Maple 2023 Questions and Posts

These are Posts and Questions associated with the product, Maple 2023

Hello,

I'm encountering an issue with the "roots of complex number" message while running my Maple code. Maple seems unable to solve this problem for me.

I would greatly appreciate any ideas or suggestions that could help me resolve this error.

Vib-code.mw

I'm trying derive the equation for a matching resistor pad.  In order for me to get a solution (eg for R2), I had to "manually" solve the one equation and then substitute the resulting value in the other.  Why doesn't solve do the same thing?  

restart

NULLeq1 := (R2+Rhi)*R1/(R1+R2+Rhi) = Rlo

(R2+Rhi)*R1/(R1+R2+Rhi) = Rlo

(1)

NULL

eq2 := R1*Rlo/(R1+Rlo)+R2 = Rhi

R1*Rlo/(R1+Rlo)+R2 = Rhi

(2)

``

R1sol := solve(eq2, R1)

-Rlo*(R2-Rhi)/(R2-Rhi+Rlo)

(3)

R2sol := solve(subs(R1 = R1sol, eq1), R2)

(Rhi^2-Rhi*Rlo)^(1/2), -(Rhi^2-Rhi*Rlo)^(1/2)

(4)

restart

NULLeq1 := (R2+Rhi)*R1/(R1+R2+Rhi) = RloNULL

(R2+Rhi)*R1/(R1+R2+Rhi) = Rlo

(5)

 

NULLeq2 := R1*Rlo/(R1+Rlo)+R2 = RhiNULL

R1*Rlo/(R1+Rlo)+R2 = Rhi

(6)

s := `assuming`([solve({eq1, eq2}, {R1, R2})], [`and`(Rhi > 0, Rlo > 0)])

{R1 = RootOf((Rhi-Rlo)*_Z^2-Rhi)*Rlo, R2 = -(RootOf((Rhi-Rlo)*_Z^2-Rhi)*Rhi-RootOf((Rhi-Rlo)*_Z^2-Rhi)*Rlo-Rhi)/(RootOf((Rhi-Rlo)*_Z^2-Rhi)-1)}

(7)
 

``

Download for_help.mw

I can't figure out what Maple is complaining about with this error.  In fact, this is an exact copy/paste from another section in my document that runs fine.  This section, however, generates the error, "Error, missing operator `;`.

I appreciate any help!

for_mapleprimes_help.mw

I am facing a kind of strange problem.  y'=y/x-5^y/x ,   y(0)=5 Cauche equation  it gives empty round brackets () . If I restart Maple engine and perform the same. Kindly help, what is this? 


restart;
with(DEtools);

de1 := diff(y(x), x) = y(x)/x - 5^(-y(x)/x)

de1 := diff(y(x), x) = y(x)/x - 5^(-y(x)/x)

an := dsolve({de1, y(0) = 5}, y(x))

an := ()

I have a complicated tensor expression that is defined wtih all indices down. However if i consider a one-up-one-down configuration it appears to introduce new terms that no longer produce the same result as the all down configuration. Not sure what to make of this. 

IndexQuestion.mw

1.mw.....can anyone hlep to sovle this equation...for omega(t)...
(-limit((1 - omega)^(k + 2), omega = 1, left) + 1)/(k + 2) = C*int((1 - `σ_a`*sin(2*pi*N))^k, N = 0 .. N)...in solution..integral didn't get rid

I keep getting an error: invalid subscript selector on specifically this part of my code:

MuligIndgange := subsop(RemoveList\[i\]=NULL, MuligIndgange).
Whenever I comment out the MuligIndgange := part it works.

I can't for the life of me see why it's happening, and whenever I use this code outside my proc it works aswell.

Any help is appreciated, and if you need more context I'll be happy to give it.

for i to numelems(MuligIndgange) do
     if M1[MuligIndgange[i][1], MuligIndgange[i][2]] =/= 0 then
         RemoveList := [op(RemoveList), i];
      end if;
end do;
for i from numelems(RemoveList) by -1 to 1 do
    MuligIndgange := subsop(RemoveList[i] = NULL, MuligIndgange);
end do;

Simple question (I'm sure) here.  I have one worksheet where the variable does not show up in the ouput of an assignment like this:

whereas I was expecting the output to include the variable being assigned like this in most other worksheets:

I am having some difficulting locating the cause (and therefore the setting) to have the behavior set back to including the variable name in the ouput.  Thanks in advance for your help.

