I would like to be able to (symbolically) compute the Jacobian matrix for the Octave lsode backward differentiation method for "stiff" differential equations. The result is considerably more complicated than I expected!
Value = "FriCAS 2014-12-18 compiled at Tue May 5 18:13:01 UTC 2015"
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Compiling function sif with type (BasicOperator,Variable(i)) -> Expression(Integer)
Compiling function sif with type (BasicOperator,Polynomial(Integer)) -> Expression(Integer)
Compiling function sigma with type (BasicOperator,Variable(i)) -> Expression(Integer)
$${{\left( {x \left( {i} \right)} -{3 \ {x \left( {{i -1}} \right)}}+{2 \ {x \left( {{i -2}} \right)}} \right)} \ {x \left( {{i+1}} \right)}} -{{{x \left( {i} \right)}} ^{2}}+{{\left( {4 \ {x \left( {{i -1}} \right)}} -{3 \ {x \left( {{i -2}} \right)}} \right)} \ {x \left( {i} \right)}} -{{{x \left( {{i -1}} \right)}} ^{2}}+{{x \left( {{i -2}} \right)} \ {x \left( {{i -1}} \right)}}$$$${\left( {x \left( {{i -1}} \right)} -{x \left( {{i -2}} \right)} \right)} \ {{{\left( {x \left( {i} \right)} -{x \left( {{i -1}} \right)} \right)}} ^{3}} \ {\left( {x \left( {{i+1}} \right)} -{x \left( {i} \right)} \right)}$$Many Worlds Interaction
Compiling function sigma with type (BasicOperator,Polynomial(Integer)) -> Expression(Integer)
Compiling function R with type (BasicOperator,Variable(i)) -> Expression(Integer)
$$-{{{hbar} ^{2}} \ {\left( {{\left( {{\left( {x \left( {i} \right)} -{3 \ {x \left( {{i -1}} \right)}}+{2 \ {x \left( {{i -2}} \right)}} \right)} \ {{{x \left( {{i+1}} \right)}} ^{3}}}+{{\left( -{3 \ {{{x \left( {i} \right)}} ^{2}}}+{{\left( {{10} \ {x \left( {{i -1}} \right)}} -{7 \ {x \left( {{i -2}} \right)}} \right)} \ {x \left( {i} \right)}} -{{{x \left( {{i -1}} \right)}} ^{2}}+{{x \left( {{i -2}} \right)} \ {x \left( {{i -1}} \right)}} \right)} \ {{{x \left( {{i+1}} \right)}} ^{2}}}+{{\left( {3 \ {{{x \left( {i} \right)}} ^{3}}}+{{\left( -{{12} \ {x \left( {{i -1}} \right)}}+{9 \ {x \left( {{i -2}} \right)}} \right)} \ {{{x \left( {i} \right)}} ^{2}}}+{{\left( {4 \ {{{x \left( {{i -1}} \right)}} ^{2}}} -{4 \ {x \left( {{i -2}} \right)} \ {x \left( {{i -1}} \right)}} \right)} \ {x \left( {i} \right)}} -{{{x \left( {{i -1}} \right)}} ^{3}}+{{x \left( {{i -2}} \right)} \ {{{x \left( {{i -1}} \right)}} ^{2}}} \right)} \ {x \left( {{i+1}} \right)}} -{{{x \left( {i} \right)}} ^{4}}+{{\left( {7 \ {x \left( {{i -1}} \right)}} -{6 \ {x \left( {{i -2}} \right)}} \right)} \ {{{x \left( {i} \right)}} ^{3}}}+{{\left( -{9 \ {{{x \left( {{i -1}} \right)}} ^{2}}}+{9 \ {x \left( {{i -2}} \right)} \ {x \left( {{i -1}} \right)}} \right)} \ {{{x \left( {i} \right)}} ^{2}}}+{{\left( {7 \ {{{x \left( {{i -1}} \right)}} ^{3}}} -{7 \ {x \left( {{i -2}} \right)} \ {{{x \left( {{i -1}} \right)}} ^{2}}} \right)} \ {x \left( {i} \right)}} -{2 \ {{{x \left( {{i -1}} \right)}} ^{4}}}+{2 \ {x \left( {{i -2}} \right)} \ {{{x \left( {{i -1}} \right)}} ^{3}}} \right)} \ {x \left( {{i+2}} \right)}}+{{\left( -{x \left( {i} \right)}+{3 \ {x \left( {{i -1}} \right)}} -{2 \ {x \left( {{i -2}} \right)}} \right)} \ {{{x \left( {{i+1}} \right)}} ^{4}}}+{{\left( {3 \ {{{x \left( {i} \right)}} ^{2}}}+{{\left( -{{10} \ {x \left( {{i -1}} \right)}}+{7 \ {x \left( {{i -2}} \right)}} \right)} \ {x \left( {i} \right)}}+{{{x \left( {{i -1}} \right)}} ^{2}} -{{x \left( {{i -2}} \right)} \ {x \left( {{i -1}} \right)}} \right)} \ {{{x \left( {{i+1}} \right)}} ^{3}}}+{{\left( -{3 \ {{{x \left( {i} \right)}} ^{3}}}+{{\left( {{12} \ {x \left( {{i -1}} \right)}} -{9 \ {x \left( {{i -2}} \right)}} \right)} \ {{{x \left( {i} \right)}} ^{2}}}+{{\left( -{4 \ {{{x \left( {{i -1}} \right)}} ^{2}}}+{4 \ {x \left( {{i -2}} \right)} \ {x \left( {{i -1}} \right)}} \right)} \ {x \left( {i} \right)}}+{{{x \left( {{i -1}} \right)}} ^{3}} -{{x \left( {{i -2}} \right)} \ {{{x \left( {{i -1}} \right)}} ^{2}}} \right)} \ {{{x \left( {{i+1}} \right)}} ^{2}}}+{{\left( {{{x \left( {i} \right)}} ^{4}}+{{\left( -{8 \ {x \left( {{i -1}} \right)}}+{7 \ {x \left( {{i -2}} \right)}} \right)} \ {{{x \left( {i} \right)}} ^{3}}}+{{\left( {{12} \ {{{x \left( {{i -1}} \right)}} ^{2}}} -{{12} \ {x \left( {{i -2}} \right)} \ {x \left( {{i -1}} \right)}} \right)} \ {{{x \left( {i} \right)}} ^{2}}}+{{\left( -{{10} \ {{{x \left( {{i -1}} \right)}} ^{3}}}+{{10} \ {x \left( {{i -2}} \right)} \ {{{x \left( {{i -1}} \right)}} ^{2}}} \right)} \ {x \left( {i} \right)}}+{3 \ {{{x \left( {{i -1}} \right)}} ^{4}}} -{3 \ {x \left( {{i -2}} \right)} \ {{{x \left( {{i -1}} \right)}} ^{3}}} \right)} \ {x \left( {{i+1}} \right)}}+{{\left( {x \left( {{i -1}} \right)} -{x \left( {{i -2}} \right)} \right)} \ {{{x \left( {i} \right)}} ^{4}}}+{{\left( -{3 \ {{{x \left( {{i -1}} \right)}} ^{2}}}+{3 \ {x \left( {{i -2}} \right)} \ {x \left( {{i -1}} \right)}} \right)} \ {{{x \left( {i} \right)}} ^{3}}}+{{\left( {3 \ {{{x \left( {{i -1}} \right)}} ^{3}}} -{3 \ {x \left( {{i -2}} \right)} \ {{{x \left( {{i -1}} \right)}} ^{2}}} \right)} \ {{{x \left( {i} \right)}} ^{2}}}+{{\left( -{{{x \left( {{i -1}} \right)}} ^{4}}+{{x \left( {{i -2}} \right)} \ {{{x \left( {{i -1}} \right)}} ^{3}}} \right)} \ {x \left( {i} \right)}} \right)}}$$$$4 \ m \ {\left( {x \left( {{i -1}} \right)} -{x \left( {{i -2}} \right)} \right)} \ {{{\left( {x \left( {i} \right)} -{x \left( {{i -1}} \right)} \right)}} ^{3}} \ {{{\left( {x \left( {{i+1}} \right)} -{x \left( {i} \right)} \right)}} ^{3}} \ {\left( {x \left( {{i+2}} \right)} -{x \left( {{i+1}} \right)} \right)}$$We let the two particles to the left be infinity far away.
