Currently I am using maple as a backend computer algebra system that is doing the heavy lifting for an application written in python. 

The procedure I currently use is:

app.py
```
from subprocess import run
my_input = 1233
cmd = 'cmaple -q -c input:={}: backend.mpl'.format(my_input) # Command Line call to cmaple
output = run(cmd, capture_output=True)
stdout = str(output.stdout) # A bytes object i.e. b'            1234\n\r\n\r'
# Do some string operations on stdout to get the output I want
output = stdout[-12:-8] # '1234'
```

backend.mpl
```
#do something with my_input
output := my_input+1:
#print to console to be recovered later
print(output);
quit:
```
This setup works reasonable well so long as I know exactly what format the ```output``` is going to be in but is not effective when I want to access more than one ```output``` or when the required ```output``` is a float.

I realise that I could likely save these variables to a file (a .csv say) and load them into ```app.py``` that way, but the dream is that there would be some way to directly access the variables in ```backend.mpl``` from within memory, an analogue of the ```Pipe``` framework in python for example?
 

Here is my try:

with(plots):
epsilon:=5*Pi/2:
gammaa:=0.4:
gammao:=0.1:
gammab:=0.002:
omegab:=100:
X:=60:
Omega:=6*Pi:
g:=10:
sigmag:=5*gammaa:
a:=1/(sigmag*sqrt(2*Pi)):
for deltao from 0 to 4 do
D7:=evalf(a*int(g*Omega*(gammao/2-I*Delta)*exp(-0.5*((Delta-deltao)/sigmag)^2)/(gammao^2/4+Delta^2),Delta=-infinity..infinity)):
D8:=evalf(0.5*a*int(g^2*gammao*exp(-0.5*((Delta-deltao)/sigmag)^2)/(gammao^2/4+Delta^2), Delta=-infinity..infinity)):
D9:=evalf(a*int(g^2*Delta*exp(-0.5*((Delta-deltao)/sigmag)^2)/(gammao^2/4+Delta^2), Delta=-infinity..infinity)):
b1:=deltao-(2*X^2*omegab*Y^2)/(omegab^2+gammab^2)-D9:
f:=epsilon-D7=Y*(gammaa+D8+I*(b1)):
P1:=implicitplot(f,Y^2=0..10,delta0=0..1,numpoints=1000,axes=boxed,thickness=2,color=black,font=[1,1,20],tickmarks=[4, 3],linestyle=1);
end do:

display(P1);

The function (f)  is an implicit function of Y^2

so my code above is an example to plot Y^2 against deltao

note that Y is complex

I appreciate valueble comments.

Hello guys, 

im not an expert of maplesim, I'm working on one of the default quarter car models (first pic).

I set a probe to measure the instant contact force between the tire and the post, but the graph shows that the force reaches both posite and negative values (as if the post were pulling back down the tire, is that right?)

What l have to do in order to see the real contact force graph? i just want to see the real positive value or 0. 

I have a variable that can take multiple values since it is the RootOf solution of a polynomial. Based on the setup of the problem, the variable should be between 0 and 1, and therefore should be only one of the four values spitted out by the allvalues of the RootOf function. How can I make Maple understand that this variable should only take one of the four values that is the outcome of allvalues of the RootOf function? Can I define this variable to be between 0 and 1 upfront? If not, how do you make Maple "pick" only one value out of multiple outcomes of allvalues evaluation?

Dear friends, please I would like to ask for your help with the following problem: 

I need to invoke the number of elements of an Array working with parallel programming in the task programming model. I've tried to used the command rtable_num_elems as it is contained in the thread safe functions lists. However, Maple does not recognize it as I obtain the error "Bad index into array". Using the same code, I've substituted the array for a list and rtable_num_elems for nops and the code works perfectly. What could I be doing wrong? I need to use arrays given the extension of the data I'm handling. 

Many thanks for your kind help. 

I have this problem, that maple wont isolate for x_1. I want to automate the prosses of any funktion, but how come it not work?

