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Examples for support purposes...

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!

sys.path.insert(0,'%s/lib/python2.7/site-packages'%os.environ['HOME'])
import pexpect
reload(pexpect)
pexpect.__version__
import expect
reload(expect)
from fricas import fricas
<module 'pexpect' from '/projects/b04b5777-e269-4c8f-a4b8-b21dbe1c93c6/lib/python2.7/site-packages/pexpect/__init__.pyc'> '3.3' <module 'expect' from './expect.pyc'>
%sage
os.environ['PATH'] = '%s/bin:%s'%(os.environ['HOME'],os.environ['PATH'])
execfile('fricas_md.py')
%default_mode fricas_md
)version
)clear completely
)set output tex on
)set output algebra off
)set output mathml off
)set message type off

Value = "FriCAS 2014-12-18 compiled at Tue May 5 18:13:01 UTC 2015"

All user variables and function definitions have been cleared.

All )browse facility databases have been cleared.

Internally cached functions and constructors have been cleared.

)clear completely is finished.

x:=operator('x);
--hbar:=;
-- Equations 24,25 of HEW paper
R(x,i) == (hbar^2/(4*m))*(sigma(x,i+1)-sigma(x,i))
sigma(x,i) == sif(x,i)^2*(sif(x,i+1)-2*sif(x,i)+sif(x,i-1))
sif(x,i) ==
  --i>N or i<2 => 0
  1/(x(i)-x(i-1))
numer sigma(x,i)
factor denom sigma(x,i)

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

Ri:=R(x,i);
factor numer Ri
factor denom Ri

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.

limit(limit(eval(eval(R(x,1),x(0)=b0),x(-1)=b1),b1=%minusInfinity),b0=%minusInfinity)

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.

limit(limit(eval(eval(R(x,N),x(N+1)=b0),x(N+2)=b1),b1=%plusInfinity),b0=%plusInfinity)

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

c:=0; b:=1; F(x) == (x-c)/(a^3*%pi)*exp(-(x-c)^2/a^2)*b
F(x(i))

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}

$$

FRx:=F(x(i))+R(x,i);
kernels FRx

$$

\left[

{{e} ^{-{{{{x

\left(

{i}

\right)}}

^{2}} \over {{a} ^{2}}}}}, : {x

\left(

{{i+2}}

\right)},

: {x

\left(

{{i+1}}

\right)},

: {x

\left(

{i}

\right)},

: {x

\left(

{{i -1}}

\right)},

: {x

\left(

{{i -2}}

\right)},

: \pi, : m, : hbar, : a

\right]

$$

%sage
def fricas2octave(name,ex):
  fr=fricas(ex).unparsed_input_form()
  f =("function result=%s(x,i)\n"%name)
  f+=("  global m hbar a;\n")
  f+=("  result= ...\n")
  i=0; cpl=80
  while i<len(fr):
    if i+cpl>=len(fr):
        f+= "    "+fr[i:i+cpl]+";\n"
        i=i+cpl
    else:
        line=fr[i:i+cpl]
        p=line.rfind('*', 0, cpl)+1
        if p==0:
            p=line.rindex('+', 0, cpl)+1
        f+= "    "+fr[i:i+p]+"...\n"
        i=i+p
  f+= "endfunction\n"
  ff = open('%s.m'%name, 'w')
  ff.write(f)
  ff.close()
  return f3

0e560dd3-ea55-4efa-9786-1bf7f0468a31s
FRx1:=eval(D(eval(FRx,x(i-2)=xm2),xm2),xm2=x(i-2));
factor numer FRx1 /factor denom FRx1

$$

-{{{hbar} ^{2}} \over {4 \ m \ {{{\left( {x

\left(

{{i -1}}

\right)}

-{x

\left(

{{i -2}}

\right)}

\right)}}

^{2}} \ {{{\left( {x

\left(

{i}

\right)}

-{x

\left(

{{i -1}}

\right)}

\right)}}

^{2}}}}

$$

%sage print fricas2octave('fr1','FRx1')
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*... a^2*m*x(i -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))*... x(i+1)^4+((16*m*x(i -1) -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*... x(i -1)^2 -32*a^2*m*x(i -2)*x(i -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*... x(i -2)*x(i -1)^4)*x(i))*x(i+1)^3+((-24*m*x(i -1)+24*m*x(i -2))*x(i)^8+(96*m*... 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*... x(i -2)*x(i -1)^3 -48*a^2*m*x(i -1)^2+48*a^2*m*x(i -2)*x(i -1))*x(i)^5+(-24*m*... 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*... x(i -1) -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*... a^2*m*x(i -2)*x(i -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)*... x(i)^3)*x(i+1)+((-4*m*x(i -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*... m*x(i -1)^2+8*a^2*m*x(i -2)*x(i -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)*... x(i -1)^4)*x(i)^4))*x(i+2)+(((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*a^2*m*x(i -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))*x(i+1)^5+((-16*m*x(i -1)+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*x(i -1)^2+32*a^2*m*x(i -2)*x(i -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*x(i -2)*x(i -1)^4)*x(i))*x(i+1)^4+((24*m*x(i -1) -24*m*... x(i -2))*x(i)^8+(-96*m*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*x(i -2)*x(i -1)^3+48*a^2*m*x(i -1)^2 -48*a^2*m*... x(i -2)*x(i -1))*x(i)^5+(24*m*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)^3+((-16*m*x(i -1)+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*a^2*m*x(i -2)*x(i -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)*x(i)^3)*x(i+1)^2+((4*m*x(i -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*m*x(i -1)^2 -8*a^2*m*x(i -2)*x(i -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)*x(i -1)^4)*x(i)^4)*x(i+1)))*exp((-1*... x(i)^2)/(a^2))+(((a^5*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)^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*... hbar^2*pi()*x(i -2)*x(i -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()*... x(i -1)^3+a^5*hbar^2*pi()*x(i -2)*x(i -1)^2))*x(i+1)^2+(-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()*x(i -2)*x(i -1)^2)*x(i)+(-1*a^5*hbar^2*pi()*... 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*... hbar^2*pi()*x(i -1)^2 -18*a^5*hbar^2*pi()*x(i -2)*x(i -1))*x(i)^3+(-22*a^5*... 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*... hbar^2*pi()*x(i -1)^5+3*a^5*hbar^2*pi()*x(i -2)*x(i -1)^4)))*x(i+2)+((-1*a^5*... 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*... pi()*x(i -2))*x(i)+(a^5*hbar^2*pi()*x(i -1)^2 -1*a^5*hbar^2*pi()*x(i -2)*... 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)*... x(i -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()*... x(i -2)*x(i -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*... pi()*x(i -2)*x(i -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)*... x(i -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)*... x(i)^3+(4*a^5*hbar^2*pi()*x(i -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()*... x(i -1)^2+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()*x(i -2)*... x(i -1)^4))*x(i+1)^4+((-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()*x(i -1)^4 -32*... a^5*m*pi()*x(i -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)^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))*... x(i)^5+(72*a^5*m*pi()*x(i -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)^2+((-8*a^5*m*pi()*... x(i -1)+8*a^5*m*pi()*x(i -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)*... x(i)^4+(-8*a^5*m*pi()*x(i -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*... m*pi()*x(i -2)*x(i -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*... pi()*x(i -1)^2 -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()*... x(i -2)*x(i -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()*... x(i -1)^4+32*a^5*m*pi()*x(i -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))*... x(i)^5+(-72*a^5*m*pi()*x(i -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()*... x(i -1) -8*a^5*m*pi()*x(i -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)*... x(i)^4+(8*a^5*m*pi()*x(i -1)^5 -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*... a^5*m*pi()*x(i -2)*x(i -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
%sage
fr1=fricas('FRx1').unparsed_input_form()
f1 =("function result=fr1(x,i)\n")
f1+=("  global m hbar;\n")
f1+=("  result= ...\n")
i=0; cpl=80
while i<len(fr1):
    if i+cpl>=len(fr1):
        f1+= fr1[i:i+cpl]+";\n"
        i=i+cpl
    else:
        line=fr1[i:i+cpl]
        p=line.rfind('+', 0, cpl)+1
        f1+= fr1[i:i+p]+"...\n"
        i=i+p
f1+= "endfunction\n"
ff = open('fr1.m', 'w')
ff.write(f1)
ff.close()
print f1
function result=fr1(x,i) global m hbar; result= ... (-1*hbar^2)/((4*m*x(i -1)^2 -8*m*x(i -2)*x(i -1)+4*m*x(i -2)^2)*x(i)^2+... (-8*m*x(i -1)^3+16*m*x(i -2)*x(i -1)^2 -8*m*x(i -2)^2*x(i -1))*x(i)+... (4*m*x(i -1)^4 -8*m*x(i -2)*x(i -1)^3+4*m*x(i -2)^2*x(i -1)^2)); endfunction
%octave
clear all
global m;
global hbar;
global a;
%octave
m = 1;
hbar = 1;
a = 1;
%octave
F1=fr1([1;2;3;4;5],3)
F1 = -0.25
FRx2:=eval(D(eval(FRx,x(i-1)=xm1),xm1),xm1=x(i-1));
factor numer FRx2/factor denom FRx2

$$

{{{hbar} ^{2}} \ {\left( {{\left( {{{x

\left(

{i}

\right)}}

^{2}}+{{\left( -{4 \ {x

\left(

{{i -1}}

\right)}}+{2

\ {x

\left(

{{i -2}}

\right)}}

\right)}

\ {x

\left(

{i}

\right)}}+{9

\ {{{x

\left(

{{i -1}}

\right)}}

^{2}}} -{{14} \ {x

\left(

{{i -2}}

\right)}

\ {x

\left(

{{i -1}}

\right)}}+{6

\ {{{x

\left(

{{i -2}}

\right)}}

^{2}}}

\right)}

\ {{{x

\left(

{{i+1}}

\right)}}

^{2}}}+{{\left( -{2 \ {{{x

\left(

{i}

\right)}}

^{3}}}+{{\left( {8 \ {x

\left(

{{i -1}}

\right)}}

-{4 \ {x

\left(

{{i -2}}

\right)}}

\right)}

\ {{{x

\left(

{i}

\right)}}

^{2}}}+{{\left( -{{20} \ {{{x

\left(

{{i -1}}

\right)}}

^{2}}}+{{32} \ {x

\left(

{{i -2}}

\right)}

\ {x

\left(

{{i -1}}

\right)}}

-{{14} \ {{{x

\left(

{{i -2}}

\right)}}

^{2}}}

\right)}

\ {x

\left(

{i}

\right)}}+{2

\ {{{x

\left(

{{i -1}}

\right)}}

^{3}}} -{4 \ {x

\left(

{{i -2}}

\right)}

\ {{{x

\left(

{{i -1}}

\right)}}

^{2}}}+{2 \ {{{x

\left(

{{i -2}}

\right)}}

^{2}} \ {x

\left(

{{i -1}}

\right)}}

\right)}

\ {x

\left(

{{i+1}}

\right)}}+{{{x

\left(

{i}

\right)}}

^{4}}+{{\left( -{4 \ {x

\left(

{{i -1}}

\right)}}+{2

\ {x

\left(

{{i -2}}

\right)}}

\right)}

\ {{{x

\left(

{i}

\right)}}

^{3}}}+{{\left( {{12} \ {{{x

\left(

{{i -1}}

\right)}}

^{2}}} -{{20} \ {x

\left(

{{i -2}}

\right)}

\ {x

\left(

{{i -1}}

\right)}}+{9

\ {{{x

\left(

{{i -2}}

\right)}}

^{2}}}

\right)}

\ {{{x

\left(

{i}

\right)}}

^{2}}}+{{\left( -{4 \ {{{x

\left(

{{i -1}}

\right)}}

^{3}}}+{8 \ {x

\left(

{{i -2}}

\right)}

\ {{{x

\left(

{{i -1}}

\right)}}

^{2}}} -{4 \ {{{x

\left(

{{i -2}}

\right)}}

^{2}} \ {x

\left(

{{i -1}}

\right)}}

\right)}

\ {x

\left(

{i}

\right)}}+{{{x

\left(

{{i -1}}

\right)}}

^{4}} -{2 \ {x

\left(

{{i -2}}

\right)}

\ {{{x

\left(

{{i -1}}

\right)}}

^{3}}}+{{{{x

\left(

{{i -2}}

\right)}}

^{2}} \ {{{x

\left(

{{i -1}}

\right)}}

^{2}}}

\right)}}

\over {4 \ m \ {{{\left( {x

\left(

{{i -1}}

\right)}

-{x

\left(

{{i -2}}

\right)}

\right)}}

^{2}} \ {{{\left( {x

\left(

{i}

\right)}

-{x

\left(

{{i -1}}

\right)}

\right)}}

^{4}} \ {{{\left( {x

\left(

{{i+1}}

\right)}

-{x

\left(

{i}

\right)}

\right)}}

^{2}}}

$$

%sage
fr2=fricas('FRx2').unparsed_input_form()
f2 =("function result=fr2(x,i)\n")
f2+=("  global m hbar;\n")
f2+=("  result= ...\n")
i=0; cpl=80
while i<len(fr2):
    if i+cpl>=len(fr2):
        f2+= fr2[i:i+cpl]+";\n"
        i=i+cpl
    else:
        line=fr2[i:i+cpl]
        p=line.rfind('+', 0, cpl)+1
        f2+= fr2[i:i+p]+"...\n"
        i=i+p
f2+= "endfunction\n"
ff = open('fr2.m', 'w')
ff.write(f2)
ff.close()
print f2
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+... (-20*hbar^2*x(i -1)^2+32*hbar^2*x(i -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)+... 9*hbar^2*x(i -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)+... 4*m*x(i -2)^2)*x(i)^4+(-16*m*x(i -1)^3+... 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)+... (4*m*x(i -1)^6 -8*m*x(i -2)*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+... (-48*m*x(i -1)^4+96*m*x(i -2)*x(i -1)^3 -48*m*x(i -2)^2*x(i -1)^2)*x(i)^3+... (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)+... ((4*m*x(i -1)^2 -8*m*x(i -2)*x(i -1)+4*m*x(i -2)^2)*x(i)^6+(-16*m*x(i -1)^3+... 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+... (4*m*x(i -1)^6 -8*m*x(i -2)*x(i -1)^5+4*m*x(i -2)^2*x(i -1)^4)*x(i)^2)); endfunction
%octave
F2=fr2([1;2;3;4;5],3)
F2 = 1

