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19 years, 358 days
Ontario, Canada

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These are answers submitted by acer

ScrollableMathTableOutput = false...

acer 32420
7 hours ago
1 0

Your worksheet contains the input,

   ScrollableMathTableOutput = false

but that would do nothing as Maple input. It's not an assignment and, more importantly, there is no such programmatic option. It can't do anything relevant here.

There can be a meaningful such line, if you add it using an external text editor (preferably while the Maple GUI is not running), in the GUI's stored configuration/preferences file. That is not a file of Maple commands. It's a file of stored GUI options/preferences.

I don't know whether that would resolve your problem. But note that your worksheet did not, in and of itself, disable matrix scrolling. So you may well not have actually successfully tried that yet.
 

ps. Your worksheet attachment was last saved using Maple 2025.0. It may not fix this particular issue, but you might otherwise benefit from the Maple 2025.1 point-release update.

the changed behavior...

acer 32420
7 hours ago
1 0

The relevant thing that changed in Maple's behavior is that lowercase int began to try floating-point quadrature (aka numeric integration) in the case that it detects floats in the integrand. (Previously, it did that if only the numeric range contained floats.) This happens to have exposed a weakness in a particular numeric integration method.

So now your example (with the float in the integrand) is attempting numeric rather than symbolic integration, and it goes wrong using the _d01amc method.

Note however that you can disable that computational route, for the int command here, by supplying the numeric=false option. Then you'd get successful symbolic integration here, even for this example with a float in the integrand.

You could also get successful numeric integration here by forcing some other method (or raising Digits).

I believe that covers the relevant details. You can see the commonalities below, run with Maple 2022.2 versus Maple 2024.2. It is only the first variant below which changed, which behaves like the OP's example.

> 

restart;
> 

kernelopts(version);

`Maple 2022.2, X86 64 LINUX, Oct 23 2022, Build ID 1657361`

> 

infolevel[`evalf/int`]:=1:
> 

int(1e6*exp(-1e6*t), t=0..infinity);

1.

> 

infolevel[`evalf/int`]:=1:
> 

int(1e6*exp(-1e6*t), t=0.0..infinity);

evalf/int/control: attempting Levin method

evalf/int/control: attempting Levin method

evalf/int/control: attempting Levin method

Control: Entering NAGInt

trying d01amc (nag_1d_quad_inf)

d01amc: result=0.

0.

> 

restart;
> 

infolevel[`evalf/int`]:=1:
> 

evalf(Int(1e6*exp(-1e6*t), t=0..infinity));

evalf/int/control: attempting Levin method

evalf/int/control: attempting Levin method

evalf/int/control: attempting Levin method

Control: Entering NAGInt

trying d01amc (nag_1d_quad_inf)

d01amc: result=0.

0.

> 

restart;
> 

infolevel[`evalf/int`]:=1:
> 

int(1e6*exp(-1e6*t), t=0.0..infinity, numeric=false);

1

> 

restart;
> 

map(M->int(1e6*exp(-1e6*t), t=0.0..infinity, method=M),
    [_d01amc,gquad,_Dexp,_d01ajc]);

[0., 1., 1.000000000, 1.]

> 

restart;
Digits:=16:
> 

map(M->int(1e6*exp(-1e6*t), t=0.0..infinity, method=M),
    [_d01amc,gquad,_Dexp,_d01ajc]);

[1., 1., 1.000000000000000, 1.]

Download int_deta_2022.2.mw

> 

restart;
> 

kernelopts(version);

`Maple 2024.2, X86 64 LINUX, Oct 29 2024, Build ID 1872373`

> 

infolevel[`evalf/int`]:=1:
> 

int(1e6*exp(-1e6*t), t=0..infinity);

evalf/int/control: attempting Levin method

evalf/int/control: attempting Levin method

evalf/int/control: attempting Levin method

Control: Entering NAGInt

trying d01amc (nag_1d_quad_inf)

d01amc: result=0.

0.

> 

infolevel[`evalf/int`]:=1:
> 

int(1e6*exp(-1e6*t), t=0.0..infinity);

evalf/int/control: attempting Levin method

evalf/int/control: attempting Levin method

evalf/int/control: attempting Levin method

Control: Entering NAGInt

trying d01amc (nag_1d_quad_inf)

d01amc: result=0.

0.

> 

restart;
> 

infolevel[`evalf/int`]:=1:
> 

evalf(Int(1e6*exp(-1e6*t), t=0..infinity));

evalf/int/control: attempting Levin method

evalf/int/control: attempting Levin method

evalf/int/control: attempting Levin method

Control: Entering NAGInt

trying d01amc (nag_1d_quad_inf)

d01amc: result=0.