Why does the Heaviside function work this way? Is this some kind of bug? The integral of this graph over the interval -1..1 cannot be equal to zero.

int_of_V-func.mw

 

Dear Power Users, I am trying to master Maple coming from another software. I encounter a problem in finding a simple way to find the best parameters for a fitting function. Would someone be so kind to help me out? Thank you in advance for your willingness to help.

FindOptimizedParametersFit.mw

Hope this is a simple question to answer but how do you use units and show 1 of something without losing the 1.  For example, it's easy enough to show 3 hours as 3h but nobody writes 1 hour as "h".  It's just silly.  Is there a way for 1 hour to render as "1h"?  Really the question is can you get 1 of any unit to show as "1 unit" and not just "unit"? Thanks.

Was working with some antenna design equations and noticed that in a certain plot definition, the addition of gridlines changes the shape of the plotted curve.  Is this a bug or is there something obvious here that I am overlooking?  This one really has me scratching my head.  The only difference between the two plots below is the addition of the gridline spec.

Many thanks!

gridlines_change_plot.mw

Is it possible overlay one column graph on top of another ? And if, how do I do it?

Regards

In a homework assignment on differential geometry, a student used Mathematica to calculate the torsion of a trefoil curve.  His result, using identical steps as mine, was significantly simpler than what I had gotten with Maple, although as we see in the attached workseet, they are mathematically equivalent.

Is there a way to coax Maple to reduce its result to something like my student has obtained?

My calculation

T1 := (-192*cos(t)^6 + 288*cos(t)^4 - 912*cos(t)^3 - 108*cos(t)^2 + 684*cos(t) - 54)/(4608*cos(t)^9 - 10368*cos(t)^7 + 6208*cos(t)^6 + 7776*cos(t)^5 - 9312*cos(t)^4 - 2440*cos(t)^3 + 3492*cos(t)^2 + 372*cos(t) - 1169);

(-192*cos(t)^6+288*cos(t)^4-912*cos(t)^3-108*cos(t)^2+684*cos(t)-54)/(4608*cos(t)^9-10368*cos(t)^7+6208*cos(t)^6+7776*cos(t)^5-9312*cos(t)^4-2440*cos(t)^3+3492*cos(t)^2+372*cos(t)-1169)

The student's calculation

T2 := 6*(10+38*cos(3*t)+cos(6*t))/(975+70*cos(3*t)-194*cos(6*t) -18*cos(9*t));

6*(10+38*cos(3*t)+cos(6*t))/(975+70*cos(3*t)-194*cos(6*t)-18*cos(9*t))

simplify(T1 - T2);

0

 

Download torsion2.mw

 

WHY DOES THE TRANSPOSE OF Vt DETERMINED BY THE FUNCTION SingularValues NOT AGREE WITH THE evectors CALCULATED BY THE FUNCTION Eigenvectors?

 

restart:
with(LinearAlgebra):

X := Matrix([[8.79,9.93,9.83,5.45,3.16],
           [6.11,6.91,5.04,-0.27,7.98],
           [-9.15,-7.93,4.86,4.85,3.01],
           [9.57,1.64,8.83,0.74,5.80],
           [-3.49,4.02,9.80,10.00,4.27],
           [9.84,0.15,-8.99,-6.02,-5.31]],
           datatype=float[8],order=Fortran_order);

Matrix(6, 5, {(1, 1) = 8.79, (1, 2) = 9.93, (1, 3) = 9.83, (1, 4) = 5.45, (1, 5) = 3.16, (2, 1) = 6.11, (2, 2) = 6.91, (2, 3) = 5.04, (2, 4) = -.27, (2, 5) = 7.98, (3, 1) = -9.15, (3, 2) = -7.93, (3, 3) = 4.86, (3, 4) = 4.85, (3, 5) = 3.01, (4, 1) = 9.57, (4, 2) = 1.64, (4, 3) = 8.83, (4, 4) = .74, (4, 5) = 5.8, (5, 1) = -3.49, (5, 2) = 4.02, (5, 3) = 9.8, (5, 4) = 10.0, (5, 5) = 4.27, (6, 1) = 9.84, (6, 2) = .15, (6, 3) = -8.99, (6, 4) = -6.02, (6, 5) = -5.31})

(1)

U,S,Vt:= SingularValues(X, output = ['U', 'S', 'Vt'],thin=true)

