Maple 2022 Questions and Posts

These are Posts and Questions associated with the product, Maple 2022

Why there is an error? Is any part missing in the if statement?

restart

rel := w+(1/2)*sqrt(960*c^6*gamma^2*k^2-336*c^4*gamma^2*k^4+64*c^2*gamma^2*k^6-4*gamma^2*k^8+576*alpha*c^6*gamma*k-288*alpha*c^4*gamma*k^3-16*alpha*c^2*gamma*k^5+8*alpha*gamma*k^7-144*alpha^2*c^4*k^2-48*alpha^2*c^2*k^4-4*alpha^2*k^6+128*c^4*gamma*k^2-40*c^2*gamma*k^4+4*gamma*k^6+48*alpha*c^4*k-16*alpha*c^2*k^3-4*alpha*k^5+4*c^2*k^2-k^4)

w+(1/2)*(960*c^6*gamma^2*k^2-336*c^4*gamma^2*k^4+64*c^2*gamma^2*k^6-4*gamma^2*k^8+576*alpha*c^6*gamma*k-288*alpha*c^4*gamma*k^3-16*alpha*c^2*gamma*k^5+8*alpha*gamma*k^7-144*alpha^2*c^4*k^2-48*alpha^2*c^2*k^4-4*alpha^2*k^6+128*c^4*gamma*k^2-40*c^2*gamma*k^4+4*gamma*k^6+48*alpha*c^4*k-16*alpha*c^2*k^3-4*alpha*k^5+4*c^2*k^2-k^4)^(1/2)

(1)

crit_points := solve(diff(rel, k) = 0, k); rel_at_crit := subs(k = crit_points, rel)

"#` determine the maxima and minima by checking the sign of the second derivative at the critical points`  for i from 1 to nops(crit_points) do    if (eval(diff(diff(rel, k), k), k = crit_points[i]) > 0) then      print("Minimum at k = ", crit_points[i], " with value ", rel_at_crit[i]);    else if (eval(diff(diff(rel, k), k), k = crit_points[i]) < 0) then      print("Maximum at k = ", crit_points[i], " with value ", rel_at_crit[i]);    else      print("Saddle point at k = ", crit_points[i], " with value ", rel_at_crit[i]);    end if;  end do; "

Error, invalid if statement termination

"#` determine the maxima and minima by checking the sign of the second derivative at the critical points`  for i from 1 to nops(crit_points) do    if (eval(diff(diff(rel, k), k), k = crit_points[i]) > 0) then   print("Minimum at k = ", crit_points[i], " with value ", rel_at_crit[i]);    else if (eval(diff(diff(rel, k), k), k = crit_points[i]) < 0) then   print("Maximum at k = ", crit_points[i], " with value ", rel_at_crit[i]);    else   print("Saddle point at k = ", crit_points[i], " with value ", rel_at_crit[i]);    end if;  end do; "

 

NULL

Download maxnmin.mw

I input this codes:

latex((4*n-1)/9-7/16*n)

\frac{n}{144}-\frac{1}{9}

This is not the output I expected.  I would like to obtain an expression similar to the one below.

\frac{4 n-1}{9}-\frac{7}{16}n

How can I achieve this, as Maple seems to have processed it internally.

Does maple over-understand the expression.

Hi, I would appreciate some help in solving the following system of partial differential equations. The particularity of the system is that only the individual variables (i.e. a, c, and l) depend on two arguments (t: current time period and v: date of birth). The other variables are either rates or aggregates. The aggregate variables (i.e. K, L, and Y) depend only on time, t, because they are the integrals of the individual variables over v. Thanks for your help.

NULL

NULL

restart; with(PDEtools)

alpha := .3306341; delta := solve(1+0.4877489e-1 = exp(delta_a)); T := 1

l0 := 42.375*(33.16667/(52*(24-9.95)*7)); L0 := l0*T

x0 := 0

IOR := .2093723865

KOR := IOR/delta

r0 := alpha/KOR-delta; rho := r0; fsolve({K0 = Y0*KOR, w0 = (1-alpha)*Y0/L0, alpha*exp(x0)*K0^(alpha-1)*L0^(1-alpha) = r0+delta}); assign(%)

0.2758153402e-1

 

{K0 = 2.510740299, Y0 = .5710794198, w0 = 1.390997088}

(1)

C0 := -K0*delta+Y0; c0 := C0/T

.4515111588

 

