MaplePrimes Questions

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

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 :)

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!

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!

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

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

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa


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

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.

 

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 :)

Hi 

I was wondering someone could help me with something.

Basically I've got a function of f(x,z) that I have plotted which comes from an integration that was taken over a large number of small steps. I have been able to plot this function to determine a Potential Field as a function of x and z. (No Problems so far)

However the next step that I want to be able to do is compute a field form this potential. apologies for my lack of knowing how to input into here as I am fairly new to this. To do this I have:

Field = - Nabla * Potential 

Again no problem, I can plot a gradient field from it which is great using the gradplot command. I beleive this comes as a result of the following:

gradplot = [diff(f,x), diff(f,z)]

HOWEVER I want to be able to plot a Field Strength plot (In essence a Gradient Field Strength) where it takes the magnitude of the vectors at each point. Firstly am I correct in saying that this should be:

Magnitude Field = |F| = sqrt( Fx^2+Fz^2)      where Fx is diff(f,x) and Fz is diff(f,z)

 

However when I try to compute this, it takes an age to evaluate and doesn't seem to make much progress. I think this may come as a result of computing square roots of large numbers/large decimal places? I was wondering whether there is any command that anyones knows of that would calculate Gradient Field Strength/Magnitude that may solve this issue? Or even who to just compute this Square root?

Hi,

i have a problem with this code ?

CodeVectorCalculus.mw

ideas ?

Thanks

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);

 

Hey guys, I am looking for a way to translate a maple code to matlab with the resultnames of codegeneration following a rule set by the loop. I tried a few ways, including with printf in the result name but no success.

Basically I need the resultname variables to be KNL(1,1) or KNL[1,1]. It doesn't let me do the way I put in the sheet, it renames the variable automatically.

Please see the sheet attached

Thanks in advance!!

restart

with(CodeGeneration)

with(LinearAlgebra)

A := RandomMatrix(6, 6)

Matrix(%id = 18446746689673050582)

(1)

``

for ii to 6 do for jj to 6 do Matlab(A[ii, jj], resultname = KNL[ii, jj]) end do end do

cg = 67;

 

``

Download Matlab_-_Resultname.mw

My problem is explained with sufficient detail in the below worksheet:

 

restart

Digits := 100:

with(StringTools); with(FileTools); with(ListTools)

``

currentdir("H:\\MAIN DIRECTORY\\ESD-USB\\my_maple_library")

L[1] := ListDirectory(currentdir()):

L[2] := [seq([k, L[1][k]], k = 1 .. nops(L[1]))]:

read L[1][15]:

currentdir("H:\\MAIN DIRECTORY\\ESD-USB\\Computer Science\\MAPLE\\Exponentiation by Squaring"):

 

B := proc (n) options operator, arrow; [seq(d(n, 2, j), j = 0 .. floor(ln(n)/ln(2)))] end proc:

 

 

Identity0 := proc (x, n) options operator, arrow; x^n = piecewise(`mod`(x, 2) = 1, x*(x^2)^((1/2)*n-1/2), `mod`(x, 2) = 0, (x^2)^((1/2)*n)) end proc

NULL

Generate_Equations_List := proc (n) global EquationsList, r, B_n, T; B_n := B(n); T := nops(B_n); r[T] := 1; return [seq(r[u-1] = r[u]^2*x^B_n[u], u = 1 .. T)] end proc:

Exp_by_squares := proc (M, Y) global R; Generate_Equations_List(M); R[1] := max([allvalues(rhs(isolate(F[0](Y, M)[1], r[1])))]); return 'x^n' = R[1]^2*X^B_n[1] end proc:

 

N := (rand(25 .. 33))():

n = 31

 

x = 34

 

x^n = 299120672332806228664106719451209941853702979584

 

x^n = 299120672332806228664106719451209941853702979584

(1)

NULL

st := time[real]():

x^n = 299120672332806228664106719451209941853702979584

 

0.40e-1

(2)

st := time[real]():

x^n = 299120672332806228664106719451209941853702979584

 

0.74e-1

(3)

is(t2 < t1)

false

(4)

``


 

Download slow.mw

 

 

So I know I have obviously done something wrong, but it has proven very difficult to establish where given how little i know about the solve function

 

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