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How to make Maple to integrate term by term?...

Asked by: emendes 515
integration differential-equations
November 08 2019
0  6

Hello

I wonder how integrate can be applied term by term to the following nonlinear differential equation

(diff(y(t), t))*(diff(y(t), t, t, t))-(diff(y(t), t))*y(t)^2-(diff(y(t), t))*(diff(y(t), t, t))-(diff(y(t), t))*A*y(t)

The expected output will be something like 

(diff(y(t), t))*(diff(y(t), t, t))-(1/3)*y(t)^3-(1/2)*A*y(t)^2-(1/2)*(diff(y(t), t))^2+C+int((diff(y(s), s, s))^2, s = 0 .. t)
map(x-> integrate(x,t),(diff(y(t), t))*(diff(y(t), t, t, t))-(diff(y(t), t))*y(t)^2-(diff(y(t), t))*(diff(y(t), t, t))-(diff(y(t), t))*A*y(t))

solves most of it but not the first part. 

Many thanks

Ed

 

Representing a hierarchical table as a tree graph

by: mmcdara 7896 Maple
graph tree table
November 08 2019
2  0

In the applications I am working on, the information are often represented by hierarchical tables (that is tables where some entries can also be tables, and so on).
To help people to understand how this information is organized, I have thought to representent this hierarchical table as a tree graph.
Once this graph built, it becomes very simple to find where a "terminal leaf", that is en entry which is no longer a table, is located in the original table (by location I mean the sequence of indices for which the entry is this "terminal leaf".

The code provided here is pretension free and I do not doubt a single second  that people here will be able to improve it.
I published it for i thought other people could face the same kind of problems that I do.


 

> 

restart
> 

with(GraphTheory):
interface(version);

`Standard Worksheet Interface, Maple 2015.2, Mac OS X, December 21 2015 Build ID 1097895`

 (1)
> 

gh := proc(T)
  global s, counter, types:
  local  i:
  if type(T, table) then
    for i in [indices(T, nolist)] do
      if type(T[i], table) then
         s := s, op(map(u -> [i, u], [indices(T[i], nolist)] ));
      else
         counter := counter+1:
         types   := types, _Z_||counter = whattype(T[i]);
         s       := s, [i, _Z_||counter];
      end if:
      thisproc(T[i]):
    end do:
  else
    return s
  end if:
end proc:
> 

t := table([a1=[alpha=1, beta=2], a2=table([a21=2, a22=table([a221=x, a222=table([a2221={1, 2, 3}, a2222=Matrix(2, 2), a2223=u3, a2224=u4])])]), a3=table([a31=u, a32=v])]);

global s, counter, types:
s       := NULL:
counter := 0:
types   := NULL:

ghres := gh(t):
types := [types]:

t := table([a1 = [alpha = 1, beta = 2], a3 = table([a32 = v, a31 = u]), a2 = table([a22 = table([a222 = table([a2222 = (Matrix(2, 2, {(1, 1) = 0, (1, 2) = 0, (2, 1) = 0, (2, 2) = 0})), a2223 = u3, a2221 = {1, 2, 3}, a2224 = u4]), a221 = x]), a21 = 2])])

 (2)


These 3 lines determine the set of edges of the form ['t', v], that are not been captured by procedure h.
They correspond to "first level" indices of table t (v in {a1, a2, a3} in the example above)

> 

L := convert(op~(1, [ghres]), set):     
R := convert(op~(2, [ghres]), set):
FirstLevelEdges := map(u -> ['t', u], L union R minus R):


Complete the set of the edges, build the graph representation TG of table t and draw TG.

> 

edges := convert~({ghres, FirstLevelEdges[]}, set):
TG := Graph(edges):

HighlightVertex(TG, Vertices(TG), white):
p := DrawGraph(TG, style=tree, root='t'):
 


The first line is used to change the the "terminal leaves" of names  _Z_n by their type.

> 

eval(t);

p       := subs(types, p):
enlarge := plottools:-transform((x,y) -> [3*x, y]):

plots:-display(enlarge(p), size=[1000, 400]);

table([a1 = [alpha = 1, beta = 2], a3 = table([a32 = v, a31 = u]), a2 = table([a22 = table([a222 = table([a2222 = (Matrix(2, 2, {(1, 1) = 0, (1, 2) = 0, (2, 1) = 0, (2, 2) = 0})), a2223 = u3, a2221 = {1, 2, 3}, a2224 = u4]), a221 = x]), a21 = 2])])

  

 


This procedure is used to find the "indices path" to a terminal leaf.
FindLeaf is then applied to all the terminal leaves.

