tomleslie

7145 Reputation

17 Badges

10 years, 292 days

MaplePrimes Activity


These are answers submitted by tomleslie

if I fix one minor typo - explain clearly what is wrong with the attached

restart

with(LinearAlgebra)

NULL

F := proc (x) options operator, arrow; x^2 end proc

F(u(t))

u(t)^2

(1)

G := proc (w) options operator, arrow; w*(diff(w, t)) end proc

G(h(t))

h(t)*(diff(h(t), t))

(2)

for n from 0 while n <= 6 do V[n] := (diff(F(sum(t^i*u[i], i = 0 .. n)), [`$`(t, n)]))/factorial(n); U[n] := (diff(G(sum(t^i*h[i], i = 0 .. n)), [`$`(t, n)]))/factorial(n) end do

t := 0

0

(3)

for i from 0 while i <= n-1 do A[i] := V[i]; B[i] := U[i] end do

u[0]^2

 

0

 

2*u[0]*u[1]

 

h[1]^2

 

2*u[0]*u[2]+u[1]^2

 

3*h[1]*h[2]

 

2*u[0]*u[3]+2*u[1]*u[2]

 

4*h[1]*h[3]+2*h[2]^2

 

2*u[0]*u[4]+2*u[1]*u[3]+u[2]^2

 

5*h[1]*h[4]+5*h[2]*h[3]

 

2*u[0]*u[5]+2*u[1]*u[4]+2*u[2]*u[3]

 

6*h[1]*h[5]+6*h[2]*h[4]+3*h[3]^2

 

2*u[0]*u[6]+2*u[1]*u[5]+2*u[2]*u[4]+u[3]^2

 

7*h[1]*h[6]+7*h[2]*h[5]+7*h[3]*h[4]

(4)

for j from 0 while j <= n-1 do u[0] := 1; u[j+1] := int(x*B[j], x)+int(A[j], x) end do

1

 

x

 

1

 

(1/2)*x^2*h[1]^2+x^2

 

1

 

(3/2)*x^2*h[1]*h[2]+(1/3)*x^3*h[1]^2+x^3

 

1

 

(1/2)*x^2*(4*h[1]*h[3]+2*h[2]^2)+x^3*h[1]*h[2]+(1/6)*x^4*h[1]^2+(1/2)*x^4+(1/2)*((1/2)*h[1]^2+1)*x^4

 

1

 

(1/2)*x^2*(5*h[1]*h[4]+5*h[2]*h[3])+(1/3)*x^3*(4*h[1]*h[3]+2*h[2]^2)+(5/4)*x^4*h[1]*h[2]+(1/15)*x^5*h[1]^2+(1/5)*x^5+(1/5)*((1/2)*h[1]^2+1)*x^5+(2/5)*((1/3)*h[1]^2+1)*x^5+(1/5)*((1/2)*h[1]^2+1)^2*x^5

 

1

 

(1/2)*x^2*(6*h[1]*h[5]+6*h[2]*h[4]+3*h[3]^2)+(1/3)*x^3*(5*h[1]*h[4]+5*h[2]*h[3])+(1/6)*x^4*(4*h[1]*h[3]+2*h[2]^2)+(9/10)*x^5*h[1]*h[2]+(1/45)*x^6*h[1]^2+(1/15)*x^6+(1/15)*((1/2)*h[1]^2+1)*x^6+(2/15)*((1/3)*h[1]^2+1)*x^6+(1/15)*((1/2)*h[1]^2+1)^2*x^6+(1/3)*((5/12)*h[1]^2+1)*x^6+(1/2)*(2*h[1]*h[3]+h[2]^2)*x^4+(1/3)*((1/2)*h[1]^2+1)*((1/3)*h[1]^2+1)*x^6+(3/5)*((1/2)*h[1]^2+1)*h[1]*h[2]*x^5

 

1

 

(1/2)*x^2*(7*h[1]*h[6]+7*h[2]*h[5]+7*h[3]*h[4])+(1/3)*x^3*(6*h[1]*h[5]+6*h[2]*h[4]+3*h[3]^2)+(1/6)*x^4*(5*h[1]*h[4]+5*h[2]*h[3])+(1/15)*x^5*(4*h[1]*h[3]+2*h[2]^2)+(43/60)*x^6*h[1]*h[2]+(2/315)*x^7*h[1]^2+(2/105)*x^7+(2/105)*((1/2)*h[1]^2+1)*x^7+(4/105)*((1/3)*h[1]^2+1)*x^7+(2/105)*((1/2)*h[1]^2+1)^2*x^7+(2/21)*((5/12)*h[1]^2+1)*x^7+(1/5)*(2*h[1]*h[3]+h[2]^2)*x^5+(2/21)*((1/2)*h[1]^2+1)*((1/3)*h[1]^2+1)*x^7+(8/15)*((1/2)*h[1]^2+1)*h[1]*h[2]*x^6+(2/7)*((3/10)*h[1]^2+4/5+(1/5)*((1/2)*h[1]^2+1)^2)*x^7+(2/5)*((4/3)*h[1]*h[3]+(2/3)*h[2]^2)*x^5+(1/2)*((5/2)*h[1]*h[4]+(5/2)*h[2]*h[3])*x^4+(2/7)*((1/2)*h[1]^2+1)*((5/12)*h[1]^2+1)*x^7+(2/5)*((1/2)*h[1]^2+1)*(2*h[1]*h[3]+h[2]^2)*x^5+(1/7)*((1/3)*h[1]^2+1)^2*x^7+(1/2)*h[1]*h[2]*((1/3)*h[1]^2+1)*x^6+(9/20)*h[1]^2*h[2]^2*x^5