Hope you can help 

Hi,

What could be an easy solution to get 2-d, 3-d etc derivatives (∂^2 V)/(∂x^2) ..,

subject to the conditions

1) 1/V(x,y) (∂V/∂x)=α(x,y)

2) -V(x,y)/diff(V(x,y),y)=beta(x,y)

More or less easy with (1), a bit tricky with (2) but is there any more or less simple and common (universal) solution(s) both for (1)-(2) and similar? I mean, find derivatives (2-d, 3-d, ...) with known first derivative.

Best

How to find the coefficient of x, x^2,and xy from the following polynomial

F:-2*x+6*y+4*x^2+12*x*y-5*y^2

coeff(F, x) gives an answer 12*y+2 but I want it as 2 etc

coeff(F, x*y) gives an error 

Error, invalid input: coeff received x*y, which is not valid for its 2nd argument, x
 

Dear maple users,

Greetings.

How to plot a contour for the below-mentioned function.

f(x):=-0.09465519086 x^3+0.02711194463 x^2+0.3862193003 x-0.00030060626-0.0003613678673 x^6-0.001538973646 x^5-0.01937304057 x^4-3.822344860 10^(-8) x^8-0.000007297718101 x^7

Anyone have any thoughts on how I can combine these two terms? (see screen shot)  The error message implies the units are somehow not really the same but there is no help page for this error.  Any insight would be appreciated.  Thanks.

Here is the file:  units_issue.mw

I want to creat a two dimisional plot of a circle.   Every time I try it gives me a parabola.

I am trying a multistart local search over a multimodal function. I need to locate around 700 local minima where the dimension of the function is very high. It will be really helpful if the computational time can be reduced. Thank you.

opt.mw

Clutch_Modell.mw

I must program exc set 3 task 2(i) and 2(ii)

Perhaps too much asked here on the mapleprime forum to come up with the solutions for this programming task ?

I did already some investigation how the code roughly works 
 

Its a graphical programming task to let show the tread-riser outlines for a right -hand rule and mid-pointrule in a graph   

exc_set_3_task_1_a_b.mw

blz_61_exc_set_3.pdf

blz_62.pdf  

This is my code:

NEUZMinus:= proc(Unten, Oben, f,G,Liste,n)::real;
  #Unten:= Untere Intervallgrenze; Oben:= Obere Intervallgrenze; f:= zu integrierende Funktion;
  #G:= Gewicht; n:= Hinzuzufügende Knoten;
  local i;
  with(LinearAlgebra);     
  with(ListTools);
  Basenwechsel:=proc(Dividend, m);
 
  print(Anfang,Dividend,p[m]);
  Koeffizient:=quo(Dividend, p[m],x);

  Rest:=rem(Dividend, p[m],x);
 
  if m=0 then
    Basenwechsel:=[Koeffizient];
  else

    Basenwechsel:=[Koeffizient,op(Basenwechsel(Rest,m-1))];
   
  end if;
 
  end proc;
p[-1]:=0;
p[0]:=1;
for i from 1 to (numelems(Liste)+n)*2 do
  p[i]:=(x^i-add(int(x^i*p[j]*diff(G,x),x=Unten..Oben)*p[j]/int(p[j]^2*diff(G,x),x=Unten..Oben),j=0..i-1));
  print(p[i]);
c[i-1]:=coeff(p[i],x,i)/coeff(p[i-1],x,i-1);
d[i-1]:=(coeff(p[i],x,(i-1))-coeff(p[i-1],x,(i-2)))/coeff(p[i-1],x,(i-1));
if i <> 1 then
  e[i-1]:=coeff(p[i]-(c[i-1]*x+d[i-1])*p[i-1],x,i-2)/coeff(p[i-2],x,i-2);
else
  e[i-1]:=0;
end if;
end do;
print(Liste[1],numelems(Liste));
Hn:=mul(x-Liste[i],i=1..numelems(Liste));
print(Hn);
 Koeffizienten:=Reverse(Basenwechsel(Hn,n)); #!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
print(Koeffizienten,HIER);