0.

> 

restart;
> 

infolevel[`evalf/int`]:=1:
> 

int(1e6*exp(-1e6*t), t=0.0..infinity, numeric=false);

1.

> 

restart;
> 

map(M->int(1e6*exp(-1e6*t), t=0.0..infinity, method=M),
    [_d01amc,gquad,_Dexp,_d01ajc]);

[0., 1., 1.000000000, 1.]

> 

restart;
Digits:=16:
> 

map(M->int(1e6*exp(-1e6*t), t=0.0..infinity, method=M),
    [_d01amc,gquad,_Dexp,_d01ajc]);

[1., 1., 1.000000000000000, 1.]

Download int_deta_2024.2.mw

structured type...

acer 32420
Yesterday at 10:36 PM
1 0

For example,

type(y(x), And(typefunc(symbol,symbol),
               satisfies(u->nops(u)=1)));

                true

If you actually intended name instead of (either instance of) symbol then you could change accordingly.

animations...

acer 32420
September 17 2025
0 0

The animate export of the solution modules returned by pdsolve,numeric is  considerately more efficient than generating frames as separate plots and thus repeatedly pushing the computation further out.

The results of separate animations can also be ripped out of each structure and then recombined so that they show together.

The following seems reasonably quick, taking about 12 seconds to do the computational work on my machine, ie. generating the 4*2*2*35=560 curves.

I've used Maple 2018, as the OP did.

> 

restart
> 

Nc := .3; M := 1.5; QG := 1.5; Thetaa := .2; n1 := 1; n2 := 0; lambda1 := .1; lambda2 := .1; lambda3 := .1p := 2; a := .5; alpha1 := (1/2)*PiNULL
> 

p1 := 0.1e-1; p2 := 0.1e-1
> 

rf := 997.1; kf := .613; cpf := 4179; betaf := 21*10^(-5)
> 

betas1 := .85*10^(-5); rs1 := 3970; ks1 := 40; cps1 := 765
> 

betas2 := 1.67*10^(-5); rs2 := 8933; ks2 := 401; cps2 := 385
> 

z1 := 1/((1-p1)^2.5*(1-p2)^2.5)
> 

knf := kf*(ks1+2*kf-2*p1*(kf-ks1))/(ks1+2*kf+p1*(kf-ks1)); khnf := knf*(ks2+2*knf-2*p2*(knf-ks2))/(ks2+2*knf+p2*(knf-ks2))
> 

z2 := 1-p1-p2+p1*rs1/rf+p2*rs2/rf
> 

z3 := 1-p1-p2+p1*rs1*cps1/(rf*cpf)+p2*rs2*cps2/(rf*cpf)
> 

z4 := khnf/kf
> 

z5 := 1-p1-p2+p1*rs1*betas1/(rf*betaf)+p2*rs2*betas2/(rf*betaf)
> 

OdeSys := z4*(X*(diff(Theta(X, tau), X, X))+diff(Theta(X, tau), X))/z3-(diff(Theta(X, tau), tau))-Nc*(Theta(X, tau)-Thetaa)^2*z5/z1-M^2*(Theta(X, tau)-Thetaa)^(p+1)*(1+n1*z2/z3)/(z3*(1-Thetaa)^p)-Nr*(Theta(X, tau)^4-Thetaa^4)/z3+QG*X*(1+lambda1*(Theta(X, tau)-Thetaa)+lambda2*(Theta(X, tau)-Thetaa)^2+lambda3*(Theta(X, tau)-Thetaa)^3)/z3; Cond := {Theta(0, tau) = 1+a*sin(alpha1), Theta(X, 0) = 0, (D[1](Theta))(1, tau) = 0}
> 

OdeSys1 := z4*(X*(diff(Theta(X, tau), X, X))+diff(Theta(X, tau), X))/z3-(diff(Theta(X, tau), tau))-Nc*(Theta(X, tau)-Thetaa)^2*z5/z1-M^2*(Theta(X, tau)-Thetaa)^(p+1)*(1+n2*z2/z3)/(z3*(1-Thetaa)^p)-Nr*(Theta(X, tau)^4-Thetaa^4)/z3+QG*X*(1+lambda1*(Theta(X, tau)-Thetaa)+lambda2*(Theta(X, tau)-Thetaa)^2+lambda3*(Theta(X, tau)-Thetaa)^3)/z3; Cond1 := {Theta(0, tau) = 1+a*sin(alpha1), Theta(X, 0) = 0, (D[1](Theta))(1, tau) = 0}
> 

