For the DE solution below, Maple returns only one option. I can't get the others. Can anyone help?

wW := unapply(piecewise(0 <= x and x < L/2, 0, L/2 <= x and x <= L, w[0]), x):

eq := k*diff(y(x), x$4) = wW(x):

dsolve({eq, y(0) = 0, y'(0) = 0, y''(L) = 0, y'''(L)=0}, y(x)) assuming 0 < L

          y(x) = -L*w[0]*x^3/(6*k) + L^2*w[0]*x^2/(4*k) + w[0]*x^4/(24*k)

Obrigado.
Oliveira

Hello interested parties!

I wish to measure the distance between points in the Cartesian plane and then export the results to Excel using a data frame routine. For the sake of example: suppose there are 2 points, A and B and 6 more points, a,b,c,d,e and f whose coordinates are known.

I am interested in measuring the distance from A to a, b, c, d, e, f and from B to a, b, c, d, e, f. So, a matrix is constructed (see attached) giving the linear separation between eack of the 8 points ... and that's ok. 

However, instead of six points of interest, suppose that the number of points becomes very large (e.g. 1,000) and I still need to export to Excel.

Does anyone know of an efficient routine that produces a rectangular matrix to produce a 2 x 6 data frame so that, in the case of large-scale problems the data frame is not overburdened?

Thanks for reading and thanks in advance for any suggestions.

Mapleprimes_Matrix.mw

given an expression such as expr:=-1/2*x*(y^2-1) which in tree form will be

I can get -1/2 using op(1,expr).   I need command to return the "rest" of the right side of the tree, all of it, not matter how big.

I tried op(2..nops(expr),expr) and that returns x, y^2 - 1 

Is there a way to return directly x*(y^2-1)*etc....  so I do not have to play around with the above expression sequence?  Another option is to type

           expr/op(1,expr)

to get the right side of the tree. But this seems like a hack. Do not like to divide. worry about zero.

The same thing if the type was `+`, I want to get  the whole right side in one command.

Again, I can do  expr-op(1,expr) to get the whole right side. But this also seems like  a hack, altought not as bad as with  the * case above

Any hints on how to best do these things?

Maple 2019.1

 

 

 

Hello,

I am trying to define a statespace object. Here my code reads:

with(DynamicSystems):

>	aSys≔StateSpace(⟨⟨1,2⟩∣∣⟨3,4⟩⟩,⟨⟨2,3⟩⟩,⟨⟨1,0⟩∣∣⟨0,1⟩⟩,⟨⟨0,0⟩⟩):

Error, (in DynamicSystems:-StateSpace) unsupported type of index, t

I do not have any clue what is wrong with my code.

 

Any help will be really appreciated.

Thanks

I never used applyrule before. Seems like a good command. I was trying to tell Maple to rewrite

as

I could not find one command to do it.  Collect does not work. The only way I figure to it, is by replacing 

by a new single unused symbol, and then use collect on the symbol, then use subs again to replace the symbol with orginal  expression. like this

restart;
expr:=(x^2 - 1)/x^2*y + (x^2 - 1)/x^2;
r:=(x^2 - 1)/x^2; #this is what I want to collect
applyrule(r=Z,expr);
collect(%,Z);
subs(Z=r,%)

In the above code, if I replace applyrule by algsubs, it does not work. Why?

restart;
expr:=(x^2 - 1)/x^2*y + (x^2 - 1)/x^2;
r:=(x^2 - 1)/x^2;
algsubs(r=Z,expr);

You see, it did not replace (x^2-1)/x by Z, like applyrule does:

restart;
expr:=(x^2 - 1)/x^2*y + (x^2 - 1)/x^2;
r:=(x^2 - 1)/x^2;
applyrule(r=Z,expr);

I will learn applyrule now more to do this. I was just wondering why algsubs failed, and if applyrule is the better tool to do this. Or may be there is a better way to do this whole thing?

Maple 2019.1

after running the command  DocumentTools:-Tabulate  as you can see it in the example below in Maple 2018.2:

DocumentTools:-Tabulate(Matrix(2, [a, b, c, d]), width=20);

Output:
                                  

 

 

I expect this proc to return a matrix of all ones but it returns a matrix of all zeros.  Why does it do that?

doit := proc()  
  local i, j, M;                                     
  M := Matrix(3,3);                    
  for i from 1 to 3 do  
    for j from 1 to 3 do  
      M[i][j] := 1;                                      
    end do;                             
  end do;              
  return M;  
end proc:                                           

doit();                            
                                 [0    0    0]
                                 [           ]
                                 [0    0    0]
                                 [           ]
                                 [0    0    0]

 

I am putting pictures into Maple 2019 Document to facilitate/document of analysis being done.  Would very much like to move pictures/images around document?  Once I place them, I can resize them, but I cannot seem to move them.  This is very restrictive.

