tomleslie

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10 years, 254 days

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These are replies submitted by tomleslie

@coopersj 

Within the VectorCalculus package a "vector" is interpreted as a quantity which represents magnitude and direction in some "space". So an obvious(?) thing you might want to know is the length/magnitude of this "vector", because in ths context, length/magnitude means something

Within the LinearAlgebra package a "vector" is a 1-dimensional data container, which could represent (say) the number of cabbages you manage to produce in your garden in successive years. Do you really want to know the"length/magnitude" of this particular "vector"? What would it mean?

@Muhammad Usman 

This prblem scales very badly.

Just because you want a calculation to be performed more quickly does not mean that it can be performed more quickly. You can't always get what you want!!

Essentially you have two choices

  1. Come up with a much better algorithm for your calculation - this will require you to think!
  2. Since the calculations of the integrals appear to be independent, you can rewrite the code to parallelize the problem. Although the number of processors (eg say 8) on a single machine is probably not going to gain you enough to make your problem tractable. The only solution is then to purchase the Maple 'Grid' toolbox and spread the problem over a "gazillion" processors. Various cloud computing companies will provide the 'gazillion processors" - for a fee

@dim____ 

As you can see from the worksheet I originally posted - everythng works perfectly

So what exactly are you doing?

Two suggestions

  1. Specify precise Maple version
  2. Upload the "failing" Maple worksheet using the big green up-arrow in the Mapleprimes toolbae

this time (I think?!)

  restart;
  randomize():
  L:=[ [-1,0],[1,0],[0,-1],[0,1]];
  r:=rand(1..4):
  numpts:=10000:

[[-1, 0], [1, 0], [0, -1], [0, 1]]

(1)

  A:=Array(1..2, 0..numpts):
  A[1,0]:=[0,0]:
  A[2,0]:=[0,0]:
  for j from 1 by 1 to numpts do
      for i from 1 by 1 to 2 do
          A[i,j]:=A[i,j-1]+L[r()];
      od:
  od:
  plot( [ convert(A[1,..], list),
          convert(A[2,..], list)
        ],
        style=line,
        color=[red, blue],
        scaling=constrained
     );

 

 


 

Download rWalk2.mw

@tomleslie 

For a bonus point, spot the logical error in the above!!

@Felipe_123 

Nothing wrong with prevoiusly supplied methods, but I'd probably use the 'combinat' package to generate the original list of vectors, rather than  the 'StringTools' approach. - as in the attached
 

  restart;

  map[2]
  ( LinearAlgebra:-Modular:-Multiply,
    5,
    Vector[row]~( combinat:-permute
                            ( [0$3, 1$3,2$3],
                              3
                            )
                ),
    Matrix( [ [2,1,0,0],
              [0,2,1,0],
              [0,0,2,1]
            ]
          )
  )

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

(1)

 


Download cv2.mw

@Anthrazit 

I'd probably be using the StringTools:-SearchAll() command, which will return a sequence of all the starting indexes of the supplied pattern, from whihc it is trivial to select the starting index for any particular occurrence. For example to obtain the start index of the third occurrence of the pattern, one wold have

[StringTools:-SearchAll("aba", "abababababababababab" )][3];

@AHSAN 

accurate answers for this problem you have to use a high setting of DIgits - Set to 30 in the attached

DIsplaying 30 Digits can make the output look a litttle cluttered so you can separately control the amount of digits which are displayed. NB this affects display only: all calculations are done to the precision set by Digits.

See the atached


 

restart

Digits := 30; interface(displayprecision = 4)

4

(1)

