7854000000*x)^2/(sin(.7854000000*x)^3*(13213.*cosh(2.250000000*pi)*pi-47382.*sinh(2.250000000*pi)))-1.249986140*sin(.2500000000*pi*x)*cosh(2.250000000*pi)*pi*y*cosh((1/4)*Pi*y)/(sin(.7854000000*x)*(13213.*cosh(2.250000000*pi)*pi-47382.*sinh(2.250000000*pi)))+0.6775145675e-4*sin(.2500000000*pi*x)*pi^2*y*sinh((1/4)*Pi*y)/sin(.7854000000*x)+0.4256959530e-3*cos(.2500000000*pi*x)*pi*y*sinh((1/4)*Pi*y)*cos(.7854000000*x)/sin(.7854000000*x)^2-0.1337366406e-2*sin(.2500000000*pi*x)*y*sinh((1/4)*Pi*y)*cos(.7854000000*x)^2/sin(.7854000000*x)^3-0.6686832031e-3*sin(.2500000000*pi*x)*y*sinh((1/4)*Pi*y)/sin(.7854000000*x))

 (30)
> 

evalf[5]( (30) );

-.61686*sin(.78540*x)*(0.11136e-1*sin(.25000*pi*x)*cosh(.78540*y)/sin(.78540*x)+38406.*sin(.25000*pi*x)*sinh(.25000*pi*y)/(sin(.78540*x)*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi)))-2.0264*sin(.25000*pi*x)*cosh(2.2500*pi)*pi*y*cosh(.78540*y)/(sin(.78540*x)*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi)))-0.10840e-2*sin(.25000*pi*x)*y*sinh(.78540*y)/sin(.78540*x))+1.5708*cos(.78540*x)*(0.27841e-2*cos(.25000*pi*x)*pi*cosh(.78540*y)/sin(.78540*x)-0.87465e-2*sin(.25000*pi*x)*cosh(.78540*y)*cos(.78540*x)/sin(.78540*x)^2-30164.*sin(.25000*pi*x)*sinh(.25000*pi*y)*cos(.78540*x)/(sin(.78540*x)^2*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi)))+9601.4*cos(.25000*pi*x)*pi*sinh(.25000*pi*y)/(sin(.78540*x)*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi)))-.50660*cos(.25000*pi*x)*pi^2*cosh(2.2500*pi)*y*cosh(.78540*y)/(sin(.78540*x)*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi)))+1.5915*sin(.25000*pi*x)*cosh(2.2500*pi)*pi*y*cosh(.78540*y)*cos(.78540*x)/(sin(.78540*x)^2*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi)))-0.27101e-3*cos(.25000*pi*x)*pi*y*sinh(.78540*y)/sin(.78540*x)+0.85139e-3*sin(.25000*pi*x)*y*sinh(.78540*y)*cos(.78540*x)/sin(.78540*x)^2)+sin(.78540*x)*(-0.69602e-3*sin(.25000*pi*x)*pi^2*cosh(.78540*y)/sin(.78540*x)-0.43733e-2*cos(.25000*pi*x)*pi*cosh(.78540*y)*cos(.78540*x)/sin(.78540*x)^2+0.13739e-1*sin(.25000*pi*x)*cosh(.78540*y)*cos(.78540*x)^2/sin(.78540*x)^3+0.68695e-2*sin(.25000*pi*x)*cosh(.78540*y)/sin(.78540*x)+47381.*sin(.25000*pi*x)*sinh(.25000*pi*y)*cos(.78540*x)^2/(sin(.78540*x)^3*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi)))-15082.*cos(.25000*pi*x)*pi*sinh(.25000*pi*y)*cos(.78540*x)/(sin(.78540*x)^2*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi)))+23691.*sin(.25000*pi*x)*sinh(.25000*pi*y)/(sin(.78540*x)*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi)))-2400.4*sin(.25000*pi*x)*pi^2*sinh(.25000*pi*y)/(sin(.78540*x)*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi)))+.12665*sin(.25000*pi*x)*pi^3*cosh(2.2500*pi)*y*cosh(.78540*y)/(sin(.78540*x)*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi)))+.79576*cos(.25000*pi*x)*pi^2*cosh(2.2500*pi)*y*cosh(.78540*y)*cos(.78540*x)/(sin(.78540*x)^2*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi)))-2.5000*sin(.25000*pi*x)*cosh(2.2500*pi)*pi*y*cosh(.78540*y)*cos(.78540*x)^2/(sin(.78540*x)^3*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi)))-1.2500*sin(.25000*pi*x)*cosh(2.2500*pi)*pi*y*cosh(.78540*y)/(sin(.78540*x)*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi)))+0.67751e-4*sin(.25000*pi*x)*pi^2*y*sinh(.78540*y)/sin(.78540*x)+0.42570e-3*cos(.25000*pi*x)*pi*y*sinh(.78540*y)*cos(.78540*x)/sin(.78540*x)^2-0.13374e-2*sin(.25000*pi*x)*y*sinh(.78540*y)*cos(.78540*x)^2/sin(.78540*x)^3-0.66868e-3*sin(.25000*pi*x)*y*sinh(.78540*y)/sin(.78540*x))