(5)

y := sum(u[l], l = 0 .. n-1)

1+x+x^3*h[1]*h[2]+(3/5)*((1/2)*h[1]^2+1)*h[1]*h[2]*x^5+(1/5)*((1/2)*h[1]^2+1)^2*x^5+(1/3)*x^3*(4*h[1]*h[3]+2*h[2]^2)+(1/15)*x^5*h[1]^2+(1/5)*((1/2)*h[1]^2+1)*x^5+(2/5)*((1/3)*h[1]^2+1)*x^5+(1/2)*x^2*(5*h[1]*h[4]+5*h[2]*h[3])+(1/2)*((1/2)*h[1]^2+1)*x^4+(1/2)*x^2*(4*h[1]*h[3]+2*h[2]^2)+(1/6)*x^4*h[1]^2+(1/3)*x^3*h[1]^2+(1/2)*x^2*h[1]^2+(1/15)*x^6+(1/15)*((1/2)*h[1]^2+1)*x^6+(2/15)*((1/3)*h[1]^2+1)*x^6+(1/15)*((1/2)*h[1]^2+1)^2*x^6+(1/3)*((5/12)*h[1]^2+1)*x^6+(1/2)*(2*h[1]*h[3]+h[2]^2)*x^4+(1/2)*x^2*(6*h[1]*h[5]+6*h[2]*h[4]+3*h[3]^2)+(1/3)*x^3*(5*h[1]*h[4]+5*h[2]*h[3])+(1/6)*x^4*(4*h[1]*h[3]+2*h[2]^2)+(1/45)*x^6*h[1]^2+(1/5)*x^5+(1/2)*x^4+x^3+x^2+(9/10)*x^5*h[1]*h[2]+(1/3)*((1/2)*h[1]^2+1)*((1/3)*h[1]^2+1)*x^6+(3/2)*x^2*h[1]*h[2]+(5/4)*x^4*h[1]*h[2]

(6)

NULL

``


 

Download adom.mw

ie just substitute the solutions obtained by fsolve() back into the original expression - the answer *ought* to be zero. In fact one gets O(10^-15) for both solutions - close enough to zero for me!

See the attached


 