P := -(9958.466892*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+2.439889255))*(0.261007e-4*k+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)^3-2.86369*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)^8-2.26*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+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+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+4.611637585*10^(-6)*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^3-0.1910578434e-3*lambda^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)^3-0.1557978257e-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+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)^6-4.610017127*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+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+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+0.2699913289e-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-2.723097*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+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)^8-2.26342*10^(-15)*k*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^7-0.158580e-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)*k*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-1.144560151*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)^4-1.150701960*10^(-6)*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^4+2.171377*10^(-10)*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^5+2.29*10^(-15)*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^7-4.54*10^(-11)*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^6-9.0*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)^6-3.054641904*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+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)^5-6.10984*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)+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)^8-4.555918*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)^3-2.26*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)^7-3.010540298*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+0.2875578036e-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)+0.2841557560e-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)+0.3073879707e-4*lambda+0.155261e-4*k*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-2.86369*10^(-16)*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^8-0.2642338092e-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)*k-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+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+0.1650484496e-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-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)^2-0.2863334102e-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)-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-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+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+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+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+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)^4-0.1674000840e-4*(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+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)^4-1.519459*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+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+1.899324*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+0.1981472958e-3*lambda^3-1.519459*10^(-15)*lambda*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^7-4.605558319*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)^3-6.11292*10^(-6)*lambda*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)+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)^7-9.3627*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)-0.1069489149e-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*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-1.445703114*10^(-10)*lambda*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^5+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+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)^4-4.559112439*10^(-6)*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)^5-8.931240077*10^(-6)*k*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)-2.16324*10^(-10)*k*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^5+4.49704*10^(-11)*k*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^6-2.86*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+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)^4-2.86*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+0.663330427e-4*lambda^5-1.14257*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+4.607967783*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)^3-0.835512256e-4*lambda^2+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)^8-0.2565264181e-4+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)^3-0.16e-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)*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^2-9.3922*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)-1.14560*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)^4-0.1069507987e-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+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)+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+2.29*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)*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^7-7.2*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)^5+7.19049*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)*k*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^5+6.110608393*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)+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+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)^6-2.687022860*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)*k*(7.056244720*lambda^5-20.62251164*lambda^4+21.33270654*lambda^3-8.876682482*lambda^2+1.340638018*lambda+.4398892548)^6+4.81577*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)^5-2.168014321*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+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+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)^6-7.637931745*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)^4-1.519459*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+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)-1.805990298*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)^3-4.82063*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+2.83*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)^8-1.519459*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)^7-2.26342*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)/((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);

 

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

-.329543248729246670859214244152, -.333666875089007736876317588707

(2)

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

-0.324354778471227278438260551979e-15

 

-0.303861053016358474098136276319e-13

(3)

 


 

Download resid2.mw

 

@Maple_lover1 

without going into the boring details of how you might want plot shading to be done ( see the options colorscheme, colorfunc and shading as mentioned beore), you basically want something as shown in the attached.

  restart;
  with(plots):
  with(plottools):
  display( [ plot3d
             ( sin(x*y),
               x=-3..3,
               y=-3..3,
               gridstyle=triangular,
               shading=zhue
             ),
             transform
             ( (x,y)->[x,y,-2] )
                      ( contourplot
                        ( sin(x*y),
                          x=-3..3,
                          y=-3..3,
                          contours=[-1/2,1/4,1/2,3/4],
                          filledregions=true,
                          coloring=[green,red]
                        )
             )
           ]
         );

 

 

Download mapPlot3.mw

You really only try to accept two simple statements: when it comes to plots

  1. If you can do it in Maple you can do it in Matlab
  2. If you can do it in Matlab you can do it in Maple

Now out of the thousands of plot possibilities available in both of these packages - will you ever be able to come with something in one package which cannot be replicated in the other - yeah, maybe? But good luck finding it!

@Maple_lover1 

that you play with the various plot3d options available, in paticular,

style
gridstyle
shading

( as well as color=colorscheme or color=colorfunc which will allow explicit shading based on coordinate values)

See the the additional execution group in the attached (which only scratches the surface of all the possibilities)