U, S, Vt := Matrix(6, 5, {(1, 1) = -.591142376412437, (1, 2) = .263167814714055, (1, 3) = .355430173862827, (1, 4) = .314264362726927, (1, 5) = .229938315364748, (2, 1) = -.397566794202426, (2, 2) = .243799027926330, (2, 3) = -.222390000685446, (2, 4) = -.753466150953458, (2, 5) = -.363589686697497, (3, 1) = -0.334789690624459e-1, (3, 2) = -.600272580693583, (3, 3) = -.450839268922308, (3, 4) = .233449657244714, (3, 5) = -.305475732747932, (4, 1) = -.429706903137018, (4, 2) = .236166806281125, (4, 3) = -.685862863873811, (4, 4) = .331860018200310, (4, 5) = .164927634884511, (5, 1) = -.469747921566658, (5, 2) = -.350891398883703, (5, 3) = .387444603099673, (5, 4) = .158735559582156, (5, 5) = -.518257437353535, (6, 1) = .293358758464403, (6, 2) = .576262119133891, (6, 3) = -0.208529179808710e-1, (6, 4) = .379077667060160, (6, 5) = -.652551600592398}), Vector(6, {(1) = 27.4687324182218, (2) = 22.6431850097747, (3) = 8.55838822848258, (4) = 5.98572320151213, (5) = 2.01489965871576, (6) = 0.}), Matrix(5, 5, {(1, 1) = -.251382792720498, (1, 2) = -.396845551776930, (1, 3) = -.692151007470363, (1, 4) = -.366170444772230, (1, 5) = -.407635238653352, (2, 1) = .814836686086339, (2, 2) = .358661500188002, (2, 3) = -.248888011159285, (2, 4) = -.368593537944618, (2, 5) = -0.979625692668875e-1, (3, 1) = -.260618505584221, (3, 2) = .700768209407253, (3, 3) = -.220811446720437, (3, 4) = .385938483188542, (3, 5) = -.493250142851024, (4, 1) = .396723777130597, (4, 2) = -.450711241216643, (4, 3) = .251321149693754, (4, 4) = .434248601436671, (4, 5) = -.622684072035804, (5, 1) = -.218027763686546, (5, 2) = .140209949871121, (5, 3) = .589119449239943, (5, 4) = -.626528250364817, (5, 5) = -.439551692342332})

(2)

SDM:= DiagonalMatrix(S[1..5],5,5)

Matrix(5, 5, {(1, 1) = 27.46873241822184, (1, 2) = 0., (1, 3) = 0., (1, 4) = 0., (1, 5) = 0., (2, 1) = 0., (2, 2) = 22.643185009774694, (2, 3) = 0., (2, 4) = 0., (2, 5) = 0., (3, 1) = 0., (3, 2) = 0., (3, 3) = 8.558388228482578, (3, 4) = 0., (3, 5) = 0., (4, 1) = 0., (4, 2) = 0., (4, 3) = 0., (4, 4) = 5.985723201512132, (4, 5) = 0., (5, 1) = 0., (5, 2) = 0., (5, 3) = 0., (5, 4) = 0., (5, 5) = 2.014899658715757})

(3)

THIS EQUALS TO ORIGINAL X MATRIX

 

U.SDM.Vt

Matrix(6, 5, {(1, 1) = 8.789999999999997, (1, 2) = 9.93, (1, 3) = 9.829999999999995, (1, 4) = 5.449999999999993, (1, 5) = 3.159999999999998, (2, 1) = 6.1099999999999985, (2, 2) = 6.9099999999999975, (2, 3) = 5.0399999999999965, (2, 4) = -.26999999999999996, (2, 5) = 7.980000000000001, (3, 1) = -9.14999999999999, (3, 2) = -7.930000000000001, (3, 3) = 4.859999999999987, (3, 4) = 4.849999999999992, (3, 5) = 3.009999999999995, (4, 1) = 9.569999999999997, (4, 2) = 1.6399999999999977, (4, 3) = 8.82999999999999, (4, 4) = .7399999999999956, (4, 5) = 5.799999999999994, (5, 1) = -3.489999999999992, (5, 2) = 4.019999999999998, (5, 3) = 9.799999999999985, (5, 4) = 9.999999999999988, (5, 5) = 4.269999999999993, (6, 1) = 9.83999999999999, (6, 2) = .15000000000000033, (6, 3) = -8.989999999999982, (6, 4) = -6.0199999999999925, (6, 5) = -5.309999999999993})

(4)