 (31)
> 

eval( (31), [y = -9]);

-.61686*sin(.78540*x)*(.810415675*sin(.25000*pi*x)/sin(.78540*x)-38406.*sin(.25000*pi*x)*sinh(2.25000*pi)/(sin(.78540*x)*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi)))+10710.06188*sin(.25000*pi*x)*cosh(2.2500*pi)*pi/(sin(.78540*x)*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi))))+1.5708*cos(.78540*x)*(.202609792*cos(.25000*pi*x)*pi/sin(.78540*x)-.636581512*sin(.25000*pi*x)*cos(.78540*x)/sin(.78540*x)^2+30164.*sin(.25000*pi*x)*sinh(2.25000*pi)*cos(.78540*x)/(sin(.78540*x)^2*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi)))-9601.4*cos(.25000*pi*x)*pi*sinh(2.25000*pi)/(sin(.78540*x)*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi)))+2677.515471*cos(.25000*pi*x)*pi^2*cosh(2.2500*pi)/(sin(.78540*x)*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi)))-8411.499945*sin(.25000*pi*x)*cosh(2.2500*pi)*pi*cos(.78540*x)/(sin(.78540*x)^2*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi))))+sin(.78540*x)*(-0.506574395e-1*sin(.25000*pi*x)*pi^2/sin(.78540*x)-.318293693*cos(.25000*pi*x)*pi*cos(.78540*x)/sin(.78540*x)^2+.999747570*sin(.25000*pi*x)*cos(.78540*x)^2/sin(.78540*x)^3+.499979490*sin(.25000*pi*x)/sin(.78540*x)-47381.*sin(.25000*pi*x)*sinh(2.25000*pi)*cos(.78540*x)^2/(sin(.78540*x)^3*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi)))+15082.*cos(.25000*pi*x)*pi*sinh(2.25000*pi)*cos(.78540*x)/(sin(.78540*x)^2*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi)))-23691.*sin(.25000*pi*x)*sinh(2.25000*pi)/(sin(.78540*x)*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi)))+2400.4*sin(.25000*pi*x)*pi^2*sinh(2.25000*pi)/(sin(.78540*x)*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi)))-669.3788677*sin(.25000*pi*x)*pi^3*cosh(2.2500*pi)/(sin(.78540*x)*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi)))-4205.802825*cos(.25000*pi*x)*pi^2*cosh(2.2500*pi)*cos(.78540*x)/(sin(.78540*x)^2*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi)))+13213.16360*sin(.25000*pi*x)*cosh(2.2500*pi)*pi*cos(.78540*x)^2/(sin(.78540*x)^3*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi)))+6606.581798*sin(.25000*pi*x)*cosh(2.2500*pi)*pi/(sin(.78540*x)*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi))))

 (32)
> 

eval( (32), [x = 6]);

0.6647677858e-4*sin(1.50000*pi)+.1251557536*sin(1.50000*pi)*sinh(2.25000*pi)/(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi))-0.2697360445e-1*sin(1.50000*pi)*cosh(2.2500*pi)*pi/(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi))+0.377220e-9*cos(1.50000*pi)*pi-0.13321e-5*cos(1.50000*pi)*pi*sinh(2.25000*pi)/(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi))-0.42401e-6*cos(1.50000*pi)*pi^2*cosh(2.2500*pi)/(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi))-0.5065743949e-1*sin(1.50000*pi)*pi^2+2400.400000*sin(1.50000*pi)*pi^2*sinh(2.25000*pi)/(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi))-669.3788676*sin(1.50000*pi)*pi^3*cosh(2.2500*pi)/(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi))