restart

Digits := 16

P := -(9958.466892*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+2.439889255))*(-0.1557978257e-4*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*k*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.261007e-4*k-9.0*10^(-6)*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*k*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)-4.48946*10^(-11)*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*k*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^6-2.26*10^(-15)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*k*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^7+1.899324*10^(-16)*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*lambda*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^8+1.899324*10^(-16)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*lambda*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^8+0.2699913289e-4*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*k+2.83*10^(-16)*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*k*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^8+0.155261e-4*k*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.1910578434e-3*lambda^4-1.519459*10^(-15)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*lambda*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^7+2.29*10^(-15)*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^7-2.26342*10^(-15)*k*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^7+2.171377*10^(-10)*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^5-6.10984*10^(-6)*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*lambda*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)-1.144560151*10^(-6)*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*k*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^4+0.2875578036e-4*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)+0.106975e-4*lambda*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-2.86369*10^(-16)*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^8+0.1981472958e-3*lambda^3+0.2841557560e-4*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)+1.150803103*10^(-6)*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^4+1.899324*10^(-16)*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*lambda*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^8+7.28416*10^(-11)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^5+1.14719*10^(-6)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^4+6.11214955*10^(-6)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*lambda*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)-1.14257*10^(-6)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*k*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^4-4.82063*10^(-11)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*lambda*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^5-2.26342*10^(-15)*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*k*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^7+1.807661*10^(-11)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*lambda*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^6+8.9899*10^(-6)*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*k*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)+8.9599*10^(-6)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*k*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)-7.64058733*10^(-7)*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*lambda*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^4+4.55915*10^(-6)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*k*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^3+2.83*10^(-16)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*k*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^8+2.29495*10^(-15)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^7+2.83*10^(-16)*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*k*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^8+1.445217*10^(-10)*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*lambda*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^5-1.519459*10^(-15)*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*lambda*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^7-0.1674000840e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.1833461551e-4*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*lambda-4.605558319*10^(-6)*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^3+1.140719237*10^(-6)*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*k*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^4-3.056762083*10^(-6)*lambda*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^3+0.183311e-4*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*lambda-2.26*10^(-15)*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*k*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^7-1.519459*10^(-15)*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*lambda*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^7+2.83*10^(-16)*k*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^8-2.86*10^(-16)*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^8+4.607967783*10^(-6)*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^3-9.3627*10^(-6)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)-0.835512256e-4*lambda^2-2.168014321*10^(-10)*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^5-0.2863334102e-4*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)-7.637931745*10^(-7)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*lambda*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^4-1.805990298*10^(-11)*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*lambda*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^6+3.055990782*10^(-6)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*lambda*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^3+0.1650484496e-4*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e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6682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^4-3.010540298*10^(-11)*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*lambda*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^6+0.1650524630e-4*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.1069507987e-4*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*lambda*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.663330427e-4*lambda^5-3.054641904*10^(-6)*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*lambda*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^3+7.64564268*10^(-7)*lambda*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^4+0.106924e-4*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*lambda*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+7.632879155*10^(-7)*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*lambda*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^4+2.169902*10^(-10)*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*k*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^5-0.2660838513e-4*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*k+3.012211408*10^(-11)*lambda*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^6+4.534365311*10^(-11)*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^6-1.519459*10^(-15)*lambda*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^7-2.86*10^(-16)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^8+1.899324*10^(-16)*lambda*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^8-1.445703114*10^(-10)*lambda*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^5-2.86369*10^(-16)*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^8+2.29495*10^(-15)*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^7+2.72995*10^(-11)*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^6-0.2565264181e-4-6.11292*10^(-6)*lambda*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)-9.3922*10^(-6)*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)+4.555659255*10^(-6)*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*k*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^3-2.723097*10^(-11)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^6-0.1833342214e-4*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*lambda-1.150701960*10^(-6)*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^4+2.69309794*10^(-11)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*k*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^6+1.14531*10^(-6)*k*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^4+0.16e-4*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*k*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+3.055413*10^(-6)*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*lambda*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^3+0.3073879707e-4*lambda-8.931240077*10^(-6)*k*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)-4.610017127*10^(-6)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^3-4.555918*10^(-6)*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*k*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^3-7.2367*10^(-11)*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^5+9.4151*10^(-6)*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)-4.54*10^(-11)*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^6+4.611637585*10^(-6)*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^3)/((0.6307162107e-4*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.2522864843e-3*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)+0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-7.999243141*exp(0.1576790527e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-0.4450487932e-3*lambda^5+0.1300695240e-2*lambda^4-0.1345488383e-2*lambda^3+0.5598667540e-3*lambda^2-0.8455621308e-4*lambda+0.1614703348e-3)-0.1780195173e-2*lambda^5+0.5202780960e-2*lambda^4-0.5381953532e-2*lambda^3+0.2239467016e-2*lambda^2-0.3382248522e-3*lambda+8.000645881)*((7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-28.22497888*lambda^5+82.49004656*lambda^4-85.33082616*lambda^3+35.50672993*lambda^2-5.362552072*lambda+10.24044298)*(0.6307162107e-4*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-1.999873857*exp(0.6307162107e-4*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+0.1261432421e-3)+2.000126143)*((7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2+2))

newP:=eval(P,[k=0.1]):

plot(newP,lambda=-1..1);

 

Digits := 30; sols := fsolve(newP, lambda = -1 .. 1, maxsols = 3)

-.329543248729246670859214244152, -.333666875089007712748988551007

(1)

evalf(eval(newP, lambda = sols[1])); evalf(eval(newP, lambda = sols[2]))

-0.324354778471225210895876344743e-15

 

-0.525926830329962261065920595552e-14

(2)

 


 

Download resid.mw

Matlab does not contain a direct equivalent for the Maple piecewise() function, so I doubt that you willl be able to "translate" your expression without manually converting it to. (Use a lot of if statements)

It is not true that Matlab offers better plotting capability - so I owuldn.t both anyway. See the Maple help here

https://www.maplesoft.com/support/help/Maple/view.aspx?path=worksheet/reference/PlottingGuide

or type

?PlottingGuide

at the Maple prompt

It is generally much more useful if you upload your complete worksheet using the big green up-arrow in the Mapleprimes toolbar. Some observations on the code snippet you have uploaded

#################################################

Are definitions for 'A' and 'old' given elsewhere in yuor worksheet or are these just 'names'? Because if these are just 'names' then the statement

new := (1/16*old) . (120*I + ((A . old) . (735*I + ((A . old) . (-861.*I + ((A . old) . (651*I + ((A . old) . (93*I + (A . (old(-15*I + (A . old))))))))))))

will define 'new' in terms of 'old'. And the subsequent statement

old := new;

will then define 'old' in terms of 'old' which is obviously recursive.

###############################################

In Maple 'I' normally designates the square root of -1 - do you perhaps want this to be an identity matris (of unspecified size!)? Hve you made this redefinition elsewhere in your worksheet?