Compiling function sif with type (BasicOperator,PositiveInteger) -> Expression(Integer)
Compiling function sif with type (BasicOperator,Integer) -> Expression(Integer)
Compiling function sigma with type (BasicOperator,PositiveInteger) -> Expression(Integer)
Compiling function R with type (BasicOperator,PositiveInteger) -> Expression(Integer)
$${{\left( -{2 \ {x \left( {3} \right)}}+{3 \ {x \left( {2} \right)}} -{x \left( {1} \right)} \right)} \ {{hbar} ^{2}}} \over {{\left( {{\left( {4 \ {{{x \left( {2} \right)}} ^{3}}} -{{12} \ {x \left( {1} \right)} \ {{{x \left( {2} \right)}} ^{2}}}+{{12} \ {{{x \left( {1} \right)}} ^{2}} \ {x \left( {2} \right)}} -{4 \ {{{x \left( {1} \right)}} ^{3}}} \right)} \ {x \left( {3} \right)}} -{4 \ {{{x \left( {2} \right)}} ^{4}}}+{{12} \ {x \left( {1} \right)} \ {{{x \left( {2} \right)}} ^{3}}} -{{12} \ {{{x \left( {1} \right)}} ^{2}} \ {{{x \left( {2} \right)}} ^{2}}}+{4 \ {{{x \left( {1} \right)}} ^{3}} \ {x \left( {2} \right)}} \right)} \ m}$$Similarly on the right.
Compiling function sif with type (BasicOperator,Variable(N)) -> Expression(Integer)
Compiling function sigma with type (BasicOperator,Variable(N)) -> Expression(Integer)
Compiling function R with type (BasicOperator,Variable(N)) -> Expression(Integer)
$${-{{{hbar} ^{2}} \ {x \left( {N} \right)}}+{3 \ {{hbar} ^{2}} \ {x \left( {{N -1}} \right)}} -{2 \ {{hbar} ^{2}} \ {x \left( {{N -2}} \right)}}} \over {{{\left( {4 \ m \ {x \left( {{N -1}} \right)}} -{4 \ m \ {x \left( {{N -2}} \right)}} \right)} \ {{{x \left( {N} \right)}} ^{3}}}+{{\left( -{{12} \ m \ {{{x \left( {{N -1}} \right)}} ^{2}}}+{{12} \ m \ {x \left( {{N -2}} \right)} \ {x \left( {{N -1}} \right)}} \right)} \ {{{x \left( {N} \right)}} ^{2}}}+{{\left( {{12} \ m \ {{{x \left( {{N -1}} \right)}} ^{3}}} -{{12} \ m \ {x \left( {{N -2}} \right)} \ {{{x \left( {{N -1}} \right)}} ^{2}}} \right)} \ {x \left( {N} \right)}} -{4 \ m \ {{{x \left( {{N -1}} \right)}} ^{4}}}+{4 \ m \ {x \left( {{N -2}} \right)} \ {{{x \left( {{N -1}} \right)}} ^{3}}}}$$Classical Force
Compiling function F with type Expression(Integer) -> Expression(Integer)
$${{x \left( {i} \right)} \ {{e} ^{-{{{{x \left( {i} \right)}} ^{2}} \over {{a} ^{2}}}}}} \over {{{a} ^{3}} \ \pi}$$function result=fr3(x,i)
global m hbar a;
result= ...
(((((-4*m*x(i -1)+4*m*x(i -2))*x(i)^6+(16*m*x(i -1)^2 -16*m*x(i -2)*x(i -1))*...
x(i)^5+(-24*m*x(i -1)^3+24*m*x(i -2)*x(i -1)^2+2*a^2*m*x(i -1) -2*a^2*m*...
x(i -2))*x(i)^4+(16*m*x(i -1)^4 -16*m*x(i -2)*x(i -1)^3 -8*a^2*m*x(i -1)^2+8*...
-2)*x(i -1))*x(i)^3+(-4*m*x(i -1)^5+4*m*x(i -2)*x(i -1)^4+12*a^2*m*...
x(i -1)^3 -12*a^2*m*x(i -2)*x(i -1)^2)*x(i)^2+(-8*a^2*m*x(i -1)^4+8*a^2*m*...
x(i -2)*x(i -1)^3)*x(i)+(2*a^2*m*x(i -1)^5 -2*a^2*m*x(i -2)*x(i -1)^4))*...
-16*m*x(i -2))*x(i)^7+(-64*m*x(i -1)^2+64*m*x(i -2)*...
x(i -1))*x(i)^6+(96*m*x(i -1)^3 -96*m*x(i -2)*x(i -1)^2 -8*a^2*m*x(i -1)+8*a^2*...
m*x(i -2))*x(i)^5+(-64*m*x(i -1)^4+64*m*x(i -2)*x(i -1)^3+32*a^2*m*...
-1))*x(i)^4+(16*m*x(i -1)^5 -16*m*x(i -2)*...
x(i -1)^4 -48*a^2*m*x(i -1)^3+48*a^2*m*x(i -2)*x(i -1)^2)*x(i)^3+(32*a^2*m*...
x(i -1)^4 -32*a^2*m*x(i -2)*x(i -1)^3)*x(i)^2+(-8*a^2*m*x(i -1)^5+8*a^2*m*...
-1)+24*m*x(i -2))*x(i)^8+(96*m*...)^3+((-24*m*x(i
x(i -1)^2 -96*m*x(i -2)*x(i -1))*x(i)^7+(-144*m*x(i -1)^3+144*m*x(i -2)*...
x(i -1)^2+12*a^2*m*x(i -1) -12*a^2*m*x(i -2))*x(i)^6+(96*m*x(i -1)^4 -96*m*...
-1))*x(i)^5+(-24*m*...-48*a^2*m*x(i -1)^2+48*a^2*m*x(i -2)*x(i
x(i -1)^5+24*m*x(i -2)*x(i -1)^4+72*a^2*m*x(i -1)^3 -72*a^2*m*x(i -2)*...
x(i -1)^2)*x(i)^4+(-48*a^2*m*x(i -1)^4+48*a^2*m*x(i -2)*x(i -1)^3)*x(i)^3+(12*...
a^2*m*x(i -1)^5 -12*a^2*m*x(i -2)*x(i -1)^4)*x(i)^2)*x(i+1)^2+((16*m*...
-16*m*x(i -2))*x(i)^9+(-64*m*x(i -1)^2+64*m*x(i -2)*x(i -1))*...
x(i)^8+(96*m*x(i -1)^3 -96*m*x(i -2)*x(i -1)^2 -8*a^2*m*x(i -1)+8*a^2*m*...
x(i -2))*x(i)^7+(-64*m*x(i -1)^4+64*m*x(i -2)*x(i -1)^3+32*a^2*m*x(i -1)^2 -32*...