 (33)
> 

eval( (32), [x = 4]);

-0.360700e7*sin(1.00000*pi)+0.113252e11*sin(1.00000*pi)*sinh(2.25000*pi)/(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi))+0.70315e10*sin(1.00000*pi)*cosh(2.2500*pi)*pi/(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi))-4.65965*cos(1.00000*pi)*pi+16453.*cos(1.00000*pi)*pi*sinh(2.25000*pi)/(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi))+5237.5*cos(1.00000*pi)*pi^2*cosh(2.2500*pi)/(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi))-0.5065743950e-1*sin(1.00000*pi)*pi^2+2400.400000*sin(1.00000*pi)*pi^2*sinh(2.25000*pi)/(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi))-669.3788677*sin(1.00000*pi)*pi^3*cosh(2.2500*pi)/(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi))

 (34)
> 

eval( (32), [x = 20]);

-144280.5*sin(5.00000*pi)+0.45300e9*sin(5.00000*pi)*sinh(2.25000*pi)/(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi))+0.281258e9*sin(5.00000*pi)*cosh(2.2500*pi)*pi/(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi))-.931934*cos(5.00000*pi)*pi+3291.2*cos(5.00000*pi)*pi*sinh(2.25000*pi)/(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi))+1047.5*cos(5.00000*pi)*pi^2*cosh(2.2500*pi)/(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi))-0.5065743950e-1*sin(5.00000*pi)*pi^2+2400.400000*sin(5.00000*pi)*pi^2*sinh(2.25000*pi)/(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi))-669.3788674*sin(5.00000*pi)*pi^3*cosh(2.2500*pi)/(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi))

 (35)
> 

eval( (32), [x = 2]);

0.6647668651e-4*sin(.50000*pi)+.1251606393*sin(.50000*pi)*sinh(2.25000*pi)/(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi))-0.2697317827e-1*sin(.50000*pi)*cosh(2.2500*pi)*pi/(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi))+0.125740e-9*cos(.50000*pi)*pi-0.44401e-6*cos(.50000*pi)*pi*sinh(2.25000*pi)/(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi))-0.14133e-6*cos(.50000*pi)*pi^2*cosh(2.2500*pi)/(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi))-0.5065743950e-1*sin(.50000*pi)*pi^2+2400.400000*sin(.50000*pi)*pi^2*sinh(2.25000*pi)/(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi))-669.3788677*sin(.50000*pi)*pi^3*cosh(2.2500*pi)/(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi))

 (36)
> 

 

> 

sxx := diff(phi1, y, y);

sin((1/4)*Pi*x)*(0.6960234862e-3*sin(.2500000000*pi*x)*cosh((1/4)*Pi*y)*Pi^2/sin(.7854000000*x)+2400.362319*sin(.2500000000*pi*x)*pi^2*sinh((1/4)*pi*y)/(sin(.7854000000*x)*(13213.*cosh(2.250000000*pi)*pi-47382.*sinh(2.250000000*pi)))-1.013195863*sin(.2500000000*pi*x)*cosh(2.250000000*pi)*pi*sinh((1/4)*Pi*y)*Pi/(sin(.7854000000*x)*(13213.*cosh(2.250000000*pi)*pi-47382.*sinh(2.250000000*pi)))-.1266494829*sin(.2500000000*pi*x)*cosh(2.250000000*pi)*pi*y*cosh((1/4)*Pi*y)*Pi^2/(sin(.7854000000*x)*(13213.*cosh(2.250000000*pi)*pi-47382.*sinh(2.250000000*pi)))-0.5420116540e-3*sin(.2500000000*pi*x)*cosh((1/4)*Pi*y)*Pi/sin(.7854000000*x)-0.6775145675e-4*sin(.2500000000*pi*x)*y*sinh((1/4)*Pi*y)*Pi^2/sin(.7854000000*x))

 (37)
> 

eval( (37), [x = 20]);

0

 (38)
> 

eval( (37), [x = 0]);

0

 (39)
> 

sxy := diff(-phi1, x, y);