> 

FindLeaf := proc(TG, leaf)
   local here:
   here := GraphTheory:-ShortestPath(TG, 't', leaf)[1..-2]:
   here := cat(convert(here[1], string), convert(here[2..-1], string)):
   here := StringTools:-SubstituteAll(here, ",", "]["):
   here := parse(here);
end proc:

# where is a2221

printf("%a\n", FindLeaf(TG, a2221));

t[a2][a22][a222]

  
> 

 


 

Download Table_Unfolding_2.mw

 

Problem solving log equation...

Asked by: mschneider 60
log user-error
November 08 2019
0  8

I was attempting to construct  a log question and noticed a problem with the answers that are being resolved by maple.

restart:
with(StringTools):
a := 2:
b := 10:
 c := -4:
d := 5:
rs := 4:
#notice I use the word filler below, in order to randomize later and replace "filler" with various "log[base]" or "ln".
equation1 := convert(filler(a*x+b)-filler(c*x+d) = rs, string):
equationAct := parse(SubstituteAll(equation1, filler, cat(ln))):
answer := [solve(equationAct, x)]:

#it appears maple is applying the log properties and suggesting solutions outside the real domain, for the individual log expressions.  The plot of the equation seems to confirm this.
plotA := plot(lhs(equationAct), x = -10 .. 10):
plotB := plot(rhs(equationAct), x = -10 .. 10):
plots[display](plotA, plotB);

Maple is not able to simplify x^3+a*x+b) -(y^3+a*y...

Asked by: HS 40
simplification
November 08 2019
0  1

Maple is not able to simplify x^3+a*x+b) -(y^3+a*y+b) )^2/(x-y)^4   into (x^2 + x*y + y^2 + a)^2/(x - y)^2 

wtf

p.s.  how do I get maple to show steps in simplifications

Error, when trying to remove a task......

Asked by: Cholong 5
worksheet task editing
November 08 2019
1  0

Hello people :) 

As the captian says, im trying to remove an old task i've made.
But i get this:

Error in Get, invalid object [_XML_reply_data_get("reference" =
"_Maplets_reference_12","parameter" =
"value",_XML_content("Task,UserTasks,Nyops",&Entity "#xc3",&Enity
"#xa6","tning"))]

And i have no idea what it is, but it won't erase my task :'D

Thanks a bunch in advance! 

Have a great weekend you all
Best regards Lucas :)

How do i work with multivariate functions?...

Asked by: Pjeter 10
economics
November 08 2019
2  2

Hi

I am a student of economics writing my thesis. I have an inverse demand function defined:

p[i,j]=1-q[i,j]-αq[i,k]-β(q[h,j]+αq[h,k])

where α,β are scalars, i{1,2,}, j {1,2,3}, h/=i and k/=j.

I wanted to know how do i input this kind of function in the program and how do i calculate the function of q[i,j] (the inverse)

Thank you!

How to extract x and y values from a list of order...

Asked by: Teep 205
November 08 2019
1  4

I would like to extract the x and y values from a list containing ordered pairs, [x,y], and display as a list.

For example, given 

  A:= [ [4,2], [9,1], [6,8] ] 

how can I obtain 

 X:=[4,9,6] and Y:=[2,1,8] 

using a simple command?

Thank you!

numtheory package lamba wtf...

Asked by: Adam Ledger 360
numtheory
November 08 2019
1  5

Why is lamba protected as something it traditionally isnt for this package?

 


 

> 

restart

lambda(n) = (-1)^Omega(n)

 

 

> 

with(numtheory)

lambda(n) = (-1)^Omega(n)

  

[GIgcd, bigomega, cfrac, cfracpol, cyclotomic, divisors, factorEQ, factorset, fermat, imagunit, index, integral_basis, invcfrac, invphi, iscyclotomic, issqrfree, ithrational, jacobi, kronecker, lambda, legendre, mcombine, mersenne, migcdex, minkowski, mipolys, mlog, mobius, mroot, msqrt, nearestp, nthconver, nthdenom, nthnumer, nthpow, order, pdexpand, phi, pi, pprimroot, primroot, quadres, rootsunity, safeprime, sigma, sq2factor, sum2sqr, tau, thue, varphi]

 (1)
> 

Omega := proc (n) options operator, arrow; bigomega(n) end proc:
> 

numtheory:-lambda(667)

308

 (2)
> 

``


 

Download main.mw

How to handle ordering problems...

Asked by: Adam Ledger 360
set condition list
November 07 2019
1  4

My learning exercise today is the Calkin-Wilf Tree, and the first worksheet I have the issue, due to needing to use a set operator and at that point of computation losing the ordering if it were to be a list (I have tried with a list, and was unsuccessful) none the less my question is, can I alter the ordering condition for Sets in a worksheet produced therein? 

