Maple 2020 Questions and Posts

Questions re using Maple cloud...

Asked by: Earl 980

July 25 2022

0 2

I want to create and modify the same worksheet at different times on two different computers in two different locations.

To avoid transferring files between the two machines, it seems most convenient to reference all objects within Maple cloud.

I am a beginner at this and have several questions:

1) I have downloaded the DirectSearch package as directed in help text but the only result from issuing the command kernelopts(toolboxdir) is " ".

How can I establish a path which enables my worksheet to execute commands within this package?

2) How can my worksheet invoke procedures within my .mla file referencing only objects in Maple cloud?

How can I update (save and delete procedures) within my .mla file?

How to integrate...

Asked by: mohammad1 15

July 20 2022

1 2

Hello my friends
Please help me solve the integration problem in the attached Maple code below (why was the integration not done in u[4]?) ... Thank you very much

>	u[1] := 1/3t^3x + 2tx + (-1)0.7522527780t^(3/2)x + (-1)0.1719434922t^(7/2)x + (-1)0.01587301587t^7x + (-1)0.1333333333t^5x

(1)

>	u[2] := subs(t=Tau,u[1]);

(1/3)*Tau^3*x+2*Tau*x-.7522527780*Tau^(3/2)*x-.1719434922*Tau^(7/2)*x-0.1587301587e-1*Tau^7*x-.1333333333*Tau^5*x

(2)

>	u[3]:= int(u[2],Tau = 0 .. t);

t^2*x+0.8333333333e-1*t^4*x-0.2222222222e-1*t^6*x-0.1984126984e-2*t^8*x-.3009011112*t^(5/2)*x-0.3820966493e-1*x*t^(9/2)

(3)

>	u[4]:= int((t-Tau)^(-0.5)*u[2],Tau = 0 .. t);

int(((1/3)*Tau^3*x+2*Tau*x-.7522527780*Tau^(3/2)*x-.1719434922*Tau^(7/2)*x-0.1587301587e-1*Tau^7*x-.1333333333*Tau^5*x)/(t-Tau)^.5, Tau = 0 .. t)

(4)

Download help.mw

Common legend for different figures...

Asked by: Mikhail Drugov 133

July 06 2022

1 0

Hello,

Is it possible to have a common legend for different figures? I can plot them as Array of Plots (below) but then they each have a legend.

Is it possible to have the two figures side by side and a common legend in the middle?

Thank you!

restart:
with(plots):
A := Array(1 .. 2):
A[1] := plot([2*sin(x), 3*sin(x)], x = -Pi .. Pi, labels = [x, b*sin(x)], color = [blue, red], legend = ["Case of b=2", "Case of b=3"]):
A[2] := plot([2*cos(x), 3*cos(x)], x = -Pi .. Pi, labels = [x, b*cos(x)], color = [blue, red], legend = ["Case of b=2", "Case of b=3"]):
display(A);

plot of function...

Asked by: Nikol 60

July 06 2022

1 4

Hey, guys! My Maple 2020 program does not build a plot. that is, it cuts it off. everything is correct in maple 2015.

plot(140^t*exp(-140)/t!, t = 0 .. 300)

Maple 2015

plot(140^t*exp(-140)/t!, t = 0 .. 300)

My maple 2020 creates

Why???????????

How to run programmatically Windows PowerShell com...

Asked by: sand15 807

June 22 2022

2 2

I use Maple 2020 on a Windows 10 PC.

The command ssystem("CMD") enables to launch any Windows command accessible from the shell.
But how to launch a PowerShell command?

For instance ssystem("get-process") returns -1 (not surprising in fact for get-process is not a shell process).
How can I tell Maple that this command is to be found in the PowerShell ?

And even, I this possible for, in the ssystem help page, it's said that not all the command can be launched by ssystem

TIA

How can these three Watt's curves be plotted in th...

Asked by: Earl 980

June 19 2022

4 10

Two of the three Watt's curves plotted in this worksheet display with gaps.