-(1/4)*cos((1/4)*Pi*x)*Pi*(0.2784093945e-2*sin(.2500000000*pi*x)*sinh((1/4)*Pi*y)*Pi/sin(.7854000000*x)+9601.449275*sin(.2500000000*pi*x)*cosh((1/4)*pi*y)*pi/(sin(.7854000000*x)*(13213.*cosh(2.250000000*pi)*pi-47382.*sinh(2.250000000*pi)))-2.026391726*sin(.2500000000*pi*x)*cosh(2.250000000*pi)*pi*cosh((1/4)*Pi*y)/(sin(.7854000000*x)*(13213.*cosh(2.250000000*pi)*pi-47382.*sinh(2.250000000*pi)))-.5065979315*sin(.2500000000*pi*x)*cosh(2.250000000*pi)*pi*y*sinh((1/4)*Pi*y)*Pi/(sin(.7854000000*x)*(13213.*cosh(2.250000000*pi)*pi-47382.*sinh(2.250000000*pi)))-0.1084023308e-2*sin(.2500000000*pi*x)*sinh((1/4)*Pi*y)/sin(.7854000000*x)-0.2710058270e-3*sin(.2500000000*pi*x)*y*cosh((1/4)*Pi*y)*Pi/sin(.7854000000*x))-sin((1/4)*Pi*x)*(0.6960234862e-3*cos(.2500000000*pi*x)*pi*sinh((1/4)*Pi*y)*Pi/sin(.7854000000*x)-0.2186627384e-2*sin(.2500000000*pi*x)*sinh((1/4)*Pi*y)*Pi*cos(.7854000000*x)/sin(.7854000000*x)^2-7540.978260*sin(.2500000000*pi*x)*cosh((1/4)*pi*y)*pi*cos(.7854000000*x)/(sin(.7854000000*x)^2*(13213.*cosh(2.250000000*pi)*pi-47382.*sinh(2.250000000*pi)))+2400.362319*cos(.2500000000*pi*x)*pi^2*cosh((1/4)*pi*y)/(sin(.7854000000*x)*(13213.*cosh(2.250000000*pi)*pi-47382.*sinh(2.250000000*pi)))-.5065979315*cos(.2500000000*pi*x)*pi^2*cosh(2.250000000*pi)*cosh((1/4)*Pi*y)/(sin(.7854000000*x)*(13213.*cosh(2.250000000*pi)*pi-47382.*sinh(2.250000000*pi)))-.1266494829*cos(.2500000000*pi*x)*pi^2*cosh(2.250000000*pi)*y*sinh((1/4)*Pi*y)*Pi/(sin(.7854000000*x)*(13213.*cosh(2.250000000*pi)*pi-47382.*sinh(2.250000000*pi)))+1.591528062*sin(.2500000000*pi*x)*cosh(2.250000000*pi)*pi*cosh((1/4)*Pi*y)*cos(.7854000000*x)/(sin(.7854000000*x)^2*(13213.*cosh(2.250000000*pi)*pi-47382.*sinh(2.250000000*pi)))+.3978820155*sin(.2500000000*pi*x)*cosh(2.250000000*pi)*pi*y*sinh((1/4)*Pi*y)*Pi*cos(.7854000000*x)/(sin(.7854000000*x)^2*(13213.*cosh(2.250000000*pi)*pi-47382.*sinh(2.250000000*pi)))-0.2710058270e-3*cos(.2500000000*pi*x)*pi*sinh((1/4)*Pi*y)/sin(.7854000000*x)-0.6775145675e-4*cos(.2500000000*pi*x)*pi*y*cosh((1/4)*Pi*y)*Pi/sin(.7854000000*x)+0.8513919061e-3*sin(.2500000000*pi*x)*sinh((1/4)*Pi*y)*cos(.7854000000*x)/sin(.7854000000*x)^2+0.2128479765e-3*sin(.2500000000*pi*x)*y*cosh((1/4)*Pi*y)*Pi*cos(.7854000000*x)/sin(.7854000000*x)^2)

 (40)
> 

evalf[5]( (40) );