OdeSysa := z4*(X*(diff(Theta(X, tau), X, X))+diff(Theta(X, tau), X))/z3-(diff(Theta(X, tau), tau))-Nc*(Theta(X, tau)-Thetaa)^2*z5/z1-M^2*(Theta(X, tau)-Thetaa)^(p+1)*(1+n1*z2/z3)/(z3*(1-Thetaa)^p)-Nr*(Theta(X, tau)^4-Thetaa^4)/z3+QG*X*(1+lambda1*(Theta(X, tau)-Thetaa)+lambda2*(Theta(X, tau)-Thetaa)^2+lambda3*(Theta(X, tau)-Thetaa)^3)/z3; Conda := {Theta(0, tau) = 1+a*cos(alpha1), Theta(X, 0) = 0, (D[1](Theta))(1, tau) = 0}
> 

OdeSysa1 := z4*(X*(diff(Theta(X, tau), X, X))+diff(Theta(X, tau), X))/z3-(diff(Theta(X, tau), tau))-Nc*(Theta(X, tau)-Thetaa)^2*z5/z1-M^2*(Theta(X, tau)-Thetaa)^(p+1)*(1+n2*z2/z3)/(z3*(1-Thetaa)^p)-Nr*(Theta(X, tau)^4-Thetaa^4)/z3+QG*X*(1+lambda1*(Theta(X, tau)-Thetaa)+lambda2*(Theta(X, tau)-Thetaa)^2+lambda3*(Theta(X, tau)-Thetaa)^3)/z3; Conda1 := {Theta(0, tau) = 1+a*cos(alpha1), Theta(X, 0) = 0, (D[1](Theta))(1, tau) = 0}
> 

colour := [cyan, black]; colour1 := [red, blue]
> 

NrVals := [2.5, 3.5]
> 

NN := 35:
str := time[real]():
for j from 1 to nops(NrVals) do
Ans := pdsolve((eval([OdeSys,Cond],Nr=NrVals[j]))[],numeric,spacestep=1/200,timestep=1/100):
Ans1 := pdsolve((eval([OdeSys1,Cond1],Nr=NrVals[j]))[],numeric,spacestep=1/200,timestep=1/100):
Ansa := pdsolve((eval([OdeSysa,Conda],Nr=NrVals[j]))[],numeric,spacestep=1/200,timestep=1/100):
Ansa1 := pdsolve((eval([OdeSysa1,Conda1], Nr=NrVals[j]))[],numeric,spacestep=1/200,timestep=1/100):

eta[j] := Ans:-animate((int(z3*z5*Nc*(Theta(X, tau)-Thetaa)^2/(z1*z4)+NrVals[j]*(Theta(X, tau)^4-Thetaa^4)/z4+M^2*(Theta(X, tau)-Thetaa)^(p+1)*(1+n1*z2/z3)/(z4*(1-Thetaa)^p), X = 0 .. 1,numeric,epsilon=1e-5,method=_Dexp))/(z3*z5*Nc*(1-Thetaa)^2/(z1*z4)+NrVals[j]*(-Thetaa^4+1)/z4+M^2*(1-Thetaa)*(1+n1*z2/z3)/z4), tau = 0 .. 2, X = 0.01..1.0, frames=NN, linestyle = "solid", 'axes' = 'boxed', labels = [" τ ", " η "], color = colour[j], title="X = %4.3f"):
eta1[j] := Ans1:-animate((int(z3*z5*Nc*(Theta(X, tau)-Thetaa)^2/(z1*z4)+NrVals[j]*(Theta(X, tau)^4-Thetaa^4)/z4+M^2*(Theta(X, tau)-Thetaa)^(p+1)*(1+n2*z2/z3)/(z4*(1-Thetaa)^p), X = 0 .. 1,numeric,epsilon=1e-5,method=_Dexp))/(z3*z5*Nc*(1-Thetaa)^2/(z1*z4)+NrVals[j]*(-Thetaa^4+1)/z4+M^2*(1-Thetaa)*(1+n2*z2/z3)/z4), tau = 0 .. 2, X = 0.01..1.0, frames=NN, linestyle = "dash", 'axes' = 'boxed', labels = [" τ ", " η "], color = colour[j], title="X = %4.3f");
etaa[j] := Ansa:-animate((int(z3*z5*Nc*(Theta(X, tau)-Thetaa)^2/(z1*z4)+NrVals[j]*(Theta(X, tau)^4- Thetaa^4)/z4+M^2*(Theta(X, tau)-Thetaa)^(p+1)*(1+n1*z2/z3)/(z4*(1-Thetaa)^p), X = 0 .. 1,numeric,epsilon=1e-5,method=_Dexp))/(z3*z5*Nc*(1-Thetaa)^2/(z1*z4)+NrVals[j]*(-Thetaa^4+1)/z4+M^2*(1-Thetaa)*(1+n1*z2/z3)/z4), tau = 0 .. 2, X = 0.01..1.0, frames=NN, linestyle = "solid", 'axes' = 'boxed', labels = [" τ ", " η "], color = colour1[j], title="X = %4.3f");
etaa1[j] := Ansa1:-animate((int(z3*z5*Nc*(Theta(X, tau)-Thetaa)^2/(z1*z4)+NrVals[j]*(Theta(X, tau)^4-Thetaa^4)/z4+M^2*(Theta(X, tau)-Thetaa)^(p+1)*(1+n2*z2/z3)/(z4*(1-Thetaa)^p), X = 0 .. 1,numeric,epsilon=1e-5,method=_Dexp))/(z3*z5*Nc*(1-Thetaa)^2/(z1*z4)+NrVals[j]*(-Thetaa^4+1)/z4+M^2*(1-Thetaa)*(1+n2*z2/z3)/z4), tau = 0 .. 2, X = 0.01..1.0, frames=NN, linestyle = "dash", 'axes' = 'boxed', labels = [" τ ", " η "], color = colour1[j], title="X = %4.3f");