X -~ U.SDM.Vt

Matrix(6, 5, {(1, 1) = 0.1776356839e-14, (1, 2) = 0., (1, 3) = 0.5329070518e-14, (1, 4) = 0.7105427358e-14, (1, 5) = 0.2220446049e-14, (2, 1) = 0.1776356839e-14, (2, 2) = 0.2664535259e-14, (2, 3) = 0.3552713679e-14, (2, 4) = -0.5551115123e-16, (2, 5) = -0.8881784197e-15, (3, 1) = -0.1065814104e-13, (3, 2) = 0.8881784197e-15, (3, 3) = 0.1332267630e-13, (3, 4) = 0.7993605777e-14, (3, 5) = 0.4884981308e-14, (4, 1) = 0.3552713679e-14, (4, 2) = 0.2220446049e-14, (4, 3) = 0.1065814104e-13, (4, 4) = 0.4440892099e-14, (4, 5) = 0.6217248938e-14, (5, 1) = -0.7993605777e-14, (5, 2) = 0.1776356839e-14, (5, 3) = 0.1598721155e-13, (5, 4) = 0.1243449788e-13, (5, 5) = 0.6217248938e-14, (6, 1) = 0.1065814104e-13, (6, 2) = -0.3330669074e-15, (6, 3) = -0.1776356839e-13, (6, 4) = -0.7105427358e-14, (6, 5) = -0.6217248938e-14})

(5)

EIGENVALUES

 

S*~S

Vector(6, {(1) = 754.5312606638714, (2) = 512.7138273868854, (3) = 73.24600906942915, (4) = 35.82888224512065, (5) = 4.059820634692874, (6) = 0.})

(6)

EIGENVECTORS

 

Transpose(Vt)

Matrix(5, 5, {(1, 1) = -.2513827927204978, (1, 2) = .8148366860863387, (1, 3) = -.2606185055842209, (1, 4) = .39672377713059703, (1, 5) = -.21802776368654583, (2, 1) = -.3968455517769299, (2, 2) = .35866150018800186, (2, 3) = .7007682094072526, (2, 4) = -.45071124121664313, (2, 5) = .1402099498711206, (3, 1) = -.6921510074703628, (3, 2) = -.2488880111592855, (3, 3) = -.22081144672043732, (3, 4) = .2513211496937536, (3, 5) = .5891194492399427, (4, 1) = -.3661704447722298, (4, 2) = -.3685935379446182, (4, 3) = .3859384831885419, (4, 4) = .434248601436671, (4, 5) = -.6265282503648171, (5, 1) = -.4076352386533523, (5, 2) = -0.979625692668875e-1, (5, 3) = -.4932501428510237, (5, 4) = -.6226840720358041, (5, 5) = -.4395516923423325})

(7)

COMPARE LINE (6) AND THE evalues OF  LINE  (8), IN AGREEMENT.

 

COMPARE LINE (7) AND THE evectors OF LINE (8), NOT IN AGREEMENT.

 

evalues, evectors:= Eigenvectors(Transpose(X).X)

evalues, evectors := Vector(5, {(1) = 754.531260663872+0.*I, (2) = 512.713827386885+0.*I, (3) = 73.2460090694292+0.*I, (4) = 35.8288822451207+0.*I, (5) = 4.05982063469289+0.*I}), Matrix(5, 5, {(1, 1) = -.251382792720496+0.*I, (1, 2) = -.814836686086340+0.*I, (1, 3) = -.260618505584220+0.*I, (1, 4) = .396723777130597+0.*I, (1, 5) = .218027763686546+0.*I, (2, 1) = -.396845551776929+0.*I, (2, 2) = -.358661500188003+0.*I, (2, 3) = .700768209407252+0.*I, (2, 4) = -.450711241216643+0.*I, (2, 5) = -.140209949871121+0.*I, (3, 1) = -.692151007470364+0.*I, (3, 2) = .248888011159284+0.*I, (3, 3) = -.220811446720437+0.*I, (3, 4) = .251321149693753+0.*I, (3, 5) = -.589119449239943+0.*I, (4, 1) = -.366170444772231+0.*I, (4, 2) = .368593537944617+0.*I, (4, 3) = .385938483188543+0.*I, (4, 4) = .434248601436671+0.*I, (4, 5) = .626528250364817+0.*I, (5, 1) = -.407635238653353+0.*I, (5, 2) = 0.979625692668865e-1+0.*I, (5, 3) = -.493250142851024+0.*I, (5, 4) = -.622684072035804+0.*I, (5, 5) = .439551692342333+0.*I})