-.78540*cos(.78540*x)*(0.76625e-2*sin(.25000*pi*x)*sinh(.78540*y)/sin(.78540*x)+9601.4*sin(.25000*pi*x)*cosh(.25000*pi*y)*pi/(sin(.78540*x)*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi)))-2.0264*sin(.25000*pi*x)*cosh(2.2500*pi)*pi*cosh(.78540*y)/(sin(.78540*x)*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi)))-1.5915*sin(.25000*pi*x)*cosh(2.2500*pi)*pi*y*sinh(.78540*y)/(sin(.78540*x)*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi)))-0.85141e-3*sin(.25000*pi*x)*y*cosh(.78540*y)/sin(.78540*x))-1.*sin(.78540*x)*(0.19156e-2*cos(.25000*pi*x)*pi*sinh(.78540*y)/sin(.78540*x)-0.60180e-2*sin(.25000*pi*x)*sinh(.78540*y)*cos(.78540*x)/sin(.78540*x)^2-7541.0*sin(.25000*pi*x)*cosh(.25000*pi*y)*pi*cos(.78540*x)/(sin(.78540*x)^2*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi)))+2400.4*cos(.25000*pi*x)*pi^2*cosh(.25000*pi*y)/(sin(.78540*x)*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi)))-.50660*cos(.25000*pi*x)*pi^2*cosh(2.2500*pi)*cosh(.78540*y)/(sin(.78540*x)*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi)))-.39788*cos(.25000*pi*x)*pi^2*cosh(2.2500*pi)*y*sinh(.78540*y)/(sin(.78540*x)*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi)))+1.5915*sin(.25000*pi*x)*cosh(2.2500*pi)*pi*cosh(.78540*y)*cos(.78540*x)/(sin(.78540*x)^2*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi)))+1.2500*sin(.25000*pi*x)*cosh(2.2500*pi)*pi*y*sinh(.78540*y)*cos(.78540*x)/(sin(.78540*x)^2*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi)))-0.21285e-3*cos(.25000*pi*x)*pi*y*cosh(.78540*y)/sin(.78540*x)+0.66869e-3*sin(.25000*pi*x)*y*cosh(.78540*y)*cos(.78540*x)/sin(.78540*x)^2)

 (41)
> 

eval( (41), [y = -9]);

-.78540*cos(.78540*x)*(0.118103e-3*sin(.25000*pi*x)/sin(.78540*x)+9601.4*sin(.25000*pi*x)*cosh(2.25000*pi)*pi/(sin(.78540*x)*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi)))-9601.494623*sin(.25000*pi*x)*cosh(2.2500*pi)*pi/(sin(.78540*x)*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi))))-1.*sin(.78540*x)*(0.30993e-4*cos(.25000*pi*x)*pi/sin(.78540*x)-0.128448e-3*sin(.25000*pi*x)*cos(.78540*x)/sin(.78540*x)^2-7541.0*sin(.25000*pi*x)*cosh(2.25000*pi)*pi*cos(.78540*x)/(sin(.78540*x)^2*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi)))+2400.4*cos(.25000*pi*x)*pi^2*cosh(2.25000*pi)/(sin(.78540*x)*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi)))-2400.400082*cos(.25000*pi*x)*pi^2*cosh(2.2500*pi)/(sin(.78540*x)*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi)))+7541.183323*sin(.25000*pi*x)*cosh(2.2500*pi)*pi*cos(.78540*x)/(sin(.78540*x)^2*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi))))

 (42)
> 

eval( (41), [y = 9]);

-.78540*cos(.78540*x)*(-0.118103e-3*sin(.25000*pi*x)/sin(.78540*x)+9601.4*sin(.25000*pi*x)*cosh(2.25000*pi)*pi/(sin(.78540*x)*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi)))-9601.494623*sin(.25000*pi*x)*cosh(2.2500*pi)*pi/(sin(.78540*x)*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi))))-1.*sin(.78540*x)*(-0.30993e-4*cos(.25000*pi*x)*pi/sin(.78540*x)+0.128448e-3*sin(.25000*pi*x)*cos(.78540*x)/sin(.78540*x)^2-7541.0*sin(.25000*pi*x)*cosh(2.25000*pi)*pi*cos(.78540*x)/(sin(.78540*x)^2*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi)))+2400.4*cos(.25000*pi*x)*pi^2*cosh(2.25000*pi)/(sin(.78540*x)*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi)))-2400.400082*cos(.25000*pi*x)*pi^2*cosh(2.2500*pi)/(sin(.78540*x)*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi)))+7541.183323*sin(.25000*pi*x)*cosh(2.2500*pi)*pi*cos(.78540*x)/(sin(.78540*x)^2*(13213.*cosh(2.2500*pi)*pi-47382.*sinh(2.2500*pi))))

 (43)
> 

``

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