Maple Questions and Posts

Subprocedure spits out the answer of the first use...

Asked by: Spirithaunter 75

June 09 2020

1 10

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

dsolve event continue the simulation after "halt"...

Asked by: panke 140

June 09 2020

0 3

I want to contnue the simulation from the point (time) that the event accure

how can I do it ?

How to solve a set equations in a matrix form?...

Asked by: pik1432 245

June 09 2020

0 6

Hello there,

When I tried to solve a set of equations, represented in a matrix form, Maple complained. After the matrix form was decomposed to row by row and solve was attempted, Maple became happy. I wonder if I can solve the set of equations in a matrix form.

Goal: solve this set of equations in terms of Xl12/Xl23/Xl13

X1 = 0.5 * ( Xl12 + Xl13 - Xl23 )
X2 = 0.5 * ( Xl12 + Xl23 - Xl13 )
X3 = 0.5 * ( Xl13 + Xl23 - Xl12 )

>	X:=<X1, X2, X3>;

Vector(3, {(1) = X1, (2) = X2, (3) = X3})

(1)

>	Xeq:= X = <1/2(xl12 + xl13-xl23), 1/2(xl12 + xl23-xl13), 1/2*(xl13 + xl23-xl12)>;

(Vector(3, {(1) = X1, (2) = X2, (3) = X3})) = (Vector(3, {(1) = (1/2)*xl12+(1/2)*xl13-(1/2)*xl23, (2) = (1/2)*xl12+(1/2)*xl23-(1/2)*xl13, (3) = (1/2)*xl13+(1/2)*xl23-(1/2)*xl12}))

(2)

>	solve(Xeq, {xl12, xl13, xl23});

Error, invalid input: solve expects its 1st argument, eqs, to be of type {`and`, `not`, `or`, algebraic, relation(algebraic), ({list, set})({`and`, `not`, `or`, algebraic, relation(algebraic)})}, but received (Vector(3, {(1) = X1, (2) = X2, (3) = X3})) = (Vector(3, {(1) = (1/2)*xl12+(1/2)*xl13-(1/2)*xl23, (2) = (1/2)*xl12+(1/2)*xl23-(1/2)*xl13, (3) = (1/2)*xl13+(1/2)*xl23-(1/2)*xl12}))

Did not work.

>	solve({X1=1/2(xl12 + xl13-xl23), X2=1/2(xl12 + xl23-xl13), X3=1/2*(xl13 + xl23-xl12)}, {xl12, xl13, xl23});

(3)

Did work.

Download Q_20200609.mw

How do I shade this?...

Asked by: anthonyfl 65

June 09 2020

1 7

I want to shade the function y=x*ln(x) on the domain of (0,1].

conflict between with() and uses...

Asked by: tomleslie 13771

June 08 2020

2 10

It would seem that if a package is loaded at the "top-level" via with() and the worksheet also has a procedure definition which contains a 'uses' statement for the same package (OK, admittedly a bit redundant), the commands from the relevant package actually "go missing".

See the output from test4() in the attached.

I can't believe that this is deliberate, because when trying to 'compartmentalise' code, then a 'uses' statement in a procedure seems like a good idea. To have this fail because the "top-level" worksheet contains a with() statement loading the same package seems perverse.

Please don't post workarounds - I already know several ways to do achieve it. I'm trying to find out if this behaviour is "deliberate" or a "bug". If the latter, it has been around for a long time because I have checked all the way back to Maple 18: every version exhibits the same behaviour

>

restart:

>

  kernelopts(version);
  test1:= proc(M::Matrix)
               uses LinearAlgebra:
               return MatrixInverse(M):
          end proc:
  test2:= proc(M::Matrix)
               return LinearAlgebra:-MatrixInverse(M):
          end proc:
  with(LinearAlgebra):
  test3:= proc(M::Matrix)
               return MatrixInverse(M):
          end proc:
  test4:= proc(M::Matrix)
               uses LinearAlgebra:
               return MatrixInverse(M):
          end proc:
  test1( Matrix( [[1,2],[3,4]]));
  test2( Matrix( [[1,2],[3,4]]));
  test3( Matrix( [[1,2],[3,4]]));
  test4( Matrix( [[1,2],[3,4]]));

Matrix(2, 2, {(1, 1) = -2, (1, 2) = 1, (2, 1) = 3/2, (2, 2) = -1/2})

MatrixInverse(Matrix(%id = 18446744074373391174))

(1)

>

Download usewith.mw

How To make Phaseportrait 3D...

