How to simplify the product of 4x4 matrices and how can we take out the expression that appears in each entry of the matrix?

MLM-1.mw

Hi,

I'm trying to use an older package but the results of the author's own example returns the error:

"Error, (in SumTools:-DefiniteSum:-ClosedForm) summand is singular in the interval of summation"

I don't have access to the source coude, but by looking at other similar issues it seems to be happening when "sum" function is used. Is there a way to force Maple use "add" instead?

Thanks!

What im trying to do is build a 14 faced polyhedron from 9 vertices however when i try to plot 1 of these faces as defined by these vectors using polygonplot3d,


 

the resulting graph plots the points, [17/2,-17/2,0],[0,0,11/2],[0,0,sqrt(166/4)] instead of how they are given by their vectors. It plots correctly if i use "polygonplot3d(Matrix([A1, A2, B1]))" but this does not scale well to my full polyhedron as Im not sure how to choose my faces in that regard. Is there any way I can force polygonplot3d to actually plot the vectors as points properly. Or is it simplist to convert all my vectors to lists first before plotting?

Thanks a lot, Seb
 

Hello there, 

Would you tell me how to treat differentiation as an operator?

Here is a simple example:

(The content of the worksheet is supposed to be here, but that did not work)

Download Q20210407.mw

The 'coeff' operation shows 'psi__d0' as the only coefficient of 'Delta__delta(t)', while what I wanted to see is the 'Desired' expression in the worksheet, '(psi__d0 + psi__q0 / omega__0 * D)' as the coefficients. Here, 'D' represents the differentiation. 

Thank you, 

In Kwon Park 

EssayTools command SpellCorrectWord("trnu") will return "run" and not return "turn".

Is there a way for Maple to only find anagrams with the same length as the given string?

Can Maple do this referencing an external dictionary located on the internet e.g. a complete Websters?

Hello all,

I am very new to Maple but it looks like a wonderful symbolic computing tool.  I am hoping to gain some familiarity with it and one of my first questions is this:  I have identified a nice formula refered to as a modified inverse gamma function.  This is a "peak function" with a couple nice features.  Firstly, it can describe both positively and negatively skewed distributions, and secondly its mode and amplitude are easily recognized as (X₀,Ym).  I have entered it into a Maple 2019 notebook as so:

Y = Ym*(c/((d + 1)*(X - X__0) + c))^(d + 1)*exp((X - X__0)*(d + 1)^2/((d + 1)*(X - X__0) + c))

What I would like to do is calculate the positions, X, of the two points where it is half-maximal.  That is, where Y=1/2Ym.  I would like to assume that all numbers are real, etc.  I should point out that in the real world, I will have optimized the values of Ym, X₀, c and d by first fitting to actual data, so this may helpfully constrain the problem.

Can someone explain how I might go about this?  If you assume I know nothing, I will not be offended.

Thank you!

I was trying to get an aproximation of an expression, but it doesnt seem to provide the correct answer. for the following

((12*sqrt(13))/13 - 3/4)/(1 + ((12*sqrt(13))/13)(3/4))

 maple provides 0.59568 and the actual answer is 0.73744

I dont know what I am doing wrong

It was interesting not to miss the solutions of such a test equation  x * (1 + 1.0001 * sin (x ^ 2)) = 0 on a fairly large arbitrary segment using NextZero.
It turned out that NextZero skips solutions.
For example, solutions in the range from 7.5 to 10 are skipped.  And two more specific solutions skipped 21.232154952 and 21.232821004.
I took Digits to help, but it didn't affect anything. Most likely the reason is that I am a bad user.  The example seems to be a good one.
 

restart: 
#Digits := 30; 
f := proc (x) options operator, arrow; x*(1+1.0001*sin(x^2)) end proc; 
RootFinding:-NextZero(f, 1.0): 
for j to 154 do RootFinding:-NextZero(f, %) end do

Let L be list say

L:=[[[1,2],3],[[1,3],4],[[1,4],4],[[1,7],7]]

The list is of this type it can be any list type and can be of any size it should be exported to excel like a table like this

A        B

(1,2)    3

(1,3)    4

(1,4)    4

(1,7)    7

First is in column A

and second is in column B

See brackets changed

kind help with the needul

Hi, dear community,
I have a Maple package "rath" for finding the traveling wave solution of differential equations. But I am not able to loading in Maple 18. Please see this attached zip folder and need help in this regard.
Kind regard

inform.txt,

PaperExp.mws

rath.txt

Anyone else experiencing problems uploading Workbooks as MaplePackage to MapleCloud.

Very often it is not possible to upload a workbook as a package, but just as a normal Maple file. Takes a couple of tries with opening the file until it is possible.