restart:
u:=1/(1. + exp(x))^2 + 1/(1. + exp(-5.*t))^2 - 0.2500000000 + x*(1/(1. + exp(1 - 5*t))^2 - 1./((1. + exp(-5*t))^2) + 0.1776705118 + 0.0415431679756514*piecewise(0. <= t and t <= 0.5000000000, 1.732050808, 0.) + 0.00922094377856479*piecewise(0. <= t and t <= 0.5000000000, 30.98386677*t - 7.745966692, 0.) + 0.0603742508215732*piecewise(0.5000000000 <= t and t <= 1., 1.732050808, 0.) - 0.00399645630498528*piecewise(0.5000000000 <= t and t <= 1., 30.98386677*t - 23.23790008, 0.)) + (-0.00243051684581302*piecewise(0. <= x and x <= 0.5000000000, 1.732050808, 0.) - 0.000809061198761621*piecewise(0. <= x and x <= 0.5000000000, 30.98386677*x - 7.745966692, 0.) - 0.0152377552205917*piecewise(0.5000000000 <= x and x <= 1., 1.732050808, 0.) - 0.00195593427342862*piecewise(0.5000000000 <= x and x <= 1., 30.98386677*x - 23.23790008, 0.))*piecewise(0. <= t and t <= 0.5000000000, 1.732050808, 0.) + (-0.000433590063316381*piecewise(0. <= x and x <= 0.5000000000, 1.732050808, 0.) - 0.000146112803263678*piecewise(0. <= x and x <= 0.5000000000, 30.98386677*x - 7.745966692, 0.) - 0.00319022339097685*piecewise(0.5000000000 <= x and x <= 1., 1.732050808, 0.) - 0.000477063086307787*piecewise(0.5000000000 <= x and x <= 1., 30.98386677*x - 23.23790008, 0.))*piecewise(0. <= t and t <= 0.5000000000, 30.98386677*t - 7.745966692, 0.) + (-0.00276114805649180*piecewise(0. <= x and x <= 0.5000000000, 1.732050808, 0.) - 0.000933166016624500*piecewise(0. <= x and x <= 0.5000000000, 30.98386677*x - 7.745966692, 0.) - 0.0207984584912892*piecewise(0.5000000000 <= x and x <= 1., 1.732050808, 0.) - 0.00314360556336114*piecewise(0.5000000000 <= x and x <= 1., 30.98386677*x - 23.23790008, 0.))*piecewise(0.5000000000 <= t and t <= 1., 1.732050808, 0.) + (0.000172746997599710*piecewise(0. <= x and x <= 0.5000000000, 1.732050808, 0.) + 0.0000586775450031145*piecewise(0. <= x and x <= 0.5000000000, 30.98386677*x - 7.745966692, 0.) + 0.00136190009033518*piecewise(0.5000000000 <= x and x <= 1., 1.732050808, 0.) + 0.000211410172315387*piecewise(0.5000000000 <= x and x <= 1., 30.98386677*x - 23.23790008, 0.))*piecewise(0.5000000000 <= t and t <= 1., 30.98386677*t - 23.23790008, 0.):

  plot3d( u,
          x=0..1,
          t=0..1,
          style=surface,
          axes=boxed,
          colorscheme=[yellow, red]
        );

 

plot3d( u,
        x=0..1,
        t=0..1,
        axes=normal,
        gridstyle=triangular,
        style=patch,
        shading=zhue
       );

 

 

 

 

 


 

Download mapPlot2.mw

 

@Maple_lover1 

the importatnt part of my original response, which is (original typos corrected)

It is not true that Matlab offers better plotting capability - so I wouldn.t bother anyway.

Now if you can explain exactly what plotting capabilyt exists within Matlab but not Maple I'd get interested. By the way I'm currently running Matlab R2020b and Maple 2020.1.1, although I do have several older versions of both packages if you think that "versions" are an issue.

From a plotting viewpoint - tell me what is worng with the following and I will fix it. NB the plot "renders" rather better in a Maple worksheet than it does on this site