I also encountered a strange result that I would appreciate an explaination for as seen below in the uploaded worksheet

 


 

> 

restart

``

https://en.wikipedia.org/wiki/Calkin–Wilf_tree

 

 

> 

Q := proc (n) options operator, arrow; (`minus`(map(rhs, solve(`union`(seq({q[0] = 1/2, q[1] = 1, q[i+1] = 1/(2*floor(q[i])-q[i]+1)}, i = 1 .. n)))), map(rhs, solve(`union`(seq({q[0] = 1/2, q[1] = 1, q[i+1] = 1/(2*floor(q[i])-q[i]+1)}, i = 1 .. n-1))))))[] end proc

proc (n) options operator, arrow; (`minus`(map(rhs, solve(`union`(seq({q[0] = 1/2, q[1] = 1, q[i+1] = 1/(2*floor(q[i])-q[i]+1)}, i = 1 .. n)))), map(rhs, solve(`union`(seq({q[0] = 1/2, q[1] = 1, q[i+1] = 1/(2*floor(q[i])-q[i]+1)}, i = 1 .. n-1))))))[] end proc

 (1)
> 

NULL
> 

delta := proc (x, y) options operator, arrow; piecewise(x = y, 1, x <> y, 0) end proc

proc (x, y) options operator, arrow; piecewise(x = y, 1, x <> y, 0) end proc

 (2)

 

 

> 

q[1] := 1

1

 (3)
> 

q[2] := 1/2

1/2

 (4)
> 

q0 := proc (n) options operator, arrow; 1/(2*floor(Q(n)*(1-delta(n, 2))+delta(n, 2)*q[2]+delta(n, 1)*q[1])-Q(n)*(1-delta(n, 2))-delta(n, 2)*q[2]-delta(n, 1)*q[1]+1) end proc

proc (n) options operator, arrow; 1/(2*floor(Q(n)*(1-delta(n, 2))+delta(n, 2)*q[2]+delta(n, 1)*q[1])-Q(n)*(1-delta(n, 2))-delta(n, 2)*q[2]-delta(n, 1)*q[1]+1) end proc

 (5)
> 

[seq(q0(k), k = 1 .. 20)][1]

1/(2*floor(()+1)+())

 (6)
> 

NULL


 

Download Q1_MP_08112019.mw

aaaaaaaaaaaaaaaaaaaaaa...

Asked by: yates91374 5
nasdaq
November 07 2019
1  3

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

How to order a list of records ...

Asked by: brian bovril 914
seq evaluation list
November 07 2019
0  2


Hello. Here is my question.

> 

 

#GIVEN:

ST := [`162` = Record(mu = 475, sigma = 41), `70` = Record(mu = 480, sigma = 42),
       `168` = Record(mu = 448, sigma = 103)]

[`162` = Record(mu = 475, sigma = 41), `70` = Record(mu = 480, sigma = 42), `168` = Record(mu = 448, sigma = 103)]

 (1)

Games:=[[`162`, `70`], [`70`, `168`], [`168`, `162`]]

[[`162`, `70`], [`70`, `168`], [`168`, `162`]]

 (2)

#I need Maple commands to follow the order of Games to auto create STO please

STO:=[`162` = Record(mu = 475, sigma = 41),`70` = Record(mu = 480, sigma = 42),
       `70` = Record(mu = 480, sigma = 42),`168` = Record(mu = 448, sigma = 103),
     `168` = Record(mu = 448, sigma = 103),`162` = Record(mu = 475, sigma = 41)]

`Non-fatal error while reading data from kernel.`

 (3)

 


 

Download ORDERED.mw

How can I vary the resolution of a simple grid in...

Asked by: Teep 205
plotting
November 07 2019
1  8

Good day.

My question involves a set of prescribed points in the Cartesian plane. The x and y ranges are fixed. The points are connected by (imaginary) horizontal and vertical lines to produce a fixed number of blocks / grids.

An example is given in the attached file.  Grid_Example.mw

Now, I wish to reduce the intervals between these points by a scaling factor, n, so as to generate more blocks within the plane that is constrained by the x and y-ranges.

In doing so, I need to find the (x,y)-location of these points in the plane and it would also be great if I could obtain a simple plot.  

As I have several scaling factors to investigate, I was hoping someone may be able to guide me towards a simple routine to help obtain these solutions.

Once again, thanks for taking the time to read this.

 

Making a package installable ? ...

