Maple 2021 Questions and Posts

These are Posts and Questions associated with the product, Maple 2021

I create and use the variable e (for elementary charge) often in my work.  I recently upgraded from version 2019 to version 2021 .  My workbooks now show the following warning when I run anything using my e vaiable.

Warning, if e is meant to be the exponential e, use command/symbol completion or palettes to enter this special symbol, or use the exp function
 

Is there a way to turn off this warning?  It is very annoying and a bit embarassing when I demo anything.

Thanks

Hi Maple Users,

Microsoft is enticing me to upgrade to Windows 11 from 10 for free. I am a bit hesitant because I don't know if Maple 2021 will continue working as well as in Windows 10. Does anyone have any thoughts or wisdom to share.

Thank you.

i have this differential equation of order 4 that i have problem with solving it,

when ever i try solving it using maple the answer comes like this [  ] with nothing inside.

the differntial equation is: u'''' - sin x u'' + uu' - u=-1-sinx.

and the inital values are: u(0)=2, u'(0)=0,u''(0)=-1,u'''(0)=0.

if you got the answer can you send the code in maple so i can try it and see where i did wrong.

Recently I saw a heated discussion on this post:https://www.mapleprimes.com/questions/233026-Write-Output-Of-For-Loop-To-txt-File

In Carl Love  's answer, I felt the power of adjacency matrix of graph. I carefully read maple's function to generate non IsomorphicGraphs:  NonIsomorphicGraphs. There was one passage that I thought was really interesting.

selectform = graph, adjacency, or bits
This specifies the form used for a graph when it is being passed to the select procedure. The forms are identical to those for outputform, but note that adjacency and bits are the most efficient forms, while graph is only reasonable for a relatively small number of comparison operations (1000 or less), as it needs to form a Graph for every comparison. Note also that when selectform=adjacency the same read-only Matrix is internally used to pass the data for every call to reduce overhead. This is not possible with a Graph structure.

I never quite understood what the advantage of this bits was. At least according to the help documentation, we have  to do many works to do to convert this into a adjacency matrix of graph.

[NonIsomorphicGraphs(8, output = graphs, restrictto = regular[2])]

bit := Vector[row](Bits:-Split(210256131, bits = (8*(8 - 1))/2));
M := Matrix(8, 8, shape = symmetric, datatype = integer[1]);
M[1, 2 .. 8] := bit[1 .. 7];

M[2, 3 .. 8] := bit[8 .. 13];

M[3, 4 .. 8] := bit[14 .. 18];
M[4, 5 .. 8] := bit[19 .. 22];

M[5, 6 .. 8] := bit[23 .. 25];

M[6, 7 .. 8] := bit[26 .. 27];
M[7, 8 .. 8] := bit[28 .. 28];
M;

From adjacency matrix of graph,  we can diractly get a lot of information about the graph, like edges, and the number of closed walks of a particular length, but from bits , what imformation of graph we can get?

If we have to convert it to an adjacency matrix fist, maybe it's a little bit more complicated from above long codes. At least there isn't a more efficient way to convert?

Hi,

I am generating several random weighted graphs using the following code:

with(GraphTheory):
with(RandomGraphs):
G:=RandomGraph(10,20,connected):
G1:=AssignEdgeWeights(G,5..25):
DrawGraph(G1,showlabels=true,stylesheet=[edgecolor=blue,weightfont = [times,bold,11]])

By default weight labels appear to be positioned at the midpoint of each edge. Is there a way to change that positioning?

Thanks!

Hey everyone ! 

I want to get the analytical function from a piecewise differential equation defined on 6 intervals but Maple returns me a numerical result... I think it hides a Runge Kutta method.. However, it returned me an analytical function for a similar piecewise differential equation defined on 3 intervals.

Do you know how I could get the analytical function defined on the 6 intervals ?

Thank you very much for your time ! 