restart:
u:=1/(1. + exp(x))^2 + 1/(1. + exp(-5.*t))^2 - 0.2500000000 + x*(1/(1. + exp(1 - 5*t))^2 - 1./((1. + exp(-5*t))^2) + 0.1776705118 + 0.0415431679756514*piecewise(0. <= t and t <= 0.5000000000, 1.732050808, 0.) + 0.00922094377856479*piecewise(0. <= t and t <= 0.5000000000, 30.98386677*t - 7.745966692, 0.) + 0.0603742508215732*piecewise(0.5000000000 <= t and t <= 1., 1.732050808, 0.) - 0.00399645630498528*piecewise(0.5000000000 <= t and t <= 1., 30.98386677*t - 23.23790008, 0.)) + (-0.00243051684581302*piecewise(0. <= x and x <= 0.5000000000, 1.732050808, 0.) - 0.000809061198761621*piecewise(0. <= x and x <= 0.5000000000, 30.98386677*x - 7.745966692, 0.) - 0.0152377552205917*piecewise(0.5000000000 <= x and x <= 1., 1.732050808, 0.) - 0.00195593427342862*piecewise(0.5000000000 <= x and x <= 1., 30.98386677*x - 23.23790008, 0.))*piecewise(0. <= t and t <= 0.5000000000, 1.732050808, 0.) + (-0.000433590063316381*piecewise(0. <= x and x <= 0.5000000000, 1.732050808, 0.) - 0.000146112803263678*piecewise(0. <= x and x <= 0.5000000000, 30.98386677*x - 7.745966692, 0.) - 0.00319022339097685*piecewise(0.5000000000 <= x and x <= 1., 1.732050808, 0.) - 0.000477063086307787*piecewise(0.5000000000 <= x and x <= 1., 30.98386677*x - 23.23790008, 0.))*piecewise(0. <= t and t <= 0.5000000000, 30.98386677*t - 7.745966692, 0.) + (-0.00276114805649180*piecewise(0. <= x and x <= 0.5000000000, 1.732050808, 0.) - 0.000933166016624500*piecewise(0. <= x and x <= 0.5000000000, 30.98386677*x - 7.745966692, 0.) - 0.0207984584912892*piecewise(0.5000000000 <= x and x <= 1., 1.732050808, 0.) - 0.00314360556336114*piecewise(0.5000000000 <= x and x <= 1., 30.98386677*x - 23.23790008, 0.))*piecewise(0.5000000000 <= t and t <= 1., 1.732050808, 0.) + (0.000172746997599710*piecewise(0. <= x and x <= 0.5000000000, 1.732050808, 0.) + 0.0000586775450031145*piecewise(0. <= x and x <= 0.5000000000, 30.98386677*x - 7.745966692, 0.) + 0.00136190009033518*piecewise(0.5000000000 <= x and x <= 1., 1.732050808, 0.) + 0.000211410172315387*piecewise(0.5000000000 <= x and x <= 1., 30.98386677*x - 23.23790008, 0.))*piecewise(0.5000000000 <= t and t <= 1., 30.98386677*t - 23.23790008, 0.):

  plot3d( u,
          x=0..1,
          t=0..1,
          style=surface,
          axes=boxed,
          colorscheme=[yellow, red]
        );

 

 

Download mapPlot.mw

@raj2018 

  1. I should probably have use fsolve() in my previous sheet, since you are only really interested in a numerical solution
  2. however even using fsolve() with guesses for the expected ranges of the unknowns - still no solution
  3. tried the DirectSearch() optimiser package ( a free add-on from the Maple Application centre). This *sometimes* works when the built-in fsolve() fails. This does provide "solutions" for a range of values for delta[d] - see the attched
  4. But are these solutions *plausible*?. DirectSearch() will just return the "best solution" it can find, which may or may not be the "actual" solution!!)

Some observations about the solutions found by by DirectSearch() - first of all the *form* of the ouput for each value of delta[d] is

  [  mean square residual error,  residual error in each equation,   values,    number of iterations taken to obtain solution]

  1. For delta[d] from 1e-04 to 1e-03, the values of u[i10] and u[i20] don't vary much at all, being around 3 and 1.5 respectively
  2. The value of phi[d0] varies by several orders of magnitude from O(10^-32) to O(10^-24)
  3. When the value of phi[d0] is O(10^-32), then the mean square residual is "pretty good", ie < O(10^-6), When the value of phi[d0] is O(10^-24), then the mean square residual is bad - up to O(10^7).
  4. The biggest contribution to the mean square residual always occurs from the error in solving the third equation in the system - from which one can conclude that this equation is numerically pretty unstable, with respect to the variable phi[d0]

What would I do next???