FRx3:=eval(D(eval(FRx,x(i)=x1),x1),x1=x(i));
factor numer FRx3

$$

-{\left( {{\left( {{\left( {{\left( {{\left( {4 \ m \ {x

\left(

{{i -1}}

\right)}}

-{4 \ m \ {x

\left(

{{i -2}}

\right)}}

\right)}

\ {{{x

\left(

{i}

\right)}}

^{6}}}+{{\left( -{{16} \ m \ {{{x

\left(

{{i -1}}

\right)}}

^{2}}}+{{16} \ m \ {x

\left(

{{i -2}}

\right)}

\ {x

\left(

{{i -1}}

\right)}}

\right)}

\ {{{x

\left(

{i}

\right)}}

^{5}}}+{{\left( {{24} \ m \ {{{x

\left(

{{i -1}}

\right)}}

^{3}}} -{{24} \ m \ {x

\left(

{{i -2}}

\right)}

\ {{{x

\left(

{{i -1}}

\right)}}

^{2}}} -{2 \ {{a} ^{2}} \ m \ {x

\left(

{{i -1}}

\right)}}+{2

\ {{a} ^{2}} \ m \ {x

\left(

{{i -2}}

\right)}}

\right)}

\ {{{x

\left(

{i}

\right)}}

^{4}}}+{{\left( -{{16} \ m \ {{{x

\left(

{{i -1}}

\right)}}

^{4}}}+{{16} \ m \ {x

\left(

{{i -2}}

\right)}

\ {{{x

\left(

{{i -1}}

\right)}}

^{3}}}+{8 \ {{a} ^{2}} \ m \ {{{x

\left(

{{i -1}}

\right)}}

^{2}}} -{8 \ {{a} ^{2}} \ m \ {x

\left(

{{i -2}}

\right)}

\ {x

\left(

{{i -1}}

\right)}}

\right)}

\ {{{x

\left(

{i}

\right)}}

^{3}}}+{{\left( {4 \ m \ {{{x

\left(

{{i -1}}

\right)}}

^{5}}} -{4 \ m \ {x

\left(

{{i -2}}

\right)}

\ {{{x

\left(

{{i -1}}

\right)}}

^{4}}} -{{12} \ {{a} ^{2}} \ m \ {{{x

\left(

{{i -1}}

\right)}}

^{3}}}+{{12} \ {{a} ^{2}} \ m \ {x

\left(

{{i -2}}

\right)}

\ {{{x

\left(

{{i -1}}

\right)}}

^{2}}}

\right)}

\ {{{x

\left(

{i}

\right)}}

^{2}}}+{{\left( {8 \ {{a} ^{2}} \ m \ {{{x

\left(

{{i -1}}

\right)}}

^{4}}} -{8 \ {{a} ^{2}} \ m \ {x

\left(

{{i -2}}

\right)}

\ {{{x

\left(

{{i -1}}

\right)}}

^{3}}}

\right)}

\ {x

\left(

{i}

\right)}}

-{2 \ {{a} ^{2}} \ m \ {{{x

\left(

{{i -1}}

\right)}}

^{5}}}+{2 \ {{a} ^{2}} \ m \ {x

\left(

{{i -2}}

\right)}

\ {{{x

\left(

{{i -1}}

\right)}}

^{4}}}

\right)}

\ {{{x

\left(

{{i+1}}

\right)}}

^{4}}}+{{\left( {{\left( -{{16} \ m \ {x

\left(

{{i -1}}

\right)}}+{{16}

\ m \ {x

\left(

{{i -2}}

\right)}}

\right)}

\ {{{x

\left(

{i}

\right)}}

^{7}}}+{{\left( {{64} \ m \ {{{x

\left(

{{i -1}}

\right)}}

^{2}}} -{{64} \ m \ {x

\left(

{{i -2}}

\right)}

\ {x

\left(

{{i -1}}

\right)}}

\right)}

\ {{{x

\left(

{i}

\right)}}

^{6}}}+{{\left( -{{96} \ m \ {{{x

\left(

{{i -1}}

\right)}}

^{3}}}+{{96} \ m \ {x

\left(

{{i -2}}

\right)}

\ {{{x

\left(

{{i -1}}

\right)}}

^{2}}}+{8 \ {{a} ^{2}} \ m \ {x

\left(

{{i -1}}

\right)}}

-{8 \ {{a} ^{2}} \ m \ {x

\left(

{{i -2}}

\right)}}

\right)}

\ {{{x

\left(

{i}

\right)}}

^{5}}}+{{\left( {{64} \ m \ {{{x

\left(

{{i -1}}

\right)}}

^{4}}} -{{64} \ m \ {x

\left(

{{i -2}}

\right)}

\ {{{x

\left(

{{i -1}}

\right)}}

^{3}}} -{{32} \ {{a} ^{2}} \ m \ {{{x

\left(

{{i -1}}

\right)}}

^{2}}}+{{32} \ {{a} ^{2}} \ m \ {x

\left(

{{i -2}}

\right)}

\ {x

\left(

{{i -1}}

\right)}}

\right)}

\ {{{x

\left(

{i}

\right)}}

^{4}}}+{{\left( -{{16} \ m \ {{{x

\left(

{{i -1}}

\right)}}

^{5}}}+{{16} \ m \ {x

\left(

{{i -2}}

\right)}

\ {{{x

\left(

{{i -1}}

\right)}}

^{4}}}+{{48} \ {{a} ^{2}} \ m \ {{{x

\left(

{{i -1}}

\right)}}

^{3}}} -{{48} \ {{a} ^{2}} \ m \ {x

\left(

{{i -2}}

\right)}

\ {{{x

\left(

{{i -1}}

\right)}}

^{2}}}

\right)}

\ {{{x

\left(

{i}

\right)}}

^{3}}}+{{\left( -{{32} \ {{a} ^{2}} \ m \ {{{x

\left(

{{i -1}}

\right)}}

^{4}}}+{{32} \ {{a} ^{2}} \ m \ {x

\left(

{{i -2}}

\right)}

\ {{{x

\left(

{{i -1}}

\right)}}

^{3}}}

\right)}

\ {{{x

\left(

{i}

\right)}}

^{2}}}+{{\left( {8 \ {{a} ^{2}} \ m \ {{{x

\left(

{{i -1}}

\right)}}

^{5}}} -{8 \ {{a} ^{2}} \ m \ {x

\left(

{{i -2}}

\right)}

\ {{{x

\left(

{{i -1}}

\right)}}

^{4}}}

\right)}

\ {x

\left(

{i}

\right)}}

\right)}

\ {{{x

\left(

{{i+1}}

\right)}}

^{3}}}+{{\left( {{\left( {{24} \ m \ {x

\left(

{{i -1}}

\right)}}

-{{24} \ m \ {x

\left(

{{i -2}}

\right)}}

\right)}

\ {{{x

\left(

{i}

\right)}}

^{8}}}+{{\left( -{{96} \ m \ {{{x

\left(

{{i -1}}

\right)}}

^{2}}}+{{96} \ m \ {x

\left(

{{i -2}}

\right)}

\ {x

\left(

{{i -1}}

\right)}}

\right)}

\ {{{x

\left(

{i}

\right)}}

^{7}}}+{{\left( {{144} \ m \ {{{x

\left(

{{i -1}}

\right)}}

^{3}}} -{{144} \ m \ {x

\left(

{{i -2}}

\right)}

\ {{{x

\left(

{{i -1}}

\right)}}

^{2}}} -{{12} \ {{a} ^{2}} \ m \ {x

\left(

{{i -1}}

\right)}}+{{12}

\ {{a} ^{2}} \ m \ {x

\left(

{{i -2}}

\right)}}

\right)}

\ {{{x

\left(

{i}

\right)}}

^{6}}}+{{\left( -{{96} \ m \ {{{x

\left(

{{i -1}}

\right)}}

^{4}}}+{{96} \ m \ {x

\left(

{{i -2}}

\right)}

\ {{{x

\left(

{{i -1}}

\right)}}

^{3}}}+{{48} \ {{a} ^{2}} \ m \ {{{x

\left(

{{i -1}}

\right)}}

^{2}}} -{{48} \ {{a} ^{2}} \ m \ {x

\left(

{{i -2}}

\right)}

\ {x

\left(

{{i -1}}

\right)}}

\right)}

\ {{{x

\left(

{i}

\right)}}

^{5}}}+{{\left( {{24} \ m \ {{{x

\left(

{{i -1}}

\right)}}

^{5}}} -{{24} \ m \ {x

\left(

{{i -2}}

\right)}

\ {{{x

\left(

{{i -1}}

\right)}}

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\ {{{x

\left(

{{i -1}}

\right)}}

^{4}}}

\right)}

\ {{{x

\left(

{i}

\right)}}

^{4}}}

\right)}

\ {x

\left(

{{i+1}}

\right)}}

\right)}

\ {{e} ^{-{{{{x

\left(

{i}

\right)}}

^{2}} \over {{a} ^{2}}}}}}+{{\left( {{\left( -{{{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{i}

\right)}}+{4

\ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -1}}

\right)}}

-{3 \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -2}}

\right)}}

\right)}

\ {{{x

\left(

{{i+1}}

\right)}}

^{4}}}+{{\left( {4 \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {{{x

\left(

{i}

\right)}}

^{2}}}+{{\left( -{{17} \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -1}}

\right)}}+{{13}

\ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -2}}

\right)}}

\right)}

\ {x

\left(

{i}

\right)}}+{{{a}

^{5}} \ {{hbar} ^{2}} \ \pi \ {{{x

\left(

{{i -1}}

\right)}}

^{2}}} -{{{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -2}}

\right)}

\ {x

\left(

{{i -1}}

\right)}}

\right)}

\ {{{x

\left(

{{i+1}}

\right)}}

^{3}}}+{{\left( -{6 \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {{{x

\left(

{i}

\right)}}

^{3}}}+{{\left( {{28} \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -1}}

\right)}}

-{{22} \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -2}}

\right)}}

\right)}

\ {{{x

\left(

{i}

\right)}}

^{2}}}+{{\left( -{5 \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {{{x

\left(

{{i -1}}

\right)}}

^{2}}}+{5 \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -2}}

\right)}

\ {x

\left(

{{i -1}}

\right)}}

\right)}

\ {x

\left(

{i}

\right)}}+{{{a}

^{5}} \ {{hbar} ^{2}} \ \pi \ {{{x

\left(

{{i -1}}

\right)}}

^{3}}} -{{{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -2}}

\right)}

\ {{{x

\left(

{{i -1}}

\right)}}

^{2}}}

\right)}

\ {{{x

\left(

{{i+1}}

\right)}}

^{2}}}+{{\left( {4 \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {{{x

\left(

{i}

\right)}}

^{4}}}+{{\left( -{{22} \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -1}}

\right)}}+{{18}

\ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -2}}

\right)}}

\right)}

\ {{{x

\left(

{i}

\right)}}

^{3}}}+{{\left( {{10} \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {{{x

\left(

{{i -1}}

\right)}}

^{2}}} -{{10} \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -2}}

\right)}

\ {x

\left(

{{i -1}}

\right)}}

\right)}

\ {{{x

\left(

{i}

\right)}}

^{2}}}+{{\left( -{5 \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {{{x

\left(

{{i -1}}

\right)}}

^{3}}}+{5 \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -2}}

\right)}

\ {{{x

\left(

{{i -1}}

\right)}}

^{2}}}

\right)}

\ {x

\left(

{i}

\right)}}+{{{a}

^{5}} \ {{hbar} ^{2}} \ \pi \ {{{x

\left(

{{i -1}}

\right)}}

^{4}}} -{{{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -2}}

\right)}

\ {{{x

\left(

{{i -1}}

\right)}}

^{3}}}

\right)}

\ {x

\left(

{{i+1}}

\right)}}

-{{{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {{{x

\left(

{i}

\right)}}

^{5}}}+{{\left( {{10} \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -1}}

\right)}}

-{9 \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -2}}

\right)}}

\right)}

\ {{{x

\left(

{i}

\right)}}

^{4}}}+{{\left( -{{18} \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {{{x