.4515111588

(2)

sigma := w0*(1-l0)/c0

2.234133040

(3)

eq1 := diff(c(t, v), t) = (r(t)-rho)*c(t, v)

eq2 := sigma*c(t, v) = w(t)*(1-l(t, v))

eq3 := r(t)*a(t, v)+w(t)*l(t, v) = c(t, v)+diff(a(t, v), t)

eq4 := Y(t) = exp(x(t))*K(t)^alpha*L(t)^(1-alpha)

eq5 := r(t)-delta = alpha*Y(t)/K(t)

eq6 := w(t) = (1-alpha)*Y(t)/L(t)

eq7 := K(t) = int(a(t, v), v = t-T .. t)

eq8 := L(t) = int(l(t, v), v = t-T .. t)

eq9 := x(t) = piecewise(t = 0, 0, t > 0, 0.1e-1)

eq := {eq1, eq2, eq3, eq4, eq5, eq6, eq7, eq8, eq9}

SV := {K(0) = K0, L(0) = L0, Y(0) = Y0, a(t, 0) = 0, c(0, 0) = c0, l(0, 0) = l0, r(0) = r0, w(0) = w0}

pdsolve(eq, SV, numeric, 'time' = t, 'range' = 0 .. T)

Error, (in pdsolve/numeric/process_PDEs) variable(s) {v} are in the PDE system but are not dependent or independent variables

 

sol := pdsolve(eq, SV, 'time' = t, 'range' = 0 .. T)

(4)

NULL

Download OLG.mw

Hi,

I have been bothered lately by the number format for axis labels in Maple. My problem existed before, but it apparently didn't bother me before. I have spent many hours trying to find an answer in the program help, in MaplePrimes, and in general online searches. I am not having any luck at all (good luck, that is).

I want to change the format of the axis numbering. Maple seems to default to 2 decimal places in my graph, and I really need more. Oddly, when I export the graph to PDF, I get another decimal place (even though I didn't explicitly ask for one). 

How do I change the axis-label format? Any idea what I might get when I export the graph?

Thanks for your help,

Jno.

 

How can I change the order of variables in a polynomial as I want? For example, I want to assign a polynomial G of 3 variables a,b,c. Then I want to compute G(a,b,c) (exchange the variable a to b, exchange variable b to a)?

I've probably asked about this long time ago but I do not remember now. But it is still a problem any way in 2022.2

Compare these two results

code is

 

restart;

alias(seq(c[k] = _C||k, k = 0..10));
c[1]*h(x);
Int(c[1]*h(x),x);


restart;
c[1]*h(x);
Int(c[1]*h(x),x);

I tried with typesetting level as extended and standard and same result.

Is this a know issue? It is not a big deal as it only affects display but it will be nice to find why it happens when using alias.

 

This a more a math question than  a maple programming question. But interesting.

I have a point P=[x,y] on a line y= 2+3x. The point maps to Pn=[f(x, y), g(x, y)]. That represents a conic.

I want to find the equation of the conic. I did it by calculating 5 points and that works fine but only because I know I'm looking for a conic. 

Can the problem by solved without having to get the five points?
I copied and pasted the equations for the lines because they were generated by commands in a pagkage I have.

restart

NULL

NULL

P := [X, Y]

[X, Y]

``

NULL

Pn := [(5*X+12*Y)*(-384+48*X+55*Y)/(225*X^2+225*Y^2-1800*X-602*Y), (2*(12*X-5*Y))*(-384+48*X+55*Y)/(225*X^2+225*Y^2-1800*X-602*Y)]

[(5*X+12*Y)*(-384+48*X+55*Y)/(225*X^2+225*Y^2-1800*X-602*Y), 2*(12*X-5*Y)*(-384+48*X+55*Y)/(225*X^2+225*Y^2-1800*X-602*Y)]

NULL

``

Y := 2+3*Xn

2+3*X

``

for i to 5 do P || i := eval(Pn, X = i) end do

[181139/51416, -19775/25708]

NULL

l12 := 153621*x*(1/68840)+169429*y*(1/27536)-15067/17210

(153621/68840)*x+(169429/27536)*y-15067/17210

NULL

l34 := -5733*x*(1/473062)+258973*y*(1/946124)+244205/946124

-(5733/473062)*x+(258973/946124)*y+244205/946124

c1 := l12*l34

((153621/68840)*x+(169429/27536)*y-15067/17210)*(-(5733/473062)*x+(258973/946124)*y+244205/946124)