Asked by: MapleUser2017 175
package
November 07 2019
1  11

Dear Maple Users, 

 

First of all I would like to thank for your great support and hints on making a package for Maple. It has made possible for me to construct this package here: 

 

restart; 
MyMat:=module()
description "My Package";
option package; 
export RegModelPlot,RegModel;
RegModelPlot :=proc(c::algebraic,xd::list,yd::list,x::algebraic)
    uses Statistics, plots:
     display
                            (  [ plot
                                 ( Fit(c, xd, yd, x),
                                   x=min(xd)..max(xd),
                                   color=blue,gridlines,
                                   title=typeset("Regressionformula\n f(x) = ", evalf[4](Fit(c, xd, yd, x))),caption=typeset("Residuals = ", Fit(c, xd, yd, x, output = residuals) ))                    
                                 ,
                            
                                 plot
                                 ( xd, yd,
                                   style=point,
                                   symbol=solidcircle,
                                   symbolsize=10,
                                   color=red
                                 )
                               ],
                               size=[800,600]
                            );
                           
                           end proc; 

    RegModel:=proc(c::algebraic,xd::list,yd::list,x::algebraic)
            uses Statistics, plots:
return  Fit(c, xd, yd, x);
end proc; 
    end module

 

My question is now. How do I make it installable ? Meaning, making it so I can be accessed using with the with() argument alene? I have tried to convert it to into an MLA-file and place it in the lib folder. 
 

But if I type with(MyMat) it gives me the error: 

Error, invalid input: with expects its 1st argument, pname, to be of type {`module`, package}, but received MyMat 
 

So anyone with an idea/hint on what I need to add to make the package installable? 

 

Thanks in advance :)

Question about Maple code ( Vector Calculus)...

Asked by: jalal 465
vector-calculus plane
November 07 2019
1  2

Hi,

i have a problem with this code ?

CodeVectorCalculus.mw

ideas ?

Thanks

why 'combine' command is not working for this expr...

Asked by: Gourav 10
exponential combine
November 07 2019
1  6

Ty4 :=combine(-(chi*omega^2+2*omega)*cos(omega*(Upsilon+b1))*P1*(3*exp(-3*omega)*kappa+exp(-omega)*kappa+exp(-omega*(2*d1+1))*kappa^2+3*exp(-omega*(2*d1+3))*kappa^2-2*exp(-omega*(2*d1+3))*omega-4*exp(-3*omega)*omega^2-2*exp(-omega*(2*d1+3))*d1*kappa*nu__p^2*omega+4*exp(-omega*(2*d1+3))*d1*kappa*nu__p*omega+2*exp(-omega*(2*d1+1))*d1*kappa*nu__p^2*omega+4*exp(-omega*(2*d1+1))*d1*kappa*nu__p*omega-exp(-3*omega)*kappa*nu__p^2+exp(-omega)*kappa*nu__p^2+exp(-omega*(2*d1+1))*kappa^2*nu__p^2-exp(-omega*(2*d1+3))*kappa^2*nu__p^2+2*exp(-omega*(2*d1+1))*d1*kappa*omega-8*exp(-omega*(2*d1+3))*d1*nu__p^2*omega^3-16*exp(-omega*(2*d1+3))*d1*nu__p*omega^3-4*exp(-omega*(2*d1+3))*kappa*nu__p^2*omega^2-8*exp(-omega*(2*d1+3))*kappa*nu__p*omega^2+6*exp(-omega*(2*d1+3))*d1*kappa*omega-4*exp(-3*omega)*kappa*nu__p*omega+4*exp(-3*omega)*d1*nu__p^2*omega^2+8*exp(-3*omega)*d1*nu__p*omega^2-2*exp(-3*omega)*kappa*nu__p^2*omega+2*exp(-3*omega)*kappa*nu__p+2*exp(-omega)*kappa*nu__p+2*exp(-omega*(2*d1+1))*kappa^2*nu__p+2*exp(-omega*(2*d1+3))*kappa^2*nu__p-8*exp(-omega*(2*d1+3))*d1*omega^3-4*exp(-omega*(2*d1+3))*nu__p*omega-2*exp(-omega*(2*d1+3))*nu__p^2*omega-4*exp(-omega*(2*d1+3))*kappa*omega^2-2*exp(-3*omega)*kappa*omega-4*exp(-3*omega)*nu__p^2*omega^2+4*exp(-3*omega)*d1*omega^2-8*exp(-3*omega)*nu__p*omega^2)*exp(-omega*(1-d1-chi))/(omega*(4*exp(-2*omega)*nu__p^2*omega^2+8*exp(-2*omega)*nu__p*omega^2-exp(-4*omega)*nu__p^2+2*exp(-2*omega)*nu__p^2+4*exp(-2*omega)*omega^2+2*exp(-4*omega)*nu__p-4*exp(-2*omega)*nu__p-nu__p^2+3*exp(-4*omega)+10*exp(-2*omega)+2*nu__p+3)*(kappa+1)*Pi),exp);

 

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