Why is this and how can these curves be displayed without gaps?

WattsCurve.mw

error, null fix?...

Asked by: PainedMushroom 35

June 19 2022

2 7

Hi

Keep getting "Error, null" on every calculation i make. It indicates hidden spaces or something weird????.

Screenshot of it is included.

https://imgur.com/a/wSdUeqe

Would be great with a fix or some help because this is driving me mad....

What is the proof that Neile's semi-cubical parabo...

Asked by: Earl 980

June 14 2022

2 12

The uploaded worksheet is a failed attempt at this proof.

Please either refer me to or show me a valid proof.

*** I have tried to upload my worksheet using the green arrow but the insert link operation of the upload failed ***

cc

Plotting a one dimensional curve with implicitplot...

Asked by: Tereso 40

June 09 2022

1 4

I want to plot the solutions of the equation (x-y)^2+(1-z)^2=0.

However, implicitplot3d is not able to plot them, at least using the default arguments. Any recommendations?

I know a priori that it is going to be a curve contained in a plane in case that makes this task easier.

"fsolve"-ing an expression containing a cosh-funct...

Asked by: krowkoster95 5

May 13 2022

1 5

Can anyone tell me what this means? (workfile maple.file.mw)

how I can convert this maple code to matlab ones?...

Asked by: 9009134 110

May 06 2022

1 1

how I can convert this maple code to Matlab ones?

1.mw

>

$restart; t1 := time(); with(LinearAlgebra); J := readstat("Please enter integer number J: "); N1 := proc (x) options operator, arrow; piecewise(0 <= x and x <= 1, 1) end proc; N2 := proc (x) options operator, arrow; piecewise(0 <= x and x <= 1, x, 1 < x and x <= 2, 2-x) end proc; N := proc (J, k) options operator, arrow; unapply(N2(2^J*x-k), x) end proc; Phi := proc (J, k) options operator, arrow; evalf((N(J, k))(x))*N1(x) end proc; PhiJ := Vector[column](2^J+1); for k from -1 to 2^J-1 do PhiJ[k+2] := Phi(J, k) end do; P := Matrix(2^J+1, 2^J+1); Map2[proc (i, j) options operator, arrow; evalb(i-j = 1) end proc](proc (x, a) options operator, arrow; x end proc, 1/6, P, inplace); Map2[proc (i, j) options operator, arrow; evalb(j-i = 1) end proc](proc (x, a) options operator, arrow; x end proc, 1/6, P, inplace); Map2[proc (i, j) options operator, arrow; evalb(i = j) end proc](proc (x, a) options operator, arrow; x end proc, 2/3, P, inplace); P[1, 1] := 1/3; P[2^J+1, 2^J+1] := 1/3; P := 2^(-J)*P; E := Matrix(2^J+1, 2^J+1); Map2[proc (i, j) options operator, arrow; evalb(i-j = 1) end proc](proc (x, a) options operator, arrow; x end proc, 1/2, E, inplace); Map2[proc (i, j) options operator, arrow; evalb(j-i = 1) end proc](proc (x, a) options operator, arrow; x end proc, -1/2, E, inplace); E[1, 1] := -1/2; E[2^J+1, 2^J+1] := 1/2; DPhi := E.(1/P); X1 := Vector[column](2^J+1, symbol = x1); X2 := Vector[column](2^J+1, symbol = x2); U := Vector[column](2^J+1, symbol = u); JJ := (1/2)*U^%T.P.U; x1t := X1^%T.PhiJ; x2t := X2^%T.PhiJ; ut := U^%T.PhiJ; for i from 0 to 2^J do PhiJxJ[i+1] := apply(unapply(PhiJ, x), i/2^J) end do; for i to 2^J+1 do eq1[i] := (X1^%T.DPhi-X2^%T).PhiJxJ[i] = 0; eq2[i] := (X2^%T.DPhi-U^%T).PhiJxJ[i] = 0 end do; for i to 2^J+1 do eq3[i] := X1^%T.PhiJxJ[i]-.1, 0 end do; eq1[0] := eval(x1t, x = 0) = 0; eq2[0] := eval(x2t, x = 0)-1 = 0; eq1[2^J+2] := eval(x1t, x = 1) = 0; eq2[2^J+2] := eval(x2t, x = 1) = -1; eqq1 := {seq(eq1[i], i = 0*.2^J+2)}; eqq2 := {seq(eq2[i], i = 0.2^J+2)}; eqq3 := {seq(eq3[i], i = 1.2^J+1)}; eq := `union`(`union`(eqq1, eqq2), eqq3); with(Optimization); S := NLPSolve(JJ, eq); assign(S[2]); uexact := piecewise(0 <= x and x <= .3, (200/9)*x-20/3, .3 <= x and x <= .7, 0, .7 <= x and x <= 1, -(200/9)*x+140/9); x2exact := piecewise(0 <= x and x <= .3, (100/9)*x^2-(20/3)*x+1, .3 <= x and x <= .7, 0, .7 <= x and x <= 1, -(100/9)*x^2+(140/9)*x-49/9); x1exact := piecewise(0 <= x and x <= .3, (100/27)*x^3-(10/3)*x^2+x, .3 <= x and x <= .7, 1/10, .7 <= x and x <= 1, -(100/27)*x^3+(70/9)*x^2-(49/9)*x+37/27); plot([x1exact, x1t], x = 0 .. 1, style = [line, point], legend = ["Exact", "Approximate"], axis = [gridlines = [colour = green, majorlines = 2]], labels = ["t", x[1](t)], labeldirections = ["horizontal", "vertical"])$