print(c,d,e);
a[0][0]:=1;
a[1][0]:=x;
a[1][1]:=-e[1]*c[0]/c[1]+(d[0]-d[1]*c[0]/c[1])*x+c[0]/c[1]*x^2;
for s from 2 to numelems(Liste)+n do
  a[s][0]:=x^s;
  a[s][1]:=-e[s]*c[0]/c[s]*x^(s-1)+(d[0]-d[s]*c[0]/c[s])*x^s+c[0]/c[s]*x^(s+1);
    print (coeff(a[s][1],x,s),as1s);
end do;
for s from 2 to numelems(Liste)+n do
  for j from 2 to s do
    
      print(c[j-1]*sum(coeff(a[s][j-1],x,k-1)/c[k-1]*x^k,k=abs(s-j)+2..s+j));  print(sum((d[j-1]-c[j-1]*d[k]/c[k])*coeff(a[s][j-1],x,k)*x^k,k=abs(s-j)+1..s+j-1));  print(c[j-1]*sum(e[k+1]*coeff(a[s][j-1],x,k+1)/c[k+1]*x^k,k=abs(s-j)..s+j-2));print(e[j-1]*sum(coeff(a[s][j-2],x,k)*x^k,k=s-j+2..s+j-2));

     a[s][j]:=c[j-1]*sum(coeff(a[s][j-1],x,k-1)/c[k-1]*x^k,k=abs(s-j)+2..s+j)+sum((d[j-1]-c[j-1]*d[k]/c[k])*coeff(a[s][j-1],x,k)*x^k,k=abs(s-j)+1..s+j-1)-c[j-1]*sum(e[k+1]*coeff(a[s][j-1],x,k+1)/c[k+1]*x^k,k=abs(s-j)..s+j-2)+e[j-1]*sum(coeff(a[s][j-2],x,k)*x^k,k=abs(s-j)+2..s+j-2);

      
   
    
  end do;
end do;
for s from 0 to numelems(Liste)-1 do
  for j from 0 to s do
    print(a[s][j], Polynom[s][j]);
  end do;
end do;
M:=Matrix(n,n);
V:=Vector(n);
 
  for s from 0 to n-1 do
    for j from 0 to s do
      M(s+1,j+1):=sum(coeff(a[s][j],x,k)*Koeffizienten[k+1],k=0..n);
      if s<>j then
        M(j+1,s+1):=M(s+1,j+1);
      end if;
      print(M,1);
    end do;
    print(testb1);print(coeff(a[n][s],x,2));print(Koeffizienten[3]);print(testb2);
    V(s+1):=-sum(coeff(a[n][s],x,k)*Koeffizienten[k+1],k=0..n);
    
    print(M,V);
  end do;
print(M,V);
K:=LinearSolve(M,V);
K(n+1):=1;
print(K);

print(test2,coeff(a[max(3,2)][min(1,2)],x,2));
print(Koeffizienten[3]);
for l from 0 to n do
  for m from 0 to numelems(Liste)do
    print(Koeffizienten[m+1]*coeff(a[7][l],x,m),a[7][l],m,Koeff,Koeffizienten[m+1])
  end do;
end do;
for l from 0 to n do
  print(K(l+1)*add(Koeffizienten[m+1]*coeff(a[max(k,l)][min(k,l)],x,m),m=0..numelems(Liste)));
end do;
    nNeu:=add(p[k]*add(K(l+1)*add(Koeffizienten[m+1]*coeff(a[max(k,l)][min(k,l)],x,m),m=0..numelems(Liste)),l=0..n),k=numelems(Liste)..numelems(Liste)+n);
fsolve(nNeu);
Em:=add(p[i]*K[i+1],i=0..n);
Hnm:=Hn*Em;
KnotenHnm:=fsolve(Hnm);
print(Hn,alt,Em,neu,Hnm);
print(Testergebnis,nNeu);
print(fsolve(Hnm),fsolve(nNeu));
KoeffizientenHnm:=Reverse(Basenwechsel(Hnm,n+numelems(Liste)));  #!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
print(KoeffizientenHnm);
h0:=int(diff(G,x),x=Unten..Oben);
b[n+numelems(Liste)+2]:=0;
b[n+numelems(Liste)+1]:=0;
  for i from 1 to n+numelems(Liste) do
    for j from n+numelems(Liste) by -1 to 1 do
      print(test21);
      b[j]:=KoeffizientenHnm[j]+(d[j]+KnotenHnm[i]*c[j])*b[j+1]+e[j+1]*b[j+2];
  print(test22);
    end do;
    print(test23);
    gxi:=quo(Hnm,x-KnotenHnm[i],x);
   print(test24);
    Gewichte[i]:=c[1]*b[2]*h0/gxi(i);
   