################################################

In the expression you provide it looks like there is a missing operator at the point highlighted below

new := (1/16*old) . (120*I + ((A . old) . (735*I + ((A . old) . (-861.*I + ((A . old) . (651*I + ((A . old) . (93*I + (A . (old(-15*I + (A . old))))))))))))

The ColumnSpace(A) command in Maple constructs a *basis* (in the form of column vectors) for the columns of A

Hence the columns of the original matrix A can be reconstructed by simple linear combinations of these basis columns.

See the attached

  restart;
  A:=Matrix([[1,2,1,3,2],[3,4,9,0,7],[2,3,5,1,8],[2,2,8,-3,5]]);
#
# Generate the basis for the column space of A
#
  cs:=LinearAlgebra:-ColumnSpace(A);
#
# Given the basis columns, produce the coefficients which
# will allow the original columns to be reconstructed
#
  cnames:= [ seq
             ( c||j,
               j=1..numelems(cs)
             )
           ];
  cvals:= seq
          ( solve
            ( [ entries
                ( A[..,k]-~add(cnames*~cs),
                 'nolist'
                )
              ],
              cnames
            )[],
            k=1..op([1,2],A)
          );
#
# From the column space basis and the above coefficients,
# reconstruct the columns of the original matrix
#
  seq
  ( add
    ( rhs~(cvals[k])*~cs),
    k=1..op([1,2],A)
  );

Matrix(4, 5, {(1, 1) = 1, (1, 2) = 2, (1, 3) = 1, (1, 4) = 3, (1, 5) = 2, (2, 1) = 3, (2, 2) = 4, (2, 3) = 9, (2, 4) = 0, (2, 5) = 7, (3, 1) = 2, (3, 2) = 3, (3, 3) = 5, (3, 4) = 1, (3, 5) = 8, (4, 1) = 2, (4, 2) = 2, (4, 3) = 8, (4, 4) = -3, (4, 5) = 5})

 

[Vector(4, {(1) = 1, (2) = 0, (3) = 0, (4) = -1}), Vector(4, {(1) = 0, (2) = 1, (3) = 0, (4) = 1}), Vector(4, {(1) = 0, (2) = 0, (3) = 1, (4) = 0})]

 

cnames := [c1, c2, c3]

 

cvals := [c1 = 1, c2 = 3, c3 = 2], [c1 = 2, c2 = 4, c3 = 3], [c1 = 1, c2 = 9, c3 = 5], [c1 = 3, c2 = 0, c3 = 1], [c1 = 2, c2 = 7, c3 = 8]

 

Vector[column](%id = 18446744074220559046), Vector[column](%id = 18446744074220559166), Vector[column](%id = 18446744074220559286), Vector[column](%id = 18446744074220559406), Vector[column](%id = 18446744074220559526)

(1)

 


 

Download colbasis.mw

 

the first thing is to check that the number of unknowns does not excedd the number of equations.

Your worksheet *looks* as if it has four equations ( either [Eq1, Eq2a, Eq3, Eq4], or [Eq1, Eq2b, Eq3, Eq4]) in the four unknowns

  {delta[d], phi[d0], u[i10], u[i20]}

However, when you insert all of your parameters into all of your equations, Eq1 works out to 0=0 and there fore is of no use in sovling for {delta[d], phi[d0], u[i10], u[i20]}, so you actually have three equations in four unknowns - which is not uniquely solvable.

See the attached (where I have made numerous corrections/simplifications to your original)

restart;
local gamma:
Eq1:=1+delta[i]+delta[d]*z[c]*phi[d0]-delta[e]=0:   

Eq2a:=C[is1]*u[i10]*(1-2*phi[d0]/u[i10]^2)+delta[i]*C[is2]*u[i20]*(1-2*phi[d0]/u[i20]^2)-sqrt(8/Pi)*delta[e]*v[te]*(beta*phi[d0]^2-4*beta*phi[d0]+(24*alpha+1)/((3*alpha+1))*exp(phi[d0]))=0:    # for phi[d0]<=0

Eq2b:=C[is1]*u[i10]*exp(2*phi[d0]/u[i10]^2)+delta[i]*C[is2]*u[i20]*exp(2*phi[d0]/u[i20]^2)-sqrt(8/Pi)*delta[e]*v[te]*((8*alpha+1)*phi[d0]/(3*alpha+1)+(24*alpha+1)/(3*alpha+1))=0:   # for phi[d0]>0

Eq3:=alpha[c1]*u[i10]^2+3*delta[e]*A[1]/(gamma[i1]*u[i10])-(lambda[Di1]/lambda[Di2])*alpha[c2]*u[i20]^2-3*(lambda[Di1]/lambda[Di2])*delta[e]*A[2]/(delta[i]*gamma[i2]*u[i20])=0:

Eq4:=delta[e]*A[1]/u[i10]+(lambda[Di1]/lambda[Di2])*delta[e]*A[2]/u[i20]-((delta[e]*(beta-1)+(delta[d]*z[c]*phi[d0]^2)/u[d0]^2))*(alpha[c1]*u[i10]^2+3*delta[e]*A[1]/(gamma[i1]*u[i10]))-delta[d]*z[c]*phi[d0]*(G/2+(F[id10]+F[id20]+F[nd10]+F[nd20])/u[d0]^2)+Pi*r[d]^2*delta[d]*lambda[Di1]*n[i10]/(C[ds]*u[d0])*(C[is1]*u[i10]*(1-2*phi[d0]/u[i10]^2)+delta[i]*C[is2]*u[i20]*(1-2*phi[d0]/u[i20]^2)-sqrt(8/Pi)*delta[e]*v[te]*(beta*phi[d0]^2-4*beta*phi[d0]+(24*alpha+1)/((3*alpha+1))*exp(phi[d0])))=0:

   # where:

#Parameters
  lambda[D]:=lambda[Di1]*(1+delta[e]/gamma[i1]+gamma[i2]*delta[i]/gamma[i1])^(-0.5):
  delta[e]:=1+delta[i]+delta[d]*z[c]*phi[d0]:
  gamma[i1]:=T[e]/T[i1]:
  gamma[i2]:=T[e]/T[i2]:
  z[c]:=r[d]*T[e]/e0^2:
  C[is1]:=sqrt(T[e]/m[i1]):
  n[i20]:=delta[i]*n[i10]:
  lambda[Di1]:=sqrt(epsilon[0]*T[i1]/(n[i10]*e0^2)):
  lambda[Di2]:=sqrt(epsilon[0]*T[i2]/(n[i20]*e0^2)):
  lambda[De]:=sqrt(epsilon[0]*T[e]/(n[e0]*e0^2)):
  delta[l]:=lambda[Di1]/lambda[Di2]:
  alpha[c1]:=lambda[Di1]*sigma[in1]*n[n1]:
  alpha[c2]:=lambda[Di2]*sigma[in2]*n[n2]:
  A[1]:=lambda[Di1]*k[i1]*n[n1]/C[is1]:
  A[2]:=lambda[Di2]*k[i2]*n[n2]/C[is2]:
  C[is2]:=sqrt(T[e]/m[i2]):
  C[is2]:=sqrt(T[e]/m[i2]):
  k[i1]:=1.75*10^(-8)*T[e]^0.5*(1+0.13*T[e])*exp(-15.76/T[e]):
  k[i2]:=0.72*10^(-8)*T[e]^0.5*(1+0.08*T[e])*exp(-24.59/T[e]):
  beta:=4*alpha/(3*alpha+1):
  v[te]:=sqrt(T[e]/m[e]):
  F[nd10]:=-lambda[Di1]*8*(2*Pi)^0.5*r[d]^2*n[n1]*T[n1]*u[d0]/(3*v[tn1]*m[d]*C[ds]):
  F[nd20]:=-lambda[Di1]*8*(2*Pi)^0.5*r[d]^2*n[n2]*T[n2]*u[d0]/(3*v[tn2]*m[d]*C[ds]):
  C[ds]:=sqrt((r[d]*T[e]/e0^2)*T[e]/m[d]):
  v[tn1]:=sqrt(T[n1]/m[n1]):
  v[tn2]:=sqrt(T[n2]/m[n2]):
  G:=2*g*lambda[Di1]/(C[ds]^2*u[d0]^2):
  F[id10]:=(Pi*n[i10]*m[i1]*u[i10]*C[is1]^2*sqrt(u[i10]^2+8/Pi)*b[c1]^2+2*Pi*n[i10]*m[i1]*u[i10]*sqrt(u[i10]^2+8/Pi)*b[1]^2*ln((b[1]^2+lambda[D]^2)/(b[1]^2+b[c1]^2)))/(z[c]*T[e]/lambda[Di1]):
  F[id20]:=(Pi*n[i20]*m[i2]*u[i20]*C[is2]^2*sqrt(u[i20]^2+8/Pi)*b[c2]^2+2*Pi*n[i20]*m[i2]*u[i20]*sqrt(u[i20]^2+8/Pi)*b[2]^2*ln((b[2]^2+lambda[D]^2)/(b[2]^2+b[c2]^2)))/(z[c]*T[e]/lambda[Di1]):
  b[c1]:=r[d]*(1-2*phi[d0]/(u[i10]^2+8/(Pi*gamma[i1])))^0.5:
  b[c2]:=r[d]*(1-2*phi[d0]/(u[i20]^2+8/(Pi*gamma[i2])))^0.5:
  b[1]:=r[d]*phi[d0]/(u[i10]^2+8/(Pi*gamma[i1])):
  b[2]:=r[d]*phi[d0]/(u[i20]^2+8/(Pi*gamma[i2])):
  m[e]:=0.91*10^(-30):
  m[i1]:=40*1.67*10^(-27):
  m[i2]:=4*1.67*10^(-27):
  m[n1]:=40*1.67*10^(-27):
  m[n2]:=4*1.67*10^(-27):
 n[i10]:=10^(15):
  sigma[in1]:=5*10^(-19):
  sigma[in2]:=1.5*10^(-19):
  r[d]:=10^(-6):
  m[d]:=0.002*(4/3)*Pi*(10^(-6))^3:
  T[e]:=3*11600:
  T[i1]:=0.05*11600:
  T[i2]:=0.1*11600:
  T[n1]:=0.01*11600:
  T[n2]:=0.02*11600:
  e0:=1.6*10^(-19):
  epsilon[0]:=8.85*10^(-12):
  u[d0]:=0.3:
  n[n1]:=0.133/(0.01*11600*1.38*10^(-23)):
  g:=9.8:
  n[n2]:=0.133/(0.02*11600*1.38*10^(-23)):