Hi dear community!

The following code produces a table, however it always has the text "Tabulate0" as an output as well. Is it possible to supress that? Ordinary : dont work unfortunately.

with(DocumentTools):
with(ArrayTools):
nUnten:=2:
nOben:=8:
InitialisierungDF:=Vector[column](nOben-nUnten+1, fill=oE): #Erstellen der auszugebenden Tabelle
InitialisierungSpalte:=Vector[row](nOben-nUnten+1, i->n=nUnten-1+i):
DF:= DataFrame( Concatenate( 2, InitialisierungDF $ 10),
                   columns = [ GKAbs, GKRel, PZPAbs, PZPRel, PZMAbs, PZMRel, PYAbs, PYRel, DAbs, DRel],
                   rows = InitialisierungSpalte);
print(Tabulate(DF));

Thank you very much!

Hi there!

The first time I compile the following code, I get the error message

"Error, cannot split rhs into multiple assignment."

when trying to solve an issue with the procedure. I then have to compile the procedure over and over again, until it finally works (which it does eventually, without changing the code.) The problematic line is

Knoten, Eigenvektoren := Eigenvectors(evalf[15](M));

it is one of the last lines within the code below. Is it possible to get rid of that issue? It is annoying and unprofessional to have to compile a code over and over again until it finally works.

GaußKronrodQuadraturKurz:= proc(Unten, Oben, f,G,n)::real;
 
  #Unten:= Untere Intervallgrenze; Oben:= Obere Intervallgrenze; G:= Gewicht;
  #f:= zu untersuchende Funktion; n:= Berechnung der Knotenanzahl mittels 2*n+1
local
A,B,P,S,T, #Listen
a,b,p,s,t, #Listenelemente
i,j,k, #Laufvariablen
M, #werdende Gauss-Kronrod-Jacobi-Matrix
m, #Matrixeinträge
u,l, #Hilfsvariablen Gemischte Momente
RekursivesZwischenergebnis,Gewichte,Knoten,Eigenvektoren,AktuellerNormierterVektor,Hilfsvariable,Endergebnis;

with(LinearAlgebra):
 
A := [seq(a[i], i = 0 .. n)];
B := [seq(b[i], i = 0 .. n)];
P := [seq(p[i], i = -1 .. ceil(3*n/2)+1)];  
S := [seq(s[i], i = -1 .. floor(n/2))];
T := [seq(t[i], i = -1 .. floor(n/2))];
p[-1]:= 0;
p[0]:=1;
for i from -1 to floor(n/2) do
  s[i]:=0;
  t[i]:=0
end do;
for j from 1 to 2*n+1 do
  RekursivesZwischenergebnis:= x^j;
  for i from 0 to j-1 do
    RekursivesZwischenergebnis:= RekursivesZwischenergebnis -
    (int(x^j*p[i],x=Unten..Oben)/int(p[i]*p[i],x=Unten..Oben))*p[i]                  #Gram-Schmidt algorithm
  end do;
  p[j]:=RekursivesZwischenergebnis;
end do;
a[0]:=-coeff(p[1],x,0);

  #p[0+1]=(x-a[0])*p[0]-b[0]*p[0-1] -> p[1]=x*p[0]-a[0]*p[0]-b[0]*p[-1] ->
  #p[1]=x*1-a[0]*1-0 -> a[0]=x-p[1] -> a[0]= -coeff(p[1],x,0), da p[1] monisch ist und von Grad 1    #ist
 
b[0]:=int(p[0]^2, x=Unten..Oben); #by definition
for j from 1 to ceil(3*n/2) do
 
  #Genau genommen muss a nur bis floor(3/(2*n)) initialisiert werden, allerdings wird der Wert       #ohnehin für die Berechnung von b gebraucht. Die Initialisierung schadet nicht.
    
                                     
  a[j]:= coeff(p[j],x,j-1)- coeff(p[j+1],x,j);
    
    #p[j+1]=(x-a[j])*p[j]-b[j]*p[j-1] -> p[j+1]=x*p[j]-a[j]*p[j]-b[j]p[j-1] ->
    #coeff(p[j+1],x,j)=coeff(x*p[j],x,j)-coeff(a[j]*p[j],x,j)
      #(da b[j]*p[j-1] vom Grad j-1 ist) ->
    #coeff(p[j+1],x,j)=coeff(x*p[j],x,j)-a[j], da p[j] monisch ist ->
    #coeff(p[j+1],x,j)=coeff(p[j],x,j-1)-a[j]->
    #a[j]=coeff(p[j],x,j-1)-coeff(p[j+1],x,j)
 
  b[j]:=  quo((x-a[j])*p[j]-p[j+1],p[j-1],x);
    