    Delta[i]:=c[1]*b[2];
  end do;
print(KnotenHnm);
print(Gewichte);
sum(Knoten[k]*Gewichte[k],k=1..n+numelems(Liste));
end proc

With the first use of the subprocedure Basenwechsel, everything works fine. With the input

NEUZMinus(-1,1,x,x,[-sqrt(3/5),0,sqrt(3/5)],4)

I get the result [0,0,0,1,0] correctly.

The following time I use it, the polynomial is different, and m is 7 in that case, so the list should have 8 entries, it just returns the same [0,0,0,1,0] again, however. Changing the polynomial in the first application to say 5*Hn results in [0,0,0,5,0] in both cases again. The procedure seems to have saved the old values and never overwrites them. How can I fix this? I have highlighted the use of the procedure with exclamation marks.

Thank you in advance!

P.S.: The lengthy result is this:

NEUZMinus(-1,1,x,x,[-sqrt(3/5),0,sqrt(3/5)],4)

                               x
                              2   1
                             x  - -
                                  3
                             3   3  
                            x  - - x
                                 5  
                          4   3    6  2
                         x  + -- - - x
                              35   7   
                        5   5      10  3
                       x  + -- x - -- x
                            21     9    
                     6    5    5   2   15  4
                    x  - --- + -- x  - -- x
                         231   11      11   
                   7   35      105  3   21  5
                  x  - --- x + --- x  - -- x
                       429     143      13   
                8    7     28   2   14  4   28  6
               x  + ---- - --- x  + -- x  - -- x
                    1287   143      13      15   
              9    63      84   3   126  5   36  7
             x  + ---- x - --- x  + --- x  - -- x
                  2431     221      85       17   
         10    63     315   2   210  4   630  6   45  8
        x   - ----- + ---- x  - --- x  + --- x  - -- x
              46189   4199      323      323      19   
         11    33      55   3   330  5   330  7   55  9
        x   - ---- x + --- x  - --- x  + --- x  - -- x
              4199     323      323      133      21   
    12    33     198   2   2475  4   660  6   495  8   66  10
   x   + ----- - ---- x  + ---- x  - --- x  + --- x  - -- x  
         96577   7429      7429      437      161      23    
 13    429       2574   3   1287  5   1716  7   429  9   78  11
x   + ------ x - ----- x  + ---- x  - ---- x  + --- x  - -- x  
      185725     37145      2185      805       115      25    
     14     143      1001   2   1001  4   1001  6   1001  8
    x   - ------- + ------ x  - ---- x  + ---- x  - ---- x
          1671525   111435      6555      1035      345    