NULL

#
# Let's check the number of unknowns - remember that
# we only have four equations, because Eq2a, Eq2b seem
# to be either/or - but definitely not both simultaneouly!
#
# Hmmmmm, 6 unknowns
#
 `union`(indets~([Eq1, Eq2a, Eq3, Eq4],name)[]) minus {Pi};
 `union`(indets~([Eq1, Eq2b, Eq3, Eq4], name)[]) minus {Pi};

{alpha, delta[d], delta[i], phi[d0], u[i10], u[i20]}

 

{alpha, delta[d], delta[i], phi[d0], u[i10], u[i20]}

(1)

#
# Now OP is prepared to assign two values, for delta[i]
# and alpha. This *ought* to reduce the above system to
# four unknowns in four variable - which has a reasonable(?)
# chance of being solvable
#
# Just one problem: having inserted all of these parameters,
# just what is Eq1? It evaluates to 0=0, which is seriously,
# non-useful!! Means one is still left with three *meaningful*
# equations (either [Eq2a, Eq3, Eq4], or [Eq2b, Eq3, Eq4]
# in four unknowns - NOT SOLVABLE
#
  Eq1;

0. = 0

(2)

 

 

``


 

Download eqSys.mw

 

on how "sophisticated" you want to get!!

A couple of options are shown in the attached

 restart:
 M1:=Matrix( [ [1,2,3],
               [4,5,6]
             ]
           ):
 M2:=Matrix( [ [1,2,a],
               [4,b,6]
             ]
           ):

 testNum1:= m-> not member
                    ( false,
                      type~(m, numeric)
                    ):
 testNum1(M1);
 testNum1(M2);

true

 

false

(1)

 testNum2:= m-> seq
                ( seq
                  ( `if`
                    ( type
                      ( m[i,j],
                        numeric
                      ),
                      NULL,
                      cat("entry ", [i,j], " is not numeric")
                    ),
                    i=1..op([1,1],m)
                  ),
                  j=1..op([1,2],m)
                ):
 testNum2(M1);
 testNum2(M2);

"entry [2, 2] is not numeric", "entry [1, 3] is not numeric"

(2)

 


 

Download tesMat.mw

as in the attached.

Note that the coomand has seveeral options depending on exactly how you want the result to "look" - the attached just shows the basics

plots:-inequal( [x>0, y>1, y<3, y<1/x], x=-1..1, y=0..4);

 

 


 

Download pltineq.mw

 


 

restart:

EXPR := (s - omega__n*(-z + sqrt(-z^2 + 1)*I))*(s - omega__n*(-z - sqrt(-z^2 + 1)*I));
expand(EXPR);

(s-omega__n*(-z+I*(-z^2+1)^(1/2)))*(s-omega__n*(-z-I*(-z^2+1)^(1/2)))

 

2*s*z*omega__n+s^2+omega__n^2

(1)

 


 

Download short.mw

You need to set some options on the "fiilled" option, and make sure that it appears in the correct position in the list provided to the display() command. See the attached


 

restart;

sine :=   plot(sin(x), x=0..4*Pi, color=black,thickness=3):
s    :=   plot(sin(x), x=0..4*Pi, color=red, filled=true):
cosine := plot(cos(x), x=0..4*Pi, color=black,thickness=3):
c      := plot(cos(x), x=0..4*Pi, color=red, filled=true):

f := x -> if cos(x)>0 and sin(x)>0 then
              min(cos(x),sin(x))
          elif cos(x)<0 and sin(x)<0 then
              max(cos(x),sin(x))
          else 0
          end if:

b := plot(f, 0..4*Pi, filled=[true, color=white, transparency=0]):
plots:-display([b, sine, cosine, s, c]);

 

 

 


 

Download fillplot.mw

differentiate both sides and solve te resulting ODE  as in the attached

restart;

V1:=t->a+b*t+c*t^2: #source voltage
ode:=diff(V2(t),t)=(V1(t)-V2(t))/RC;
dsolve([ode, V2(0)=Vstart]);

diff(V2(t), t) = (c*t^2+b*t+a-V2(t))/RC

 

V2(t) = 2*RC^2*c-2*RC*c*t+c*t^2-RC*b+b*t+a+exp(-t/RC)*(-2*RC^2*c+RC*b+Vstart-a)

(1)

 


 

Download RC.mw

see the attached

NULL

printlevel:=2:

1

"servus"

2

"servus"

3

"servus"

"hei"

"hello"

4

"servus"

5

"servus"

6

NULL


 

Download printlev.mw

by preceding the necessary operators with the '%' character. Note that iv you actually then want the expression to evaluate, you will have to use the value() command.