Plots1[j] := Ans1:-animate(Theta(X, tau), tau = 0..2, linestyle = "dash", labels = ["Y", Theta(Y, tau)], color = colour[j], 'axes' = 'boxed', frames=NN, title="tau = %4.3f");
 Plotsa[j] := Ansa:-animate(Theta(X, tau), tau = 0..2, linestyle = "solid", labels = ["Y", Theta(Y, tau)], color = colour1[j], 'axes' = 'boxed', frames=NN, title="tau = %4.3f");
 Plots[j] := Ans:-animate(Theta(X, tau), tau = 0..2, linestyle = "solid", labels = ["Y", Theta(Y, tau)], color = colour[j], 'axes' = 'boxed', frames=NN, title="tau = %4.3f");
 Plotsa1[j] := Ansa1:-animate(Theta(X, tau), tau = 0..2, linestyle = "dash", labels = ["Y", Theta(Y, tau)], color = colour1[j], 'axes' = 'boxed', frames=NN, title="tau = %4.3f");

end do:
(time[real]()-str)*`seconds`;

11.645*seconds

> 

plots:-display(seq(plots:-display(seq([seq(PLOT(op([1,KK,..],RR[j]),op(2..,RR[j])),
                                           RR=[Plots,Plotsa,Plots1,Plotsa1])][],
                                      j=1..nops(NrVals))),
                   KK=1..NN),insequence,size=[700,700]);
> 

plots:-display(seq(plots:-display(seq([seq(PLOT(op([1,KK,..],RR[j]),op(2..,RR[j])),
                                           RR=[eta,etaa,eta1,etaa1])][],
                                      j=1..nops(NrVals))),
                   KK=1..NN),insequence,size=[700,700]);

``

Download paper2_new_efficiency_plots_2025_acc.mw

ranges...

acer 32420
September 09 2025
1 0

You can even get a nice closed form for the expression that represents this curve, in terms of either variable.

> 

restart;

> 

f3:=-1/(((-qh-1)*Tch+qc+1)*deltac+(qh+1)*Tch)*(6*alpha^2*(alpha-1)*(alpha+1)*(((-qh-1)*Tch+qc+1)^2*deltac^2+((-7/3*(qh^2)-10/3*qh-1)*Tch^2+(2*(qh+1))*(qc+1)*Tch+(1/3)*qc^2-2*qc*(1/3)-1)*deltac+4*qh*Tch^2*(qh+1)*(1/3)))=0:
> 

params:=[qh=0.64,deltac=0.5,deltah=0.5,alpha=0.8,gamma=0.1,M=1.6205];

[qh = .64, deltac = .5, deltah = .5, alpha = .8, gamma = .1, M = 1.6205]

> 

Eq1:=eval(collect(f3,[Tch,qc]), params);

1.3824*(0.27333334e-1*Tch^2+(.8200*qc+.8200)*Tch+.4166666667*qc^2+.1666666667*qc-.25)/(.820*Tch+.5*qc+.5) = 0

> 

plots:-implicitplot(Eq1, qc=0..1, Tch=0..1);

> 

S1:=solve({(lhs-rhs)(eval(f3,convert(params,rational)))=0,
                qc>0, Tch>0}, [qc,Tch]);

[[qc < 3/5, 0 < qc, Tch = -15*qc-15+(10/41)*(3526*qc^2+7462*qc+3936)^(1/2)]]

> 

S2:=solve({(lhs-rhs)(eval(f3,convert(params,rational)))=0,
                qc>0, Tch>0}, [Tch,qc]);

[[Tch < -15+(40/41)*246^(1/2), 0 < Tch, qc = -(123/125)*Tch-1/5+(2/125)*(3526*Tch^2-6150*Tch+2500)^(1/2)]]

> 

indets([S1,S2],`<`);
evalf(%);

{0 < Tch, 0 < qc, Tch < -15+(40/41)*246^(1/2), qc < 3/5}

{0. < Tch, 0. < qc, Tch < .30184111, qc < .6000000000}

Download 1_6_ac.mw

The range qc=0.34..0.5, Tch=0.01..0.05 that you were using doesn't contain what you're after. It just misses the curve where the expression is zero...