\left(

{{i -1}}

\right)}}

^{2}}}+{{18} \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -2}}

\right)}

\ {x

\left(

{{i -1}}

\right)}}

\right)}

\ {{{x

\left(

{i}

\right)}}

^{3}}}+{{\left( {{22} \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {{{x

\left(

{{i -1}}

\right)}}

^{3}}} -{{22} \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -2}}

\right)}

\ {{{x

\left(

{{i -1}}

\right)}}

^{2}}}

\right)}

\ {{{x

\left(

{i}

\right)}}

^{2}}}+{{\left( -{{13} \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {{{x

\left(

{{i -1}}

\right)}}

^{4}}}+{{13} \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -2}}

\right)}

\ {{{x

\left(

{{i -1}}

\right)}}

^{3}}}

\right)}

\ {x

\left(

{i}

\right)}}+{3

\ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {{{x

\left(

{{i -1}}

\right)}}

^{5}}} -{3 \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -2}}

\right)}

\ {{{x

\left(

{{i -1}}

\right)}}

^{4}}}

\right)}

\ {x

\left(

{{i+2}}

\right)}}+{{\left(

{{{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{i}

\right)}}

-{4 \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -1}}

\right)}}+{3

\ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -2}}

\right)}}

\right)}

\ {{{x

\left(

{{i+1}}

\right)}}

^{5}}}+{{\left( -{4 \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {{{x

\left(

{i}

\right)}}

^{2}}}+{{\left( {{17} \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -1}}

\right)}}

-{{13} \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -2}}

\right)}}

\right)}

\ {x

\left(

{i}

\right)}}

-{{{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {{{x

\left(

{{i -1}}

\right)}}

^{2}}}+{{{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -2}}

\right)}

\ {x

\left(

{{i -1}}

\right)}}

\right)}

\ {{{x

\left(

{{i+1}}

\right)}}

^{4}}}+{{\left( {6 \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {{{x

\left(

{i}

\right)}}

^{3}}}+{{\left( -{{28} \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -1}}

\right)}}+{{22}

\ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -2}}

\right)}}

\right)}

\ {{{x

\left(

{i}

\right)}}

^{2}}}+{{\left( {5 \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {{{x

\left(

{{i -1}}

\right)}}

^{2}}} -{5 \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -2}}

\right)}

\ {x

\left(

{{i -1}}

\right)}}

\right)}

\ {x

\left(

{i}

\right)}}

-{{{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {{{x

\left(

{{i -1}}

\right)}}

^{3}}}+{{{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -2}}

\right)}

\ {{{x

\left(

{{i -1}}

\right)}}

^{2}}}

\right)}

\ {{{x

\left(

{{i+1}}

\right)}}

^{3}}}+{{\left( -{4 \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {{{x

\left(

{i}

\right)}}

^{4}}}+{{\left( {{22} \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -1}}

\right)}}

-{{18} \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -2}}

\right)}}

\right)}

\ {{{x

\left(

{i}

\right)}}

^{3}}}+{{\left( -{{10} \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {{{x

\left(

{{i -1}}

\right)}}

^{2}}}+{{10} \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -2}}

\right)}

\ {x

\left(

{{i -1}}

\right)}}

\right)}

\ {{{x

\left(

{i}

\right)}}

^{2}}}+{{\left( {5 \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {{{x

\left(

{{i -1}}

\right)}}

^{3}}} -{5 \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -2}}

\right)}

\ {{{x

\left(

{{i -1}}

\right)}}

^{2}}}

\right)}

\ {x

\left(

{i}

\right)}}

-{{{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {{{x

\left(

{{i -1}}

\right)}}

^{4}}}+{{{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -2}}

\right)}

\ {{{x

\left(

{{i -1}}

\right)}}

^{3}}}

\right)}

\ {{{x

\left(

{{i+1}}

\right)}}

^{2}}}+{{\left( {{{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {{{x

\left(

{i}

\right)}}

^{5}}}+{{\left( -{{11} \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -1}}

\right)}}+{{10}

\ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -2}}

\right)}}

\right)}

\ {{{x

\left(

{i}

\right)}}

^{4}}}+{{\left( {{22} \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {{{x

\left(

{{i -1}}

\right)}}

^{2}}} -{{22} \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -2}}

\right)}

\ {x

\left(

{{i -1}}

\right)}}

\right)}

\ {{{x

\left(

{i}

\right)}}

^{3}}}+{{\left( -{{28} \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {{{x

\left(

{{i -1}}

\right)}}

^{3}}}+{{28} \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -2}}

\right)}

\ {{{x

\left(

{{i -1}}

\right)}}

^{2}}}

\right)}

\ {{{x

\left(

{i}

\right)}}

^{2}}}+{{\left( {{17} \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {{{x

\left(

{{i -1}}

\right)}}

^{4}}} -{{17} \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -2}}

\right)}

\ {{{x

\left(

{{i -1}}

\right)}}

^{3}}}

\right)}

\ {x

\left(

{i}

\right)}}

-{4 \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {{{x

\left(

{{i -1}}

\right)}}

^{5}}}+{4 \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -2}}

\right)}

\ {{{x

\left(

{{i -1}}

\right)}}

^{4}}}

\right)}

\ {x

\left(

{{i+1}}

\right)}}+{{\left(

{{{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -1}}

\right)}}

-{{{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -2}}

\right)}}

\right)}

\ {{{x

\left(

{i}

\right)}}

^{5}}}+{{\left( -{4 \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {{{x

\left(

{{i -1}}

\right)}}

^{2}}}+{4 \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -2}}

\right)}

\ {x

\left(

{{i -1}}

\right)}}

\right)}

\ {{{x

\left(

{i}

\right)}}

^{4}}}+{{\left( {6 \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {{{x

\left(

{{i -1}}

\right)}}

^{3}}} -{6 \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -2}}

\right)}

\ {{{x

\left(

{{i -1}}

\right)}}

^{2}}}

\right)}

\ {{{x

\left(

{i}

\right)}}

^{3}}}+{{\left( -{4 \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {{{x

\left(

{{i -1}}

\right)}}

^{4}}}+{4 \ {{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -2}}

\right)}

\ {{{x

\left(

{{i -1}}

\right)}}

^{3}}}

\right)}

\ {{{x

\left(

{i}

\right)}}

^{2}}}+{{\left( {{{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {{{x

\left(

{{i -1}}

\right)}}

^{5}}} -{{{a} ^{5}} \ {{hbar} ^{2}} \ \pi \ {x

\left(

{{i -2}}

\right)}

\ {{{x

\left(

{{i -1}}

\right)}}

^{4}}}

\right)}

\ {x

\left(

{i}

\right)}}

\right)}

$$

factor denom FRx3

$$

2 \ {{a} ^{5}} \ m \ \pi \ {\left( {x

\left(

{{i -1}}

\right)}

-{x

\left(

{{i -2}}

\right)}

\right)}

\ {{{\left( {x

\left(

{i}

\right)}

-{x

\left(

{{i -1}}

\right)}

\right)}}

^{4}} \ {{{\left( {x

\left(

{{i+1}}

\right)}

-{x

\left(

{i}

\right)}

\right)}}

^{4}} \ {\left( {x

\left(

{{i+2}}

\right)}

-{x

\left(

{{i+1}}

\right)}

\right)}

$$

%sage
def fricas2octave(name,ex)
  fr=fricas(ex).unparsed_input_form()
  f =("function result=%s(x,i)\n"%name)
  f+=("  global m hbar a;\n")
  f+=("  result= ...\n")
  i=0; cpl=80
  while i<len(fr):
    if i+cpl>=len(fr):
        f+= "    "+fr[i:i+cpl]+";\n"
        i=i+cpl
    else:
        line=fr[i:i+cpl]
        p=line.rfind('*', 0, cpl)+1
        if p==0:
            p=line.rindex('+', 0, cpl)+1
        f+= "    "+fr[i:i+p]+"...\n"
        i=i+p
  f+= "endfunction\n"
  ff = open('%s.m'%name, 'w')
  ff.write(f)
  ff.close()
  return f3
f8fc4d51-c1d3-439f-8b78-5069d5034e0ds
%sage print fricas2octave('fr3','FR')
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*... a^2*m*x(i -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))*... x(i+1)^4+((16*m*x(i -1) -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*... x(i -1)^2 -32*a^2*m*x(i -2)*x(i -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*... x(i -2)*x(i -1)^4)*x(i))*x(i+1)^3+((-24*m*x(i -1)+24*m*x(i -2))*x(i)^8+(96*m*... 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*... x(i -2)*x(i -1)^3 -48*a^2*m*x(i -1)^2+48*a^2*m*x(i -2)*x(i -1))*x(i)^5+(-24*m*... 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*... x(i -1) -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*... a^2*m*x(i -2)*x(i -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)*... x(i)^3)*x(i+1)+((-4*m*x(i -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*... m*x(i -1)^2+8*a^2*m*x(i -2)*x(i -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)*... x(i -1)^4)*x(i)^4))*x(i+2)+(((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*a^2*m*x(i -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))*x(i+1)^5+((-16*m*x(i -1)+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*x(i -1)^2+32*a^2*m*x(i -2)*x(i -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*x(i -2)*x(i -1)^4)*x(i))*x(i+1)^4+((24*m*x(i -1) -24*m*... x(i -2))*x(i)^8+(-96*m*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*x(i -2)*x(i -1)^3+48*a^2*m*x(i -1)^2 -48*a^2*m*... x(i -2)*x(i -1))*x(i)^5+(24*m*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)^3+((-16*m*x(i -1)+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*a^2*m*x(i -2)*x(i -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)*x(i)^3)*x(i+1)^2+((4*m*x(i -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*m*x(i -1)^2 -8*a^2*m*x(i -2)*x(i -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)*x(i -1)^4)*x(i)^4)*x(i+1)))*exp((-1*... x(i)^2)/(a^2))+(((a^5*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)^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*... hbar^2*pi()*x(i -2)*x(i -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()*... x(i -1)^3+a^5*hbar^2*pi()*x(i -2)*x(i -1)^2))*x(i+1)^2+(-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()*x(i -2)*x(i -1)^2)*x(i)+(-1*a^5*hbar^2*pi()*... 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*... hbar^2*pi()*x(i -1)^2 -18*a^5*hbar^2*pi()*x(i -2)*x(i -1))*x(i)^3+(-22*a^5*... 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*... hbar^2*pi()*x(i -1)^5+3*a^5*hbar^2*pi()*x(i -2)*x(i -1)^4)))*x(i+2)+((-1*a^5*... 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*... pi()*x(i -2))*x(i)+(a^5*hbar^2*pi()*x(i -1)^2 -1*a^5*hbar^2*pi()*x(i -2)*... 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)*... x(i -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()*... x(i -2)*x(i -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*... pi()*x(i -2)*x(i -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)*... x(i -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)*... x(i)^3+(4*a^5*hbar^2*pi()*x(i -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()*... x(i -1)^2+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()*x(i -2)*... x(i -1)^4))*x(i+1)^4+((-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()*x(i -1)^4 -32*... a^5*m*pi()*x(i -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)^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))*... x(i)^5+(72*a^5*m*pi()*x(i -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)^2+((-8*a^5*m*pi()*... x(i -1)+8*a^5*m*pi()*x(i -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)*... x(i)^4+(-8*a^5*m*pi()*x(i -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*... m*pi()*x(i -2)*x(i -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*... pi()*x(i -1)^2 -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()*... x(i -2)*x(i -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()*... x(i -1)^4+32*a^5*m*pi()*x(i -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))*... x(i)^5+(-72*a^5*m*pi()*x(i -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()*... x(i -1) -8*a^5*m*pi()*x(i -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)*... x(i)^4+(8*a^5*m*pi()*x(i -1)^5 -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*... a^5*m*pi()*x(i -2)*x(i -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
%octave
F3=fr3([1;2;3;4;5],3)
error: 'FR3' undefined near line 4 column 5 error: called from: error: /projects/b04b5777-e269-4c8f-a4b8-b21dbe1c93c6/fr3.m at line 3, column 9
factor numer eval(D(eval(FRx,x(i+1)=x1),x1),x1=x(i+1))/factor denom eval(D(eval(FRx,x(i+1)=x1),x1),x1=x(i+1))

$$

{\left( {{hbar} ^{2}} \ {\left( {{\left( {{{x

\left(

{{i+1}}

\right)}}

^{2}}+{{\left( -{4 \ {x

\left(

{i}

\right)}}+{2

\ {x

\left(

{{i -1}}

\right)}}

\right)}

\ {x

\left(

{{i+1}}

\right)}}+{9

\ {{{x

\left(

{i}

\right)}}

^{2}}} -{{14} \ {x

\left(

{{i -1}}

\right)}

\ {x

\left(

{i}

\right)}}+{6

\ {{{x

\left(

{{i -1}}

\right)}}

^{2}}}

\right)}

\ {{{x

\left(

{{i+2}}

\right)}}

^{2}}}+{{\left( -{2 \ {{{x

\left(

{{i+1}}

\right)}}

^{3}}}+{{\left( {8 \ {x

\left(

{i}

\right)}}

-{4 \ {x

\left(

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\right)}}

\right)}

\ {{{x

\left(

{{i+1}}

\right)}}

^{2}}}+{{\left( -{{20} \ {{{x

\left(

{i}

\right)}}

^{2}}}+{{32} \ {x

\left(

{{i -1}}

\right)}

\ {x

\left(

{i}

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-{{14} \ {{{x

\left(

{{i -1}}

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^{2}}}

\right)}

\ {x

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\ {{{x

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^{3}}} -{4 \ {x

\left(

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\ {{{x

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{i}

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^{2}}}+{2 \ {{{x

\left(

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^{2}} \ {x

\left(

{i}

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\right)}

\ {x

\left(

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\right)}}+{{{x

\left(

{{i+1}}

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^{4}}+{{\left( -{4 \ {x

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{i}

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\ {x

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\right)}

\ {{{x

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^{3}}}+{{\left( {{12} \ {{{x