See the attached


 

NULL

NULL

NULL

 

``

restart

randomize()

A := RandomTools:-Generate(integer(range = 2 .. 7))

B := RandomTools:-Generate(integer(range = 8 .. 13))

C := RandomTools:-Generate(integer(range = 2 .. 13))

F := B/A

Eq := F*(7*x/C-A)

(28/11)*x-8

(1)

sol:=F%*(7%/C%*x-A);
value(sol);

`%*`(4, `%*`(`%/`(7, 11), x)-2)

 

(28/11)*x-8

(2)

 

 

 

NULL


 

Download inert.mw

As in the attached.

Setting Digits:=30, and using the 'fulldigits' option in the fsolve() command is probably not strictly necessary, but *may* avoid rounding isuues in the floating point calculations


 

restart

eq1 := 1-0.7936507937e-3*r+a-b+2.710370855*10^(-8)*a^3*b*c-2.086985558*10^(-6)*a^2*b*c-2.683267146*10^(-6)*b*a^2*d-4.472111910*10^(-7)*a*b*n+8.944223819*10^(-7)*a*b^2*c+6.559097467*10^(-6)*b*c^2-3.279548734*10^(-6)*b*r+0.1377410468e-3*a*b*c-1.355185427*10^(-8)*a^3*n+0.6887052342e-4*b*a*d+5.962815879*10^(-7)*a^2*c^2-8.131112564*10^(-8)*a^4*d+3.279548734*10^(-6)*c*n+1.043492779*10^(-6)*a^2*n+6.260956674*10^(-6)*a^3*d-4.934230142*10^(-7)*a^2*r+6.887052341*10^(-6)*a*c+0.4040404040e-2*n+.9997474747*c-.9998917749*d+0.5903187721e-4*a*c*d-0.7575757576e-2*b*c+0.2410468320e-4*a*r-0.4132231405e-3*a^2*d-0.4591368227e-4*a*c^2+0.2272727273e-1*a*d+0.1147842057e-4*b*n-0.2295684114e-4*b^2*c-0.3030303030e-2*c*d+0.1298701299e-2*d^2-0.7575757576e-4*a*n+0.3030303030e-2*c^2 = 0

eq2 := 5.691778795*10^(-7)*a^4*d-4.173971115*10^(-6)*a^2*c^2-6.260956674*10^(-6)*a^2*n+3.453961099*10^(-6)*a^2*r+0.4040404040e-2*r+b+3.130478337*10^(-6)*a*b*n-6.260956673*10^(-6)*a*b^2*c+0.1252191335e-4*a^2*b*c+0.1878287002e-4*b*a^2*d-0.4132231405e-3*a*c*d-0.1666666666e-1*n-1.998484848*c+2.999242424*d-0.6887052340e-3*a*b*c-0.4132231405e-3*b*a*d+9.486297989*10^(-8)*a^3*n-1.897259598*10^(-7)*a^3*b*c+0.2066115702e-2*a^2*d-0.9090909092e-1*a*d+0.3030303030e-1*b*c-0.1446280992e-3*a*r+0.2754820936e-3*a*c^2-0.4820936639e-4*a*c-0.3756574004e-4*a^3*d+0.1377410468e-3*b^2*c+0.1818181818e-1*c*d-0.9090909093e-2*d^2-0.4591368227e-4*b*c^2-0.2295684114e-4*c*n+0.3925619835e-3*a*n-0.6887052342e-4*b*n+0.2295684114e-4*b*r-0.1515151515e-1*c^2 = 0

eq3 := -0.1252191335e-4*a^2*b*c+0.1878287002e-4*b*a^2*d+0.4040404040e-2*r+b-0.4132231405e-3*a*c*d+0.1666666666e-1*n+1.998484848*c+2.999242424*d+0.1446280992e-3*a*r+0.2066115702e-2*a^2*d+0.9090909092e-1*a*d-0.3030303030e-1*b*c-0.1377410468e-3*b^2*c-0.1818181818e-1*c*d-0.2754820936e-3*a*c^2-0.4820936639e-4*a*c-0.2295684114e-4*c*n+0.3925619835e-3*a*n+0.6887052342e-4*b*n+0.3756574004e-4*a^3*d+0.2295684114e-4*b*r-0.4591368227e-4*b*c^2+6.260956674*10^(-6)*a^2*n+3.453961099*10^(-6)*a^2*r+0.4132231405e-3*b*a*d+5.691778795*10^(-7)*a^4*d-4.173971115*10^(-6)*a^2*c^2+9.486297989*10^(-8)*a^3*n-0.6887052340e-3*a*b*c+3.130478337*10^(-6)*a*b*n-6.260956673*10^(-6)*a*b^2*c-1.897259598*10^(-7)*a^3*b*c-0.9090909093e-2*d^2-0.1515151515e-1*c^2 = 0