  1. Are the values obtained for the three unknowns vaguely plausible ie is phi[d0]~10^-30, u[i10]~2, and u[i20]~1.5 a "believable" solution
  2. If the answer to (1) above is "No" - then it means that you have some idea what the solution should be - so appropriately adjust the constraints on the variables in the DirectSearch() command (or possibly even fsolve()?) in order to assist the solution process
  3. If this system of equations represents a "physical situation" rather than a mathematical abstraction, then consider whether an appropriate choice of 'units' for various parameters/variables might reduce numerical instabilities. Any equation system which simultaneously contains coefficients/parameters of O(10^-48) and O(10^36) is just asking for trouble
  4. If (3) above is impossible then consider raisin the setting of Digits, wihc will force numerical calculations to be performed more accurately - althugh if the setting is high enough that hardware floats cannot be used (Digits=15, roughly) then computation times will increase substantially

See the attached - Note that you will not be able to re-execute this worksheet unless you first install the DirectSearch() add-on
 

restart;

Eq1:=-2.356739746*10^(-48)*(4.682096432*10^11*exp(phi[d0])*u[i10]*u[i20]-7.21774261*10^8*u[i10]^2*u[i20]-1.141225310*10^9*u[i10]*u[i20]^2+2.282450620*10^9*phi[d0]*u[i10]+1.443548522*10^9*phi[d0]*u[i20])/(exp(phi[d0])*phi[d0]*u[i10]*u[i20]=delta[d]);

Eq2:=1.839080460*10^(-38)*(8.117630990*10^9*u[i10]^3*u[i20]-1.217644649*10^9*u[i10]*u[i20]^3-3.988316460*10^9*u[i10]+2.490971436*10^10*u[i20])/(phi[d0]*(6.6471941*10^7*u[i10]-4.15161906*10^8*u[i20]))=delta[d]:


Eq3:=3.321295248*10^(-13)*(1.359375000*10^36*delta[d]*phi[d0]+1.5)/u[i10]+1.329438820*10^(-14)*(1.359375000*10^36*delta[d]*phi[d0]+1.5)/u[i20]-(-1.359375000*10^36*delta[d]*phi[d0]-1.5+1.510416667*10^37*delta[d]*phi[d0]^2)*(8.117630990*10^(-15)*u[i10]^2+1.660647624*10^(-14)*(1.359375000*10^36*delta[d]*phi[d0]+1.5)/u[i10])-1.359375000*10^36*delta[d]*phi[d0]*(-6.189239034*10^(-29)+3.634239206*10^(-25)*u[i10]*sqrt(u[i10]^2+2.547770701)*(1-2*phi[d0]/(u[i10]^2+0.4246284503e-1))^1.0+1.395213672*10^(-54)*u[i10]*sqrt(u[i10]^2+2.547770701)*phi[d0]^2*ln((phi[d0]^2/(1000000000000*(u[i10]^2+0.4246284503e-1)^2)+2.005078125*10^14/(1.275000000+2.265625000*10^34*delta[d]*phi[d0]))/(phi[d0]^2/(1000000000000*(u[i10]^2+0.4246284503e-1)^2)+(1/1000000000000)*(1-2*phi[d0]/(u[i10]^2+0.4246284503e-1))^1.0))/(u[i10]^2+0.4246284503e-1)^2+1.817119603*10^(-25)*u[i20]*sqrt(u[i20]^2+2.547770701)*(1-2*phi[d0]/(u[i20]^2+0.8492569001e-1))^1.0+6.976068361*10^(-56)*u[i20]*sqrt(u[i20]^2+2.547770701)*phi[d0]^2*ln((phi[d0]^2/(1000000000000*(u[i20]^2+0.8492569001e-1)^2)+2.005078125*10^14/(1.275000000+2.265625000*10^34*delta[d]*phi[d0]))/(phi[d0]^2/(1000000000000*(u[i20]^2+0.8492569001e-1)^2)+(1/1000000000000)*(1-2*phi[d0]/(u[i20]^2+0.8492569001e-1))^1.0))/(u[i20]^2+0.8492569001e-1)^2)+6.235395017*10^(-20)*delta[d]*(7.217742610*10^14*u[i10]*(1-2*phi[d0]/u[i10]^2)+1.141225310*10^15*u[i20]*(1-2*phi[d0]/u[i20]^2)-2.207161425*10^17*sqrt(2)*(1.359375000*10^36*delta[d]*phi[d0]+1.5)*exp(phi[d0]))= 0;

sys:=[ Eq1,Eq2,Eq3]:
 