-1))*x(i)^6+(16*m*x(i -1)^5 -16*m*x(i -2)*x(i -1)^4 -48*a^2*...
m*x(i -1)^3+48*a^2*m*x(i -2)*x(i -1)^2)*x(i)^5+(32*a^2*m*x(i -1)^4 -32*a^2*m*...
x(i -2)*x(i -1)^3)*x(i)^4+(-8*a^2*m*x(i -1)^5+8*a^2*m*x(i -2)*x(i -1)^4)*...
-1)+4*m*x(i -2))*x(i)^10+(16*m*x(i -1)^2 -16*m*...
x(i -2)*x(i -1))*x(i)^9+(-24*m*x(i -1)^3+24*m*x(i -2)*x(i -1)^2+2*a^2*m*...
x(i -1) -2*a^2*m*x(i -2))*x(i)^8+(16*m*x(i -1)^4 -16*m*x(i -2)*x(i -1)^3 -8*a^2*...
-1))*x(i)^7+(-4*m*x(i -1)^5+4*m*x(i -2)*...
x(i -1)^4+12*a^2*m*x(i -1)^3 -12*a^2*m*x(i -2)*x(i -1)^2)*x(i)^6+(-8*a^2*m*...
x(i -1)^4+8*a^2*m*x(i -2)*x(i -1)^3)*x(i)^5+(2*a^2*m*x(i -1)^5 -2*a^2*m*x(i -2)*...
-2))*x(i)^6+(-16*m*...)*x(i+2)+(((4*m*x(i -1) -4*m*x(i
x(i -1)^2+16*m*x(i -2)*x(i -1))*x(i)^5+(24*m*x(i -1)^3 -24*m*x(i -2)*...
x(i -1)^2 -2*a^2*m*x(i -1)+2*a^2*m*x(i -2))*x(i)^4+(-16*m*x(i -1)^4+16*m*...
x(i -2)*x(i -1)^3+8*a^2*m*x(i -1)^2 -8*a^2*m*x(i -2)*x(i -1))*x(i)^3+(4*m*...
-4*m*x(i -2)*x(i -1)^4 -12*a^2*m*x(i -1)^3+12*a^2*m*x(i -2)*...
x(i -1)^2)*x(i)^2+(8*a^2*m*x(i -1)^4 -8*a^2*m*x(i -2)*x(i -1)^3)*x(i)+(-2*a^2*m*...
x(i -1)^5+2*a^2*m*x(i -2)*x(i -1)^4))*x(i+1)^5+((-16*m*x(i -1)+16*m*x(i -2))*...
-64*m*x(i -2)*x(i -1))*x(i)^6+(-96*m*x(i -1)^3+96*m*...
x(i -2)*x(i -1)^2+8*a^2*m*x(i -1) -8*a^2*m*x(i -2))*x(i)^5+(64*m*x(i -1)^4 -64*...
m*x(i -2)*x(i -1)^3 -32*a^2*m*x(i -1)^2+32*a^2*m*x(i -2)*x(i -1))*x(i)^4+(-16*m*...
-1)^4+48*a^2*m*x(i -1)^3 -48*a^2*m*x(i -2)*...
x(i -1)^2)*x(i)^3+(-32*a^2*m*x(i -1)^4+32*a^2*m*x(i -2)*x(i -1)^3)*x(i)^2+(8*...
a^2*m*x(i -1)^5 -8*a^2*m*x(i -2)*x(i -1)^4)*x(i))*x(i+1)^4+((24*m*x(i -1) -24*m*...
-2)*x(i -1))*x(i)^7+(144*m*... -1)^2+96*m*x(i
x(i -1)^3 -144*m*x(i -2)*x(i -1)^2 -12*a^2*m*x(i -1)+12*a^2*m*x(i -2))*...
x(i)^6+(-96*m*x(i -1)^4+96*m*x(i -2)*x(i -1)^3+48*a^2*m*x(i -1)^2 -48*a^2*m*...
-72*a^2*m*...(i -1))*x(i)^5+(24*m*x(i -1)^5 -24*m*x(i -2)*x(i -1)^4
x(i -1)^3+72*a^2*m*x(i -2)*x(i -1)^2)*x(i)^4+(48*a^2*m*x(i -1)^4 -48*a^2*m*...
x(i -2)*x(i -1)^3)*x(i)^3+(-12*a^2*m*x(i -1)^5+12*a^2*m*x(i -2)*x(i -1)^4)*...
x(i)^2)*x(i+1)^3+((-16*m*x(i -1)+16*m*x(i -2))*x(i)^9+(64*m*x(i -1)^2 -64*m*...
-2)*x(i -1))*x(i)^8+(-96*m*x(i -1)^3+96*m*x(i -2)*x(i -1)^2+8*a^2*m*...
x(i -1) -8*a^2*m*x(i -2))*x(i)^7+(64*m*x(i -1)^4 -64*m*x(i -2)*x(i -1)^3 -32*...
a^2*m*x(i -1)^2+32*a^2*m*x(i -2)*x(i -1))*x(i)^6+(-16*m*x(i -1)^5+16*m*x(i -2)*...
-1)^4+48*a^2*m*x(i -1)^3 -48*a^2*m*x(i -2)*x(i -1)^2)*x(i)^5+(-32*a^2*m*...
x(i -1)^4+32*a^2*m*x(i -2)*x(i -1)^3)*x(i)^4+(8*a^2*m*x(i -1)^5 -8*a^2*m*...
x(i -2)*x(i -1)^4)*x(i)^3)*x(i+1)^2+((4*m*x(i -1) -4*m*x(i -2))*x(i)^10+(-16*m*...
-2)*x(i -1))*x(i)^9+(24*m*x(i -1)^3 -24*m*x(i -2)*...
x(i -1)^2 -2*a^2*m*x(i -1)+2*a^2*m*x(i -2))*x(i)^8+(-16*m*x(i -1)^4+16*m*...
x(i -2)*x(i -1)^3+8*a^2*m*x(i -1)^2 -8*a^2*m*x(i -2)*x(i -1))*x(i)^7+(4*m*...
-1)^3+12*a^2*m*x(i -2)*...*x(i -1)^4 -12*a^2*m*x(i
x(i -1)^2)*x(i)^6+(8*a^2*m*x(i -1)^4 -8*a^2*m*x(i -2)*x(i -1)^3)*x(i)^5+(-2*a^2*...
m*x(i -1)^5+2*a^2*m*x(i -2)*x(i -1)^4)*x(i)^4)*x(i+1)))*exp((-1*...
-1)+3*a^5*...a^2))+(((a^5*hbar^2*pi()*x(i)+(-4*a^5*hbar^2*pi()*x(i
hbar^2*pi()*x(i -2)))*x(i+1)^4+(-4*a^5*hbar^2*pi()*x(i)^2+(17*a^5*hbar^2*pi()*...
x(i -1) -13*a^5*hbar^2*pi()*x(i -2))*x(i)+(-1*a^5*hbar^2*pi()*x(i -1)^2+a^5*...
-1)))*x(i+1)^3+(6*a^5*hbar^2*pi()*x(i)^3+(-28*a^5*...
hbar^2*pi()*x(i -1)+22*a^5*hbar^2*pi()*x(i -2))*x(i)^2+(5*a^5*hbar^2*pi()*...
x(i -1)^2 -5*a^5*hbar^2*pi()*x(i -2)*x(i -1))*x(i)+(-1*a^5*hbar^2*pi()*...
-1)^2))*x(i+1)^2+(-4*a^5*hbar^2*pi()*...i
x(i)^4+(22*a^5*hbar^2*pi()*x(i -1) -18*a^5*hbar^2*pi()*x(i -2))*x(i)^3+(-10*a^5*...
hbar^2*pi()*x(i -1)^2+10*a^5*hbar^2*pi()*x(i -2)*x(i -1))*x(i)^2+(5*a^5*hbar^2*...