Alex

eq := diff(Uy(x), x, x)-piecewise(x < d1, 12*F*x/(E*b*h^3), d1 < x and x < d2, 12*((F+F1)*x-F1*d1)/(E*b*h^3), d2 < x and x < d3, 12*((F+F1+F2)*x-F1*d1-F2*d2)/(E*b*h^3), d3 < x and x < d4, 12*((F5+F4-F)*x+F*L-F5*d5-F4*d4)/(E*b*h^3), d4 < x and x < d5, 12*((F5-F)*x+F*L-F5*d5)/(E*b*h^3), 12*F*(L-x)/(E*b*h^3))

diff(diff(Uy(x), x), x)-piecewise(x < d1, 12*F*x/(E*b*h^3), d1 < x and x < d2, 12*((F+F1)*x-F1*d1)/(E*b*h^3), d2 < x and x < d3, 12*((F+F1+F2)*x-F1*d1-F2*d2)/(E*b*h^3), d3 < x and x < d4, 12*((F5+F4-F)*x+F*L-F5*d5-F4*d4)/(E*b*h^3), d4 < x and x < d5, 12*((F5-F)*x+F*L-F5*d5)/(E*b*h^3), 12*F*(L-x)/(E*b*h^3))

(1)

dsolve({eq, Uy(0) = 0, Uy(L) = 0}, Uy(x))

assign(dsolve({eq, Uy(0) = 0, Uy(L) = 0}, Uy(x)))

Uy_sol := unapply(Uy(x), x)

proc (x) options operator, arrow; Uy(x) end proc

(2)

E := 210*10^9; L := 4; d1 := (1/6)*L; d2 := 2*L*(1/6); d3 := 3*L*(1/6); d4 := 4*L*(1/6); d5 := 5*L*(1/6); b := 0.1e-1; h := 0.5e-2

210000000000

 

4

 

2/3

 

4/3

 

2

 

8/3

 

10/3

 

0.1e-1

 

0.5e-2

(3)

eq

diff(diff(Uy(x), x), x)-piecewise(x < 2/3, 0.4571428572e-1*F*x, 2/3 < x and x < 4/3, 0.4571428572e-1*(F+F1)*x-0.3047619048e-1*F1, 4/3 < x and x < 2, 0.4571428572e-1*(F+F1+F2)*x-0.3047619048e-1*F1-0.6095238096e-1*F2, 2 < x and x < 8/3, 0.4571428572e-1*(F5+F4-F)*x+.1828571429*F-.1523809524*F5-.1219047619*F4, 8/3 < x and x < 10/3, 0.4571428572e-1*(F5-F)*x+.1828571429*F-.1523809524*F5, 0.4571428572e-1*F*(4-x))

(4)

dsolve({eq, Uy(0) = 0, Uy(L) = 0}, Uy(x))

Uy(x) = -(1/4)*(Int(Int(piecewise(_z1 < 2/3, (1142857143/25000000000)*F*_z1, _z1 < 4/3, (1142857143/25000000000)*F*_z1-(380952381/12500000000)*F1+(1142857143/25000000000)*F1*_z1, _z1 < 2, (1142857143/25000000000)*F*_z1-(380952381/6250000000)*F2-(380952381/12500000000)*F1+(1142857143/25000000000)*F1*_z1+(1142857143/25000000000)*_z1*F2, _z1 < 8/3, -(1142857143/25000000000)*F*_z1-(1219047619/10000000000)*F4-(380952381/2500000000)*F5+(1828571429/10000000000)*F+(1142857143/25000000000)*F4*_z1+(1142857143/25000000000)*_z1*F5, _z1 < 10/3, -(1142857143/25000000000)*F*_z1-(380952381/2500000000)*F5+(1828571429/10000000000)*F+(1142857143/25000000000)*_z1*F5, 10/3 <= _z1, -(1142857143/25000000000)*F*_z1+(1142857143/6250000000)*F), _z1 = 0 .. _z1), _z1 = 0 .. 4))*x+Int(Int(piecewise(_z1 < 2/3, (1142857143/25000000000)*F*_z1, _z1 < 4/3, (1142857143/25000000000)*F*_z1-(380952381/12500000000)*F1+(1142857143/25000000000)*F1*_z1, _z1 < 2, (1142857143/25000000000)*F*_z1-(380952381/6250000000)*F2-(380952381/12500000000)*F1+(1142857143/25000000000)*F1*_z1+(1142857143/25000000000)*_z1*F2, _z1 < 8/3, -(1142857143/25000000000)*F*_z1-(1219047619/10000000000)*F4-(380952381/2500000000)*F5+(1828571429/10000000000)*F+(1142857143/25000000000)*F4*_z1+(1142857143/25000000000)*_z1*F5, _z1 < 10/3, -(1142857143/25000000000)*F*_z1-(380952381/2500000000)*F5+(1828571429/10000000000)*F+(1142857143/25000000000)*_z1*F5, 10/3 <= _z1, -(1142857143/25000000000)*F*_z1+(1142857143/6250000000)*F), _z1 = 0 .. _z1), _z1 = 0 .. x)