NULL

l13 := 5499*x*(1/2360)+6539*y*(1/944)-793/472

(5499/2360)*x+(6539/944)*y-793/472

l24 := 596115*x*(1/6899489)+7228091*y*(1/6899489)+195364/363131

(596115/6899489)*x+(7228091/6899489)*y+195364/363131

plots:-implicitplot([l12, l34, l13, l24])

c2 := l13*l24

((5499/2360)*x+(6539/944)*y-793/472)*((596115/6899489)*x+(7228091/6899489)*y+195364/363131)

c := simplify(c2*lambda+c1)

(655607277/3256558808)*(x+(2515/846)*y-305/423)*(x+(556007/45855)*y+285532/45855)*lambda-(880709193/32565588080)*(x-(19921/882)*y-18785/882)*(x+(65165/23634)*y-4636/11817)

lambda := solve(eval(c, [x = P5[1], y = P5[2]]), lambda)

-1/4

simplify(c)

-(5039454771/65131176160)*x^2+(1/130262352320)*(-29130506847*y+40315638168)*x-(423368829/3256558808)*y^2+(111619143207/130262352320)*y

plt1 := plot(Y, X = -10 .. 10)

NULL

NULL

plt2 := plots:-implicitplot([c])

plots:-display(plt1, plt2, colour = ["Red", "Green"])

NULL

for i in [-7, 13/3, 42*(1/7)] do x := eval(Pn[1], X = i); y := eval(Pn[2], X = i); simplify(c) end do

0

NULL

Download Q_23-03-04_how_to_find_conic_from_mapping.mw

Maple continuously shows 'Evaluating' and there is no output. How to fix it?

restart

with(LinearAlgebra)

assume(x::real); assume(t::real); assume(`&alpha;__1`::real); assume(`&alpha;__2`::real); assume(nu::real)

A2s := Matrix([[H__11*exp(I*v__11)/(`&lambda;__1`-conjugate(`&lambda;__1`))+H__13*exp(I*v__21)/(`&lambda;__1`-conjugate(`&lambda;__2`))+1, H__12*exp(-I*v__11)/(`&lambda;__1`-conjugate(`&lambda;__1`))+H__14*exp(-I*v__21)/(`&lambda;__1`-conjugate(`&lambda;__2`)), H__11*exp(I*v__12)/(`&lambda;__2`-conjugate(`&lambda;__1`))+H__13*exp(I*v__22)/(`&lambda;__2`-conjugate(`&lambda;__2`)), H__12*exp(-I*v__12)/(`&lambda;__2`-conjugate(`&lambda;__1`))+H__14*exp(-I*v__22)/(`&lambda;__2`-conjugate(`&lambda;__2`))], [H__12*exp(I*v__11)/(`&lambda;__1`-conjugate(`&lambda;__1`))+H__14*exp(I*v__21)/(`&lambda;__1`-conjugate(`&lambda;__2`)), 1+H__11*exp(-I*v__11)/(`&lambda;__1`-conjugate(`&lambda;__1`))+H__13*exp(-I*v__21)/(`&lambda;__1`-conjugate(`&lambda;__2`)), H__12*exp(I*v__12)/(`&lambda;__2`-conjugate(`&lambda;__1`))+H__14*exp(I*v__22)/(`&lambda;__2`-conjugate(`&lambda;__2`)), H__11*exp(-I*v__12)/(`&lambda;__2`-conjugate(`&lambda;__1`))+H__13*exp(-I*v__22)/(`&lambda;__2`-conjugate(`&lambda;__2`))], [H__13*exp(I*v__11)/(`&lambda;__1`-conjugate(`&lambda;__1`))+H__33*exp(I*v__21)/(`&lambda;__1`-conjugate(`&lambda;__2`)), H__14*exp(-I*v__11)/(`&lambda;__1`-conjugate(`&lambda;__1`))+H__34*exp(-I*v__21)/(`&lambda;__1`-conjugate(`&lambda;__2`)), 1+H__13*exp(I*v__12)/(`&lambda;__2`-conjugate(`&lambda;__1`))+H__33*exp(I*v__22)/(`&lambda;__2`-conjugate(`&lambda;__2`)), H__14*exp(-I*v__12)/(`&lambda;__2`-conjugate(`&lambda;__1`))+H__34*exp(-I*v__22)/(`&lambda;__2`-conjugate(`&lambda;__2`))], [H__14*exp(I*v__11)/(`&lambda;__1`-conjugate(`&lambda;__1`))+H__34*exp(I*v__21)/(`&lambda;__1`-conjugate(`&lambda;__2`)), H__13*exp(-I*v__11)/(`&lambda;__1`-conjugate(`&lambda;__1`))+H__33*exp(-I*v__21)/(`&lambda;__1`-conjugate(`&lambda;__2`)), H__14*exp(I*v__12)/(`&lambda;__2`-conjugate(`&lambda;__1`))+H__34*exp(I*v__22)/(`&lambda;__2`-conjugate(`&lambda;__2`)), H__13*exp(-I*v__12)/(`&lambda;__2`-conjugate(`&lambda;__1`))+H__33*exp(-I*v__22)/(`&lambda;__2`-conjugate(`&lambda;__2`))+1]])