N2 := proc (x) options operator, arrow; piecewise(0 <= x and x <= 1, x, 1 < x and x <= 2, 2-x) end proc

_rtable[36893490566539206892]

PhiJ[1] := piecewise(16.*x <= 0. and 0. <= 16.*x+1., 16.*x+1., 0. < 16.*x and 16.*x <= 1., 1.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)

PhiJ[2] := piecewise(0. <= 16.*x and 16.*x <= 1., 16.*x, 1. < 16.*x and 16.*x <= 2., 2.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)

PhiJ[3] := piecewise(`and`(0. <= 16.*x-1., 16.*x <= 2.), 16.*x-1., `and`(0. < 16.*x-2., 16.*x <= 3.), 3.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)

PhiJ[4] := piecewise(`and`(0. <= 16.*x-2., 16.*x <= 3.), 16.*x-2., `and`(0. < 16.*x-3., 16.*x <= 4.), 4.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)

PhiJ[5] := piecewise(`and`(0. <= 16.*x-3., 16.*x <= 4.), 16.*x-3., `and`(0. < 16.*x-4., 16.*x <= 5.), 5.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)

PhiJ[6] := piecewise(`and`(0. <= 16.*x-4., 16.*x <= 5.), 16.*x-4., `and`(0. < 16.*x-5., 16.*x <= 6.), 6.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)

PhiJ[7] := piecewise(`and`(0. <= 16.*x-5., 16.*x <= 6.), 16.*x-5., `and`(0. < 16.*x-6., 16.*x <= 7.), 7.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)

PhiJ[8] := piecewise(`and`(0. <= 16.*x-6., 16.*x <= 7.), 16.*x-6., `and`(0. < 16.*x-7., 16.*x <= 8.), 8.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)

PhiJ[9] := piecewise(`and`(0. <= 16.*x-7., 16.*x <= 8.), 16.*x-7., `and`(0. < 16.*x-8., 16.*x <= 9.), 9.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)

PhiJ[10] := piecewise(`and`(0. <= 16.*x-8., 16.*x <= 9.), 16.*x-8., `and`(0. < 16.*x-9., 16.*x <= 10.), 10.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)