> 

plots:-implicitplot(Eq1, qc=0.34..0.5, Tch=0.01..0.1, rangeasview);

convert example...

acer 32420
September 08 2025
0 0

You could augment the convert command.

> 

restart;
> 

`convert/sinc` := proc(ee)
   evalindets(
     evalindets(
       evalindets(ee,
                  specfunc(sin),x -> op(x)*sinc(op(x))),
       specfunc(cos),x -> (op(x)+Pi/2)*sinc(op(x)+Pi/2)),
     specfunc(tan),x -> op(x)*sinc(op(x))/(op(x)+Pi/2)/sinc(op(x)+Pi/2));
end proc:

 

> 

convert(sin(s), sinc);

s*sinc(s)

> 

convert(cos(s), sinc);

(s+(1/2)*Pi)*sinc(s+(1/2)*Pi)

> 

convert(tan(s), sinc);

s*sinc(s)/((s+(1/2)*Pi)*sinc(s+(1/2)*Pi))

Download conv_sinc_ex.mw

And you could also make such a convert(...,sinc) call for a compound expression involving a mix of sin&cos&tan, naturally.

ps. I changed your Post into a Question.

pps. You could also handle csc/sec/cot , in a few ways, eg. by converting to sincos as intermediate form.

ppps. It's possible to simply replace name sin/cos/tan by your operators, under eval. I deliberately used evalindets instead, to target only function calls of those names, and not any (other) instances of the bare names. Examples where is might matter could be rare, and possibly look contrived...

Explore...

acer 32420
September 08 2025
1 4

An Explore example, using your attachment g1.mw .

The signifant first change here is to remove the fixed view option from the plot3d call (since the surface's scale changes so much with the parameters) and to supply the adaptview=false option to Explore so that it allow each frame to get its own view independently. See magenta text edits.

g1_ac.mw

> 

restart
> 

_local(gamma)
> 

M := 2*sqrt(7*a^6*alpha[4]^2-8*a^4*l^2*alpha[4]*alpha[5]+a^2*l^4*alpha[5]^2+12*a^5*alpha[3]*alpha[4]-8*a^3*l^2*alpha[1]*alpha[4]-6*a^3*l^2*alpha[3]*alpha[5]+2*a*l^4*alpha[1]*alpha[5]+10*a^4*alpha[2]*alpha[4]+5*a^4*alpha[3]^2-6*a^2*l^2*alpha[1]*alpha[3]-4*a^2*l^2*alpha[2]*alpha[5]+l^4*alpha[1]^2-8*a^4*alpha[4]+8*a^3*alpha[2]*alpha[3]+2*a^2*l^2*alpha[5]-4*a*l^2*alpha[1]*alpha[2]-6*a^3*alpha[3]+3*a^2*alpha[2]^2+2*a*l^2*alpha[1]-4*a^2*alpha[2]+a^2)
> 

G := proc( alpha__1,alpha__2,alpha__3,alpha__4,alpha__5 )
   global last;
   last := [[:-alpha[1] = alpha__1,:-alpha[2] = alpha__2,:-alpha[3] = alpha__3,
             :-alpha[4] = alpha__4,:-alpha[5] = alpha__5],
            eval(M, [:-alpha[1] = alpha__1,:-alpha[2] = alpha__2,:-alpha[3] = alpha__3,
                     :-alpha[4] = alpha__4,:-alpha[5] = alpha__5])];
   plot3d(Im(eval(last[2])), a = -10 .. 10, l = -10 .. 10,
          #view = -10 .. 10,
          grid = [100, 100],
          colorscheme="turbo",
          style = surface, adaptmesh = false, size = [500, 500]); end proc:
> 

last := 'last'; Explore(G(`&alpha;__1`, `&alpha;__2`, `&alpha;__3`, `&alpha;__4`, `&alpha;__5`), `&alpha;__1` = -5.00000001 .. 5.000000001, `&alpha;__2` = -5.00000001 .. 5.000000001, `&alpha;__3` = -5.00000001 .. 5.000000001, `&alpha;__4` = -5.00000001 .. 5.000000001, `&alpha;__5` = -5.00000001 .. 5.000000001, initialvalues = [`&alpha;__1` = 1, `&alpha;__2` = 1, `&alpha;__3` = 1, `&alpha;__4` = 1, `&alpha;__5` = 5], placement = right, adaptview = false)

 

 

 

 

alpha__1

 

 
 

 

alpha__2

 

 
 

 

alpha__3

 

 
 

 

alpha__4

 

 
 

 

alpha__5

 

 
 

 
 

 
 

 
 

 
 

 
 

 

example...

acer 32420
September 07 2025
2 1

The following tests that the first indices (yours have just one) of the elements are four distinct values.
 