         1001  10   91  12
       + ---- x   - -- x  
         225        27    
                           1   (1/2)   
                         - - 15     , 3
                           5           
               /    1   (1/2)\   /    1   (1/2)\
               |x + - 15     | x |x - - 15     |
               \    5        /   \    5        /
           /    1   (1/2)\   /    1   (1/2)\   4   3    6  2
   Anfang, |x + - 15     | x |x - - 15     |, x  + -- - - x
           \    5        /   \    5        /       35   7   
                            3   3     3   3  
                   Anfang, x  - - x, x  - - x
                                5         5  
                                   2   1
                       Anfang, 0, x  - -
                                       3
                          Anfang, 0, x
                          Anfang, 0, 1
                     [0, 0, 0, 1, 0], HIER #!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
                            c, d, e
                            0, as1s
                            0, as1s
                            0, as1s
                            0, as1s
                            0, as1s
                            0, as1s
                           4   2    4
                           -- x  + x
                           15        
                               0
                            4    9   2
                          - -- - -- x
                            45   35   
                               1  2
                             - - x
                               3   
                           9   3    5
                           -- x  + x
                           35        
                               0
                          12      16  3
                        - --- x - -- x
                          175     63   
                               1  3
                             - - x
                               3   
                      12   2   8   4    6
                      --- x  + -- x  + x
                      175      45        
                               0
                        4     8   2   25  4
                     - --- - --- x  - -- x
                       175   175      99   
                          12   2   4   4
                        - --- x  - -- x
                          175      15   
                           16  4    6
                           -- x  + x
                           63        
                               0
                          16   2   25  4
                        - --- x  - -- x
                          245      99   
                               1  4
                             - - x
                               3   
                      16   3   40   5    7
                      --- x  + --- x  + x
                      245      231        
                               0
                     64       640   3   36   5
                  - ---- x - ----- x  - --- x
                    3675     14553      143   
                          64   3   4   5
                        - --- x  - -- x
                          945      15   
                  64   2   16   4   72   6    8
                 ---- x  + --- x  + --- x  + x
                 3675      385      455        
                               0
                64      144   2    40   4   49   6
             - ----- - ----- x  - ---- x  - --- x
               11025   13475      1001      195   
                     24   4   9   6   144   2
                   - --- x  - -- x  - ---- x
                     539      35      8575   
                           25  5    7
                           -- x  + x
                           99        
                               0
                         400   3   36   5
                       - ---- x  - --- x
                         6237      143   
                               1  5
                             - - x
                               3   
                     400   4   20   6    8
                     ---- x  + --- x  + x
                     6237      117        
                               0
                    80   2    500   4   49   6
                 - ---- x  - ----- x  - --- x
                   4851      11583      195   
                          20   4   4   6
                        - --- x  - -- x
                          297      15   
                  80   3    40   5   7   7    9
                 ---- x  + ---- x  + -- x  + x
                 4851      1001      45        
                               0
                64        640   3   28   5   64   7
             - ----- x - ----- x  - --- x  - --- x
               14553     63063      715      255   
                     4   5   9   7    80   3
                   - -- x  - -- x  - ---- x
                     91      35      4851   
           64    2    640   4   16   6   160   8    10
          ----- x  + ----- x  + --- x  + ---- x  + x  
          14553      63063      455      1071         
                               0
           64      128   2    80   4   224   6   81   8
        - ----- - ----- x  - ---- x  - ---- x  - --- x
          43659   49049      9009      5967      323   
               640   4   16   6   16  8    1280   2
            - ----- x  - --- x  - -- x  - ------ x
              63063      405      63      305613   
                          36   6    8
                          --- x  + x
                          143        
                               0
                         100   4   49   6
                       - ---- x  - --- x
                         1573      195   
                               1  6
                             - - x
                               3   
                     100   5   28   7    9
                     ---- x  + --- x  + x
                     1573      165        
                               0
                   1600   3   336   5   64   7
                 - ----- x  - ---- x  - --- x
                   99099      7865      255   
                          48   5   4   7
                        - --- x  - -- x
                          715      15   
                1600   4   28   6   144  8    10
                ----- x  + --- x  + --- x  + x  
                99099      715      935         
                               0
              320   2    140   4   2352   6   81   8
           - ----- x  - ----- x  - ----- x  - --- x
             77077      14157      60775      323   
                    12   6   9   8    180   4
                  - --- x  - -- x  - ----- x
                    275      35      11011   
           320   3    320   5   32   7   216   9    11
          ----- x  + ----- x  + --- x  + ---- x  + x  
          77077      33033      935      1463         
                               0
       256        5120    3    1152   5    4608   7   100  9
    - ------ x - ------- x  - ------ x  - ------ x  - --- x
      231231     2081079      133705      124355      399   
               64   5   256   7   16  9    25600   3
            - ---- x  - ---- x  - -- x  - ------- x
              6435      6545      63      6243237   
   256    2    320    4    1280   6    800   8   100  10    12
  ------ x  + ------ x  + ------ x  + ----- x  + --- x   + x  
  231231      127413      153153      24871      693          
                               0
   256      64    2    32000    4    1120   6    900   8   121  10
- ------ - ----- x  - -------- x  - ------ x  - ----- x  - --- x  
  693693   99099      15162147      138567      24871      483    
       8000    4    160   6    600   8   25  10    8000    2
    - ------- x  - ----- x  - ----- x  - -- x   - ------- x
      3270267      18513      16093      99       7630623   
                          49   7    9
                          --- x  + x
                          195        
                               0
                         588   5   64   7
                       - ---- x  - --- x
                         9295      255   
                               1  7
                             - - x
                               3   
                     588   6   112  8    10
                     ---- x  + --- x  + x  
                     9295      663         
                               0
                   980   4    5488   6   81   8
                - ----- x  - ------ x  - --- x
                  61347      129285      323   
                         196   6   4   8
                       - ---- x  - -- x
                         2925      15   
               980   5   2352   7   189   9    11
              ----- x  + ----- x  + ---- x  + x  
              61347      60775      1235         
                               0
            2240   3    84672   5    4032   7   100  9
         - ------ x  - ------- x  - ------ x  - --- x
           552123      8690825      104975      399   
                     48   7   9   9    756   5
                  - ---- x  - -- x  - ----- x
                    1105      35      46475   
         2240   4    896   6    7776   8   40   10    12
        ------ x  + ----- x  + ------ x  + --- x   + x  
        552123      94809      230945      273          
                               0
      64    2    22400   4    127008   6   1080   8   121  10
   - ----- x  - ------- x  - -------- x  - ----- x  - --- x  
     61347      9386091      15011425      29393      483    
              1792   6    48   8   16  10    2240   4
           - ------ x  - ---- x  - -- x   - ------ x
             182325      1235      63       552123   
  64    3    22400   5    1120   7    600   9   385   11    13
 ----- x  + ------- x  + ------ x  + ----- x  + ---- x   + x  
 61347      9386091      138567      19019      2691          
                               0
    256        51200    3    13440   5    2560   7    5500   9
 - ------ x - -------- x  - ------- x  - ------ x  - ------ x
   920205     84474819      6605027      323323      153387   