PhiJ[11] := piecewise(`and`(0. <= 16.*x-9., 16.*x <= 10.), 16.*x-9., `and`(0. < 16.*x-10., 16.*x <= 11.), 11.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)

PhiJ[12] := piecewise(`and`(0. <= 16.*x-10., 16.*x <= 11.), 16.*x-10., `and`(0. < 16.*x-11., 16.*x <= 12.), 12.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)

PhiJ[13] := piecewise(`and`(0. <= 16.*x-11., 16.*x <= 12.), 16.*x-11., `and`(0. < 16.*x-12., 16.*x <= 13.), 13.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)

PhiJ[14] := piecewise(`and`(0. <= 16.*x-12., 16.*x <= 13.), 16.*x-12., `and`(0. < 16.*x-13., 16.*x <= 14.), 14.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)

PhiJ[15] := piecewise(`and`(0. <= 16.*x-13., 16.*x <= 14.), 16.*x-13., `and`(0. < 16.*x-14., 16.*x <= 15.), 15.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)

PhiJ[16] := piecewise(`and`(0. <= 16.*x-14., 16.*x <= 15.), 16.*x-14., `and`(0. < 16.*x-15., 16.*x <= 16.), 16.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)

PhiJ[17] := piecewise(`and`(0. <= 16.*x-15., 16.*x <= 16.), 16.*x-15., `and`(0. < 16.*x-16., 16.*x <= 17.), 17.-16.*x)*piecewise(0 <= x and x <= 1, 1, 0)

_rtable[36893490566536466172]

_rtable[36893490566563670004]

_rtable[36893490566563682652]

_rtable[36893490566592433196]

_rtable[36893490566592446084]

_rtable[36893490566592458492]

_rtable[36893490566592462708]

_rtable[36893490566593511164]

_rtable[36893490566474385156]

_rtable[36893490566474387196]

_rtable[36893490566474274564]

_rtable[36893490566474276604]

_rtable[36893490566471927556]

_rtable[36893490566471929596]

_rtable[36893490566439466756]

_rtable[36893490566439468796]

_rtable[36893490566581483268]

_rtable[36893490566581485308]

_rtable[36893490566581487364]

_rtable[36893490566581489404]

_rtable[36893490566581491460]

_rtable[36893490566581493500]

_rtable[36893490566581561092]

_rtable[36893490566581563132]

eq1[1] := -20.28718708*x1[1]+25.72312247*x1[2]-6.892489894*x1[3]+1.846837101*x1[4]-.4948585097*x1[5]+.1325969380*x1[6]-0.3552924247e-1*x1[7]+0.9520031827e-2*x1[8]-0.2550884838e-2*x1[9]+0.6835075261e-3*x1[10]-0.1831452664e-3*x1[11]+0.4907353932e-4*x1[12]-0.1314889092e-4*x1[13]+3.522024353*10^(-6)*x1[14]-9.392064942*10^(-7)*x1[15]+2.348016235*10^(-7)*x1[16]-3.913360392*10^(-8)*x1[17]-1.*x2[1] = 0

eq2[1] := -20.28718708*x2[1]+25.72312247*x2[2]-6.892489894*x2[3]+1.846837101*x2[4]-.4948585097*x2[5]+.1325969380*x2[6]-0.3552924247e-1*x2[7]+0.9520031827e-2*x2[8]-0.2550884838e-2*x2[9]+0.6835075261e-3*x2[10]-0.1831452664e-3*x2[11]+0.4907353932e-4*x2[12]-0.1314889092e-4*x2[13]+3.522024353*10^(-6)*x2[14]-9.392064942*10^(-7)*x2[15]+2.348016235*10^(-7)*x2[16]-3.913360392*10^(-8)*x2[17]-1.*u[1] = 0