-1)^2)*x(i)+(-1*a^5*hbar^2*pi()*...()*x(i -2)*x(i
x(i -1)^4+a^5*hbar^2*pi()*x(i -2)*x(i -1)^3))*x(i+1)+(a^5*hbar^2*pi()*...
x(i)^5+(-10*a^5*hbar^2*pi()*x(i -1)+9*a^5*hbar^2*pi()*x(i -2))*x(i)^4+(18*a^5*...
-1))*x(i)^3+(-22*a^5*...2 -18*a^5*hbar^2*pi()*x(i -2)*x(i
hbar^2*pi()*x(i -1)^3+22*a^5*hbar^2*pi()*x(i -2)*x(i -1)^2)*x(i)^2+(13*a^5*...
hbar^2*pi()*x(i -1)^4 -13*a^5*hbar^2*pi()*x(i -2)*x(i -1)^3)*x(i)+(-3*a^5*...
-1)^4)))*x(i+2)+((-1*a^5*...a^5*hbar^2*pi()*x(i -2)*x(i
hbar^2*pi()*x(i)+(4*a^5*hbar^2*pi()*x(i -1) -3*a^5*hbar^2*pi()*x(i -2)))*...
x(i+1)^5+(4*a^5*hbar^2*pi()*x(i)^2+(-17*a^5*hbar^2*pi()*x(i -1)+13*a^5*hbar^2*...
-2)*...)*x(i -2))*x(i)+(a^5*hbar^2*pi()*x(i -1)^2 -1*a^5*hbar^2*pi()*x(i
x(i -1)))*x(i+1)^4+(-6*a^5*hbar^2*pi()*x(i)^3+(28*a^5*hbar^2*pi()*x(i -1) -22*...
a^5*hbar^2*pi()*x(i -2))*x(i)^2+(-5*a^5*hbar^2*pi()*x(i -1)^2+5*a^5*hbar^2*pi()*...
x(i -2)*x(i -1))*x(i)+(a^5*hbar^2*pi()*x(i -1)^3 -1*a^5*hbar^2*pi()*x(i -2)*...
-1)^2))*x(i+1)^3+(4*a^5*hbar^2*pi()*x(i)^4+(-22*a^5*hbar^2*pi()*x(i -1)+18*...
a^5*hbar^2*pi()*x(i -2))*x(i)^3+(10*a^5*hbar^2*pi()*x(i -1)^2 -10*a^5*hbar^2*...
pi()*x(i -2)*x(i -1))*x(i)^2+(-5*a^5*hbar^2*pi()*x(i -1)^3+5*a^5*hbar^2*pi()*...
-1)^2)*x(i)+(a^5*hbar^2*pi()*x(i -1)^4 -1*a^5*hbar^2*pi()*x(i -2)*...
x(i -1)^3))*x(i+1)^2+(-1*a^5*hbar^2*pi()*x(i)^5+(11*a^5*hbar^2*pi()*x(i -1) -10*...
a^5*hbar^2*pi()*x(i -2))*x(i)^4+(-22*a^5*hbar^2*pi()*x(i -1)^2+22*a^5*hbar^2*...
-1))*x(i)^3+(28*a^5*hbar^2*pi()*x(i -1)^3 -28*a^5*hbar^2*pi()*...
x(i -2)*x(i -1)^2)*x(i)^2+(-17*a^5*hbar^2*pi()*x(i -1)^4+17*a^5*hbar^2*pi()*...
x(i -2)*x(i -1)^3)*x(i)+(4*a^5*hbar^2*pi()*x(i -1)^5 -4*a^5*hbar^2*pi()*x(i -2)*...
-1)^4))*x(i+1)+((-1*a^5*hbar^2*pi()*x(i -1)+a^5*hbar^2*pi()*x(i -2))*...
x(i)^5+(4*a^5*hbar^2*pi()*x(i -1)^2 -4*a^5*hbar^2*pi()*x(i -2)*x(i -1))*...
x(i)^4+(-6*a^5*hbar^2*pi()*x(i -1)^3+6*a^5*hbar^2*pi()*x(i -2)*x(i -1)^2)*...
-1)^4 -4*a^5*hbar^2*pi()*x(i -2)*x(i -1)^3)*...
x(i)^2+(-1*a^5*hbar^2*pi()*x(i -1)^5+a^5*hbar^2*pi()*x(i -2)*x(i -1)^4)*...
x(i)))))/((((2*a^5*m*pi()*x(i -1) -2*a^5*m*pi()*x(i -2))*x(i)^4+(-8*a^5*m*pi()*...
-1))*x(i)^3+(12*a^5*m*pi()*x(i -1)^3 -12*...
a^5*m*pi()*x(i -2)*x(i -1)^2)*x(i)^2+(-8*a^5*m*pi()*x(i -1)^4+8*a^5*m*pi()*...
x(i -2)*x(i -1)^3)*x(i)+(2*a^5*m*pi()*x(i -1)^5 -2*a^5*m*pi()*x(i -2)*...
-1)+8*a^5*m*pi()*x(i -2))*x(i)^5+(32*...*x(i
a^5*m*pi()*x(i -1)^2 -32*a^5*m*pi()*x(i -2)*x(i -1))*x(i)^4+(-48*a^5*m*pi()*...
x(i -1)^3+48*a^5*m*pi()*x(i -2)*x(i -1)^2)*x(i)^3+(32*a^5*m*pi()*x(i -1)^4 -32*...
-1)^3)*x(i)^2+(-8*a^5*m*pi()*x(i -1)^5+8*a^5*m*pi()*...
x(i -2)*x(i -1)^4)*x(i))*x(i+1)^3+((12*a^5*m*pi()*x(i -1) -12*a^5*m*pi()*...
x(i -2))*x(i)^6+(-48*a^5*m*pi()*x(i -1)^2+48*a^5*m*pi()*x(i -2)*x(i -1))*...
-72*a^5*m*pi()*x(i -2)*x(i -1)^2)*x(i)^4+(-48*...
a^5*m*pi()*x(i -1)^4+48*a^5*m*pi()*x(i -2)*x(i -1)^3)*x(i)^3+(12*a^5*m*pi()*...
x(i -1)^5 -12*a^5*m*pi()*x(i -2)*x(i -1)^4)*x(i)^2)*x(i+1)^2+((-8*a^5*m*pi()*...
-2))*x(i)^7+(32*a^5*m*pi()*x(i -1)^2 -32*a^5*m*pi()*...
x(i -2)*x(i -1))*x(i)^6+(-48*a^5*m*pi()*x(i -1)^3+48*a^5*m*pi()*x(i -2)*...
x(i -1)^2)*x(i)^5+(32*a^5*m*pi()*x(i -1)^4 -32*a^5*m*pi()*x(i -2)*x(i -1)^3)*...
-1)^5+8*a^5*m*pi()*x(i -2)*x(i -1)^4)*x(i)^3)*...
x(i+1)+((2*a^5*m*pi()*x(i -1) -2*a^5*m*pi()*x(i -2))*x(i)^8+(-8*a^5*m*pi()*...
x(i -1)^2+8*a^5*m*pi()*x(i -2)*x(i -1))*x(i)^7+(12*a^5*m*pi()*x(i -1)^3 -12*a^5*...
-1)^2)*x(i)^6+(-8*a^5*m*pi()*x(i -1)^4+8*a^5*m*pi()*x(i -2)*...
x(i -1)^3)*x(i)^5+(2*a^5*m*pi()*x(i -1)^5 -2*a^5*m*pi()*x(i -2)*x(i -1)^4)*...
x(i)^4))*x(i+2)+(((-2*a^5*m*pi()*x(i -1)+2*a^5*m*pi()*x(i -2))*x(i)^4+(8*a^5*m*...