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^{2}}} -{{20} \ {x

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\ {x

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\ {{{x

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\ {{{x

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^{2}}}+{{\left( -{4 \ {{{x

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\ {x

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\ {{{x

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^{3}}}+{{{{x

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^{2}} \ {{{x

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\right)}/{\left(

4 \ m \ {{{\left( {x

\left(

{i}

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-{x

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^{2}} \ {{{\left( {x

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^{4}} \ {{{\left( {x

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\right)}

-{x

\left(

{{i+1}}

\right)}

\right)}}

^{2}}

\right)}

$$

factor numer eval(D(eval(FRx,x(i+2)=x1),x1),x1=x(i+2))/factor denom eval(D(eval(FRx,x(i+2)=x1),x1),x1=x(i+2))

$$

{\left( -{{hbar} ^{2}}

\right)}/{\left(

4 \ m \ {{{\left( {x

\left(

{{i+1}}

\right)}

-{x

\left(

{i}

\right)}

\right)}}

^{2}} \ {{{\left( {x

\left(

{{i+2}}

\right)}

-{x

\left(

{{i+1}}

\right)}

\right)}}

^{2}}

\right)}

$$

xdot:=concat([x(N+i) for i in 1..N],[F(x(i))+R(x,i) for i in 1..N]);
# xdot

$$

10

$$

xdot(6)

$$

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\right)}}

^{2}}}+{{\left( {{10} \ {x

\left(

{0}

\right)}}

-{7 \ {x

\left(

{-1}

\right)}}

\right)}

\ {x

\left(

{1}

\right)}}

-{{{x

\left(

{0}

\right)}}

^{2}}+{{x

\left(

{-1}

\right)}

\ {x

\left(

{0}

\right)}}

\right)}

\ {{{x

\left(

{2}

\right)}}

^{3}}}+{{\left( {3 \ {{{x

\left(

{1}

\right)}}

^{3}}}+{{\left( -{{12} \ {x

\left(

{0}

\right)}}+{9

\ {x

\left(

{-1}

\right)}}

\right)}

\ {{{x

\left(

{1}

\right)}}

^{2}}}+{{\left( {4 \ {{{x

\left(

{0}

\right)}}

^{2}}} -{4 \ {x

\left(

{-1}

\right)}

\ {x

\left(

{0}

\right)}}

\right)}

\ {x

\left(

{1}

\right)}}

-{{{x

\left(

{0}

\right)}}

^{3}}+{{x

\left(

{-1}

\right)}

\ {{{x

\left(

{0}

\right)}}

^{2}}}

\right)}

\ {{{x

\left(

{2}

\right)}}

^{2}}}+{{\left( -{{{x

\left(

{1}

\right)}}

^{4}}+{{\left( {8 \ {x

\left(

{0}

\right)}}

-{7 \ {x

\left(

{-1}

\right)}}

\right)}

\ {{{x

\left(

{1}

\right)}}

^{3}}}+{{\left( -{{12} \ {{{x

\left(

{0}

\right)}}

^{2}}}+{{12} \ {x

\left(

{-1}

\right)}

\ {x

\left(

{0}

\right)}}

\right)}

\ {{{x

\left(

{1}

\right)}}

^{2}}}+{{\left( {{10} \ {{{x

\left(

{0}

\right)}}

^{3}}} -{{10} \ {x

\left(

{-1}

\right)}

\ {{{x

\left(

{0}

\right)}}

^{2}}}

\right)}

\ {x

\left(

{1}

\right)}}

-{3 \ {{{x

\left(

{0}

\right)}}

^{4}}}+{3 \ {x

\left(

{-1}

\right)}

\ {{{x

\left(

{0}

\right)}}

^{3}}}

\right)}

\ {x

\left(

{2}

\right)}}+{{\left(

-{x

\left(

{0}

\right)}+{x

\left(

{-1}

\right)}

\right)}

\ {{{x

\left(

{1}

\right)}}

^{4}}}+{{\left( {3 \ {{{x

\left(

{0}

\right)}}

^{2}}} -{3 \ {x

\left(

{-1}

\right)}

\ {x

\left(

{0}

\right)}}

\right)}

\ {{{x

\left(

{1}

\right)}}

^{3}}}+{{\left( -{3 \ {{{x

\left(

{0}

\right)}}

^{3}}}+{3 \ {x

\left(

{-1}

\right)}

\ {{{x

\left(

{0}

\right)}}

^{2}}}

\right)}

\ {{{x

\left(

{1}

\right)}}

^{2}}}+{{\left( {{{x

\left(

{0}

\right)}}

^{4}} -{{x

\left(

{-1}

\right)}

\ {{{x

\left(

{0}

\right)}}

^{3}}}

\right)}

\ {x

\left(

{1}

\right)}}

\right)}

\ {{a} ^{3}} \ {{hbar} ^{2}} \ \pi}

\right)}/{\left(

{\left( {{\left( {{\left( {{\left( {4 \ {x

\left(

{0}

\right)}}

-{4 \ {x

\left(

{-1}

\right)}}

\right)}

\ {{{x

\left(

{1}

\right)}}

^{3}}}+{{\left( -{{12} \ {{{x

\left(

{0}

\right)}}

^{2}}}+{{12} \ {x

\left(

{-1}

\right)}

\ {x

\left(

{0}

\right)}}

\right)}

\ {{{x

\left(

{1}

\right)}}

^{2}}}+{{\left( {{12} \ {{{x

\left(

{0}

\right)}}

^{3}}} -{{12} \ {x

\left(

{-1}

\right)}

\ {{{x

\left(

{0}

\right)}}

^{2}}}

\right)}

\ {x

\left(

{1}

\right)}}

-{4 \ {{{x

\left(

{0}

\right)}}

^{4}}}+{4 \ {x

\left(

{-1}

\right)}

\ {{{x

\left(

{0}

\right)}}

^{3}}}

\right)}

\ {{{x

\left(

{2}

\right)}}

^{3}}}+{{\left( {{\left( -{{12} \ {x

\left(

{0}

\right)}}+{{12}

\ {x

\left(

{-1}

\right)}}

\right)}

\ {{{x

\left(

{1}

\right)}}

^{4}}}+{{\left( {{36} \ {{{x

\left(

{0}

\right)}}

^{2}}} -{{36} \ {x

\left(

{-1}

\right)}

\ {x

\left(

{0}

\right)}}

\right)}

\ {{{x

\left(

{1}

\right)}}

^{3}}}+{{\left( -{{36} \ {{{x

\left(

{0}

\right)}}

^{3}}}+{{36} \ {x

\left(

{-1}

\right)}

\ {{{x

\left(

{0}

\right)}}

^{2}}}

\right)}

\ {{{x

\left(

{1}

\right)}}

^{2}}}+{{\left( {{12} \ {{{x

\left(

{0}

\right)}}

^{4}}} -{{12} \ {x

\left(

{-1}

\right)}

\ {{{x

\left(

{0}

\right)}}

^{3}}}

\right)}

\ {x

\left(

{1}

\right)}}

\right)}

\ {{{x

\left(

{2}

\right)}}

^{2}}}+{{\left( {{\left( {{12} \ {x

\left(

{0}

\right)}}

-{{12} \ {x

\left(

{-1}

\right)}}

\right)}

\ {{{x

\left(

{1}

\right)}}

^{5}}}+{{\left( -{{36} \ {{{x

\left(

{0}

\right)}}

^{2}}}+{{36} \ {x

\left(

{-1}

\right)}

\ {x

\left(

{0}

\right)}}

\right)}

\ {{{x

\left(

{1}

\right)}}

^{4}}}+{{\left( {{36} \ {{{x

\left(

{0}

\right)}}

^{3}}} -{{36} \ {x

\left(

{-1}

\right)}

\ {{{x

\left(

{0}

\right)}}

^{2}}}

\right)}

\ {{{x

\left(

{1}

\right)}}

^{3}}}+{{\left( -{{12} \ {{{x

\left(

{0}

\right)}}

^{4}}}+{{12} \ {x

\left(

{-1}

\right)}

\ {{{x

\left(

{0}

\right)}}

^{3}}}

\right)}

\ {{{x

\left(

{1}

\right)}}

^{2}}}

\right)}

\ {x

\left(

{2}

\right)}}+{{\left(

-{4 \ {x

\left(

{0}

\right)}}+{4

\ {x

\left(

{-1}

\right)}}

\right)}

\ {{{x

\left(

{1}

\right)}}

^{6}}}+{{\left( {{12} \ {{{x

\left(

{0}

\right)}}

^{2}}} -{{12} \ {x

\left(

{-1}

\right)}

\ {x

\left(

{0}

\right)}}

\right)}

\ {{{x

\left(

{1}

\right)}}

^{5}}}+{{\left( -{{12} \ {{{x

\left(

{0}

\right)}}

^{3}}}+{{12} \ {x

\left(

{-1}

\right)}

\ {{{x

\left(

{0}

\right)}}

^{2}}}

\right)}

\ {{{x

\left(

{1}

\right)}}

^{4}}}+{{\left( {4 \ {{{x

\left(

{0}

\right)}}

^{4}}} -{4 \ {x

\left(

{-1}

\right)}

\ {{{x

\left(

{0}

\right)}}

^{3}}}

\right)}

\ {{{x

\left(

{1}

\right)}}

^{3}}}

\right)}

\ {x

\left(

{3}

\right)}}+{{\left(

{{\left( -{4 \ {x

\left(

{0}

\right)}}+{4

\ {x

\left(

{-1}

\right)}}

\right)}

\ {{{x

\left(

{1}

\right)}}

^{3}}}+{{\left( {{12} \ {{{x

\left(

{0}

\right)}}

^{2}}} -{{12} \ {x

\left(

{-1}

\right)}

\ {x

\left(

{0}

\right)}}

\right)}

\ {{{x

\left(

{1}

\right)}}

^{2}}}+{{\left( -{{12} \ {{{x

\left(

{0}

\right)}}

^{3}}}+{{12} \ {x

\left(

{-1}

\right)}

\ {{{x

\left(

{0}

\right)}}

^{2}}}

\right)}

\ {x

\left(

{1}

\right)}}+{4

\ {{{x

\left(

{0}

\right)}}

^{4}}} -{4 \ {x

\left(

{-1}

\right)}

\ {{{x

\left(

{0}

\right)}}

^{3}}}

\right)}

\ {{{x

\left(

{2}

\right)}}

^{4}}}+{{\left( {{\left( {{12} \ {x

\left(

{0}

\right)}}

-{{12} \ {x

\left(

{-1}

\right)}}

\right)}

\ {{{x

\left(

{1}

\right)}}

^{4}}}+{{\left( -{{36} \ {{{x

\left(

{0}

\right)}}

^{2}}}+{{36} \ {x

\left(

{-1}

\right)}

\ {x

\left(

{0}

\right)}}

\right)}

\ {{{x

\left(

{1}

\right)}}

^{3}}}+{{\left( {{36} \ {{{x

\left(

{0}

\right)}}

^{3}}} -{{36} \ {x

\left(

{-1}

\right)}

\ {{{x

\left(

{0}

\right)}}

^{2}}}

\right)}

\ {{{x

\left(

{1}

\right)}}

^{2}}}+{{\left( -{{12} \ {{{x

\left(

{0}

\right)}}

^{4}}}+{{12} \ {x

\left(

{-1}

\right)}

\ {{{x

\left(

{0}

\right)}}

^{3}}}

\right)}

\ {x

\left(

{1}

\right)}}

\right)}

\ {{{x

\left(

{2}

\right)}}

^{3}}}+{{\left( {{\left( -{{12} \ {x

\left(

{0}

\right)}}+{{12}

\ {x

\left(

{-1}

\right)}}

\right)}

\ {{{x

\left(

{1}

\right)}}

^{5}}}+{{\left( {{36} \ {{{x

\left(

{0}

\right)}}

^{2}}} -{{36} \ {x

\left(

{-1}

\right)}

\ {x

\left(

{0}

\right)}}

\right)}

\ {{{x

\left(

{1}

\right)}}

^{4}}}+{{\left( -{{36} \ {{{x

\left(

{0}

\right)}}

^{3}}}+{{36} \ {x

\left(

{-1}

\right)}

\ {{{x

\left(

{0}

\right)}}

^{2}}}

\right)}

\ {{{x

\left(

{1}

\right)}}

^{3}}}+{{\left( {{12} \ {{{x

\left(

{0}

\right)}}

^{4}}} -{{12} \ {x

\left(

{-1}

\right)}

\ {{{x

\left(

{0}

\right)}}

^{3}}}

\right)}

\ {{{x

\left(

{1}

\right)}}

^{2}}}

\right)}

\ {{{x

\left(

{2}

\right)}}

^{2}}}+{{\left( {{\left( {4 \ {x

\left(

{0}

\right)}}

-{4 \ {x

\left(

{-1}

\right)}}

\right)}

\ {{{x

\left(

{1}

\right)}}

^{6}}}+{{\left( -{{12} \ {{{x

\left(

{0}

\right)}}

^{2}}}+{{12} \ {x

\left(

{-1}

\right)}

\ {x

\left(

{0}

\right)}}

\right)}

\ {{{x

\left(

{1}

\right)}}

^{5}}}+{{\left( {{12} \ {{{x

\left(

{0}

\right)}}

^{3}}} -{{12} \ {x

\left(

{-1}

\right)}

\ {{{x

\left(

{0}

\right)}}

^{2}}}

\right)}

\ {{{x

\left(

{1}

\right)}}

^{4}}}+{{\left( -{4 \ {{{x

\left(

{0}

\right)}}

^{4}}}+{4 \ {x

\left(

{-1}

\right)}

\ {{{x

\left(

{0}

\right)}}

^{3}}}

\right)}

\ {{{x

\left(

{1}

\right)}}

^{3}}}

\right)}

\ {x

\left(

{2}

\right)}}

\right)}

\ {{a} ^{3}} \ m \ \pi

\right)}

$$

limit(limit(eval(eval(xdot(6),x(0)=b0),x(-1)=b1),b1=%minusInfinity),b0=%minusInfinity)