Asked by: Pemudahijrah01 25

June 08 2020

2 17

Please everybody, help me to make phaseportrait 3D

Solving multi-span Euler beams with the Method...

by: Rouben Rostamian 7711 Product: Maple 2020

June 08 2020

14 15

Maple's pdsolve() is quite capable of solving the PDE that describes the motion of a single-span Euler beam. As far as I have been able to ascertain, there is no obvious way of applying pdsolve() to solve multi-span beams. The worksheet attached to this post provides tools for solving multi-span Euler beams. Shown below are a few demos. The worksheet contains more demos.

A module for solving the Euler beam with the method of lines

beamsolve

The beamsolve proc solves a (possibly multi-span) Euler beam equation:

subject to initial and boundary conditions. The solution is the

transverse deflection of the beam at point at time , subject to the load
density (i.e., load per unit length) given by . The coefficient

is the beam's mass density (mass per unit length), is the Young's modulus of

the beam's material, and is the beam's cross-sectional moment of inertia

about the neutral axis. The figure below illustrates a 3-span beam (drawn in green)
supported on four supports, and loaded by a variable density load (drawn in gray)
which may vary in time. The objective is to determine the deformed shape of the
beam as a function of time.

The number of spans, their lengths, and the nature of the supports may be specified

as arguments to beamsolve.

In this worksheet we assume that are constants for simplicity. Since only
the product of the coefficients and enters the calculations, we lump the two

together into a single variable which we indicate with the two-letter symbol .

Commonly, is referred to as the beam's rigidity.

The PDE needs to be supplied with boundary conditions, two at each end, each

condition prescribing a value (possibly time-dependent) for one of
(that's 36 possible combinations!) where I have used subscripts to indicate

derivatives. Thus, for a single-span beam of length , the following is an admissible

set of boundary conditions:
. (Oops, coorection, that last
condition was meant to be u_xxx(L,t) = sin t.)
Additionally, the PDE needs to be supplied with initial conditions which express

the initial displacement and the initial velocity:

The PDE is solved through the Method of Lines. Thus, each span is subdivided into

subintervals and the PDE's spatial derivatives are approximated through finite differences.

The time derivatives, however, are not discretized. This reduces the PDE into a set of

ODEs which are solved with Maple's dsolve().

Calling sequence:

beamsolve(, options)

Parameters:

: List of span lengths, in order from left to right, as in .

The number of subintervals in the shortest span (for the finite difference approximation)

Notes:

•	It is assumed that the spans are laid back-to-back along the axis, with the left end of the overall beam at .

•

The interior supports, that is, those supports where any two spans meet, are assumed
to be of the so-called simple type. A simple support is immobile and it doesn't exert
a bending moment on the beam. Supports at the far left and far right of the beam can
be of general type; see the BC_left and BC_right options below.

•	If the beam consists of a single span, then the argument may be entered as a number rather than as a list. That is, is equivalent to .

Options:

All options are of the form option_name=value, and have built-in default values.

Only options that are other than the defaults need be specified.

rho: the beam's (constant) mass density per unit length (default: rho = 1)

EI: the beam's (constant) rigidity (default: EI = 1)

T: solve the PDE over the time interval (default: T = 1)

        F: an expression in and that describes the applied force   (default: F = 0)
        IC: the list of the initial displacement and velocity, as
                expressions in (default: IC = [0,0])

        BC_left: a list consisting of a pair of boundary conditions at the left end of
                the overall (possibly multi-span beam. These can be any two of
                . The right-hand sides of these equations

can be any expression in . The left-hand sides should be entered literally as indicated.

If a right-hand side is omitted, it is taken to be zero. (default: BC_left = which

corresponds to a simple support).