-8*a^5*m*pi()*x(i -2)*x(i -1))*x(i)^3+(-12*a^5*m*pi()*...
x(i -1)^3+12*a^5*m*pi()*x(i -2)*x(i -1)^2)*x(i)^2+(8*a^5*m*pi()*x(i -1)^4 -8*...
a^5*m*pi()*x(i -2)*x(i -1)^3)*x(i)+(-2*a^5*m*pi()*x(i -1)^5+2*a^5*m*pi()*...
-1)^4))*x(i+1)^5+((8*a^5*m*pi()*x(i -1) -8*a^5*m*pi()*x(i -2))*...
x(i)^5+(-32*a^5*m*pi()*x(i -1)^2+32*a^5*m*pi()*x(i -2)*x(i -1))*x(i)^4+(48*a^5*...
m*pi()*x(i -1)^3 -48*a^5*m*pi()*x(i -2)*x(i -1)^2)*x(i)^3+(-32*a^5*m*pi()*...
-2)*x(i -1)^3)*x(i)^2+(8*a^5*m*pi()*x(i -1)^5 -8*...
a^5*m*pi()*x(i -2)*x(i -1)^4)*x(i))*x(i+1)^4+((-12*a^5*m*pi()*x(i -1)+12*a^5*m*...
pi()*x(i -2))*x(i)^6+(48*a^5*m*pi()*x(i -1)^2 -48*a^5*m*pi()*x(i -2)*x(i -1))*...
-1)^3+72*a^5*m*pi()*x(i -2)*x(i -1)^2)*x(i)^4+(48*...
a^5*m*pi()*x(i -1)^4 -48*a^5*m*pi()*x(i -2)*x(i -1)^3)*x(i)^3+(-12*a^5*m*pi()*...
x(i -1)^5+12*a^5*m*pi()*x(i -2)*x(i -1)^4)*x(i)^2)*x(i+1)^3+((8*a^5*m*pi()*...
-2))*x(i)^7+(-32*a^5*m*pi()*x(i -1)^2+32*a^5*m*pi()*...
x(i -2)*x(i -1))*x(i)^6+(48*a^5*m*pi()*x(i -1)^3 -48*a^5*m*pi()*x(i -2)*...
x(i -1)^2)*x(i)^5+(-32*a^5*m*pi()*x(i -1)^4+32*a^5*m*pi()*x(i -2)*x(i -1)^3)*...
-8*a^5*m*pi()*x(i -2)*x(i -1)^4)*x(i)^3)*...
x(i+1)^2+((-2*a^5*m*pi()*x(i -1)+2*a^5*m*pi()*x(i -2))*x(i)^8+(8*a^5*m*pi()*...
x(i -1)^2 -8*a^5*m*pi()*x(i -2)*x(i -1))*x(i)^7+(-12*a^5*m*pi()*x(i -1)^3+12*...
-1)^2)*x(i)^6+(8*a^5*m*pi()*x(i -1)^4 -8*a^5*m*pi()*...
x(i -2)*x(i -1)^3)*x(i)^5+(-2*a^5*m*pi()*x(i -1)^5+2*a^5*m*pi()*x(i -2)*...
x(i -1)^4)*x(i)^4)*x(i+1)));
endfunction
function result=fr2(x,i)
global m hbar;
result= ...
((hbar^2*x(i)^2+(-4*hbar^2*x(i -1)+2*hbar^2*x(i -2))*x(i)+...
(9*hbar^2*x(i -1)^2 -14*hbar^2*x(i -2)*x(i -1)+6*hbar^2*x(i -2)^2))*x(i+1)^2+...
(-2*hbar^2*x(i)^3+(8*hbar^2*x(i -1) -4*hbar^2*x(i -2))*x(i)^2+...
-2)*x(i -1) -14*hbar^2*x(i -2)^2)*x(i)+...
(2*hbar^2*x(i -1)^3 -4*hbar^2*x(i -2)*x(i -1)^2+...
2*hbar^2*x(i -2)^2*x(i -1)))*x(i+1)+(hbar^2*x(i)^4+(-4*hbar^2*x(i -1)+...
2*hbar^2*x(i -2))*x(i)^3+(12*hbar^2*x(i -1)^2 -20*hbar^2*x(i -2)*x(i -1)+...
-2)^2)*x(i)^2+(-4*hbar^2*x(i -1)^3+...
8*hbar^2*x(i -2)*x(i -1)^2 -4*hbar^2*x(i -2)^2*x(i -1))*x(i)+...
(hbar^2*x(i -1)^4 -2*hbar^2*x(i -2)*x(i -1)^3+...
hbar^2*x(i -2)^2*x(i -1)^2)))/(((4*m*x(i -1)^2 -8*m*x(i -2)*x(i -1)+...
-1)^3+...2)^2)*x(i)^4+(-16*m*x(i
32*m*x(i -2)*x(i -1)^2 -16*m*x(i -2)^2*x(i -1))*x(i)^3+...
(24*m*x(i -1)^4 -48*m*x(i -2)*x(i -1)^3+24*m*x(i -2)^2*x(i -1)^2)*x(i)^2+...
(-16*m*x(i -1)^5+32*m*x(i -2)*x(i -1)^4 -16*m*x(i -2)^2*x(i -1)^3)*x(i)+...
-1)^5+4*m*x(i -2)^2*x(i -1)^4))*x(i+1)^2+...
((-8*m*x(i -1)^2+16*m*x(i -2)*x(i -1) -8*m*x(i -2)^2)*x(i)^5+...
(32*m*x(i -1)^3 -64*m*x(i -2)*x(i -1)^2+32*m*x(i -2)^2*x(i -1))*x(i)^4+...
-1)^2)*x(i)^3+...96*m*x(i -2)*x(i -1)^3 -48*m*x(i -2)^2*x(i
(32*m*x(i -1)^5 -64*m*x(i -2)*x(i -1)^4+32*m*x(i -2)^2*x(i -1)^3)*x(i)^2+...
(-8*m*x(i -1)^6+16*m*x(i -2)*x(i -1)^5 -8*m*x(i -2)^2*x(i -1)^4)*x(i))*x(i+1)+...
-1)^3+... -1)^2 -8*m*x(i -2)*x(i -1)+4*m*x(i -2)^2)*x(i)^6+(-16*m*x(i
32*m*x(i -2)*x(i -1)^2 -16*m*x(i -2)^2*x(i -1))*x(i)^5+...
(24*m*x(i -1)^4 -48*m*x(i -2)*x(i -1)^3+24*m*x(i -2)^2*x(i -1)^2)*x(i)^4+...
(-16*m*x(i -1)^5+32*m*x(i -2)*x(i -1)^4 -16*m*x(i -2)^2*x(i -1)^3)*x(i)^3+...
-1)^5+4*m*x(i -2)^2*x(i -1)^4)*x(i)^2));
endfunction
function result=fr3(x,i)
global m hbar a;
result= ...
(((((-4*m*x(i -1)+4*m*x(i -2))*x(i)^6+(16*m*x(i -1)^2 -16*m*x(i -2)*x(i -1))*...
x(i)^5+(-24*m*x(i -1)^3+24*m*x(i -2)*x(i -1)^2+2*a^2*m*x(i -1) -2*a^2*m*...
x(i -2))*x(i)^4+(16*m*x(i -1)^4 -16*m*x(i -2)*x(i -1)^3 -8*a^2*m*x(i -1)^2+8*...