eq1[3] := 1.989690448*x1[1]-11.93814269*x1[2]-.2474292549*x1[3]+12.92785971*x1[4]-3.464009568*x1[5]+.9281785663*x1[6]-.2487046973*x1[7]+0.6664022279e-1*x1[8]-0.1785619387e-1*x1[9]+0.4784552683e-2*x1[10]-0.1282016864e-2*x1[11]+0.3435147752e-3*x1[12]-0.9204223643e-4*x1[13]+0.2465417047e-4*x1[14]-6.574445459*10^(-6)*x1[15]+1.643611365*10^(-6)*x1[16]-2.739352275*10^(-7)*x1[17]-1.000000000*x2[3] = 0

eq2[3] := 1.989690448*x2[1]-11.93814269*x2[2]-.2474292549*x2[3]+12.92785971*x2[4]-3.464009568*x2[5]+.9281785663*x2[6]-.2487046973*x2[7]+0.6664022279e-1*x2[8]-0.1785619387e-1*x2[9]+0.4784552683e-2*x2[10]-0.1282016864e-2*x2[11]+0.3435147752e-3*x2[12]-0.9204223643e-4*x2[13]+0.2465417047e-4*x2[14]-6.574445459*10^(-6)*x2[15]+1.643611365*10^(-6)*x2[16]-2.739352275*10^(-7)*x2[17]-1.000000000*u[3] = 0

eq1[4] := -.5331359486*x1[1]+3.198815692*x1[2]-12.79526277*x1[3]-0.1776462123e-1*x1[4]+12.86632125*x1[5]-3.447520389*x1[6]+.9237603042*x1[7]-.2475208275*x1[8]+0.6632300579e-1*x1[9]-0.1777119568e-1*x1[10]+0.4761776926e-2*x1[11]-0.1275912022e-2*x1[12]+0.3418711639e-3*x1[13]-0.9157263318e-4*x1[14]+0.2441936885e-4*x1[15]-6.104842212*10^(-6)*x1[16]+1.017473702*10^(-6)*x1[17]-1.000000000*x2[4] = 0

eq2[4] := -.5331359486*x2[1]+3.198815692*x2[2]-12.79526277*x2[3]-0.1776462123e-1*x2[4]+12.86632125*x2[5]-3.447520389*x2[6]+.9237603042*x2[7]-.2475208275*x2[8]+0.6632300579e-1*x2[9]-0.1777119568e-1*x2[10]+0.4761776926e-2*x2[11]-0.1275912022e-2*x2[12]+0.3418711639e-3*x2[13]-0.9157263318e-4*x2[14]+0.2441936885e-4*x2[15]-6.104842212*10^(-6)*x2[16]+1.017473702*10^(-6)*x2[17]-1.000000000*u[4] = 0

eq1[5] := .1428533469*x1[1]-.8571200814*x1[2]+3.428480326*x1[3]-12.85680122*x1[4]-0.1275442419e-2*x1[5]+12.86190299*x1[6]-3.446336519*x1[7]+.9234430872*x1[8]-.2474358293*x1[9]+0.6630023004e-1*x1[10]-0.1776509084e-1*x1[11]+0.4760133314e-2*x1[12]-0.1275442419e-2*x1[13]+0.3416363623e-3*x1[14]-0.9110302994e-4*x1[15]+0.2277575748e-4*x1[16]-3.795959581*10^(-6)*x1[17]-1.000000000*x2[5] = 0

eq2[5] := .1428533469*x2[1]-.8571200814*x2[2]+3.428480326*x2[3]-12.85680122*x2[4]-0.1275442419e-2*x2[5]+12.86190299*x2[6]-3.446336519*x2[7]+.9234430872*x2[8]-.2474358293*x2[9]+0.6630023004e-1*x2[10]-0.1776509084e-1*x2[11]+0.4760133314e-2*x2[12]-0.1275442419e-2*x2[13]+0.3416363623e-3*x2[14]-0.9110302994e-4*x2[15]+0.2277575748e-4*x2[16]-3.795959581*10^(-6)*x2[17]-1.000000000*u[5] = 0