(8)

sdm:= DiagonalMatrix(evalues[1..5],5,5)

Matrix(5, 5, {(1, 1) = 754.5312606638715+0.*I, (1, 2) = 0.*I, (1, 3) = 0.*I, (1, 4) = 0.*I, (1, 5) = 0.*I, (2, 1) = 0.*I, (2, 2) = 512.7138273868852+0.*I, (2, 3) = 0.*I, (2, 4) = 0.*I, (2, 5) = 0.*I, (3, 1) = 0.*I, (3, 2) = 0.*I, (3, 3) = 73.2460090694292+0.*I, (3, 4) = 0.*I, (3, 5) = 0.*I, (4, 1) = 0.*I, (4, 2) = 0.*I, (4, 3) = 0.*I, (4, 4) = 35.82888224512066+0.*I, (4, 5) = 0.*I, (5, 1) = 0.*I, (5, 2) = 0.*I, (5, 3) = 0.*I, (5, 4) = 0.*I, (5, 5) = 4.0598206346928905+0.*I})

(9)

THIS SHOULD EQUAL TO THE ORIGINAL X MATRIX??

 

U.sdm.Transpose(evectors)

Matrix(6, 5, {(1, 1) = 0.6552908001635141e-1+0.*I, (1, 2) = 141.65095872384822+0.*I, (1, 3) = 338.83755003799257+0.*I, (1, 4) = 228.5810832324622+0.*I, (1, 5) = 175.59568314998398+0.*I, (2, 1) = -33.23139659260195+0.*I, (2, 2) = 75.17135144556929+0.*I, (2, 3) = 236.421687561631+0.*I, (2, 4) = 136.98207278415265+0.*I, (2, 5) = 158.72195870452097+0.*I, (3, 1) = 268.7849531650388+0.*I, (3, 2) = 93.67237457619457+0.*I, (3, 3) = -48.99100376421241+0.*I, (3, 4) = -114.08088481922744+0.*I, (3, 5) = -9.317711776596651+0.*I, (4, 1) = .7955765643196264+0.*I, (4, 2) = 44.582065761106776+0.*I, (4, 3) = 268.23773062231106+0.*I, (4, 4) = 149.54848119026994+0.*I, (4, 5) = 161.6981236670314+0.*I, (5, 1) = 230.09623253311864+0.*I, (5, 2) = 222.80201293072588+0.*I, (5, 3) = 196.9514995697131+0.*I, (5, 4) = 75.57668964466434+0.*I, (5, 5) = 108.39382140065305+0.*I, (6, 1) = -291.18409102891843+0.*I, (6, 2) = -200.6307865795955+0.*I, (6, 3) = -74.35923030344051+0.*I, (6, 4) = 31.501149679670085+0.*I, (6, 5) = -70.1539507795088+0.*I})

(10)

X -~ U.sdm.Transpose(evectors)

Matrix(6, 5, {(1, 1) = 8.724470919983649+0.*I, (1, 2) = -131.7209587238482+0.*I, (1, 3) = -329.0075500379926+0.*I, (1, 4) = -223.1310832324622+0.*I, (1, 5) = -172.435683149984+0.*I, (2, 1) = 39.34139659260195+0.*I, (2, 2) = -68.26135144556929+0.*I, (2, 3) = -231.381687561631+0.*I, (2, 4) = -137.25207278415266+0.*I, (2, 5) = -150.74195870452098+0.*I, (3, 1) = -277.9349531650388+0.*I, (3, 2) = -101.60237457619456+0.*I, (3, 3) = 53.85100376421241+0.*I, (3, 4) = 118.93088481922743+0.*I, (3, 5) = 12.32771177659665+0.*I, (4, 1) = 8.774423435680374+0.*I, (4, 2) = -42.942065761106775+0.*I, (4, 3) = -259.4077306223111+0.*I, (4, 4) = -148.80848119026993+0.*I, (4, 5) = -155.8981236670314+0.*I, (5, 1) = -233.58623253311865+0.*I, (5, 2) = -218.78201293072587+0.*I, (5, 3) = -187.15149956971308+0.*I, (5, 4) = -65.57668964466434+0.*I, (5, 5) = -104.12382140065306+0.*I, (6, 1) = 301.0240910289184+0.*I, (6, 2) = 200.7807865795955+0.*I, (6, 3) = 65.36923030344052+0.*I, (6, 4) = -37.52114967967009+0.*I, (6, 5) = 64.8439507795088+0.*I})

(11)

 

Download SVD_test.mw

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