-2)*x(i -1))*x(i)^3+(-4*m*x(i -1)^5+4*m*x(i -2)*x(i -1)^4+12*a^2*m*...
x(i -1)^3 -12*a^2*m*x(i -2)*x(i -1)^2)*x(i)^2+(-8*a^2*m*x(i -1)^4+8*a^2*m*...
x(i -2)*x(i -1)^3)*x(i)+(2*a^2*m*x(i -1)^5 -2*a^2*m*x(i -2)*x(i -1)^4))*...
-16*m*x(i -2))*x(i)^7+(-64*m*x(i -1)^2+64*m*x(i -2)*...
x(i -1))*x(i)^6+(96*m*x(i -1)^3 -96*m*x(i -2)*x(i -1)^2 -8*a^2*m*x(i -1)+8*a^2*...
m*x(i -2))*x(i)^5+(-64*m*x(i -1)^4+64*m*x(i -2)*x(i -1)^3+32*a^2*m*...
-1))*x(i)^4+(16*m*x(i -1)^5 -16*m*x(i -2)*...
x(i -1)^4 -48*a^2*m*x(i -1)^3+48*a^2*m*x(i -2)*x(i -1)^2)*x(i)^3+(32*a^2*m*...
x(i -1)^4 -32*a^2*m*x(i -2)*x(i -1)^3)*x(i)^2+(-8*a^2*m*x(i -1)^5+8*a^2*m*...
-1)+24*m*x(i -2))*x(i)^8+(96*m*...)^3+((-24*m*x(i
x(i -1)^2 -96*m*x(i -2)*x(i -1))*x(i)^7+(-144*m*x(i -1)^3+144*m*x(i -2)*...
x(i -1)^2+12*a^2*m*x(i -1) -12*a^2*m*x(i -2))*x(i)^6+(96*m*x(i -1)^4 -96*m*...
-1))*x(i)^5+(-24*m*...-48*a^2*m*x(i -1)^2+48*a^2*m*x(i -2)*x(i
x(i -1)^5+24*m*x(i -2)*x(i -1)^4+72*a^2*m*x(i -1)^3 -72*a^2*m*x(i -2)*...
x(i -1)^2)*x(i)^4+(-48*a^2*m*x(i -1)^4+48*a^2*m*x(i -2)*x(i -1)^3)*x(i)^3+(12*...
a^2*m*x(i -1)^5 -12*a^2*m*x(i -2)*x(i -1)^4)*x(i)^2)*x(i+1)^2+((16*m*...
-16*m*x(i -2))*x(i)^9+(-64*m*x(i -1)^2+64*m*x(i -2)*x(i -1))*...
x(i)^8+(96*m*x(i -1)^3 -96*m*x(i -2)*x(i -1)^2 -8*a^2*m*x(i -1)+8*a^2*m*...
x(i -2))*x(i)^7+(-64*m*x(i -1)^4+64*m*x(i -2)*x(i -1)^3+32*a^2*m*x(i -1)^2 -32*...
-1))*x(i)^6+(16*m*x(i -1)^5 -16*m*x(i -2)*x(i -1)^4 -48*a^2*...
m*x(i -1)^3+48*a^2*m*x(i -2)*x(i -1)^2)*x(i)^5+(32*a^2*m*x(i -1)^4 -32*a^2*m*...
x(i -2)*x(i -1)^3)*x(i)^4+(-8*a^2*m*x(i -1)^5+8*a^2*m*x(i -2)*x(i -1)^4)*...
-1)+4*m*x(i -2))*x(i)^10+(16*m*x(i -1)^2 -16*m*...
x(i -2)*x(i -1))*x(i)^9+(-24*m*x(i -1)^3+24*m*x(i -2)*x(i -1)^2+2*a^2*m*...
x(i -1) -2*a^2*m*x(i -2))*x(i)^8+(16*m*x(i -1)^4 -16*m*x(i -2)*x(i -1)^3 -8*a^2*...
-1))*x(i)^7+(-4*m*x(i -1)^5+4*m*x(i -2)*...
x(i -1)^4+12*a^2*m*x(i -1)^3 -12*a^2*m*x(i -2)*x(i -1)^2)*x(i)^6+(-8*a^2*m*...
x(i -1)^4+8*a^2*m*x(i -2)*x(i -1)^3)*x(i)^5+(2*a^2*m*x(i -1)^5 -2*a^2*m*x(i -2)*...
-2))*x(i)^6+(-16*m*...)*x(i+2)+(((4*m*x(i -1) -4*m*x(i
x(i -1)^2+16*m*x(i -2)*x(i -1))*x(i)^5+(24*m*x(i -1)^3 -24*m*x(i -2)*...
x(i -1)^2 -2*a^2*m*x(i -1)+2*a^2*m*x(i -2))*x(i)^4+(-16*m*x(i -1)^4+16*m*...
x(i -2)*x(i -1)^3+8*a^2*m*x(i -1)^2 -8*a^2*m*x(i -2)*x(i -1))*x(i)^3+(4*m*...
-4*m*x(i -2)*x(i -1)^4 -12*a^2*m*x(i -1)^3+12*a^2*m*x(i -2)*...
x(i -1)^2)*x(i)^2+(8*a^2*m*x(i -1)^4 -8*a^2*m*x(i -2)*x(i -1)^3)*x(i)+(-2*a^2*m*...
x(i -1)^5+2*a^2*m*x(i -2)*x(i -1)^4))*x(i+1)^5+((-16*m*x(i -1)+16*m*x(i -2))*...
-64*m*x(i -2)*x(i -1))*x(i)^6+(-96*m*x(i -1)^3+96*m*...
x(i -2)*x(i -1)^2+8*a^2*m*x(i -1) -8*a^2*m*x(i -2))*x(i)^5+(64*m*x(i -1)^4 -64*...
m*x(i -2)*x(i -1)^3 -32*a^2*m*x(i -1)^2+32*a^2*m*x(i -2)*x(i -1))*x(i)^4+(-16*m*...
-1)^4+48*a^2*m*x(i -1)^3 -48*a^2*m*x(i -2)*...
x(i -1)^2)*x(i)^3+(-32*a^2*m*x(i -1)^4+32*a^2*m*x(i -2)*x(i -1)^3)*x(i)^2+(8*...
a^2*m*x(i -1)^5 -8*a^2*m*x(i -2)*x(i -1)^4)*x(i))*x(i+1)^4+((24*m*x(i -1) -24*m*...
-2)*x(i -1))*x(i)^7+(144*m*... -1)^2+96*m*x(i
x(i -1)^3 -144*m*x(i -2)*x(i -1)^2 -12*a^2*m*x(i -1)+12*a^2*m*x(i -2))*...
x(i)^6+(-96*m*x(i -1)^4+96*m*x(i -2)*x(i -1)^3+48*a^2*m*x(i -1)^2 -48*a^2*m*...
-72*a^2*m*...(i -1))*x(i)^5+(24*m*x(i -1)^5 -24*m*x(i -2)*x(i -1)^4
x(i -1)^3+72*a^2*m*x(i -2)*x(i -1)^2)*x(i)^4+(48*a^2*m*x(i -1)^4 -48*a^2*m*...
x(i -2)*x(i -1)^3)*x(i)^3+(-12*a^2*m*x(i -1)^5+12*a^2*m*x(i -2)*x(i -1)^4)*...
x(i)^2)*x(i+1)^3+((-16*m*x(i -1)+16*m*x(i -2))*x(i)^9+(64*m*x(i -1)^2 -64*m*...
-2)*x(i -1))*x(i)^8+(-96*m*x(i -1)^3+96*m*x(i -2)*x(i -1)^2+8*a^2*m*...
x(i -1) -8*a^2*m*x(i -2))*x(i)^7+(64*m*x(i -1)^4 -64*m*x(i -2)*x(i -1)^3 -32*...
a^2*m*x(i -1)^2+32*a^2*m*x(i -2)*x(i -1))*x(i)^6+(-16*m*x(i -1)^5+16*m*x(i -2)*...