eq1[6] := -0.3827743894e-1*x1[1]+.2296646336*x1[2]-.9186585345*x1[3]+3.444969504*x1[4]-12.86121948*x1[5]-0.9157263318e-4*x1[6]+12.86158577*x1[7]-3.446251521*x1[8]+.9234203114*x1[9]-.2474297245*x1[10]+0.6629858642e-1*x1[11]-0.1776462123e-1*x1[12]+0.4759898512e-2*x1[13]-0.1274972816e-2*x1[14]+0.3399927509e-3*x1[15]-0.8499818772e-4*x1[16]+0.1416636462e-4*x1[17]-1.000000000*x2[6] = 0

eq2[6] := -0.3827743894e-1*x2[1]+.2296646336*x2[2]-.9186585345*x2[3]+3.444969504*x2[4]-12.86121948*x2[5]-0.9157263318e-4*x2[6]+12.86158577*x2[7]-3.446251521*x2[8]+.9234203114*x2[9]-.2474297245*x2[10]+0.6629858642e-1*x2[11]-0.1776462123e-1*x2[12]+0.4759898512e-2*x2[13]-0.1274972816e-2*x2[14]+0.3399927509e-3*x2[15]-0.8499818772e-4*x2[16]+0.1416636462e-4*x2[17]-1.000000000*u[6] = 0

eq1[7] := 0.1025640885e-1*x1[1]-0.6153845311e-1*x1[2]+.2461538124*x1[3]-.9230767966*x1[4]+3.446153374*x1[5]-12.86153670*x1[6]-6.574445459*10^(-6)*x1[7]+12.86156300*x1[8]-3.446245416*x1[9]+.9234186678*x1[10]-.2474292549*x1[11]+0.6629835162e-1*x1[12]-0.1776415163e-1*x1[13]+0.4758254901e-2*x1[14]-0.1268867974e-2*x1[15]+0.3172169934e-3*x1[16]-0.5286949890e-4*x1[17]-1.000000000*x2[7] = 0

eq2[7] := 0.1025640885e-1*x2[1]-0.6153845311e-1*x2[2]+.2461538124*x2[3]-.9230767966*x2[4]+3.446153374*x2[5]-12.86153670*x2[6]-6.574445459*10^(-6)*x2[7]+12.86156300*x2[8]-3.446245416*x2[9]+.9234186678*x2[10]-.2474292549*x2[11]+0.6629835162e-1*x2[12]-0.1776415163e-1*x2[13]+0.4758254901e-2*x2[14]-0.1268867974e-2*x2[15]+0.3172169934e-3*x2[16]-0.5286949890e-4*x2[17]-1.000000000*u[7] = 0

eq1[8] := -0.2748196469e-2*x1[1]+0.1648917882e-1*x1[2]-0.6595671526e-1*x1[3]+.2473376822*x1[4]-.9233940136*x1[5]+3.446238372*x1[6]-12.86155948*x1[7]-4.696032471*10^(-7)*x1[8]+12.86156135*x1[9]-3.446244947*x1[10]+.9234184330*x1[11]-.2474287852*x1[12]+0.6629670801e-1*x1[13]-0.1775804679e-1*x1[14]+0.4735479144e-2*x1[15]-0.1183869786e-2*x1[16]+0.1973116310e-3*x1[17]-1.000000000*x2[8] = 0

eq2[8] := -0.2748196469e-2*x2[1]+0.1648917882e-1*x2[2]-0.6595671526e-1*x2[3]+.2473376822*x2[4]-.9233940136*x2[5]+3.446238372*x2[6]-12.86155948*x2[7]-4.696032471*10^(-7)*x2[8]+12.86156135*x2[9]-3.446244947*x2[10]+.9234184330*x2[11]-.2474287852*x2[12]+0.6629670801e-1*x2[13]-0.1775804679e-1*x2[14]+0.4735479144e-2*x2[15]-0.1183869786e-2*x2[16]+0.1973116310e-3*x2[17]-1.000000000*u[8] = 0