      144  11
    - --- x  
      575    
      22400   5    4320   7   1000   9   25  11    56000    3
   - ------- x  - ------ x  - ----- x  - -- x   - -------- x
     9386091      508079      27027      99       54660177   
  256    2     7168    4    13440   6    80000    8   100   10
 ------ x  + -------- x  + ------- x  + -------- x  + ---- x  
 920205      11471889      6605027      10669659      3289    

      504   12    14
    + ---- x   + x  
      3575          
                               0
    256       3072    2    112000    4    112000   6    8100    8
- ------- - -------- x  - --------- x  - -------- x  - ------- x
  2760615   19119815      217965891      59445243      1062347   

     264   10   169  12
   - ---- x   - --- x  
     7475       675    
     89600    4    13440   6    21600   8   140   10   36   12
 - --------- x  - ------- x  - ------- x  - ---- x   - --- x  
   149134557      6605027      2719717      3887       143    

        768    2
    - ------- x
      2924207   
                        1, Polynom[0][0]
                        x, Polynom[1][0]
                     1    2               
                     - + x , Polynom[1][1]
                     3                    
                        2               
                       x , Polynom[2][0]
                    4       3               
                    -- x + x , Polynom[2][1]
                    15                      
                 4   2    4   4                
                 -- x  + x  + --, Polynom[2][2]
                 21           45               
             Matrix(%id = 18446745693991291350), 1
                             testb1
                               0
                               0
                             testb2
          Matrix(%id = 18446745693991291350),

            Vector[column](%id = 18446745693991291470)
             Matrix(%id = 18446745693991291350), 1
             Matrix(%id = 18446745693991291350), 1
                             testb1
                               0
                               0
                             testb2
          Matrix(%id = 18446745693991291350),

            Vector[column](%id = 18446745693991291470)
             Matrix(%id = 18446745693991291350), 1
             Matrix(%id = 18446745693991291350), 1
             Matrix(%id = 18446745693991291350), 1
                             testb1
                              16
                              ---
                              245
                               0
                             testb2
          Matrix(%id = 18446745693991291350),