> 

L:=[ [F[1], F[2], F[3], F[4]],
     [F[1], F[2], F[3], M[1]],
     [F[1], F[2], F[3], M[2]],
     [F[1], F[2], F[3], M[3]],
     [F[1], F[2], F[3], M[4]],
     [F[1], F[2], F[4], M[1]],
     [F[1], F[2], F[4], M[2]],
     [F[1], F[2], F[4], M[3]],
     [F[1], F[2], F[4], M[4]],
     [F[1], F[2], M[1], M[2]] ]:
 
> 

select(LL->nops({map2(op,1,LL)[]})=4,L);

[[F[1], F[2], F[3], F[4]], [F[1], F[2], F[3], M[4]], [F[1], F[2], F[4], M[3]]]


Download map_op_ex.mw

You haven't stated explicitly that all the lists in L will always have elements that are indexed by at least one value, but I have presumed it so.

ps. I didn't see dharr's Answer before posting my own. The fact that they are so similar is really because it's a natural way to approach it.
[edit] dharr's Answer seems to have gone missing. But it was fine, IMO, (presuming all elements have exactly one index, which is also reasonable in the absence of stated details),
    select(x->nops({map(op,x)[]})=4,L);

[edit] Some explanation of the steps, so that next time you might build your own,

> 

Turn the inner lists of indexed items into
lists of just their indices.

map( LL -> map2(op,1,LL), L );

[[1, 2, 3, 4], [1, 2, 3, 1], [1, 2, 3, 2], [1, 2, 3, 3], [1, 2, 3, 4], [1, 2, 4, 1], [1, 2, 4, 2], [1, 2, 4, 3], [1, 2, 4, 4], [1, 2, 1, 2]]

> 

But now also make them sets of the indices, to
get rid of duplicates.

map( LL -> {map2(op,1,LL)[]}, L );

[{1, 2, 3, 4}, {1, 2, 3}, {1, 2, 3}, {1, 2, 3}, {1, 2, 3, 4}, {1, 2, 4}, {1, 2, 4}, {1, 2, 3, 4}, {1, 2, 4}, {1, 2}]

> 

But now take the nops of those sets, and set equal to 4.

map( LL -> nops({map2(op,1,LL)[]})=4, L );

[4 = 4, 3 = 4, 3 = 4, 3 = 4, 4 = 4, 3 = 4, 3 = 4, 4 = 4, 3 = 4, 2 = 4]

> 

Now use those equations as boolean valued tests,
in order to select with this action.

select(LL->nops({map2(op,1,LL)[]})=4,L);

[[F[1], F[2], F[3], F[4]], [F[1], F[2], F[3], M[4]], [F[1], F[2], F[4], M[3]]]

> 

Similarly, but without using select.

map( LL -> ifelse(nops({map2(op,1,LL)[]})=4, LL, NULL), L );

[[F[1], F[2], F[3], F[4]], [F[1], F[2], F[3], M[4]], [F[1], F[2], F[4], M[3]]]

some ideas...

acer 32420
August 29 2025
1 4

I'm guessing that you'd prefer to have the Product call be shown with the assigned name, rather than with the Vector or list to which that name is assigned.

Here is something that gets that, for Vector or list, in Maple 2021.

> 

restart;
> 

kernelopts(version);

`Maple 2021.2, X86 64 LINUX, Nov 23 2021, Build ID 1576349`

> 

with(Statistics):
> 

Dist := proc(N::{posint, name}, alpha::evaln)
  local K;
  uses Statistics;

  K := numelems(eval(alpha));
  
  Distribution( ':-PDF' = (z -> Product(('alpha'[k]+z[k])^N, k=1..K)) )
end proc:
> 

P := Vector(3, [13,2,4]);

Vector(3, {(1) = 13, (2) = 2, (3) = 4})

> 

X := RandomVariable(Dist(N, P)):
> 

res1 := PDF(X, x);

Product((P[k]+x[k])^N, k = 1 .. 3)

> 

eval(res1,1);