BC_right: like BC_left, but for the right end of the overall beam (default: BC_right =

The returned module:

A call to beamsolve returns a module which presents three methods. The methods are:

plot (t, refine=val, options)

plots the solution at time . If the discretization in the direction

is too coarse and the graph looks non-smooth, the refine option

(default: refine=1) may be specified to smooth out the graph by introducing

val number of intermediate points within each discretized subinterval.

All other options are assumed to be plot options and are passed to plots:-display.

plot3d (m=val, options)

plots the surface . The optional specification requests

a grid consisting of subintervals in the time direction (default:

Note that this grid is for plotting purposes only; the solution is computed

as a continuous (not discrete) function of time. All other options are assumed

to be plot3d options and are passed to plots:-display.

animate (frames=val, refine=val, options)

produces an animation of the beam's motion. The frames option (default = 50)

                specifies the number of animation frames. The refine option is passed to plot
                (see the description above. All other options are assumed to be plot options and
                are passed to plots:-display.

Note:

In specifying the boundary conditions, the following reminder can be helpful. If the beam

is considered to be horizontal, then is the vertical displacement, is the slope,

is the bending moment, and is the transverse shear force.

>

A single-span simply-supported beam with initial velocity

The function is an exact solution of a simply supported beam with

The solution is periodic in time with period .

>	sol := beamsolve(1, 25, 'T'=2/Pi, 'IC'=[0, Pi^2sin(Pix)]): sol:-animate(size=[600,250]);

The initial condition does not lead to a separable form, and

therefore the motion is more complex.

>	sol := beamsolve(1, 25, 'T'=2/Pi, 'IC'=[0, 1]): sol:-animate(frames=200, size=[600,250]);

>

A single-span cantilever beam

A cantilever beam with initial condition where is the
first eigenmode of its free vibration (calculated in another spreadsheet). The motion is
periodic in time, with period

>	g := 0.5cos(1.875104069x) - 0.5cosh(1.875104069x) - 0.3670477570sin(1.875104069x) + 0.3670477570sinh(1.875104069x): sol := beamsolve(1, 25, 'T'=1.787018777, 'BC_left'=[u,u_x], 'BC_right'=[u_xx,u_xxx], 'IC'=[g, 0]): sol:-animate(size=[600,250]);

If the initial condition is not an eigenmode, then the solution is rather chaotic.

>	sol := beamsolve(1, 25, 'T'=3.57, 'BC_left'=[u,u_x], 'BC_right'=[u_xx,u_xxx], 'IC'=[-x^2, 0]): sol:-animate(size=[600,250], frames=100);

>

A single-span cantilever beam with a weight hanging from its free end

>	sol := beamsolve(1, 25, 'T'=3.57, 'BC_left'=[u,u_x], 'BC_right'=[u_xx,u_xxx=1]): sol:-animate(size=[600,250], frames=100);

>

A single-span cantilever beam with oscillating support

>	sol := beamsolve(1, 25, 'T'=Pi, 'BC_left'=[u=0.1sin(10t),u_x], 'BC_right'=[u_xx,u_xxx]): sol:-animate(size=[600,250], frames=100);

>

A dual-span simply-supported beam with moving load

Load moves across a dual-span beam.

The beam continues oscillating after the load leaves.

>

d := 0.4: T := 4: nframes := 100:
myload := - max(0, -6*(x - t)*(d + x - t)/d^3):
sol := beamsolve([1,1], 20, 'T'=T, 'F'=myload):
sol:-animate(frames=nframes):
plots:-animate(plot, [2e-3*myload(x,t), x=0..2, thickness=1, filled=[color="Green"]], t=0..T, frames=nframes):
plots:-display([%%,%], size=[600,250]);

>

A triple-span simply-supported beam with moving load

Load moves across a triple-span beam.

The beam continues oscillating after the load leaves.