-0.2356739746e-47*(0.4682096432e12*exp(phi[d0])*u[i10]*u[i20]-721774261.0*u[i10]^2*u[i20]-1141225310.*u[i10]*u[i20]^2+2282450620.*phi[d0]*u[i10]+1443548522.*phi[d0]*u[i20])/(exp(phi[d0])*phi[d0]*u[i10]*u[i20]) = -0.2356739746e-47*(0.4682096432e12*exp(phi[d0])*u[i10]*u[i20]-721774261.0*u[i10]^2*u[i20]-1141225310.*u[i10]*u[i20]^2+2282450620.*phi[d0]*u[i10]+1443548522.*phi[d0]*u[i20])/delta[d]

 

0.3321295248e-12*(0.1359375000e37*delta[d]*phi[d0]+1.5)/u[i10]+0.1329438820e-13*(0.1359375000e37*delta[d]*phi[d0]+1.5)/u[i20]-(-0.1359375000e37*delta[d]*phi[d0]-1.5+0.1510416667e38*delta[d]*phi[d0]^2)*(0.8117630990e-14*u[i10]^2+0.1660647624e-13*(0.1359375000e37*delta[d]*phi[d0]+1.5)/u[i10])-0.1359375000e37*delta[d]*phi[d0]*(-0.6189239034e-28+0.3634239206e-24*u[i10]*(u[i10]^2+2.547770701)^(1/2)*(1-2*phi[d0]/(u[i10]^2+0.4246284503e-1))^1.0+0.1395213672e-53*u[i10]*(u[i10]^2+2.547770701)^(1/2)*phi[d0]^2*ln(((1/1000000000000)*phi[d0]^2/(u[i10]^2+0.4246284503e-1)^2+0.2005078125e15/(1.275000000+0.2265625000e35*delta[d]*phi[d0]))/((1/1000000000000)*phi[d0]^2/(u[i10]^2+0.4246284503e-1)^2+(1/1000000000000)*(1-2*phi[d0]/(u[i10]^2+0.4246284503e-1))^1.0))/(u[i10]^2+0.4246284503e-1)^2+0.1817119603e-24*u[i20]*(u[i20]^2+2.547770701)^(1/2)*(1-2*phi[d0]/(u[i20]^2+0.8492569001e-1))^1.0+0.6976068361e-55*u[i20]*(u[i20]^2+2.547770701)^(1/2)*phi[d0]^2*ln(((1/1000000000000)*phi[d0]^2/(u[i20]^2+0.8492569001e-1)^2+0.2005078125e15/(1.275000000+0.2265625000e35*delta[d]*phi[d0]))/((1/1000000000000)*phi[d0]^2/(u[i20]^2+0.8492569001e-1)^2+(1/1000000000000)*(1-2*phi[d0]/(u[i20]^2+0.8492569001e-1))^1.0))/(u[i20]^2+0.8492569001e-1)^2)+0.6235395017e-19*delta[d]*(0.7217742610e15*u[i10]*(1-2*phi[d0]/u[i10]^2)+0.1141225310e16*u[i20]*(1-2*phi[d0]/u[i20]^2)-0.2207161425e18*2^(1/2)*(0.1359375000e37*delta[d]*phi[d0]+1.5)*exp(phi[d0])) = 0

(1)