Matrix(%id = 36893490803012390908)

(1)

vvalue := {v__11 = (conjugate(`&lambda;__1`)-`#msub(mi("&lambda;",fontstyle = "normal"),mn("1"))`)*x+(4*`&alpha;__1`*(conjugate(`&lambda;__1`)^3-`&lambda;__1`^3)+2*`&alpha;__2`*(conjugate(`&lambda;__1`)^2-`&lambda;__1`^2)-8*nu*(conjugate(`&lambda;__1`)^4-`&lambda;__1`^4))*t, v__12 = (conjugate(`&lambda;__1`)-`#msub(mi("&lambda;",fontstyle = "normal"),mn("2"))`)*x+(4*`&alpha;__1`*(conjugate(`&lambda;__1`)^3-`&lambda;__2`^3)+2*`&alpha;__2`*(conjugate(`&lambda;__1`)^2-`&lambda;__2`^2)-8*nu*(conjugate(`&lambda;__1`)^4-`&lambda;__2`^4))*t, v__21 = (conjugate(`&lambda;__2`)-`#msub(mi("&lambda;",fontstyle = "normal"),mn("1"))`)*x+(4*`&alpha;__1`*(conjugate(`&lambda;__2`)^3-`&lambda;__1`^3)+2*`&alpha;__2`*(conjugate(`&lambda;__2`)^2-`&lambda;__1`^2)-8*nu*(conjugate(`&lambda;__2`)^4-`&lambda;__1`^4))*t, v__22 = (conjugate(`&lambda;__2`)-`#msub(mi("&lambda;",fontstyle = "normal"),mn("2"))`)*x+(4*`&alpha;__1`*(conjugate(`&lambda;__2`)^3-`&lambda;__2`^3)+2*`&alpha;__2`*(conjugate(`&lambda;__2`)^2-`&lambda;__2`^2)-8*nu*(conjugate(`&lambda;__2`)^4-`&lambda;__2`^4))*t}

{v__11 = (conjugate(lambda__1)-`#msub(mi("&lambda;",fontstyle = "normal"),mn("1"))`)*x+(4*alpha__1*(conjugate(lambda__1)^3-lambda__1^3)+2*alpha__2*(conjugate(lambda__1)^2-lambda__1^2)-8*nu*(conjugate(lambda__1)^4-lambda__1^4))*t, v__12 = (conjugate(lambda__1)-`#msub(mi("&lambda;",fontstyle = "normal"),mn("2"))`)*x+(4*alpha__1*(conjugate(lambda__1)^3-lambda__2^3)+2*alpha__2*(conjugate(lambda__1)^2-lambda__2^2)-8*nu*(conjugate(lambda__1)^4-lambda__2^4))*t, v__21 = (conjugate(lambda__2)-`#msub(mi("&lambda;",fontstyle = "normal"),mn("1"))`)*x+(4*alpha__1*(conjugate(lambda__2)^3-lambda__1^3)+2*alpha__2*(conjugate(lambda__2)^2-lambda__1^2)-8*nu*(conjugate(lambda__2)^4-lambda__1^4))*t, v__22 = (conjugate(lambda__2)-`#msub(mi("&lambda;",fontstyle = "normal"),mn("2"))`)*x+(4*alpha__1*(conjugate(lambda__2)^3-lambda__2^3)+2*alpha__2*(conjugate(lambda__2)^2-lambda__2^2)-8*nu*(conjugate(lambda__2)^4-lambda__2^4))*t}

(2)

NULL

A2s2 := Determinant(A2s); dets22 := simplify(A2s2, size); length(%)

8949

(3)

dets22f := simplify(subs(vvalue, dets22))

NULL

Download sol1det.mw

Hi,

I am trying to automatically combine plots that I created with an index: ex. IP[i] := plot(...