Is there a solution?

Thank you in advance for your help.

In equation(19), the value for F = 14.616.. is wrong. It was produced by a bult execution of the whole program. However, executing only equation(19) in one step results in the correct answer F=24.665. The values for SSE,SSR, which are 1 x 1 matrices, are correct. Indices(1x1) provide access to the elements as constants so that arithmetic operations can be performed.

The correct result follows an execution at eqn(19) as a stand alone. An incorrect result follows execution of the entire program.

  restart:               

interface(rtablesize = 50); with(LinearAlgebra); with(plots); with(Statistics); with(ArrayTools);

Y := Matrix(12, 1, [2, 3, 2, 7, 6, 8, 10, 7, 8, 12, 11, 14]); n := ArrayNumElems(Y);

This is the data, with n rows and one column.

                                [2 ]

                                [  ]

                                [3 ]

                                [  ]

                                [2 ]

                                [  ]

                                [7 ]

                                [  ]

                                [6 ]

                                [  ]

                                [8 ]

                           Y := [  ]

                                [10]

                                [  ]

                                [7 ]

                                [  ]

                                [8 ]

                                [  ]

                                [12]

                                [  ]

                                [11]

                                [  ]

                                [14]

                            n := 12

type(Y, Matrix);

                              true

X := Matrix(12, 3, [1, 0, 2, 1, 2, 6, 1, 2, 7, 1, 2, 5, 1, 4, 9, 1, 4, 8, 1, 4, 7, 1, 6, 10, 1, 6, 11, 1, 6, 9, 1, 8, 15, 1, 8, 13]); k := NumElems(X)/n;

                             [1  0  2 ]

                             [        ]

                             [1  2  6 ]

                             [        ]

                             [1  2  7 ]

                             [        ]

                             [1  2  5 ]

                             [        ]

                             [1  4  9 ]

                             [        ]

                             [1  4  8 ]

                        X := [        ]

                             [1  4  7 ]

                             [        ]

                             [1  6  10]

                             [        ]

                             [1  6  11]

                             [        ]

                             [1  6  9 ]

                             [        ]

                             [1  8  15]

                             [        ]

                             [1  8  13]

                             k := 3

Xprimed := Transpose(X);

                                                                                                                                                                                                     Calculate Multiple Linear Regression in x1, and x2

                 [1  1  1  1  1  1  1  1   1   1  1   1 ]

                 [                                      ]

      Xprimed := [0  2  2  2  4  4  4  6   6   6  8   8 ]

                 [                                      ]

                 [2  6  7  5  9  8  7  10  11  9  15  13]

XprimedX := Xprimed . X;

                              [12   52   102 ]

                              [              ]

                  XprimedX := [52   296  536 ]

                              [              ]

                              [102  536  1004]

XprimedXinverse := MatrixInverse(XprimedX);

                      [   309          77              145 ]

                      [   ---          ---      uminus0--- ]

                      [   317          317             634 ]

                      [                                    ]

                      [    77          411             141 ]

   XprimedXinverse := [   ---         ----      uminus0----]

                      [   317         2536             1268]

                      [                                    ]

                      [       145         141       53     ]

                      [uminus0---  uminus0----      ---    ]

                      [       634         1268      634    ]

XprimedY := Xprimed . Y;

                                   [90 ]

                                   [   ]

                       XprimedY := [482]

                                   [   ]

                                   [872]

Betahat := XprimedXinverse . XprimedY;

                               [   1704   ]

                               [   ----   ]

                               [   317    ]

                               [          ]

                               [   3819   ]

                    Betahat := [   ----   ]

                               [   1268   ]

                               [          ]

                               [       815]

                               [uminus0---]

                               [       634]

Betahat := convert(Betahat, float);

                          [    5.375394322     ]

                          [                    ]

               Betahat := [    3.011829653     ]

                          [                    ]

                          [&uminus0;1.285488959]

 We choose the Null Hypothesis that Y= β0+Β1*x1+Β2*x2+ϵ . 