-1)^4+48*a^2*m*x(i -1)^3 -48*a^2*m*x(i -2)*x(i -1)^2)*x(i)^5+(-32*a^2*m*...
x(i -1)^4+32*a^2*m*x(i -2)*x(i -1)^3)*x(i)^4+(8*a^2*m*x(i -1)^5 -8*a^2*m*...
x(i -2)*x(i -1)^4)*x(i)^3)*x(i+1)^2+((4*m*x(i -1) -4*m*x(i -2))*x(i)^10+(-16*m*...
-2)*x(i -1))*x(i)^9+(24*m*x(i -1)^3 -24*m*x(i -2)*...
x(i -1)^2 -2*a^2*m*x(i -1)+2*a^2*m*x(i -2))*x(i)^8+(-16*m*x(i -1)^4+16*m*...
x(i -2)*x(i -1)^3+8*a^2*m*x(i -1)^2 -8*a^2*m*x(i -2)*x(i -1))*x(i)^7+(4*m*...
-1)^3+12*a^2*m*x(i -2)*...*x(i -1)^4 -12*a^2*m*x(i
x(i -1)^2)*x(i)^6+(8*a^2*m*x(i -1)^4 -8*a^2*m*x(i -2)*x(i -1)^3)*x(i)^5+(-2*a^2*...
m*x(i -1)^5+2*a^2*m*x(i -2)*x(i -1)^4)*x(i)^4)*x(i+1)))*exp((-1*...
-1)+3*a^5*...a^2))+(((a^5*hbar^2*pi()*x(i)+(-4*a^5*hbar^2*pi()*x(i
hbar^2*pi()*x(i -2)))*x(i+1)^4+(-4*a^5*hbar^2*pi()*x(i)^2+(17*a^5*hbar^2*pi()*...
x(i -1) -13*a^5*hbar^2*pi()*x(i -2))*x(i)+(-1*a^5*hbar^2*pi()*x(i -1)^2+a^5*...
-1)))*x(i+1)^3+(6*a^5*hbar^2*pi()*x(i)^3+(-28*a^5*...
hbar^2*pi()*x(i -1)+22*a^5*hbar^2*pi()*x(i -2))*x(i)^2+(5*a^5*hbar^2*pi()*...
x(i -1)^2 -5*a^5*hbar^2*pi()*x(i -2)*x(i -1))*x(i)+(-1*a^5*hbar^2*pi()*...
-1)^2))*x(i+1)^2+(-4*a^5*hbar^2*pi()*...i
x(i)^4+(22*a^5*hbar^2*pi()*x(i -1) -18*a^5*hbar^2*pi()*x(i -2))*x(i)^3+(-10*a^5*...
hbar^2*pi()*x(i -1)^2+10*a^5*hbar^2*pi()*x(i -2)*x(i -1))*x(i)^2+(5*a^5*hbar^2*...
-1)^2)*x(i)+(-1*a^5*hbar^2*pi()*...()*x(i -2)*x(i
x(i -1)^4+a^5*hbar^2*pi()*x(i -2)*x(i -1)^3))*x(i+1)+(a^5*hbar^2*pi()*...
x(i)^5+(-10*a^5*hbar^2*pi()*x(i -1)+9*a^5*hbar^2*pi()*x(i -2))*x(i)^4+(18*a^5*...
-1))*x(i)^3+(-22*a^5*...2 -18*a^5*hbar^2*pi()*x(i -2)*x(i
hbar^2*pi()*x(i -1)^3+22*a^5*hbar^2*pi()*x(i -2)*x(i -1)^2)*x(i)^2+(13*a^5*...
hbar^2*pi()*x(i -1)^4 -13*a^5*hbar^2*pi()*x(i -2)*x(i -1)^3)*x(i)+(-3*a^5*...
-1)^4)))*x(i+2)+((-1*a^5*...a^5*hbar^2*pi()*x(i -2)*x(i
hbar^2*pi()*x(i)+(4*a^5*hbar^2*pi()*x(i -1) -3*a^5*hbar^2*pi()*x(i -2)))*...
x(i+1)^5+(4*a^5*hbar^2*pi()*x(i)^2+(-17*a^5*hbar^2*pi()*x(i -1)+13*a^5*hbar^2*...
-2)*...)*x(i -2))*x(i)+(a^5*hbar^2*pi()*x(i -1)^2 -1*a^5*hbar^2*pi()*x(i
x(i -1)))*x(i+1)^4+(-6*a^5*hbar^2*pi()*x(i)^3+(28*a^5*hbar^2*pi()*x(i -1) -22*...
a^5*hbar^2*pi()*x(i -2))*x(i)^2+(-5*a^5*hbar^2*pi()*x(i -1)^2+5*a^5*hbar^2*pi()*...
x(i -2)*x(i -1))*x(i)+(a^5*hbar^2*pi()*x(i -1)^3 -1*a^5*hbar^2*pi()*x(i -2)*...
-1)^2))*x(i+1)^3+(4*a^5*hbar^2*pi()*x(i)^4+(-22*a^5*hbar^2*pi()*x(i -1)+18*...
a^5*hbar^2*pi()*x(i -2))*x(i)^3+(10*a^5*hbar^2*pi()*x(i -1)^2 -10*a^5*hbar^2*...
pi()*x(i -2)*x(i -1))*x(i)^2+(-5*a^5*hbar^2*pi()*x(i -1)^3+5*a^5*hbar^2*pi()*...
-1)^2)*x(i)+(a^5*hbar^2*pi()*x(i -1)^4 -1*a^5*hbar^2*pi()*x(i -2)*...
x(i -1)^3))*x(i+1)^2+(-1*a^5*hbar^2*pi()*x(i)^5+(11*a^5*hbar^2*pi()*x(i -1) -10*...
a^5*hbar^2*pi()*x(i -2))*x(i)^4+(-22*a^5*hbar^2*pi()*x(i -1)^2+22*a^5*hbar^2*...
-1))*x(i)^3+(28*a^5*hbar^2*pi()*x(i -1)^3 -28*a^5*hbar^2*pi()*...
x(i -2)*x(i -1)^2)*x(i)^2+(-17*a^5*hbar^2*pi()*x(i -1)^4+17*a^5*hbar^2*pi()*...
x(i -2)*x(i -1)^3)*x(i)+(4*a^5*hbar^2*pi()*x(i -1)^5 -4*a^5*hbar^2*pi()*x(i -2)*...
-1)^4))*x(i+1)+((-1*a^5*hbar^2*pi()*x(i -1)+a^5*hbar^2*pi()*x(i -2))*...
x(i)^5+(4*a^5*hbar^2*pi()*x(i -1)^2 -4*a^5*hbar^2*pi()*x(i -2)*x(i -1))*...
x(i)^4+(-6*a^5*hbar^2*pi()*x(i -1)^3+6*a^5*hbar^2*pi()*x(i -2)*x(i -1)^2)*...
-1)^4 -4*a^5*hbar^2*pi()*x(i -2)*x(i -1)^3)*...
x(i)^2+(-1*a^5*hbar^2*pi()*x(i -1)^5+a^5*hbar^2*pi()*x(i -2)*x(i -1)^4)*...
x(i)))))/((((2*a^5*m*pi()*x(i -1) -2*a^5*m*pi()*x(i -2))*x(i)^4+(-8*a^5*m*pi()*...