I can combine them manually, but the maximum value of i can be almost any number greater than 1, and I don’t want to edit things all the time. i can also be very big. I have tried several random ways of embedding the index, but I’ve had no success.

Any ideas? Thanks.

Jno.

This is my current code:

with~([NumberTheory, DocumentTools]):
tb := Tabulate([seq]([galois](CyclotomicPolynomial(i, x),x), i = 1 .. 10)):

I hope to export it into SVG file, but this code will report a error information:

Export("aatest.svg", tb)
printf("%", [[]]);

Yeah, it is incompatible with the Maple syntax. But I don't know why this command actually causes a serious logic error here. Actually, this seems fairly trifling in my view. Can you produce it again? 

restart

printf("%", [[]]);

NULL

Download printfIssue.mws

after updating to latest Physics package, I find now latex geneated is invalid as it gives compile error.

I looked at old files I have and I see the latex generated before was correct. so something changed in the latex() command to cause this and now none of my files compile when I run my Maple program.

Before, same code used to generate this

 \left(-x^{2}+1\right) \left(y^{\prime}\right)^{2} = 1-y^{2} 

which compiled correctly.

Here is worksheet
 

interface(version)

`Standard Worksheet Interface, Maple 2022.2, Windows 10, October 23 2022 Build ID 1657361`

Physics:-Version()

`The "Physics Updates" version in the MapleCloud is 1378 and is the same as the version installed in this computer, created 2023, January 29, 12:4 hours Pacific Time.`

latex:-Settings(useimaginaryunit=i,
      usecolor = false,
      powersoftrigonometricfunctions= mixed, ## computernotation,
      leavespaceafterfunctionname = true,
      cacheresults = false,
      spaceaftersqrt = true,
      linelength=10000  
);
Typesetting:-Unsuppress('all'); #always do this.
Typesetting:-Settings(prime=x,'typesetprime'=true); #this says to use y'(x) instead of dy/dx    
Typesetting:-Suppress(y(x)); # this says to use y' and not y'(x)

[useimaginaryunit = i, usecolor = false, powersoftrigonometricfunctions = mixed, leavespaceafterfunctionname = true, cacheresults = false, spaceaftersqrt = true, linelength = 10000]

x, false

ode:=(-x^2+1)*diff(y(x),x)^2 = 1-y(x)^2;

(-x^2+1)*(diff(y(x), x))^2 = 1-y(x)^2

latex(ode)

\left(-x^{2}+1\right) y^{\prime}^{2} = 1-y^{2}

 

 

The error from the latex compiler is 

 

\documentclass[12pt]{book}
\usepackage{breqn}
\usepackage{amsmath}
\begin{document}

\begin{dmath*}
\left(-x^{2}+1\right) y^{\prime}^{2} = 1-y^{2}
\end{dmath*}

\end{document}

compiled using texlive lualatex command gives

(/usr/local/texlive/2022/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg))
! Double superscript.
<recently read> \mathsup 
         
l.12 \left(-x^{2}+1\right) y^{\prime}^{2}
                                        = 1-y^{2}
? 

The fix is to keep same latex as before or use an extra {} like this  {y^{\prime}}^{2} 

but I think \left(y^{\prime}\right)^{2} looks better. But y^{\prime}^{2} is definitly wrong latex.

Download latex_problem.mw

Hello guys
I'm having trouble solving a PDE using pdsolve-numerical. Here's a notebook attached.

I'm grateful if anyone can help.

Regards,

Oliveira

                   PDE1.mw

x := 19.073*Unit('m'^4*'kg'^2/('s'^6*'A'^2)); simplify(x); Units:-Simple:-simplify(x); Units:-Standard:-simplify(x); Units:-Natural:-simplify(x); convert(x, units, V^2); # None of the simplify commands do anything. Is there a way to get the last result?

interface(version);

`Standard Worksheet Interface, Maple 2022.2, Windows 10, October 23 2022 Build ID 1657361`

restart;
ode := diff(y(x),x)/y(x)-(3*(4*x^2+y(x)^2+1))/(2*x*(4*x^2+y(x)^2-2-2*x))=0;
DEtools:-odeadvisor(ode);
sol:=dsolve(ode,y(x));

(diff(y(x), x))/y(x)-(3/2)*(4*x^2+y(x)^2+1)/(x*(4*x^2+y(x)^2-2-2*x)) = 0

[_rational]

Error, (in dsolve) invalid subscript selector

 

Download error_jan_27_2023.mw

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