     #p[j+1]=(x-a[j])*p[j]-b[j]*p[j-1] -> -p[j+1]+(x-a[j])*p[j]= b[j]*p[j-1]
     #b[j]=((x-a[j])*p[j]-p[j+1])/p[j-1]

end do;    
t[0]:=b[n+1]; #t[0]:= /hat{b}[0], Beginn der ostwärtigen Phase
for i from 0 to n-2 do # n-2 ist die Anzahl der zu berechnenden Diagonalen
  u:=0;
  for k from floor((i+1)/2) to 0 by -1 do # aufgrund des diagonalen Vorgehens ist nur bei jedem
                                          # zweiten Schleifendurchlauf eine Inkrementierung
                                          # vorzunehmen
    l:=i-k;
    u:=u+(a[k+n+1]-a[l])*t[k]+b[k+n+1]*s[k-1]-b[l]*s[k]; # Ausrechnen gemischter Momente über die
                                                         # fünfgliedrige Rekursion
    s[k]:=u
  end do;
  for j from -1 to floor(n/2) do  # Durchrotieren der Werte der gemischten Momente, da ein                                           # jeweiliges gemischtes Moment beim zweiten auf die Generierung                                    # folgenden
                                  # Schleifendurchlauf das letzte mal benötigt und danach über-
                                  # schrieben wird. Die am Ende vorliegenden Werte sind gerade
                                  # die, die bei der südwärtigen Phase benötigt werden.
    Hilfsvariable:=s[j];
    s[j]:=t[j];
    t[j]:=Hilfsvariable
  end do;
end do;
for j from floor(n/2) to 0 by -1 do
    s[j]:=s[j-1]
end do;
for i from n-1 to 2*n-3 do #entspricht der Anzahl der restlichen Diagonalen
  u:=0;
  for k from i+1-n to floor((i-1)/2) do #berechnet die gemischten Momente innerhalb einer
                                        #Diagonalen, von oben rechts nach unten links.
    l:=i-k;
    j:=n-1-l;
    u:=u-(a[k+n+1]-a[l])*t[j]-b[k+n+1]*s[j]+b[l]*s[j+1];
    s[j]:=u
  end do;
  if i mod 2 = 0 then #Ausrechnen eines fehlenden Koeffizienzen über die fünfgliedrige Rekursion                         #am Eintrag (k,k)
    k:= i/2;
    a[k+n+1]:=a[k]+(s[j]-b[k+n+1]*s[j+1])/t[j+1]
  else                #Ausrechnen eines fehlenden Koeffizienzen über die fünfgliedrige Rekursion                         #am Eintrag (k,k-1)
    k:=(i+1)/2;
    b[k+n+1]:=s[j]/s[j+1]
  end if;
  for j from -1 to floor(n/2) do #Erneutes Durchrotieren der Werte der gemischten Momente
    Hilfsvariable:=s[j];
    s[j]:=t[j];
    t[j]:=Hilfsvariable
  end do;
end do;
a[2*n]:=a[n-1]-b[2*n]*s[0]/t[0]; #Berechnung des letzten fehlenden Koeffizienten über die                                           #fünfgliedrige Rekursion am Eintrag (n-1,n-1)

M:=Matrix(2*n+1, shape=symmetric);#definieren der werdenden Gauß-Krondrod-Matrix
M(1,1):=a[0];
for m from 2 to (2*n+1) do #generieren der Gauss-Kronrod-Matrix
  M(m-1,m):= sqrt(b[m-1]);
  M(m,m-1):= sqrt(b[m-1]);
  M(m,m):= a[m-1];
end do;
Knoten, Eigenvektoren := Eigenvectors(evalf[15](M));# "Die gesuchten Knoten sind die Eigenwerte #dieser Matrix, und die Gewichte sind proportional zu den ersten Komponenten der normalisierten #Eigenvektoren"

for m from 1 to 2*n+1 do
  AktuellerNormierterVektor:= Normalize(Column(Eigenvektoren,m),Euclidean);
 
 
  Gewichte[m]:=AktuellerNormierterVektor[1]^2*b[0]

end do;

Endergebnis:=Re(add(Gewichte[i]*eval(f*diff(G,x),x=Knoten[i]),i=1..2*n+1));

end proc

An example of an application of the procedure is

GaußKronrodQuadraturKurz(-2, 1, 3*x*3*x^2*sin(x),x,3)

Thank you very much!

Hi,

How to add a moving texte ( for example  notation of vector v and vector a ) to my animation ?

Thanks

TESTAnimVitesse.mw