-1))*x(i)^3+(12*a^5*m*pi()*x(i -1)^3 -12*...
a^5*m*pi()*x(i -2)*x(i -1)^2)*x(i)^2+(-8*a^5*m*pi()*x(i -1)^4+8*a^5*m*pi()*...
x(i -2)*x(i -1)^3)*x(i)+(2*a^5*m*pi()*x(i -1)^5 -2*a^5*m*pi()*x(i -2)*...
-1)+8*a^5*m*pi()*x(i -2))*x(i)^5+(32*...*x(i
a^5*m*pi()*x(i -1)^2 -32*a^5*m*pi()*x(i -2)*x(i -1))*x(i)^4+(-48*a^5*m*pi()*...
x(i -1)^3+48*a^5*m*pi()*x(i -2)*x(i -1)^2)*x(i)^3+(32*a^5*m*pi()*x(i -1)^4 -32*...
-1)^3)*x(i)^2+(-8*a^5*m*pi()*x(i -1)^5+8*a^5*m*pi()*...
x(i -2)*x(i -1)^4)*x(i))*x(i+1)^3+((12*a^5*m*pi()*x(i -1) -12*a^5*m*pi()*...
x(i -2))*x(i)^6+(-48*a^5*m*pi()*x(i -1)^2+48*a^5*m*pi()*x(i -2)*x(i -1))*...
-72*a^5*m*pi()*x(i -2)*x(i -1)^2)*x(i)^4+(-48*...
a^5*m*pi()*x(i -1)^4+48*a^5*m*pi()*x(i -2)*x(i -1)^3)*x(i)^3+(12*a^5*m*pi()*...
x(i -1)^5 -12*a^5*m*pi()*x(i -2)*x(i -1)^4)*x(i)^2)*x(i+1)^2+((-8*a^5*m*pi()*...
-2))*x(i)^7+(32*a^5*m*pi()*x(i -1)^2 -32*a^5*m*pi()*...
x(i -2)*x(i -1))*x(i)^6+(-48*a^5*m*pi()*x(i -1)^3+48*a^5*m*pi()*x(i -2)*...
x(i -1)^2)*x(i)^5+(32*a^5*m*pi()*x(i -1)^4 -32*a^5*m*pi()*x(i -2)*x(i -1)^3)*...
-1)^5+8*a^5*m*pi()*x(i -2)*x(i -1)^4)*x(i)^3)*...
x(i+1)+((2*a^5*m*pi()*x(i -1) -2*a^5*m*pi()*x(i -2))*x(i)^8+(-8*a^5*m*pi()*...
x(i -1)^2+8*a^5*m*pi()*x(i -2)*x(i -1))*x(i)^7+(12*a^5*m*pi()*x(i -1)^3 -12*a^5*...
-1)^2)*x(i)^6+(-8*a^5*m*pi()*x(i -1)^4+8*a^5*m*pi()*x(i -2)*...
x(i -1)^3)*x(i)^5+(2*a^5*m*pi()*x(i -1)^5 -2*a^5*m*pi()*x(i -2)*x(i -1)^4)*...
x(i)^4))*x(i+2)+(((-2*a^5*m*pi()*x(i -1)+2*a^5*m*pi()*x(i -2))*x(i)^4+(8*a^5*m*...
-8*a^5*m*pi()*x(i -2)*x(i -1))*x(i)^3+(-12*a^5*m*pi()*...
x(i -1)^3+12*a^5*m*pi()*x(i -2)*x(i -1)^2)*x(i)^2+(8*a^5*m*pi()*x(i -1)^4 -8*...
a^5*m*pi()*x(i -2)*x(i -1)^3)*x(i)+(-2*a^5*m*pi()*x(i -1)^5+2*a^5*m*pi()*...
-1)^4))*x(i+1)^5+((8*a^5*m*pi()*x(i -1) -8*a^5*m*pi()*x(i -2))*...
x(i)^5+(-32*a^5*m*pi()*x(i -1)^2+32*a^5*m*pi()*x(i -2)*x(i -1))*x(i)^4+(48*a^5*...
m*pi()*x(i -1)^3 -48*a^5*m*pi()*x(i -2)*x(i -1)^2)*x(i)^3+(-32*a^5*m*pi()*...
-2)*x(i -1)^3)*x(i)^2+(8*a^5*m*pi()*x(i -1)^5 -8*...
a^5*m*pi()*x(i -2)*x(i -1)^4)*x(i))*x(i+1)^4+((-12*a^5*m*pi()*x(i -1)+12*a^5*m*...
pi()*x(i -2))*x(i)^6+(48*a^5*m*pi()*x(i -1)^2 -48*a^5*m*pi()*x(i -2)*x(i -1))*...
-1)^3+72*a^5*m*pi()*x(i -2)*x(i -1)^2)*x(i)^4+(48*...
a^5*m*pi()*x(i -1)^4 -48*a^5*m*pi()*x(i -2)*x(i -1)^3)*x(i)^3+(-12*a^5*m*pi()*...
x(i -1)^5+12*a^5*m*pi()*x(i -2)*x(i -1)^4)*x(i)^2)*x(i+1)^3+((8*a^5*m*pi()*...
-2))*x(i)^7+(-32*a^5*m*pi()*x(i -1)^2+32*a^5*m*pi()*...
x(i -2)*x(i -1))*x(i)^6+(48*a^5*m*pi()*x(i -1)^3 -48*a^5*m*pi()*x(i -2)*...
x(i -1)^2)*x(i)^5+(-32*a^5*m*pi()*x(i -1)^4+32*a^5*m*pi()*x(i -2)*x(i -1)^3)*...
-8*a^5*m*pi()*x(i -2)*x(i -1)^4)*x(i)^3)*...
x(i+1)^2+((-2*a^5*m*pi()*x(i -1)+2*a^5*m*pi()*x(i -2))*x(i)^8+(8*a^5*m*pi()*...
x(i -1)^2 -8*a^5*m*pi()*x(i -2)*x(i -1))*x(i)^7+(-12*a^5*m*pi()*x(i -1)^3+12*...
-1)^2)*x(i)^6+(8*a^5*m*pi()*x(i -1)^4 -8*a^5*m*pi()*...
x(i -2)*x(i -1)^3)*x(i)^5+(-2*a^5*m*pi()*x(i -1)^5+2*a^5*m*pi()*x(i -2)*...
x(i -1)^4)*x(i)^4)*x(i+1)));
endfunction
Type: List(Kernel(Expression(Integer)))
Type: Factored(SparseMultivariatePolynomial(Integer,Kernel(Expression(Integer))))
Type: SparseMultivariatePolynomial(Integer,Kernel(Expression(Integer)))
Type: Factored(SparseMultivariatePolynomial(Integer,Kernel(Expression(Integer))))
Type: SparseMultivariatePolynomial(Integer,Kernel(Expression(Integer)))
Type: Factored(SparseMultivariatePolynomial(Integer,Kernel(Expression(Integer))))
Type: SparseMultivariatePolynomial(Integer,Kernel(Expression(Integer)))
Type: Factored(SparseMultivariatePolynomial(Integer,Kernel(Expression(Integer))))
Type: String
Type: Factored(SparseMultivariatePolynomial(Integer,Kernel(Expression(Integer))))
-12*a^5*m*pi()*x3*x4^2)*x5^2+(-8*a^5*m*pi()*x4^4+8*a^5*m*pi()*x3*x4^3)*x5+(2*a^5*m*pi()*x4^5 -2*a^5*m*pi()*x3*x4^4)),0,0,0,0,0]])^5*m*pi()*x3)*x5^4+(-8*a^5*m*pi()*x4^2+8*a^5*m*pi()*x3*x4)*x5^3+(12*a^5*m*pi()*x4^3 2*m*x3)*x5^4+(16*m*x4^4 *x3^3 ^4