(5)

Uy(x)[0]

Uy(x)[0]

(6)

assign(dsolve({eq, Uy(0) = 0, Uy(L) = 0}, Uy(x)))

Uy(x)[0]

(-(1/4)*(Int(Int(piecewise(_z1 < 2/3, (1142857143/25000000000)*F*_z1, _z1 < 4/3, (1142857143/25000000000)*F*_z1-(380952381/12500000000)*F1+(1142857143/25000000000)*F1*_z1, _z1 < 2, (1142857143/25000000000)*F*_z1-(380952381/6250000000)*F2-(380952381/12500000000)*F1+(1142857143/25000000000)*F1*_z1+(1142857143/25000000000)*_z1*F2, _z1 < 8/3, -(1142857143/25000000000)*F*_z1-(1219047619/10000000000)*F4-(380952381/2500000000)*F5+(1828571429/10000000000)*F+(1142857143/25000000000)*F4*_z1+(1142857143/25000000000)*_z1*F5, _z1 < 10/3, -(1142857143/25000000000)*F*_z1-(380952381/2500000000)*F5+(1828571429/10000000000)*F+(1142857143/25000000000)*_z1*F5, 10/3 <= _z1, -(1142857143/25000000000)*F*_z1+(1142857143/6250000000)*F), _z1 = 0 .. _z1), _z1 = 0 .. 4))*x+Int(Int(piecewise(_z1 < 2/3, (1142857143/25000000000)*F*_z1, _z1 < 4/3, (1142857143/25000000000)*F*_z1-(380952381/12500000000)*F1+(1142857143/25000000000)*F1*_z1, _z1 < 2, (1142857143/25000000000)*F*_z1-(380952381/6250000000)*F2-(380952381/12500000000)*F1+(1142857143/25000000000)*F1*_z1+(1142857143/25000000000)*_z1*F2, _z1 < 8/3, -(1142857143/25000000000)*F*_z1-(1219047619/10000000000)*F4-(380952381/2500000000)*F5+(1828571429/10000000000)*F+(1142857143/25000000000)*F4*_z1+(1142857143/25000000000)*_z1*F5, _z1 < 10/3, -(1142857143/25000000000)*F*_z1-(380952381/2500000000)*F5+(1828571429/10000000000)*F+(1142857143/25000000000)*_z1*F5, 10/3 <= _z1, -(1142857143/25000000000)*F*_z1+(1142857143/6250000000)*F), _z1 = 0 .. _z1), _z1 = 0 .. x))[0]

(7)

Uy(x < d1)

Uy(x < 2/3)

(8)

Uy(x)[x < d1]