$$

{\left( {{\left( {{\left( {4 \ {x

\left(

{1}

\right)}

\ {{{x

\left(

{2}

\right)}}

^{3}}} -{{12} \ {{{x

\left(

{1}

\right)}}

^{2}} \ {{{x

\left(

{2}

\right)}}

^{2}}}+{{12} \ {{{x

\left(

{1}

\right)}}

^{3}} \ {x

\left(

{2}

\right)}}

-{4 \ {{{x

\left(

{1}

\right)}}

^{4}}}

\right)}

\ {x

\left(

{3}

\right)}}

-{4 \ {x

\left(

{1}

\right)}

\ {{{x

\left(

{2}

\right)}}

^{4}}}+{{12} \ {{{x

\left(

{1}

\right)}}

^{2}} \ {{{x

\left(

{2}

\right)}}

^{3}}} -{{12} \ {{{x

\left(

{1}

\right)}}

^{3}} \ {{{x

\left(

{2}

\right)}}

^{2}}}+{4 \ {{{x

\left(

{1}

\right)}}

^{4}} \ {x

\left(

{2}

\right)}}

\right)}

\ m \ {{e} ^{{{\left( -{{{x

\left(

{1}

\right)}}

^{2}}

\right)}/{\left(

{a} ^{2}

\right)}}}}}+{{\left(

-{2 \ {x

\left(

{3}

\right)}}+{3

\ {x

\left(

{2}

\right)}}

-{x

\left(

{1}

\right)}

\right)}

\ {{a} ^{3}} \ {{hbar} ^{2}} \ \pi}

\right)}/{\left(

{\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)}

\ {{a} ^{3}} \ m \ \pi

\right)}

$$

jac:=map(f+->map(g+->eval(D(eval(f,g=x1),x1),x1=g),[x(i) for i in 1..2*N]),xdot);
jac1:=map(f+->eval(f,[x(0)=b0,x(-1)=b1,x(N+1)=c0,x(N+2)=c1]),jac);
jac2:=map(g+->map(f+->limit(limit(f,b0=%minusInfinity)::Expression(Integer),b1=%minusInfinity)::Expression(Integer),g),jac1);
jac3:=map(g+->map(f+->limit(limit(f,c0=%plusInfinity)::Expression(Integer),c1=%plusInfinity)::Expression(Integer),g),jac1);
)set message type on
variables(numer jac(6,1))
factor denom(jac3(6,1))

$$

\left[

{{e} ^{{{\left( -{{{x

\left(

{1}

\right)}}

^{2}}

\right)}/{\left(

{a} ^{2}

\right)}}}},

: \pi, : m, : hbar, : a, : {x

\left(

{3}

\right)},

: {x

\left(

{2}

\right)},

: {x

\left(

{1}

\right)},

: {x

\left(

{0}

\right)},

: {x

\left(

{-1}

\right)}

\right]

$$

Type: List(Kernel(Expression(Integer)))

$$

2 \ {{{\left( {x

\left(

{2}

\right)}

-{x

\left(

{1}

\right)}

\right)}}

^{4}} \ {\left( {x

\left(

{3}

\right)}

-{x

\left(

{2}

\right)}

\right)}

\ {{a} ^{5}} \ {{{\left( b0 -{x

\left(

{1}

\right)}

\right)}}

^{4}} \ {\left( b1 -b0

\right)}

\ m \ \pi

$$

Type: Factored(SparseMultivariatePolynomial(Integer,Kernel(Expression(Integer))))

numer jac3(6,2)
factor denom(jac3(6,2))

$$

{\left( {{\left( {6 \ {{{x

\left(

{3}

\right)}}

^{2}}}+{{\left( -{{14} \ {x

\left(

{2}

\right)}}+{2

\ {x

\left(

{1}

\right)}}

\right)}

\ {x

\left(

{3}

\right)}}+{9

\ {{{x

\left(

{2}

\right)}}

^{2}}} -{4 \ {x

\left(

{1}

\right)}

\ {x

\left(

{2}

\right)}}+{{{x

\left(

{1}

\right)}}

^{2}}

\right)}

\ {{b0} ^{2}}}+{{\left( {{\left( {2 \ {x

\left(

{2}

\right)}}

-{{14} \ {x

\left(

{1}

\right)}}

\right)}

\ {{{x

\left(

{3}

\right)}}

^{2}}}+{{\left( -{4 \ {{{x

\left(

{2}

\right)}}

^{2}}}+{{32} \ {x

\left(

{1}

\right)}

\ {x

\left(

{2}

\right)}}

-{4 \ {{{x

\left(

{1}

\right)}}

^{2}}}

\right)}

\ {x

\left(

{3}

\right)}}+{2

\ {{{x

\left(

{2}

\right)}}

^{3}}} -{{20} \ {x

\left(

{1}

\right)}

\ {{{x

\left(

{2}

\right)}}

^{2}}}+{8 \ {{{x

\left(

{1}

\right)}}

^{2}} \ {x

\left(

{2}

\right)}}

-{2 \ {{{x

\left(

{1}

\right)}}

^{3}}}

\right)}

\ b0}+{{\left( {{{x

\left(

{2}

\right)}}

^{2}} -{4 \ {x

\left(

{1}

\right)}

\ {x

\left(

{2}

\right)}}+{9

\ {{{x

\left(

{1}

\right)}}

^{2}}}

\right)}

\ {{{x

\left(

{3}

\right)}}

^{2}}}+{{\left( -{2 \ {{{x

\left(

{2}

\right)}}

^{3}}}+{8 \ {x

\left(

{1}

\right)}

\ {{{x

\left(

{2}

\right)}}

^{2}}} -{{20} \ {{{x

\left(

{1}

\right)}}

^{2}} \ {x

\left(

{2}

\right)}}+{2

\ {{{x

\left(

{1}

\right)}}

^{3}}}

\right)}

\ {x

\left(

{3}

\right)}}+{{{x

\left(

{2}

\right)}}

^{4}} -{4 \ {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)}}+{{{x

\left(

{1}

\right)}}

^{4}}

\right)}

\ {{hbar} ^{2}}

$$

Type: SparseMultivariatePolynomial(Integer,Kernel(Expression(Integer)))

$$

4 \ {{{\left( {x

\left(

{2}

\right)}

-{x

\left(

{1}

\right)}

\right)}}

^{4}} \ {{{\left( {x

\left(

{3}

\right)}

-{x

\left(

{2}

\right)}

\right)}}

^{2}} \ {{{\left( b0 -{x

\left(

{1}

\right)}

\right)}}

^{2}} \ m

$$

Type: Factored(SparseMultivariatePolynomial(Integer,Kernel(Expression(Integer))))

numer jac3(6,3)
factor denom(jac3(6,3))

$$

-{{hbar} ^{2}}

$$

Type: SparseMultivariatePolynomial(Integer,Kernel(Expression(Integer)))

$$

4 \ {{{\left( {x

\left(

{2}

\right)}

-{x

\left(

{1}

\right)}

\right)}}

^{2}} \ {{{\left( {x

\left(

{3}

\right)}

-{x

\left(

{2}

\right)}

\right)}}

^{2}} \ m

$$

Type: Factored(SparseMultivariatePolynomial(Integer,Kernel(Expression(Integer))))

numer jac3(6,4)
factor denom(jac3(6,4))

$$

0

$$

Type: SparseMultivariatePolynomial(Integer,Kernel(Expression(Integer)))

$$

1

$$

Type: Factored(SparseMultivariatePolynomial(Integer,Kernel(Expression(Integer))))

unparse(numer jac3(8,2)::InputForm)
factor denom(jac3(8,2))

$$

\verb#"((x(3)^2+(-4x(2)+2x(1))x(3)+(9x(2)^2 -14x(1)x(2)+6x(1)^2))x(4)^2+(-2x(3)^3+(8x(2) -4x(1))x(3)^2+(-20x(2)^2+32x(1)x(2) -14x(1)^2)x(3)+(2x(2)^3 -4x(1)x(2)^2+2x(1)^2x(2)))x(4)+(x(3)^4+(-4x(2)+2*x(1))x(3)^3+(12x(2)^2

-20x(1)x(2)+9x(1)^2)x(3)^2+(-4x(2)^3+8x(1)x(2)^2 -4x(1)^2*x(2))x(3)+(x(2)^4 -2x(1)x(2)^3+x(1)^2x(2)^2)))*hbar^2"#

$$

Type: String

$$

4 \ {{{\left( {x

\left(

{2}

\right)}

-{x

\left(

{1}

\right)}

\right)}}

^{2}} \ {{{\left( {x

\left(

{3}

\right)}

-{x

\left(

{2}

\right)}

\right)}}

^{4}} \ {{{\left( {x

\left(

{4}

\right)}

-{x

\left(

{3}

\right)}

\right)}}

^{2}} \ m

$$

Type: Factored(SparseMultivariatePolynomial(Integer,Kernel(Expression(Integer))))