            Vector[column](%id = 18446745693991291470)
             Matrix(%id = 18446745693991291350), 1
             Matrix(%id = 18446745693991291350), 1
             Matrix(%id = 18446745693991291350), 1
             Matrix(%id = 18446745693991291350), 1
                             testb1
                               0
                               0
                             testb2
          Matrix(%id = 18446745693991291350),

            Vector[column](%id = 18446745693991291470)
          Matrix(%id = 18446745693991291350),

            Vector[column](%id = 18446745693991291470)
           Vector[column](%id = 18446745693991291830)
                                  9
                           test2, --
                                  35
                               0
                           7             
                       0, x , 0, Koeff, 0
                           7             
                       0, x , 1, Koeff, 0
                           7             
                       0, x , 2, Koeff, 0
                           7             
                       0, x , 3, Koeff, 1
                     49   6    8             
                  0, --- x  + x , 0, Koeff, 0
                     195                     
                     49   6    8             
                  0, --- x  + x , 1, Koeff, 0
                     195                     
                     49   6    8             
                  0, --- x  + x , 2, Koeff, 0
                     195                     
                     49   6    8             
                  0, --- x  + x , 3, Koeff, 1
                     195                     
                112  7    9   588   5             
             0, --- x  + x  + ---- x , 0, Koeff, 0
                663           9295                
                112  7    9   588   5             
             0, --- x  + x  + ---- x , 1, Koeff, 0
                663           9295                
                112  7    9   588   5             
             0, --- x  + x  + ---- x , 2, Koeff, 0
                663           9295                
                112  7    9   588   5             
             0, --- x  + x  + ---- x , 3, Koeff, 1
                663           9295                
         2352   6   189   8    10    980   4             
      0, ----- x  + ---- x  + x   + ----- x , 0, Koeff, 0
         60775      1235            61347                
         2352   6   189   8    10    980   4             
      0, ----- x  + ---- x  + x   + ----- x , 1, Koeff, 0
         60775      1235            61347                
         2352   6   189   8    10    980   4             
      0, ----- x  + ---- x  + x   + ----- x , 2, Koeff, 0
         60775      1235            61347                
         2352   6   189   8    10    980   4             
      0, ----- x  + ---- x  + x   + ----- x , 3, Koeff, 1
         60775      1235            61347                
    896   5    7776   7   40   9    11    2240   3             
0, ----- x  + ------ x  + --- x  + x   + ------ x , 0, Koeff, 0
   94809      230945      273            552123                
    896   5    7776   7   40   9    11    2240   3             
0, ----- x  + ------ x  + --- x  + x   + ------ x , 1, Koeff, 0
   94809      230945      273            552123                
    896   5    7776   7   40   9    11    2240   3             
0, ----- x  + ------ x  + --- x  + x   + ------ x , 2, Koeff, 0
   94809      230945      273            552123                
   2240    896   5    7776   7   40   9    11    2240   3     
  ------, ----- x  + ------ x  + --- x  + x   + ------ x , 3,
  552123  94809      230945      273            552123        

    Koeff, 1
                               0
                               0
                               0
                               0
                               0
/    1   (1/2)\   /    1   (1/2)\       155   10  2    4       
|x + - 15     | x |x - - 15     |, alt, --- - -- x  + x , neu,
\    5        /   \    5        /       891   9                

  /    1   (1/2)\   /    1   (1/2)\ /155   10  2    4\
  |x + - 15     | x |x - - 15     | |--- - -- x  + x |
  \    5        /   \    5        / \891   9         /
 Testergebnis,

      2459840   5    80254400        188027200   3    2240   7
   - --------- x  - ----------- x + ----------- x  + ------ x
     193795173      44766684963     19185722127      552123   
-0.9604912687, -0.7745966692, -0.4342437493, 0., 0.4342437493,

  0.7745966692, 0.9604912687, -1.435338337, -0.8946894490,

  -0.5176357564, 0., 0.5176357564, 0.8946894490, 1.435338337
                        [0, 0, 0, 1, 0] #!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
                             test21
Error, (in NEUZMinus) invalid subscript selector