(-(1/4)*(Int(Int(piecewise(_z1 < 2/3, (1142857143/25000000000)*F*_z1, _z1 < 4/3, (1142857143/25000000000)*F*_z1-(380952381/12500000000)*F1+(1142857143/25000000000)*F1*_z1, _z1 < 2, (1142857143/25000000000)*F*_z1-(380952381/6250000000)*F2-(380952381/12500000000)*F1+(1142857143/25000000000)*F1*_z1+(1142857143/25000000000)*_z1*F2, _z1 < 8/3, -(1142857143/25000000000)*F*_z1-(1219047619/10000000000)*F4-(380952381/2500000000)*F5+(1828571429/10000000000)*F+(1142857143/25000000000)*F4*_z1+(1142857143/25000000000)*_z1*F5, _z1 < 10/3, -(1142857143/25000000000)*F*_z1-(380952381/2500000000)*F5+(1828571429/10000000000)*F+(1142857143/25000000000)*_z1*F5, 10/3 <= _z1, -(1142857143/25000000000)*F*_z1+(1142857143/6250000000)*F), _z1 = 0 .. _z1), _z1 = 0 .. 4))*x+Int(Int(piecewise(_z1 < 2/3, (1142857143/25000000000)*F*_z1, _z1 < 4/3, (1142857143/25000000000)*F*_z1-(380952381/12500000000)*F1+(1142857143/25000000000)*F1*_z1, _z1 < 2, (1142857143/25000000000)*F*_z1-(380952381/6250000000)*F2-(380952381/12500000000)*F1+(1142857143/25000000000)*F1*_z1+(1142857143/25000000000)*_z1*F2, _z1 < 8/3, -(1142857143/25000000000)*F*_z1-(1219047619/10000000000)*F4-(380952381/2500000000)*F5+(1828571429/10000000000)*F+(1142857143/25000000000)*F4*_z1+(1142857143/25000000000)*_z1*F5, _z1 < 10/3, -(1142857143/25000000000)*F*_z1-(380952381/2500000000)*F5+(1828571429/10000000000)*F+(1142857143/25000000000)*_z1*F5, 10/3 <= _z1, -(1142857143/25000000000)*F*_z1+(1142857143/6250000000)*F), _z1 = 0 .. _z1), _z1 = 0 .. x))[x < 2/3]

(9)

NULL

Download cas_5v_F_inconnues.mw

Hi,

I try to display a different steps of an mathematical developpement with ShowSteps command, but But the command gives nothing in the new version Maple 2021?

Thanks for your Help

QShowSteps.mw

I do not know why int() on this integrand fails always first time, and works second time it is called. seems like something is not loaded correctly first time?

integrand:=(((-3*x^2-18*x-27)*exp(2)^2+(30*x^3+330*x^2+1170*x+1350)*exp(2)-75*x^4-1200*x^3-7050*x^2-18000*x-16875)*ln(x)+(12*x^2+54*x+81)*exp(2)^2+(-120*x^3-1106*x^2-3510*x-4050)*exp(2)+225*x^4+3560*x^3+20990*x^2+54000*x+50625)/((3*x^4+18*x^3+27*x^2)*exp(2)^2+(-30*x^5-330*x^4-1170*x^3-1350*x^2)*exp(2)+75*x^6+1200*x^5+7050*x^4+18000*x^3+16875*x^2):

print("First time");
int(integrand,x);

print("second time");
int(integrand,x);

Worksheet attached.

Update

Here is a movie. it is few minutes long. This happens by random and not each time. This movie shows the command starting from "restart" are repated 4 times. First two times, no error. Then the error shows up.  So it is random. Maybe it depends if Maple is busy with other things or not. I have each worksheet set to use its own server though. So I have no idea why this happens sometimes and not other times.

 

 

 

issue_int_nov_11_2021.mw

I think there is a problem here

restart;
the_integrand:=(((-2*x^2+2)*exp(exp(exp(3)))^2+(4*x^3-4*x)*exp(exp(exp(3)))-2*x^4-6*x^2+8)*exp(ln(x)-x^2)*ln(exp(exp(exp(3)))^2-2*x*exp(exp(exp(3)))+x^2+4)+((2*x^2-2)*exp(2)*exp(exp(exp(3)))^2+((-4*x^3+4*x)*exp(2)-2*x)*exp(exp(exp(3)))+(2*x^4+6*x^2-8)*exp(2)+2*x^2)*exp(ln(x)-x^2))/(exp(exp(exp(3)))^2-2*x*exp(exp(exp(3)))+x^2+4);

int(the_integrand,x,method=_RETURNVERBOSE)

#try MeijerG
int(the_integrand,x,method=MeijerG);

gives

I do not know if this known or not.

Maple 2021.1 on windows

This is Maple 2021.1 on windows.

===================
restart;
expr:=x^(6+1/3);
res:=series(expr,x=0,6);
==============

gives
        O(x^(19/3))

But type of the above is not series:

===========
type(res,'series');
        false
===========

Yet convert(res,polynom) works

================
convert(res,polynom)
          0
================

Which is correct conversion. But help says that

"convert/polynom
convert a series to polynomial form"

Notice, it says "series" there.