eq4 := -1+1.043492779*10^(-6)*a^2*n+6.260956674*10^(-6)*a^3*d+4.934230142*10^(-7)*a^2*r-6.887052341*10^(-6)*a*c+0.7936507937e-3*r+a+b-0.5903187721e-4*a*c*d+0.4040404040e-2*n+.9997474747*c+.9998917749*d-0.4591368227e-4*a*c^2+0.2272727273e-1*a*d-0.7575757576e-2*b*c+0.2410468320e-4*a*r+0.4132231405e-3*a^2*d+0.7575757576e-4*a*n+0.1147842057e-4*b*n-0.2295684114e-4*b^2*c-0.3030303030e-2*c*d-0.3030303030e-2*c^2+4.472111910*10^(-7)*a*b*n-8.944223819*10^(-7)*a*b^2*c-2.086985558*10^(-6)*a^2*b*c+2.683267146*10^(-6)*b*a^2*d-2.710370855*10^(-8)*a^3*b*c-0.1298701299e-2*d^2-3.279548734*10^(-6)*c*n+0.6887052342e-4*b*a*d+1.355185427*10^(-8)*a^3*n-6.559097467*10^(-6)*b*c^2+3.279548734*10^(-6)*b*r-0.1377410468e-3*a*b*c-5.962815879*10^(-7)*a^2*c^2+8.131112564*10^(-8)*a^4*d = 0

eq5 := -1.365909091*r-1.166666667*c+2.162878788*n-0.2892561983e-3*a*b*c-0.1666666666e-4*a^3*n+0.1000000000e-1*c*n-8.333333336*10^(-7)*a^4*r-0.3985537190e-1*a*n+0.8333333332e-3*a^2*n+0.1000000000e-1*d*r+0.1666666666e-4*a^3*c-0.8333333332e-3*a^2*c+0.4166666668e-4*a^3*r-0.8333333333e-2*c*r+0.4000000000e-1*a*c-0.2166666667e-2*a^2*r-0.4772727273e-1*a*d+0.7575757576e-2*b*c+0.6666666667e-1*a*r+0.1367768595e-2*a^2*d+1.100000000*d-0.1303030303e-1*c^2+0.6666666667e-3*a*c*r = 0

eq6 := 1.365909091*r-1.166666667*c+2.162878788*n+0.2892561983e-3*a*b*c+0.1666666666e-4*a^3*n-0.1000000000e-1*c*n+8.333333336*10^(-7)*a^4*r+0.3985537190e-1*a*n+0.8333333332e-3*a^2*n-0.1000000000e-1*d*r-0.1666666666e-4*a^3*c-0.8333333332e-3*a^2*c+0.4166666668e-4*a^3*r-0.8333333333e-2*c*r-0.4000000000e-1*a*c+0.2166666667e-2*a^2*r-0.4772727273e-1*a*d+0.7575757576e-2*b*c+0.6666666667e-1*a*r-0.1367768595e-2*a^2*d-1.100000000*d+0.1303030303e-1*c^2-0.6666666667e-3*a*c*r = 0

Digits := 30; interface(displayprecision = 10); sols := fsolve({eq1, eq2, eq3, eq4, eq5, eq6}, {a, b, c, d, n, r}, fulldigits)

{a = 0., b = 1.49912650488968266591327896509, c = 0., d = -.498538232677434994493493391119, n = 0., r = -.400024995807580723958535659599}

(1)

 

NULL

``


 

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Looks like some "order-of-calculation" issue. If you supply 'deps' as a set rather than a list, then both dsolve(sys) and dsolve(sys,deps) give the same answer. Check the attached


 

restart;
sys:=[ diff(x(t),t) = 2*x(t)-z(t),
       diff(y(t),t) = 2*y(t)+z(t),
       diff(z(t),t)=2*z(t),
       diff(w(t),t)=-z(t)+2*w(t)
     ];
deps:={x(t),y(t),z(t),w(t)};

dsolve(sys);

dsolve(sys,deps);

[diff(x(t), t) = 2*x(t)-z(t), diff(y(t), t) = 2*y(t)+z(t), diff(z(t), t) = 2*z(t), diff(w(t), t) = -z(t)+2*w(t)]

 

{w(t), x(t), y(t), z(t)}

 

{w(t) = (-_C4*t+_C3)*exp(2*t), x(t) = (-_C4*t+_C2)*exp(2*t), y(t) = (_C4*t+_C1)*exp(2*t), z(t) = _C4*exp(2*t)}

 

{w(t) = (-_C4*t+_C3)*exp(2*t), x(t) = (-_C4*t+_C2)*exp(2*t), y(t) = (_C4*t+_C1)*exp(2*t), z(t) = _C4*exp(2*t)}

(1)

 


 

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