%sage fricas('eval(jac3(8,5),xs)').sage()
-1/4*hbar^2/(m*x3^2*x4^2 - 2*m*x3*x4^3 + m*x4^4 + (m*x3^2 - 2*m*x3*x4 + m*x4^2)*x5^2 - 2*(m*x3^2*x4 - 2*m*x3*x4^2 + m*x4^3)*x5)
%sage m=fricas('eval(jac3,xs)').sage()
matrix([[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1],[(((((-4*b1+4*b0)*m*x1^6+(16*b0*b1 -16*b0^2)*m*x1^5+((-24*b0^2+2*a^2)*b1+(24*b0^3 -2*a^2*b0))*m*x1^4+((16*b0^3 -8*a^2*b0)*b1+(-16*b0^4+8*a^2*b0^2))*m*x1^3+((-4*b0^4+12*a^2*b0^2)*b1+(4*b0^5 -12*a^2*b0^3))*m*x1^2+(-8*a^2*b0^3*b1+8*a^2*b0^4)*m*x1+(2*a^2*b0^4*b1 -2*a^2*b0^5)*m)*x2^4+((16*b1 -16*b0)*m*x1^7+(-64*b0*b1+64*b0^2)*m*x1^6+((96*b0^2 -8*a^2)*b1+(-96*b0^3+8*a^2*b0))*m*x1^5+((-64*b0^3+32*a^2*b0)*b1+(64*b0^4 -32*a^2*b0^2))*m*x1^4+((16*b0^4 -48*a^2*b0^2)*b1+(-16*b0^5+48*a^2*b0^3))*m*x1^3+(32*a^2*b0^3*b1 -32*a^2*b0^4)*m*x1^2+(-8*a^2*b0^4*b1+8*a^2*b0^5)*m*x1)*x2^3+((-24*b1+24*b0)*m*x1^8+(96*b0*b1 -96*b0^2)*m*x1^7+((-144*b0^2+12*a^2)*b1+(144*b0^3 -12*a^2*b0))*m*x1^6+((96*b0^3 -48*a^2*b0)*b1+(-96*b0^4+48*a^2*b0^2))*m*x1^5+((-24*b0^4+72*a^2*b0^2)*b1+(24*b0^5 -72*a^2*b0^3))*m*x1^4+(-48*a^2*b0^3*b1+48*a^2*b0^4)*m*x1^3+(12*a^2*b0^4*b1 -12*a^2*b0^5)*m*x1^2)*x2^2+((16*b1 -16*b0)*m*x1^9+(-64*b0*b1+64*b0^2)*m*x1^8+((96*b0^2 -8*a^2)*b1+(-96*b0^3+8*a^2*b0))*m*x1^7+((-64*b0^3+32*a^2*b0)*b1+(64*b0^4 -32*a^2*b0^2))*m*x1^6+((16*b0^4 -48*a^2*b0^2)*b1+(-16*b0^5+48*a^2*b0^3))*m*x1^5+(32*a^2*b0^3*b1 -32*a^2*b0^4)*m*x1^4+(-8*a^2*b0^4*b1+8*a^2*b0^5)*m*x1^3)*x2+((-4*b1+4*b0)*m*x1^10+(16*b0*b1 -16*b0^2)*m*x1^9+((-24*b0^2+2*a^2)*b1+(24*b0^3 -2*a^2*b0))*m*x1^8+((16*b0^3 -8*a^2*b0)*b1+(-16*b0^4+8*a^2*b0^2))*m*x1^7+((-4*b0^4+12*a^2*b0^2)*b1+(4*b0^5 -12*a^2*b0^3))*m*x1^6+(-8*a^2*b0^3*b1+8*a^2*b0^4)*m*x1^5+(2*a^2*b0^4*b1 -2*a^2*b0^5)*m*x1^4))*x3+(((4*b1 -4*b0)*m*x1^6+(-16*b0*b1+16*b0^2)*m*x1^5+((24*b0^2 -2*a^2)*b1+(-24*b0^3+2*a^2*b0))*m*x1^4+((-16*b0^3+8*a^2*b0)*b1+(16*b0^4 -8*a^2*b0^2))*m*x1^3+((4*b0^4 -12*a^2*b0^2)*b1+(-4*b0^5+12*a^2*b0^3))*m*x1^2+(8*a^2*b0^3*b1 -8*a^2*b0^4)*m*x1+(-2*a^2*b0^4*b1+2*a^2*b0^5)*m)*x2^5+((-16*b1+16*b0)*m*x1^7+(64*b0*b1 -64*b0^2)*m*x1^6+((-96*b0^2+8*a^2)*b1+(96*b0^3 -8*a^2*b0))*m*x1^5+((64*b0^3 -32*a^2*b0)*b1+(-64*b0^4+32*a^2*b0^2))*m*x1^4+((-16*b0^4+48*a^2*b0^2)*b1+(16*b0^5 -48*a^2*b0^3))*m*x1^3+(-32*a^2*b0^3*b1+32*a^2*b0^4)*m*x1^2+(8*a^2*b0^4*b1 -8*a^2*b0^5)*m*x1)*x2^4+((24*b1 -24*b0)*m*x1^8+(-96*b0*b1+96*b0^2)*m*x1^7+((144*b0^2 -12*a^2)*b1+(-144*b0^3+12*a^2*b0))*m*x1^6+((-96*b0^3+48*a^2*b0)*b1+(96*b0^4 -48*a^2*b0^2))*m*x1^5+((24*b0^4 -72*a^2*b0^2)*b1+(-24*b0^5+72*a^2*b0^3))*m*x1^4+(48*a^2*b0^3*b1 -48*a^2*b0^4)*m*x1^3+(-12*a^2*b0^4*b1+12*a^2*b0^5)*m*x1^2)*x2^3+((-16*b1+16*b0)*m*x1^9+(64*b0*b1 -64*b0^2)*m*x1^8+((-96*b0^2+8*a^2)*b1+(96*b0^3 -8*a^2*b0))*m*x1^7+((64*b0^3 -32*a^2*b0)*b1+(-64*b0^4+32*a^2*b0^2))*m*x1^6+((-16*b0^4+48*a^2*b0^2)*b1+(16*b0^5 -48*a^2*b0^3))*m*x1^5+(-32*a^2*b0^3*b1+32*a^2*b0^4)*m*x1^4+(8*a^2*b0^4*b1 -8*a^2*b0^5)*m*x1^3)*x2^2+((4*b1 -4*b0)*m*x1^10+(-16*b0*b1+16*b0^2)*m*x1^9+((24*b0^2 -2*a^2)*b1+(-24*b0^3+2*a^2*b0))*m*x1^8+((-16*b0^3+8*a^2*b0)*b1+(16*b0^4 -8*a^2*b0^2))*m*x1^7+((4*b0^4 -12*a^2*b0^2)*b1+(-4*b0^5+12*a^2*b0^3))*m*x1^6+(8*a^2*b0^3*b1 -8*a^2*b0^4)*m*x1^5+(-2*a^2*b0^4*b1+2*a^2*b0^5)*m*x1^4)*x2))*exp((-1*x1^2)/(a^2))+(((-1*a^5*hbar^2*pi()*x1+(-3*a^5*b1+4*a^5*b0)*hbar^2*pi())*x2^4+(4*a^5*hbar^2*pi()*x1^2+(13*a^5*b1 -17*a^5*b0)*hbar^2*pi()*x1+(-1*a^5*b0*b1+a^5*b0^2)*hbar^2*pi())*x2^3+(-6*a^5*hbar^2*pi()*x1^3+(-22*a^5*b1+28*a^5*b0)*hbar^2*pi()*x1^2+(5*a^5*b0*b1 -5*a^5*b0^2)*hbar^2*pi()*x1+(-1*a^5*b0^2*b1+a^5*b0^3)*hbar^2*pi())*x2^2+(4*a^5*hbar^2*pi()*x1^4+(18*a^5*b1 -22*a^5*b0)*hbar^2*pi()*x1^3+(-10*a^5*b0*b1+10*a^5*b0^2)*hbar^2*pi()*x1^2+(5*a^5*b0^2*b1 -5*a^5*b0^3)*hbar^2*pi()*x1+(-1*a^5*b0^3*b1+a^5*b0^4)*hbar^2*pi())*x2+(-1*a^5*hbar^2*pi()*x1^5+(-9*a^5*b1+10*a^5*b0)*hbar^2*pi()*x1^4+(18*a^5*b0*b1 -18*a^5*b0^2)*hbar^2*pi()*x1^3+(-22*a^5*b0^2*b1+22*a^5*b0^3)*hbar^2*pi()*x1^2+(13*a^5*b0^3*b1 -13*a^5*b0^4)*hbar^2*pi()*x1+(-3*a^5*b0^4*b1+3*a^5*b0^5)*hbar^2*pi()))*x3+((a^5*hbar^2*pi()*x1+(3*a^5*b1 -4*a^5*b0)*hbar^2*pi())*x2^5+(-4*a^5*hbar^2*pi()*x1^2+(-13*a^5*b1+17*a^5*b0)*hbar^2*pi()*x1+(a^5*b0*b1 -1*a^5*b0^2)*hbar^2*pi())*x2^4+(6*a^5*hbar^2*pi()*x1^3+(22*a^5*b1 -28*a^5*b0)*hbar^2*pi()*x1^2+(-5*a^5*b0*b1+5*a^5*b0^2)*hbar^2*pi()*x1+(a^5*b0^2*b1 -1*a^5*b0^3)*hbar^2*pi())*x2^3+(-4*a^5*hbar^2*pi()*x1^4+(-18*a^5*b1+22*a^5*b0)*hbar^2*pi()*x1^3+(10*a^5*b0*b1 -10*a^5*b0^2)*hbar^2*pi()*x1^2+(-5*a^5*b0^2*b1+5*a^5*b0^3)*hbar^2*pi()*x1+(a^5*b0^3*b1 -1*a^5*b0^4)*hbar^2*pi())*x2^2+(a^5*hbar^2*pi()*x1^5+(10*a^5*b1 -11*a^5*b0)*hbar^2*pi()*x1^4+(-22*a^5*b0*b1+22*a^5*b0^2)*hbar^2*pi()*x1^3+(28*a^5*b0^2*b1 -28*a^5*b0^3)*hbar^2*pi()*x1^2+(-17*a^5*b0^3*b1+17*a^5*b0^4)*hbar^2*pi()*x1+(4*a^5*b0^4*b1 -4*a^5*b0^5)*hbar^2*pi())*x2+((-1*a^5*b1+a^5*b0)*hbar^2*pi()*x1^5+(4*a^5*b0*b1 -4*a^5*b0^2)*hbar^2*pi()*x1^4+(-6*a^5*b0^2*b1+6*a^5*b0^3)*hbar^2*pi()*x1^3+(4*a^5*b0^3*b1 -4*a^5*b0^4)*hbar^2*pi()*x1^2+(-1*a^5*b0^4*b1+a^5*b0^5)*hbar^2*pi()*x1))))/((((2*a^5*b1 -2*a^5*b0)*m*pi()*x1^4+(-8*a^5*b0*b1+8*a^5*b0^2)*m*pi()*x1^3+(12*a^5*b0^2*b1 -12*a^5*b0^3)*m*pi()*x1^2+(-8*a^5*b0^3*b1+8*a^5*b0^4)*m*pi()*x1+(2*a^5*b0^4*b1 -2*a^5*b0^5)*m*pi())*x2^4+((-8*a^5*b1+8*a^5*b0)*m*pi()*x1^5+(32*a^5*b0*b1 -32*a^5*b0^2)*m*pi()*x1^4+(-48*a^5*b0^2*b1+48*a^5*b0^3)*m*pi()*x1^3+(32*a^5*b0^3*b1 -32*a^5*b0^4)*m*pi()*x1^2+(-8*a^5*b0^4*b1+8*a^5*b0^5)*m*pi()*x1)*x2^3+((12*a^5*b1 -12*a^5*b0)*m*pi()*x1^6+(-48*a^5*b0*b1+48*a^5*b0^2)*m*pi()*x1^5+(72*a^5*b0^2*b1 -72*a^5*b0^3)*m*pi()*x1^4+(-48*a^5*b0^3*b1+48*a^5*b0^4)*m*pi()*x1^3+(12*a^5*b0^4*b1 -12*a^5*b0^5)*m*pi()*x1^2)*x2^2+((-8*a^5*b1+8*a^5*b0)*m*pi()*x1^7+(32*a^5*b0*b1 -32*a^5*b0^2)*m*pi()*x1^6+(-48*a^5*b0^2*b1+48*a^5*b0^3)*m*pi()*x1^5+(32*a^5*b0^3*b1 -32*a^5*b0^4)*m*pi()*x1^4+(-8*a^5*b0^4*b1+8*a^5*b0^5)*m*pi()*x1^3)*x2+((2*a^5*b1 -2*a^5*b0)*m*pi()*x1^8+(-8*a^5*b0*b1+8*a^5*b0^2)*m*pi()*x1^7+(12*a^5*b0^2*b1 -12*a^5*b0^3)*m*pi()*x1^6+(-8*a^5*b0^3*b1+8*a^5*b0^4)*m*pi()*x1^5+(2*a^5*b0^4*b1 -2*a^5*b0^5)*m*pi()*x1^4))*x3+(((-2*a^5*b1+2*a^5*b0)*m*pi()*x1^4+(8*a^5*b0*b1 -8*a^5*b0^2)*m*pi()*x1^3+(-12*a^5*b0^2*b1+12*a^5*b0^3)*m*pi()*x1^2+(8*a^5*b0^3*b1 -8*a^5*b0^4)*m*pi()*x1+(-2*a^5*b0^4*b1+2*a^5*b0^5)*m*pi())*x2^5+((8*a^5*b1 -8*a^5*b0)*m*pi()*x1^5+(-32*a^5*b0*b1+32*a^5*b0^2)*m*pi()*x1^4+(48*a^5*b0^2*b1 -48*a^5*b0^3)*m*pi()*x1^3+(-32*a^5*b0^3*b1+32*a^5*b0^4)*m*pi()*x1^2+(8*a^5*b0^4*b1 -8*a^5*b0^5)*m*pi()*x1)*x2^4+((-12*a^5*b1+12*a^5*b0)*m*pi()*x1^6+(48*a^5*b0*b1 -48*a^5*b0^2)*m*pi()*x1^5+(-72*a^5*b0^2*b1+72*a^5*b0^3)*m*pi()*x1^4+(48*a^5*b0^3*b1 -48*a^5*b0^4)*m*pi()*x1^3+(-12*a^5*b0^4*b1+12*a^5*b0^5)*m*pi()*x1^2)*x2^3+((8*a^5*b1 -8*a^5*b0)*m*pi()*x1^7+(-32*a^5*b0*b1+32*a^5*b0^2)*m*pi()*x1^6+(48*a^5*b0^2*b1 -48*a^5*b0^3)*m*pi()*x1^5+(-32*a^5*b0^3*b1+32*a^5*b0^4)*m*pi()*x1^4+(8*a^5*b0^4*b1 -8*a^5*b0^5)*m*pi()*x1^3)*x2^2+((-2*a^5*b1+2*a^5*b0)*m*pi()*x1^8+(8*a^5*b0*b1 -8*a^5*b0^2)*m*pi()*x1^7+(-12*a^5*b0^2*b1+12*a^5*b0^3)*m*pi()*x1^6+(8*a^5*b0^3*b1 -8*a^5*b0^4)*m*pi()*x1^5+(-2*a^5*b0^4*b1+2*a^5*b0^5)*m*pi()*x1^4)*x2)),((hbar^2*x2^2+(-4*hbar^2*x1+2*b0*hbar^2)*x2+(9*hbar^2*x1^2 -14*b0*hbar^2*x1+6*b0^2*hbar^2))*x3^2+(-2*hbar^2*x2^3+(8*hbar^2*x1 -4*b0*hbar^2)*x2^2+(-20*hbar^2*x1^2+32*b0*hbar^2*x1 -14*b0^2*hbar^2)*x2+(2*hbar^2*x1^3 -4*b0*hbar^2*x1^2+2*b0^2*hbar^2*x1))*x3+(hbar^2*x2^4+(-4*hbar^2*x1+2*b0*hbar^2)*x2^3+(12*hbar^2*x1^2 -20*b0*hbar^2*x1+9*b0^2*hbar^2)*x2^2+(-4*hbar^2*x1^3+8*b0*hbar^2*x1^2 -4*b0^2*hbar^2*x1)*x2+(hbar^2*x1^4 -2*b0*hbar^2*x1^3+b0^2*hbar^2*x1^2)))/(((4*m*x1^2 -8*b0*m*x1+4*b0^2*m)*x2^4+(-16*m*x1^3+32*b0*m*x1^2 -16*b0^2*m*x1)*x2^3+(24*m*x1^4 -48*b0*m*x1^3+24*b0^2*m*x1^2)*x2^2+(-16*m*x1^5+32*b0*m*x1^4 -16*b0^2*m*x1^3)*x2+(4*m*x1^6 -8*b0*m*x1^5+4*b0^2*m*x1^4))*x3^2+((-8*m*x1^2+16*b0*m*x1 -8*b0^2*m)*x2^5+(32*m*x1^3 -64*b0*m*x1^2+32*b0^2*m*x1)*x2^4+(-48*m*x1^4+96*b0*m*x1^3 -48*b0^2*m*x1^2)*x2^3+(32*m*x1^5 -64*b0*m*x1^4+32*b0^2*m*x1^3)*x2^2+(-8*m*x1^6+16*b0*m*x1^5 -8*b0^2*m*x1^4)*x2)*x3+((4*m*x1^2 -8*b0*m*x1+4*b0^2*m)*x2^6+(-16*m*x1^3+32*b0*m*x1^2 -16*b0^2*m*x1)*x2^5+(24*m*x1^4 -48*b0*m*x1^3+24*b0^2*m*x1^2)*x2^4+(-16*m*x1^5+32*b0*m*x1^4 -16*b0^2*m*x1^3)*x2^3+(4*m*x1^6 -8*b0*m*x1^5+4*b0^2*m*x1^4)*x2^2)),(-1*hbar^2)/((4*m*x2^2 -8*m*x1*x2+4*m*x1^2)*x3^2+(-8*m*x2^3+16*m*x1*x2^2 -8*m*x1^2*x2)*x3+(4*m*x2^4 -8*m*x1*x2^3+4*m*x1^2*x2^2)),0,0,0,0,0,0,0],[((hbar^2*x2^2+(-4*hbar^2*x1+2*b0*hbar^2)*x2+(9*hbar^2*x1^2 -14*b0*hbar^2*x1+6*b0^2*hbar^2))*x3^2+(-2*hbar^2*x2^3+(8*hbar^2*x1 -4*b0*hbar^2)*x2^2+(-20*hbar^2*x1^2+32*b0*hbar^2*x1 -14*b0^2*hbar^2)*x2+(2*hbar^2*x1^3 -4*b0*hbar^2*x1^2+2*b0^2*hbar^2*x1))*x3+(hbar^2*x2^4+(-4*hbar^2*x1+2*b0*hbar^2)*x2^3+(12*hbar^2*x1^2 -20*b0*hbar^2*x1+9*b0^2*hbar^2)*x2^2+(-4*hbar^2*x1^3+8*b0*hbar^2*x1^2 -4*b0^2*hbar^2*x1)*x2+(hbar^2*x1^4 -2*b0*hbar^2*x1^3+b0^2*hbar^2*x1^2)))/(((4*m*x1^2 -8*b0*m*x1+4*b0^2*m)*x2^4+(-16*m*x1^3+32*b0*m*x1^2 -16*b0^2*m*x1)*x2^3+(24*m*x1^4 -48*b0*m*x1^3+24*b0^2*m*x1^2)*x2^2+(-16*m*x1^5+32*b0*m*x1^4 -16*b0^2*m*x1^3)*x2+(4*m*x1^6 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-48*a^2*b0*m*x1^3)*x2^3+(-12*a^2*m*x1^5+12*a^2*b0*m*x1^4)*x2^2)*x3^3+((-16*m*x1+16*b0*m)*x2^9+(64*m*x1^2 -64*b0*m*x1)*x2^8+(-96*m*x1^3+96*b0*m*x1^2+8*a^2*m*x1 -8*a^2*b0*m)*x2^7+(64*m*x1^4 -64*b0*m*x1^3 -32*a^2*m*x1^2+32*a^2*b0*m*x1)*x2^6+(-16*m*x1^5+16*b0*m*x1^4+48*a^2*m*x1^3 -48*a^2*b0*m*x1^2)*x2^5+(-32*a^2*m*x1^4+32*a^2*b0*m*x1^3)*x2^4+(8*a^2*m*x1^5 -8*a^2*b0*m*x1^4)*x2^3)*x3^2+((4*m*x1 -4*b0*m)*x2^10+(-16*m*x1^2+16*b0*m*x1)*x2^9+(24*m*x1^3 -24*b0*m*x1^2 -2*a^2*m*x1+2*a^2*b0*m)*x2^8+(-16*m*x1^4+16*b0*m*x1^3+8*a^2*m*x1^2 -8*a^2*b0*m*x1)*x2^7+(4*m*x1^5 -4*b0*m*x1^4 -12*a^2*m*x1^3+12*a^2*b0*m*x1^2)*x2^6+(8*a^2*m*x1^4 -8*a^2*b0*m*x1^3)*x2^5+(-2*a^2*m*x1^5+2*a^2*b0*m*x1^4)*x2^4)*x3))*exp((-1*x2^2)/(a^2))+(((a^5*hbar^2*pi()*x2+(-4*a^5*hbar^2*pi()*x1+3*a^5*b0*hbar^2*pi()))*x3^4+(-4*a^5*hbar^2*pi()*x2^2+(17*a^5*hbar^2*pi()*x1 -13*a^5*b0*hbar^2*pi())*x2+(-1*a^5*hbar^2*pi()*x1^2+a^5*b0*hbar^2*pi()*x1))*x3^3+(6*a^5*hbar^2*pi()*x2^3+(-28*a^5*hbar^2*pi()*x1+22*a^5*b0*hbar^2*pi())*x2^2+(5*a^5*hbar^2*pi()*x1^2 -5*a^5*b0*hbar^2*pi()*x1)*x2+(-1*a^5*hbar^2*pi()*x1^3+a^5*b0*hbar^2*pi()*x1^2))*x3^2+(-4*a^5*hbar^2*pi()*x2^4+(22*a^5*hbar^2*pi()*x1 -18*a^5*b0*hbar^2*pi())*x2^3+(-10*a^5*hbar^2*pi()*x1^2+10*a^5*b0*hbar^2*pi()*x1)*x2^2+(5*a^5*hbar^2*pi()*x1^3 -5*a^5*b0*hbar^2*pi()*x1^2)*x2+(-1*a^5*hbar^2*pi()*x1^4+a^5*b0*hbar^2*pi()*x1^3))*x3+(a^5*hbar^2*pi()*x2^5+(-10*a^5*hbar^2*pi()*x1+9*a^5*b0*hbar^2*pi())*x2^4+(18*a^5*hbar^2*pi()*x1^2 -18*a^5*b0*hbar^2*pi()*x1)*x2^3+(-22*a^5*hbar^2*pi()*x1^3+22*a^5*b0*hbar^2*pi()*x1^2)*x2^2+(13*a^5*hbar^2*pi()*x1^4 -13*a^5*b0*hbar^2*pi()*x1^3)*x2+(-3*a^5*hbar^2*pi()*x1^5+3*a^5*b0*hbar^2*pi()*x1^4)))*x4+((-1*a^5*hbar^2*pi()*x2+(4*a^5*hbar^2*pi()*x1 -3*a^5*b0*hbar^2*pi()))*x3^5+(4*a^5*hbar^2*pi()*x2^2+(-17*a^5*hbar^2*pi()*x1+13*a^5*b0*hbar^2*pi())*x2+(a^5*hbar^2*pi()*x1^2 -1*a^5*b0*hbar^2*pi()*x1))*x3^4+(-6*a^5*hbar^2*pi()*x2^3+(28*a^5*hbar^2*pi()*x1 -22*a^5*b0*hbar^2*pi())*x2^2+(-5*a^5*hbar^2*pi()*x1^2+5*a^5*b0*hbar^2*pi()*x1)*x2+(a^5*hbar^2*pi()*x1^3 -1*a^5*b0*hbar^2*pi()*x1^2))*x3^3+(4*a^5*hbar^2*pi()*x2^4+(-22*a^5*hbar^2*pi()*x1+18*a^5*b0*hbar^2*pi())*x2^3+(10*a^5*hbar^2*pi()*x1^2 -10*a^5*b0*hbar^2*pi()*x1)*x2^2+(-5*a^5*hbar^2*pi()*x1^3+5*a^5*b0*hbar^2*pi()*x1^2)*x2+(a^5*hbar^2*pi()*x1^4 -1*a^5*b0*hbar^2*pi()*x1^3))*x3^2+(-1*a^5*hbar^2*pi()*x2^5+(11*a^5*hbar^2*pi()*x1 -10*a^5*b0*hbar^2*pi())*x2^4+(-22*a^5*hbar^2*pi()*x1^2+22*a^5*b0*hbar^2*pi()*x1)*x2^3+(28*a^5*hbar^2*pi()*x1^3 -28*a^5*b0*hbar^2*pi()*x1^2)*x2^2+(-17*a^5*hbar^2*pi()*x1^4+17*a^5*b0*hbar^2*pi()*x1^3)*x2+(4*a^5*hbar^2*pi()*x1^5 -4*a^5*b0*hbar^2*pi()*x1^4))*x3+((-1*a^5*hbar^2*pi()*x1+a^5*b0*hbar^2*pi())*x2^5+(4*a^5*hbar^2*pi()*x1^2 -4*a^5*b0*hbar^2*pi()*x1)*x2^4+(-6*a^5*hbar^2*pi()*x1^3+6*a^5*b0*hbar^2*pi()*x1^2)*x2^3+(4*a^5*hbar^2*pi()*x1^4 -4*a^5*b0*hbar^2*pi()*x1^3)*x2^2+(-1*a^5*hbar^2*pi()*x1^5+a^5*b0*hbar^2*pi()*x1^4)*x2))))/((((2*a^5*m*pi()*x1 -2*a^5*b0*m*pi())*x2^4+(-8*a^5*m*pi()*x1^2+8*a^5*b0*m*pi()*x1)*x2^3+(12*a^5*m*pi()*x1^3 -12*a^5*b0*m*pi()*x1^2)*x2^2+(-8*a^5*m*pi()*x1^4+8*a^5*b0*m*pi()*x1^3)*x2+(2*a^5*m*pi()*x1^5 -2*a^5*b0*m*pi()*x1^4))*x3^4+((-8*a^5*m*pi()*x1+8*a^5*b0*m*pi())*x2^5+(32*a^5*m*pi()*x1^2 -32*a^5*b0*m*pi()*x1)*x2^4+(-48*a^5*m*pi()*x1^3+48*a^5*b0*m*pi()*x1^2)*x2^3+(32*a^5*m*pi()*x1^4 -32*a^5*b0*m*pi()*x1^3)*x2^2+(-8*a^5*m*pi()*x1^5+8*a^5*b0*m*pi()*x1^4)*x2)*x3^3+((12*a^5*m*pi()*x1 -12*a^5*b0*m*pi())*x2^6+(-48*a^5*m*pi()*x1^2+48*a^5*b0*m*pi()*x1)*x2^5+(72*a^5*m*pi()*x1^3 -72*a^5*b0*m*pi()*x1^2)*x2^4+(-48*a^5*m*pi()*x1^4+48*a^5*b0*m*pi()*x1^3)*x2^3+(12*a^5*m*pi()*x1^5 -12*a^5*b0*m*pi()*x1^4)*x2^2)*x3^2+((-8*a^5*m*pi()*x1+8*a^5*b0*m*pi())*x2^7+(32*a^5*m*pi()*x1^2 -32*a^5*b0*m*pi()*x1)*x2^6+(-48*a^5*m*pi()*x1^3+48*a^5*b0*m*pi()*x1^2)*x2^5+(32*a^5*m*pi()*x1^4 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-8*a^2*m*x1*x2^4)*x3^3)*x4^2+((4*m*x2 -4*m*x1)*x3^10+(-16*m*x2^2+16*m*x1*x2)*x3^9+(24*m*x2^3 -24*m*x1*x2^2 -2*a^2*m*x2+2*a^2*m*x1)*x3^8+(-16*m*x2^4+16*m*x1*x2^3+8*a^2*m*x2^2 -8*a^2*m*x1*x2)*x3^7+(4*m*x2^5 -4*m*x1*x2^4 -12*a^2*m*x2^3+12*a^2*m*x1*x2^2)*x3^6+(8*a^2*m*x2^4 -8*a^2*m*x1*x2^3)*x3^5+(-2*a^2*m*x2^5+2*a^2*m*x1*x2^4)*x3^4)*x4))*exp((-1*x3^2)/(a^2))+(((a^5*hbar^2*pi()*x3+(-4*a^5*hbar^2*pi()*x2+3*a^5*hbar^2*pi()*x1))*x4^4+(-4*a^5*hbar^2*pi()*x3^2+(17*a^5*hbar^2*pi()*x2 -13*a^5*hbar^2*pi()*x1)*x3+(-1*a^5*hbar^2*pi()*x2^2+a^5*hbar^2*pi()*x1*x2))*x4^3+(6*a^5*hbar^2*pi()*x3^3+(-28*a^5*hbar^2*pi()*x2+22*a^5*hbar^2*pi()*x1)*x3^2+(5*a^5*hbar^2*pi()*x2^2 -5*a^5*hbar^2*pi()*x1*x2)*x3+(-1*a^5*hbar^2*pi()*x2^3+a^5*hbar^2*pi()*x1*x2^2))*x4^2+(-4*a^5*hbar^2*pi()*x3^4+(22*a^5*hbar^2*pi()*x2 -18*a^5*hbar^2*pi()*x1)*x3^3+(-10*a^5*hbar^2*pi()*x2^2+10*a^5*hbar^2*pi()*x1*x2)*x3^2+(5*a^5*hbar^2*pi()*x2^3 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-2*hbar^2*x2*x3^3+hbar^2*x2^2*x3^2)))/(((4*m*x3^2 -8*m*x2*x3+4*m*x2^2)*x4^4+(-16*m*x3^3+32*m*x2*x3^2 -16*m*x2^2*x3)*x4^3+(24*m*x3^4 -48*m*x2*x3^3+24*m*x2^2*x3^2)*x4^2+(-16*m*x3^5+32*m*x2*x3^4 -16*m*x2^2*x3^3)*x4+(4*m*x3^6 -8*m*x2*x3^5+4*m*x2^2*x3^4))*x5^2+((-8*m*x3^2+16*m*x2*x3 -8*m*x2^2)*x4^5+(32*m*x3^3 -64*m*x2*x3^2+32*m*x2^2*x3)*x4^4+(-48*m*x3^4+96*m*x2*x3^3 -48*m*x2^2*x3^2)*x4^3+(32*m*x3^5 -64*m*x2*x3^4+32*m*x2^2*x3^3)*x4^2+(-8*m*x3^6+16*m*x2*x3^5 -8*m*x2^2*x3^4)*x4)*x5+((4*m*x3^2 -8*m*x2*x3+4*m*x2^2)*x4^6+(-16*m*x3^3+32*m*x2*x3^2 -16*m*x2^2*x3)*x4^5+(24*m*x3^4 -48*m*x2*x3^3+24*m*x2^2*x3^2)*x4^4+(-16*m*x3^5+32*m*x2*x3^4 -16*m*x2^2*x3^3)*x4^3+(4*m*x3^6 -8*m*x2*x3^5+4*m*x2^2*x3^4)*x4^2)),((((-4*m*x3+4*m*x2)*x4^6+(16*m*x3^2 -16*m*x2*x3)*x4^5+(-24*m*x3^3+24*m*x2*x3^2+2*a^2*m*x3 -2*a^2*m*x2)*x4^4+(16*m*x3^4 -16*m*x2*x3^3 -8*a^2*m*x3^2+8*a^2*m*x2*x3)*x4^3+(-4*m*x3^5+4*m*x2*x3^4+12*a^2*m*x3^3 -12*a^2*m*x2*x3^2)*x4^2+(-8*a^2*m*x3^4+8*a^2*m*x2*x3^3)*x4+(2*a^2*m*x3^5 -2*a^2*m*x2*x3^4))*x5^4+((16*m*x3 -16*m*x2)*x4^7+(-64*m*x3^2+64*m*x2*x3)*x4^6+(96*m*x3^3 -96*m*x2*x3^2 -8*a^2*m*x3+8*a^2*m*x2)*x4^5+(-64*m*x3^4+64*m*x2*x3^3+32*a^2*m*x3^2 -32*a^2*m*x2*x3)*x4^4+(16*m*x3^5 -16*m*x2*x3^4 -48*a^2*m*x3^3+48*a^2*m*x2*x3^2)*x4^3+(32*a^2*m*x3^4 -32*a^2*m*x2*x3^3)*x4^2+(-8*a^2*m*x3^5+8*a^2*m*x2*x3^4)*x4)*x5^3+((-24*m*x3+24*m*x2)*x4^8+(96*m*x3^2 -96*m*x2*x3)*x4^7+(-144*m*x3^3+144*m*x2*x3^2+12*a^2*m*x3 -12*a^2*m*x2)*x4^6+(96*m*x3^4 -96*m*x2*x3^3 -48*a^2*m*x3^2+48*a^2*m*x2*x3)*x4^5+(-24*m*x3^5+24*m*x2*x3^4+72*a^2*m*x3^3 -72*a^2*m*x2*x3^2)*x4^4+(-48*a^2*m*x3^4+48*a^2*m*x2*x3^3)*x4^3+(12*a^2*m*x3^5 -12*a^2*m*x2*x3^4)*x4^2)*x5^2+((16*m*x3 -16*m*x2)*x4^9+(-64*m*x3^2+64*m*x2*x3)*x4^8+(96*m*x3^3 -96*m*x2*x3^2 -8*a^2*m*x3+8*a^2*m*x2)*x4^7+(-64*m*x3^4+64*m*x2*x3^3+32*a^2*m*x3^2 -32*a^2*m*x2*x3)*x4^6+(16*m*x3^5 -16*m*x2*x3^4 -48*a^2*m*x3^3+48*a^2*m*x2*x3^2)*x4^5+(32*a^2*m*x3^4 -32*a^2*m*x2*x3^3)*x4^4+(-8*a^2*m*x3^5+8*a^2*m*x2*x3^4)*x4^3)*x5+((-4*m*x3+4*m*x2)*x4^10+(16*m*x3^2 -16*m*x2*x3)*x4^9+(-24*m*x3^3+24*m*x2*x3^2+2*a^2*m*x3 -2*a^2*m*x2)*x4^8+(16*m*x3^4 -16*m*x2*x3^3 -8*a^2*m*x3^2+8*a^2*m*x2*x3)*x4^7+(-4*m*x3^5+4*m*x2*x3^4+12*a^2*m*x3^3 -12*a^2*m*x2*x3^2)*x4^6+(-8*a^2*m*x3^4+8*a^2*m*x2*x3^3)*x4^5+(2*a^2*m*x3^5 -2*a^2*m*x2*x3^4)*x4^4))*exp((-1*x4^2)/(a^2))+((a^5*hbar^2*pi()*x4+(-4*a^5*hbar^2*pi()*x3+3*a^5*hbar^2*pi()*x2))*x5^4+(-4*a^5*hbar^2*pi()*x4^2+(17*a^5*hbar^2*pi()*x3 -13*a^5*hbar^2*pi()*x2)*x4+(-1*a^5*hbar^2*pi()*x3^2+a^5*hbar^2*pi()*x2*x3))*x5^3+(6*a^5*hbar^2*pi()*x4^3+(-28*a^5*hbar^2*pi()*x3+22*a^5*hbar^2*pi()*x2)*x4^2+(5*a^5*hbar^2*pi()*x3^2 -5*a^5*hbar^2*pi()*x2*x3)*x4+(-1*a^5*hbar^2*pi()*x3^3+a^5*hbar^2*pi()*x2*x3^2))*x5^2+(-4*a^5*hbar^2*pi()*x4^4+(22*a^5*hbar^2*pi()*x3 -18*a^5*hbar^2*pi()*x2)*x4^3+(-10*a^5*hbar^2*pi()*x3^2+10*a^5*hbar^2*pi()*x2*x3)*x4^2+(5*a^5*hbar^2*pi()*x3^3 -5*a^5*hbar^2*pi()*x2*x3^2)*x4+(-1*a^5*hbar^2*pi()*x3^4+a^5*hbar^2*pi()*x2*x3^3))*x5+(a^5*hbar^2*pi()*x4^5+(-10*a^5*hbar^2*pi()*x3+9*a^5*hbar^2*pi()*x2)*x4^4+(18*a^5*hbar^2*pi()*x3^2 -18*a^5*hbar^2*pi()*x2*x3)*x4^3+(-22*a^5*hbar^2*pi()*x3^3+22*a^5*hbar^2*pi()*x2*x3^2)*x4^2+(13*a^5*hbar^2*pi()*x3^4 -13*a^5*hbar^2*pi()*x2*x3^3)*x4+(-3*a^5*hbar^2*pi()*x3^5+3*a^5*hbar^2*pi()*x2*x3^4))))/(((2*a^5*m*pi()*x3 -2*a^5*m*pi()*x2)*x4^4+(-8*a^5*m*pi()*x3^2+8*a^5*m*pi()*x2*x3)*x4^3+(12*a^5*m*pi()*x3^3 -12*a^5*m*pi()*x2*x3^2)*x4^2+(-8*a^5*m*pi()*x3^4+8*a^5*m*pi()*x2*x3^3)*x4+(2*a^5*m*pi()*x3^5 -2*a^5*m*pi()*x2*x3^4))*x5^4+((-8*a^5*m*pi()*x3+8*a^5*m*pi()*x2)*x4^5+(32*a^5*m*pi()*x3^2 -32*a^5*m*pi()*x2*x3)*x4^4+(-48*a^5*m*pi()*x3^3+48*a^5*m*pi()*x2*x3^2)*x4^3+(32*a^5*m*pi()*x3^4 -32*a^5*m*pi()*x2*x3^3)*x4^2+(-8*a^5*m*pi()*x3^5+8*a^5*m*pi()*x2*x3^4)*x4)*x5^3+((12*a^5*m*pi()*x3 -12*a^5*m*pi()*x2)*x4^6+(-48*a^5*m*pi()*x3^2+48*a^5*m*pi()*x2*x3)*x4^5+(72*a^5*m*pi()*x3^3 -72*a^5*m*pi()*x2*x3^2)*x4^4+(-48*a^5*m*pi()*x3^4+48*a^5*m*pi()*x2*x3^3)*x4^3+(12*a^5*m*pi()*x3^5 -12*a^5*m*pi()*x2*x3^4)*x4^2)*x5^2+((-8*a^5*m*pi()*x3+8*a^5*m*pi()*x2)*x4^7+(32*a^5*m*pi()*x3^2 -32*a^5*m*pi()*x2*x3)*x4^6+(-48*a^5*m*pi()*x3^3+48*a^5*m*pi()*x2*x3^2)*x4^5+(32*a^5*m*pi()*x3^4 -32*a^5*m*pi()*x2*x3^3)*x4^4+(-8*a^5*m*pi()*x3^5+8*a^5*m*pi()*x2*x3^4)*x4^3)*x5+((2*a^5*m*pi()*x3 -2*a^5*m*pi()*x2)*x4^8+(-8*a^5*m*pi()*x3^2+8*a^5*m*pi()*x2*x3)*x4^7+(12*a^5*m*pi()*x3^3 -12*a^5*m*pi()*x2*x3^2)*x4^6+(-8*a^5*m*pi()*x3^4+8*a^5*m*pi()*x2*x3^3)*x4^5+(2*a^5*m*pi()*x3^5 -2*a^5*m*pi()*x2*x3^4)*x4^4)),(hbar^2*x5^2+(-4*hbar^2*x4+2*hbar^2*x3)*x5+(9*hbar^2*x4^2 -14*hbar^2*x3*x4+6*hbar^2*x3^2))/((4*m*x4^2 -8*m*x3*x4+4*m*x3^2)*x5^4+(-16*m*x4^3+32*m*x3*x4^2 -16*m*x3^2*x4)*x5^3+(24*m*x4^4 -48*m*x3*x4^3+24*m*x3^2*x4^2)*x5^2+(-16*m*x4^5+32*m*x3*x4^4 -16*m*x3^2*x4^3)*x5+(4*m*x4^6 -8*m*x3*x4^5+4*m*x3^2*x4^4)),0,0,0,0,0],[0,0,(-1*hbar^2)/((4*m*x4^2 -8*m*x3*x4+4*m*x3^2)*x5^2+(-8*m*x4^3+16*m*x3*x4^2 -8*m*x3^2*x4)*x5+(4*m*x4^4 -8*m*x3*x4^3+4*m*x3^2*x4^2)),(hbar^2*x5^2+(-4*hbar^2*x4+2*hbar^2*x3)*x5+(9*hbar^2*x4^2 -14*hbar^2*x3*x4+6*hbar^2*x3^2))/((4*m*x4^2 -8*m*x3*x4+4*m*x3^2)*x5^4+(-16*m*x4^3+32*m*x3*x4^2 -16*m*x3^2*x4)*x5^3+(24*m*x4^4 -48*m*x3*x4^3+24*m*x3^2*x4^2)*x5^2+(-16*m*x4^5+32*m*x3*x4^4 -16*m*x3^2*x4^3)*x5+(4*m*x4^6 -8*m*x3*x4^5+4*m*x3^2*x4^4)),(((-4*m*x4+4*m*x3)*x5^6+(16*m*x4^2 -16*m*x3*x4)*x5^5+(-24*m*x4^3+24*m*x3*x4^2+2*a^2*m*x4 -2*a^2*m*x3)*x5^4+(16*m*x4^4 -16*m*x3*x4^3 -8*a^2*m*x4^2+8*a^2*m*x3*x4)*x5^3+(-4*m*x4^5+4*m*x3*x4^4+12*a^2*m*x4^3 -12*a^2*m*x3*x4^2)*x5^2+(-8*a^2*m*x4^4+8*a^2*m*x3*x4^3)*x5+(2*a^2*m*x4^5 -2*a^2*m*x3*x4^4))*exp((-1*x5^2)/(a^2))+(a^5*hbar^2*pi()*x5+(-4*a^5*hbar^2*pi()*x4+3*a^5*hbar^2*pi()*x3)))/((2*a^5*m*pi()*x4 -2*a^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 -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]])
Error in lines 1-1 Traceback (most recent call last): File "/projects/b04b5777-e269-4c8f-a4b8-b21dbe1c93c6/.sagemathcloud/sage_server.py", line 879, in execute exec compile(block+'\n', '', 'single') in namespace, locals File "", line 1, in <module> File "/projects/sage/sage-6.7/local/lib/python2.7/site-packages/sage/interfaces/interface.py", line 840, in sage return self._sage_() File "./axiom.py", line 1018, in _sage_ raise NotImplementedError NotImplementedError
%sage
matrix([[1,2],[3,4]])
[1 2] [3 4]