Performing multiple linear regression leads to the best fit linear equation:  

  Y= 5.38+3.01*x1-1.29x2

fit := plot3d(5.38+3.01*X1-1.29*X2, X1 = 0 .. 8, X2 = 2 .. 15);

data := pointplot3d({[0, 2, 2], [2, 5, 7], [2, 6, 3], [2, 7, 2], [4, 7, 10], [4, 8, 8], [4, 9, 6], [6, 9, 12], [6, 10, 7], [6, 11, 8], [8, 13, 14], [8, 15, 11]}, axes = normal, color = red, symbol = soliddiamond, symbolsize = 40, scaling = unconstrained, title = `\` Data vs Best Fit ' `);

display({data, fit});

                                                                                                               Comparison of Data and Best Fit

 

Yprimed := Transpose(Y); YprimedY := Yprimed . Y; BetahatPrime := Transpose(Betahat);

      Yprimed := [2  3  2  7  6  8  10  7  8  12  11  14]

                       YprimedY := [840]

BetahatPrime := [5.375394322  3.011829653  &uminus0;1.285488959]

SSE := YprimedY-BetahatPrime . XprimedY; SampleVariance := (YprimedY-BetahatPrime . XprimedY)/(n-k-1);

                   SSE := [25.4589905220000]

              SampleVariance := [3.18237381525000]

SSE (below) is a 1x1 vector which has been changed into a constant                                                  Covariance of β                                                                                                                                                     

`cov&beta;` := Typesetting[delayDotProduct](SSE(1, 1), XprimedXinverse, true);

cov&beta; := [

 

  [24.8164923384795, 6.18404501638486, &uminus0;5.82263978815458], 

 

  [6.18404501638486, 4.12604302229574, &uminus0;2.83100762113723], 

 

  [&uminus0;5.82263978815458, &uminus0;2.83100762113723, 

 

  2.12827523291167]]

SSR := Transpose(Betahat) . Transpose(X) . Y-n*MeanY(1, 1)^2;

                   SSR := [139.541009478000]

SST := SSR+SSE; F := SSR(1, 1)*(n-k-1)/(k*SSE);

F is found in textbook eqn (8.5)

                         SST := [165.]

                    F := [14.6160295824160]

RsquaredNonCentered := Determinant(SSR)/Determinant(SST); R := sqrt(%);

            RsquaredNonCentered := 0.845703087745454

                     R := 0.919621165342259

MeanY := Mean(Y);

                  MeanY := [7.50000000000000]

RsquaredCentered := `~`[`.`](Transpose(Betahat) . Transpose(X) . Y-n*MeanY(1, 1)^2, 1/(Yprimed . Y-n*MeanY(1, 1)^2));

            RsquaredCentered := [0.845703087745454]

                                                                                                         We note the same value for R -data not centered, and that for R-data which is centered.

 

Transpose(Betahat) . Transpose(X) . Y; MeanY(1, 1)^2; Yprimed . Y;

# Compare SSR, Mean of Y (data), and SST to results in the book. 

                       [814.541009478000]

                        56.2500000000000

                             [840]

                                                     Table 8.2 on Page 189 of textbook

                                    ANOVA for Overall Regression Test for Data in Table 7.1

________________________________________________________________________________________________________

 Source           df                                                   SS                                                        MS                                                 F

 _________________________________________________________________________________________________________

 Include β1    2                                        139.5410                                    69.7705                                24.665

Error           9                                          25.4590                                      2.8288

         Total                                             165.0000

_________________________________________________________________________________________

and from calculations using the defining equations in step(12) through step(13) and summarized in Step(19):

 

F := SSR(1, 1)*(n-k-1)/(k*SSE(1, 1)); SSE, SSR, SSR+SSE; Total := Yprimed . Y-n*MeanY(1, 1)^2;

                     F := 14.6160295824160

         [25.4589905220000], [139.541009478000], [165.]

                        Total := [165.]

Hi, 

When creating a user random variable, I would like to instanciate some of its attributes, for instance ParentName.
But it seems that it's not always possible.

​​​​​​​Is it a Maple's limitation or am I not doing the things correctly ?
​​​​​​​
Example:
 