#
# Use fsolve() to try for a numerical solution, using a value
# for delta[d] somewhere in the middle of the required range
#
# Apply ranges to the remaining unknown variables to assist the
# calculation. NB these ranges are complete GUESSWORK on my part.
# Any better knowledge of expected ranges of answers would be
# very useful and *may* allow an answer to be obtained
#
# Hmmmm - still no solution
#
    fsolve( eval(sys, delta[d]=1e-03),
            { phi[d0]=0..10, u[i10]=0..10, u[i20]=0..10}
          )

fsolve([-0.2356739746e-47*(0.4682096432e12*exp(phi[d0])*u[i10]*u[i20]-721774261.0*u[i10]^2*u[i20]-1141225310.*u[i10]*u[i20]^2+2282450620.*phi[d0]*u[i10]+1443548522.*phi[d0]*u[i20])/(exp(phi[d0])*phi[d0]*u[i10]*u[i20]) = -0.1103448276e-32*exp(phi[d0])*u[i10]*u[i20]+0.1701034089e-35*u[i10]^2*u[i20]+0.2689571047e-35*u[i10]*u[i20]^2-0.5379142094e-35*phi[d0]*u[i10]-0.3402068177e-35*phi[d0]*u[i20], 0.1839080460e-37*(8117630990.*u[i10]^3*u[i20]-1217644649.*u[i10]*u[i20]^3-3988316460.*u[i10]+0.2490971436e11*u[i20])/(phi[d0]*(66471941.00*u[i10]-415161906.0*u[i20])) = 0.1e-2, 0.3321295248e-12*(0.1359375000e34*phi[d0]+1.5)/u[i10]+0.1329438820e-13*(0.1359375000e34*phi[d0]+1.5)/u[i20]-(-0.1359375000e34*phi[d0]-1.5+0.1510416667e35*phi[d0]^2)*(0.8117630990e-14*u[i10]^2+0.1660647624e-13*(0.1359375000e34*phi[d0]+1.5)/u[i10])-0.1359375000e34*phi[d0]*(-0.6189239034e-28+0.3634239206e-24*u[i10]*(u[i10]^2+2.547770701)^(1/2)*(1-2*phi[d0]/(u[i10]^2+0.4246284503e-1))^1.0+0.1395213672e-53*u[i10]*(u[i10]^2+2.547770701)^(1/2)*phi[d0]^2*ln(((1/1000000000000)*phi[d0]^2/(u[i10]^2+0.4246284503e-1)^2+0.2005078125e15/(1.275000000+0.2265625000e32*phi[d0]))/((1/1000000000000)*phi[d0]^2/(u[i10]^2+0.4246284503e-1)^2+(1/1000000000000)*(1-2*phi[d0]/(u[i10]^2+0.4246284503e-1))^1.0))/(u[i10]^2+0.4246284503e-1)^2+0.1817119603e-24*u[i20]*(u[i20]^2+2.547770701)^(1/2)*(1-2*phi[d0]/(u[i20]^2+0.8492569001e-1))^1.0+0.6976068361e-55*u[i20]*(u[i20]^2+2.547770701)^(1/2)*phi[d0]^2*ln(((1/1000000000000)*phi[d0]^2/(u[i20]^2+0.8492569001e-1)^2+0.2005078125e15/(1.275000000+0.2265625000e32*phi[d0]))/((1/1000000000000)*phi[d0]^2/(u[i20]^2+0.8492569001e-1)^2+(1/1000000000000)*(1-2*phi[d0]/(u[i20]^2+0.8492569001e-1))^1.0))/(u[i20]^2+0.8492569001e-1)^2)+0.4500547630e-7*u[i10]*(1-2*phi[d0]/u[i10]^2)+0.7115990611e-7*u[i20]*(1-2*phi[d0]/u[i20]^2)-0.1376252335e-4*2^(1/2)*(0.1359375000e34*phi[d0]+1.5)*exp(phi[d0]) = 0], {phi[d0], u[i10], u[i20]}, {phi[d0] = 0 .. 10, u[i10] = 0 .. 10, u[i20] = 0 .. 10})

(2)

#
# Use the DirectSearch add-on optimisation package with the
# same constraints to determine whether solutions can be obtained
# for various values of delta[d] across the required range
#
  seq( [ DirectSearch:-SolveEquations
                       ( eval(sys, delta[d]=j),
                         [ phi[d0]=0..10, u[i10]=0..10, u[i20]=0..10 ]
                       )
       ],
       j= 1e-04..1e-03, 1e-04
     );