Product((P[k]+x[k])^N, k = 1 .. 3)

> 

value(eval(res1,1));

(13+x[1])^N*(2+x[2])^N*(4+x[3])^N

> 

L := [3,17,22];
X2 := RandomVariable(Dist(N, L)):

[3, 17, 22]

> 

res2 := PDF(X2, y);

Product((L[k]+y[k])^N, k = 1 .. 3)

> 

value(eval(res2,1));
value(res2);

(3+y[1])^N*(17+y[2])^N*(22+y[3])^N

(3+y[1])^N*(17+y[2])^N*(22+y[3])^N

> 

eval(res2,1);
res2;

Product((L[k]+y[k])^N, k = 1 .. 3)

Product(([3, 17, 22][k]+y[k])^N, k = 1 .. 3)

> 

V := Vector([1/2,1/3,1/4]):
subs('P'='V', eval(res1,1));
value(eval(%,1));

Product((V[k]+x[k])^N, k = 1 .. 3)

(1/2+x[1])^N*(1/3+x[2])^N*(1/4+x[3])^N

Download Product_error_ac.mw

and a variant on that: Product_error_ac2.mw

Here is something that behaves ok for a list (but not Vector), in Maple 2015: Product_error_ac_2015_list.mw

one way...

acer 32420
August 26 2025
4 0

With a little effort one can guard against collision of the textplots.

> 

restart
> 

L := [sin(x), sin(x)^2, sin(x)^3, sin(x)^4, sin(x)^5, sin(x)^6, surd(sin(x), 2), surd(sin(x), 3), surd(sin(x), 4), surd(sin(x), 5), surd(sin(x), 6)]
> 

Typesetting:-mrow(Typesetting:-mi("clist", italic = "true", mathvariant = "italic"), Typesetting:-mo("&coloneq;", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("plots", italic = "true", mathvariant = "italic"), Typesetting:-mo(":-", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("setcolors", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi(""), Typesetting:-ms("Niagara"), Typesetting:-mi("")), mathvariant = "normal"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-ms("Black"), Typesetting:-mi("")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(":", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("if", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("not", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("nops", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("L", italic = "true", mathvariant = "italic")), mathvariant = "normal"), Typesetting:-mo("&leq;", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mi("nops", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("clist", italic = "true", mathvariant = "italic")), mathvariant = "normal"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("then", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("error", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-ms("add more colors to clist"), Typesetting:-mo(";", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.2777778em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("end", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("if", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(";", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.2777778em"))
> 

plots:-animate(proc (T) local i, j, TL; TL := []; for i to nops(L) do if 0.5e-1 < min(100, seq(eval(abs(L[i]-rhs(TL[j])), x = T), j = 1 .. nops(TL))) then TL := [TL[], i = L[i]] end if end do; plots:-display(plot(L, x = 0 .. T, ':-thickness' = 2.5, ':-color' = clist), ifelse(0.1e-2 < T and T < Pi-0.1e-2, seq(plots:-textplot([T, eval(rhs(TL[i]), x = T), rhs(TL[i])], ':-align' = ':-right', ':-color' = clist[lhs(TL[i])]), i = 1 .. nops(TL)), NULL), ':-xtickmarks' = ':-piticks') end proc, [x], x = 0 .. Pi, frames = 100, size = [800, 500])

NULL

Download Animation_Trigo_ac.mw

examples...

acer 32420
August 26 2025
0 0

Your curves don't change much for such small changes in E1, it seems.

AGM_method_single_line_plot_ac.mw

There's quite a bit of duplicated effort in your approaches (which I didn't try to improve, though I showed a couple or alternative syntax blobs).

example...

acer 32420
August 26 2025
0 0

It's not clear what your definition of "simplify" is here.

But there are several ways to rationalize the denominator (including just using the rationalize command...).

> 

restart;
> 

expr:=(2500*I*w)/(1+5*I*w)+(200*I*w)/(1-10*I*w)+5;

(2500*I)*w/(1+(5*I)*w)+(200*I)*w/(1-(10*I)*w)+5

> 

rationalize(expr);

-5*(-4850*w^2-(535*I)*w-1)*((5*I)*w+50*w^2+1)/(2500*w^4+125*w^2+1)

> 

map(factor,rationalize(expr));

5*(-4850*w^2-(535*I)*w-1)*(-10*w+I)*(5*w+I)/((25*w^2+1)*(100*w^2+1))

Download rat_ex.mw

one way...

acer 32420
August 26 2025
1 0

I notice that converting the DE to sincos form allows both to work in stock Maple 2025.1.