So the input must be type series. But Maple says
O(x^(19/3)) is not type series. I think this is wrong. The
type returned should be series. Now the type returned is 'function'
from the series command.

What Am I overlooking here?

fyi;

Maple 2021.1 on windows 10.

Screen in worksheet displays this (correct)

But latex generated when compiled using lualatex from TEXLIVE 2021 shows this

code 

sol:=(Vector(2, [x(t),y(t)])) = (Vector(2, [8*c[1]*exp((1/2+1/2*89^(1/2))*t)/(-3+89^(1/2))-8*c[2]*exp((1/2-1/2*89^(1/2))*t)/(3+89^(1/2))+2/11*t^2-3/11*exp(t)-2/121*t+23/1331,c[1]*exp((1/2+1/2*89^(1/2))*t)+c[2]*exp((1/2-1/2*89^(1/2))*t)-1/11*t^2-15/22*exp(t)+12/121*t-17/1331])):

sol:=simplify(sol);

latex(sol)

`Standard Worksheet Interface, Maple 2021.1, Windows 10, May 19 2021 Build ID 1539851`

`The "Physics Updates" version in the MapleCloud is 1105 and is the same as the version installed in this computer, created 2021, November 8, 23:55 hours Pacific Time.`

zip file attached include the latex file and worksheet used.

issue_latex_nov_6_2021.zip

restart; p := .5; n := 10; nseq := 2; with(Statistics); randomize(); x1 := seq(Sample(RandomVariable(BernoulliDistribution(p)), n), i = 1 .. nseq); x2 := seq(convert(x1[i], list), i = 1 .. nseq)

[HFloat(0.0), HFloat(1.0), HFloat(0.0), HFloat(0.0), HFloat(0.0), HFloat(1.0), HFloat(0.0), HFloat(0.0), HFloat(0.0), HFloat(1.0)], [HFloat(0.0), HFloat(1.0), HFloat(1.0), HFloat(1.0), HFloat(0.0), HFloat(0.0), HFloat(1.0), HFloat(0.0), HFloat(0.0), HFloat(0.0)]

(1)

x2[1]

[HFloat(0.0), HFloat(1.0), HFloat(0.0), HFloat(0.0), HFloat(0.0), HFloat(1.0), HFloat(0.0), HFloat(0.0), HFloat(0.0), HFloat(1.0)]

(2)

whattype(x2[1])

list

(3)

numboccur(x2[1], {0.})

0

(4)

NULL

But, when I plugged the list at (2) it works...  

numboccur([0., 0., 1., 1., 0., 0., 1., 0., 0., 0.], 0.)

7

(5)

``

NULL

NULL

Download numboccur.mwnumboccur.mw

restart;In this code "add" is a trouble.
A := Matrix([[1, 2, 1, 3], [1, 1, 2, 1], [1, -2, 5, -11]]);
cs := LinearAlgebra:-ColumnSpace(A);
cnames := [seq(c || j, j = 1 .. numelems(cs))];
cvals := seq(solve([entries(A[() .. (), k] -~ add(`*`~(cnames, cs)), 'nolist')], cnames)[], k = 1 .. op([1, 2], A));
seq(add*rhs~(cvals[k]) *~ cs, k = 1 .. op([1, 2], A));
add does not play its role. Why. Thank you.

The timelimit command of Maple can be used to do a computation if it uses less than a given amount of time, otherwise generating an error message that can be cought by try ... catch. Now my question is that there exists any similar command, but with a limitation on memory usage, not the time usage. I don't mean what datalimit in kernelopts can does, because I am not going to limit the memory usage of the whole Maple session, but just a command which may be used inside a larger procedure etc.

First sorry I didn't "invent" this series.It comes from another newsgroup which I will not tell.

It is irrelevant.

My question is twofold :

How to prove it with pen and paper that it diverges

How to prove it with Maple.

Maple seems very...quiet with this series.

Thanks a lot.

Kind regards to all

Jean-Michel

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