>  restart: >  with(Statistics): >  U := RandomVariable(Uniform(0, 1)): >  interface(warnlevel=0): >  A := attributes(U)[3] (1) >  AllAttributes := with(A); (2) >  A:-ParentName (3) >  # Define a user random variable v := Distribution(PDF = (z -> piecewise(0 <= t and t < 1, 1, 0))): V := RandomVariable(v): A := attributes(V)[3]; AllAttributes := with(A); A:-Conditions; (4) >  # its definition can be augmented by adding some recognized attributes... # even if the result returned by Mean is strange v := Distribution(PDF = (z -> piecewise(0 <= t and t < 1, 1, 0)), 'Mean'=1/Pi, 'Median'=exp(-1)): V := RandomVariable(v): A := attributes(V)[3]; AllAttributes := with(A); [Median, Mean](V) (5) >  # but not all the recognized attributes seem to be able to be instanciated: v := Distribution(PDF = (z -> piecewise(a <= t and t < b, 1/(b-a), 0)), 'Parameters'=[a, b]); v := Distribution(PDF = (z -> piecewise(a <= t and t < b, 1/(b-a), 0)), 'ParentNames'=MyDistribution); Error, (in Statistics:-Distribution) invalid input: too many and/or wrong type of arguments passed to NewDistribution; first unused argument is Parameters = [a, b]   Error, (in Statistics:-Distribution) invalid input: too many and/or wrong type of arguments passed to NewDistribution; first unused argument is ParentNames = MyDistribution   >

 

Download Attributes.mw

How to get a plot for different values of Mh.

like Mh=[1 2 3 4]

Code:

restart;
with(DEtools,odeadvisor);

m:=10;H:=1;Mh:=1;b:=0.02; a:=0.05;V:=array(0..m); V[0]:=1-exp(-t);

for k from 1 to m do

if k=1 then chi:=0;

 chi:=1;

 fi;

 p:=0;

 for j from 0 to k-1 do

   p:=p+(V[k-1-j]*diff(V[j],t$2)-diff(V[k-1-j],t)*diff(V[j],t)-a*(2*diff(V[k-1-j],t)*diff(V[j],t$3)-diff(V[k-1-j],t$2)*diff(V[j],t$2)-V[k-1-j]*diff(V[j],t$4)));  od;

p:=(p+diff(V[k-1],t$3)-b*(diff(V[k-1],t$2)+t*diff(V[k-1],t$3))-Mh*diff(V[k-1],t))*h*H;

p:=factor(p);

V[k]:=(-int(p,t)+0.5*exp(t)*int(exp(-t)*p,t)+0.5*exp(-t)*int(exp(t)*p,t)+chi*V[k-1]+C1+C3*exp(-t));

v:=unapply(V[k],t);

V[k]:=frontend(expand,[V[k]]);  V[k]:=subs(C3=solve(eval(subs(t=0,diff(V[k],t))),C3),V[k]); V[k]:=frontend(expand,[V[k]]);

V[k]:=subs(C1=solve(eval(subs(t=0,-V[k]-diff(V[k],t))),C1),V[k]);

od:

appr:=0;

for k from 0 to m do

 appr:=appr+V[k];

od:

u_appr:=unapply(appr,(h,t)):

u_appr_1:=unapply(diff(u_appr(h,t),t),(h,t)):

evalf(u_appr_1(-0.4,t)):

with(plots);

plot([u_appr_1(-0.4,t)],t=0..4,0..1.2,color=[black],axes=frame):

 

 

this plot for Mh=1:

 

Hi, 

How do I change the definition of g to get the result f(1, 2)(x) = 2*t+3 ?

f := a*x+b;
g := (a,b) -> x -> f;
g(a, b)(x);   # answer a*t+b
g(2, 3)(x);   # answer a*t+b

Thanks in advance

 

Hey, I need to modify a differential equation passed to a procedure. My problem is that this code works fine:

restart;
ode := diff(y(x), x) = y(x):
y := unapply(exp(x), x):
ode;
                        exp(x) = exp(x)

But this doesn't:

restart;
ode := diff(y(x), x) = y(x);
p1 := proc (eq)
    local y;
    y := unapply(exp(x), x);
    eq
end proc:
p1(ode);
                         d             
                        --- y(x) = y(x)
                         dx            

How to solve this problem? 

May I know any command that able to support the large number even up to 2000 bits? 

I made a typo below, I did not mean to put [...] around the solution. But why Maple throws an error on this only?

restart;
ode:=diff(y(x),x) = exp(x)*sin(x)+y(x)*cot(x);
my_sol:=[sin(x)*(exp(x)+_C1)];
odetest( y(x)=my_sol,ode) assuming x::real

          Error, (in type/algext) too many levels of recursion

But on other ODE's, it works

restart;
ode:=diff(y(x),x) = y(x);
my_sol:=[_C1*exp(x)];
odetest( y(x)=my_sol,ode) assuming x::real

                [0]

I'll correct my type and remove the []. But the question is, should Maple have thrown an error? And why only on this one? Would this be considered a bug?

Removing the [] from the first example above, the error is gone and 0 is returned.

Maple 2019.1, Physics V 395 on windows 10