[[3.19460803484165*10^(-8), Vector(3, {(1) = -0.2487088061e-5, (2) = -0.133061047429682e-3, (3) = -0.119309062515421e-3}), [phi[d0] = 4.39999368528266*10^(-31), u[i10] = 2.98360668673353, u[i20] = 1.50800349885015], 771]], [[379008.267349024, Vector(3, {(1) = -0.6500013806e-12, (2) = -0.200000008640510e-3, (3) = -615.636473374494}), [phi[d0] = 1.68356130893318*10^(-24), u[i10] = 2.98360623089539, u[i20] = 1.50800427090504], 494]], [[2.59642027567093*10^(-7), Vector(3, {(1) = -0.101865773046122e-4, (2) = -0.435410816534470e-3, (3) = -0.264491364801759e-3}), [phi[d0] = 1.07427366636149*10^(-31), u[i10] = 2.98360616776824, u[i20] = 1.50800438081475], 773]], [[4.97583555741889*10^(-7), Vector(3, {(1) = -0.104446673180020e-4, (2) = -0.538841500887854e-3, (3) = -0.455109109541250e-3}), [phi[d0] = 1.04772812768309*10^(-31), u[i10] = 2.98360563725389, u[i20] = 1.50800528660184], 828]], [[1.22611706447686*10^(-6), Vector(3, {(1) = -0.445466164536864e-4, (2) = -0.109216128236589e-2, (3) = -0.176964393990126e-3}), [phi[d0] = 2.45656631825036*10^(-32), u[i10] = 2.98360646440409, u[i20] = 1.50800387665753], 820]], [[1.27212378604264*10^(-6), Vector(3, {(1) = -0.129541832316612e-4, (2) = -0.772200695800547e-3, (3) = -0.821986654748474e-3}), [phi[d0] = 8.44759684568413*10^(-32), u[i10] = 2.98360588229276, u[i20] = 1.50800486182296], 771]], [[1.50550033690128*10^(-6), Vector(3, {(1) = -0.332753272328057e-4, (2) = -0.114233248967109e-2, (3) = -0.446620165846419e-3}), [phi[d0] = 3.28867443728915*10^(-32), u[i10] = 2.98360814940436, u[i20] = 1.50800098608150], 811]], [[7.95992034093232*10^6, Vector(3, {(1) = -0.4572396327e-12, (2) = -0.800000006078140e-3, (3) = -2821.33307869377}), [phi[d0] = 2.39331217921800*10^(-24), u[i10] = 2.98360855438924, u[i20] = 1.50800028790066], 601]], [[2.34387556435520*10^(-6), Vector(3, {(1) = -0.295772909747718e-4, (2) = -0.129317346188895e-2, (3) = -0.818964679140646e-3}), [phi[d0] = 3.69985601029048*10^(-32), u[i10] = 2.98360717829695, u[i20] = 1.50800264816345], 899]], [[3.27345103272978*10^(-6), Vector(3, {(1) = -0.540071925813580e-4, (2) = -0.171792077937664e-2, (3) = -0.565050839894256e-3}), [phi[d0] = 2.02624339828116*10^(-32), u[i10] = 2.98360595919939, u[i20] = 1.50800473331530], 912]]

(3)

 

``


 

Download solveSys2.mw

@raj2018 

If I had three equations in three unknowns (x,y,z) and a "parameter " such as "tau", and I wanted to obtain values for (x,y,z) as tau varied over a substantial range (say 10^-2.. 10^3), I'd probably be using a semilogplot().

Something like the attached "toy" example

sys:=[ x + y + z = 2+tau,
       2*x + y = 3+tau,
       z=1+tau
     ];
plots:-semilogplot
       ( rhs~( solve
               ( eval
                 ( sys,
                   tau=t
                 ),
                 [x,y,z]
              )[]),
         t=1e-06..1e6
       );

[x+y+z = 2+tau, 2*x+y = 3+tau, z = 1+tau]

 

 

 

Download solveSys.mw

of why you would choose to set the options

minstep=500,maxstep=1000

when the independent variable range in which you are interesed appears to be 0..10

@raj2018 

since I can't read the paper (which you don't provide)

I can only state the mathematically obvious - that no-one can obtain numerical solutions from three equations in four unknowns

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