>

d := 0.4: T := 6: nframes := 100:
myload := - max(0, -6*(x - t)*(d + x - t)/d^3):
sol := beamsolve([1,1,1], 20, 'T'=T, 'F'=myload):
sol:-plot3d(m=50);
sol:-animate(frames=nframes):
plots:-animate(plot, [2e-3*myload(x,t), x=0..3, thickness=1, filled=[color="Green"]], t=0..T, frames=nframes):
plots:-display([%%,%], size=[600,250]);

>

z3d;

>

A triple-span beam, moving load falling off the cantilever end

In this demo the load move across a multi-span beam with a cantilever section at the right.

As it skips past the cantilever end, the beam snaps back violently.

>

d := 0.4: T := 8: nframes := 200:
myload := - max(0, -6*(x - t/2)*(d + x - t/2)/d^3):
sol := beamsolve([1,1,1/2], 10, 'T'=T, 'F'=myload, BC_right=[u_xx, u_xxx]):
sol:-animate(frames=nframes):
plots:-animate(plot, [1e-2*myload(x,t), x=0..3, thickness=1, filled=[color="Green"]], t=0..T, frames=nframes):
plots:-display([%%,%], size=[600,250]);

>

Download worksheet: euler-beam-with-method-of-lines.mw

Extending the Graph...

Asked by: anthonyfl 65

June 08 2020

0 3

f:= (ln(4x-4)/4)-(ln(4x+4)/4)+(arctan(x)/2)

When I do plots([f(x),f(x)-2,f(x)+2]), the graphs don't extend infinitely like I want. They stop just themselves. How get I the plots to extended more? I attached a picture.

hello guys, i really wondered if there any way to ...

Asked by: shimaa sadk 45

June 08 2020

0 4

it really confused, with generating different sample some times the command fsolve is working and some times don't . is there any other way to solve this system of equations. because I am going to generate 1000 samples and for each sample, I supposed to solve this system.

>

with(LinearAlgebra):

>

(1)

>

(2)

>

W := GenerateUniform(n_x, 0, 1):

>

(3)

>

Download ask_maple.mw

why this application don't work ?...

Asked by: panke 140

June 08 2020

0 8

plotproc.mw

apparently non-existential procedure called by ran...

Asked by: Adam Ledger 360

June 08 2020

0 5

I just need someone to explain to me why the following occurs:

>

rand := proc(r::{posint, numeric .. numeric}, $)
   1   if nargs = 0 then
   2     RandomTools:-MersenneTwister:-GenerateInteger()
       else
   3     try
   4       if type(r,('numeric') .. ('numeric')) then
   5         if rhs(r) < lhs(r) then
   6           error "invalid range, end points are out of order"
             elif not type(r,('integer') .. ('integer')) then
   7           return () -> RandomTools:-Generate(float(('range') = r,('method') = ('uniform')))
             end if
           end if;
   8       return RandomTools:-MersenneTwister:-NewGenerator(('range') = r)
         catch :
   9       error
         end try
       end if
end proc

>

RandomTools:-MersenneTwister:-GenerateInteger := proc({range::{integer, integer .. integer} := 1000000000000}, $)
local bits, divisor, offset;
   1   if nargs = 0 then
   2     return MTKernelInterface(4)
       end if;
   3   if type(range,'integer') then
   4     divisor := range;
   5     offset := 0
       else
   6     if rhs(range) < lhs(range) then
   7       error "illegal range, end points out of order"
         end if;
   8     if lhs(range) = rhs(range) then
   9       return lhs(range)
         end if;
  10     offset := lhs(range);
  11     divisor := rhs(range)-offset+1
       end if;
  12   if divisor = 0 then
  13     return offset
       end if;
  14   bits := MTKernelInterface(5,divisor);
  15   MTKernelInterface(6,divisor,bits)+offset
end proc

>

Error, (in showstat) procedure name expected

>

Download rand_showstat.mw

Saddle point in maple...

Asked by: radaar 202

June 08 2020

0 8

Does maple provide any method for finding the saddle point of a function? Thank you

How do I make nested for loop in Maple? ...

Asked by: abdgafartunde 20

June 08 2020

0 8

I am trying to write maple program for Gauss Siedel method. I needed two for loop. One for running the iterative method and the other for checking where (the number of iteration required) the results converge.

Please, I need help.

Thanks.