This makes me suspect that it might not be a hard fix.

restart;

kernelopts(version);

          Maple 2025.1, X86 64 LINUX, Jun 12 2025, Build ID 1932578

ode:=diff(y(x),x) = (2*sin(2*x)-tan(y(x)))/x/sec(y(x))^2:

dsolve(convert(ode,sincos));

    y(x) = -arctan((cos(2*x)-2*c__1)/x)

dsolve(convert(ode,sincos),implicit);

    -c__1+x*tan(y(x))+cos(2*x) = 0

one way...

acer 32420
August 21 2025
3 8

There was quite a lot of invalid syntax in your code attempt.

But, here is one way.

> 

restart;
> 

kernelopts(version);

`Maple 2015.2, X86 64 LINUX, Dec 20 2015, Build ID 1097895`

> 

with(plots):

> 

aa := 4: bb := 2:  
> 

f := -(x^2/(aa^2)+y^2/(bb^(2))-1) * aa^2*bb^2/(aa^2+bb^2);

-(1/5)*x^2-(4/5)*y^2+16/5

> 

ell := (2*x/aa)^2 + (2*y/bb)^2 <= 1;

(1/4)*x^2+y^2 <= 1

> 

plot3d(f, x = 0 .. sqrt(-4*y^2+4), y = 0 .. bb/(2),
       axes = boxed,style = patchcontour, grid = [50, 50],
       orientation = [-115, 70], shading = zhue,
       title = "f(x,y) over quarter ellipse domain",
       labels=[x,y,"f"]);

> 

contourplot(f, x = 0 .. sqrt(-4*y^2+4), y = 0 .. bb/(2),
            contours = 15, filled = true, coloring = [blue, green],
            axes = boxed, title = "Contour plot over quarter ellipse",
            grid = [100,100]);

Download Usman_contplot1.mw

example...

acer 32420
August 11 2025
3 4

Is this the kind of effect you're after?

[edited]

> 

restart
> 

with(PDEtools, declare); with(PDEtools, undeclare)
> 

undeclare(prime, quiet)
> 

declare(u(x, y, t), quiet); declare(v(x, y, t), quiet)
> 

pde1 := diff(u(x, y, t), t)+diff(u(x, y, t), `$`(x, 3))+diff(u(x, y, t)*v(x, y, t), x)

diff(u(x, y, t), t)+diff(diff(diff(u(x, y, t), x), x), x)+(diff(u(x, y, t), x))*v(x, y, t)+u(x, y, t)*(diff(v(x, y, t), x))

> 

pde2 := diff(u(x, y, t), x)-(diff(v(x, y, t), y))

diff(u(x, y, t), x)-(diff(v(x, y, t), y))

> 

V1 := [indets(pde1, And(specfunc(diff), satisfies(proc (fn) options operator, arrow; depends(fn, {t, x, y}) end proc)))[], `~`[apply]([u, v], x, y, t)[]]; Z1 := map(proc (v) options operator, arrow; v = freeze(v) end proc, V1)

[diff(diff(diff(u(x, y, t), x), x), x), diff(diff(u(x, y, t), x), x), diff(u(x, y, t), t), diff(u(x, y, t), x), diff(v(x, y, t), x), u(x, y, t), v(x, y, t)]

> 

pde_linear1,pde_nonlinear1 := thaw([selectremove(type,eval(pde1,Z1)+__f,
                                                 Or(linear(rhs~(Z1)),
                                                    satisfies(f->not depends(f,[rhs~(Z1)[],x,y,t]))))])[]:
pde_linear1:=pde_linear1-__f:
> 

V2 := [indets(pde2, And(specfunc(diff), satisfies(proc (fn) options operator, arrow; depends(fn, {t, x, y}) end proc)))[], `~`[apply]([u, v], x, y, t)[]]; Z2 := map(proc (v) options operator, arrow; v = freeze(v) end proc, V2)

[diff(u(x, y, t), x), diff(v(x, y, t), y), u(x, y, t), v(x, y, t)]

> 

pde_linear2,pde_nonlinear2 := thaw([selectremove(type,eval(pde2,Z2)+__f,
                                                 Or(linear(rhs~(Z2)),
                                                    satisfies(f->not depends(f,rhs~(Z2)))))])[]:
pde_linear2:=pde_linear2-__f:
> 

pde_linear1;
pde_nonlinear1;
pde_linear2;
pde_nonlinear2;

diff(diff(diff(u(x, y, t), x), x), x)+diff(u(x, y, t), t)

(diff(u(x, y, t), x))*v(x, y, t)+u(x, y, t)*(diff(v(x, y, t), x))

diff(u(x, y, t), x)-(diff(v(x, y, t), y))

0

Download linear_ac.mw

nb. You may wish to apply normal (or expand, possibly frontend'd) first, to get the addends of the DE separated.

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