eq1[9] := 0.7363770250e-3*x1[1]-0.4418262150e-2*x1[2]+0.1767304860e-1*x1[3]-0.6627393225e-1*x1[4]+.2474226804*x1[5]-.9234167894*x1[6]+3.446244477*x1[7]-12.86156112*x1[8]+12.86156112*x1[10]-3.446244477*x1[11]+.9234167894*x1[12]-.2474226804*x1[13]+0.6627393225e-1*x1[14]-0.1767304860e-1*x1[15]+0.4418262150e-2*x1[16]-0.7363770250e-3*x1[17]-1.000000000*x2[9] = 0

eq2[9] := 0.7363770250e-3*x2[1]-0.4418262150e-2*x2[2]+0.1767304860e-1*x2[3]-0.6627393225e-1*x2[4]+.2474226804*x2[5]-.9234167894*x2[6]+3.446244477*x2[7]-12.86156112*x2[8]+12.86156112*x2[10]-3.446244477*x2[11]+.9234167894*x2[12]-.2474226804*x2[13]+0.6627393225e-1*x2[14]-0.1767304860e-1*x2[15]+0.4418262150e-2*x2[16]-0.7363770250e-3*x2[17]-1.000000000*u[9] = 0

eq1[10] := -0.1973116310e-3*x1[1]+0.1183869786e-2*x1[2]-0.4735479144e-2*x1[3]+0.1775804679e-1*x1[4]-0.6629670801e-1*x1[5]+.2474287852*x1[6]-.9234184330*x1[7]+3.446244947*x1[8]-12.86156135*x1[9]+4.696032471*10^(-7)*x1[10]+12.86155948*x1[11]-3.446238372*x1[12]+.9233940136*x1[13]-.2473376822*x1[14]+0.6595671526e-1*x1[15]-0.1648917882e-1*x1[16]+0.2748196469e-2*x1[17]-1.000000000*x2[10] = 0

eq2[10] := -0.1973116310e-3*x2[1]+0.1183869786e-2*x2[2]-0.4735479144e-2*x2[3]+0.1775804679e-1*x2[4]-0.6629670801e-1*x2[5]+.2474287852*x2[6]-.9234184330*x2[7]+3.446244947*x2[8]-12.86156135*x2[9]+4.696032471*10^(-7)*x2[10]+12.86155948*x2[11]-3.446238372*x2[12]+.9233940136*x2[13]-.2473376822*x2[14]+0.6595671526e-1*x2[15]-0.1648917882e-1*x2[16]+0.2748196469e-2*x2[17]-1.000000000*u[10] = 0

eq1[11] := 0.5286949890e-4*x1[1]-0.3172169934e-3*x1[2]+0.1268867974e-2*x1[3]-0.4758254901e-2*x1[4]+0.1776415163e-1*x1[5]-0.6629835162e-1*x1[6]+.2474292549*x1[7]-.9234186678*x1[8]+3.446245416*x1[9]-12.86156300*x1[10]+6.574445459*10^(-6)*x1[11]+12.86153670*x1[12]-3.446153374*x1[13]+.9230767966*x1[14]-.2461538124*x1[15]+0.6153845311e-1*x1[16]-0.1025640885e-1*x1[17]-1.00000000*x2[11] = 0

eq2[11] := 0.5286949890e-4*x2[1]-0.3172169934e-3*x2[2]+0.1268867974e-2*x2[3]-0.4758254901e-2*x2[4]+0.1776415163e-1*x2[5]-0.6629835162e-1*x2[6]+.2474292549*x2[7]-.9234186678*x2[8]+3.446245416*x2[9]-12.86156300*x2[10]+6.574445459*10^(-6)*x2[11]+12.86153670*x2[12]-3.446153374*x2[13]+.9230767966*x2[14]-.2461538124*x2[15]+0.6153845311e-1*x2[16]-0.1025640885e-1*x2[17]-1.00000000*u[11] = 0

eq1[12] := -0.1416636462e-4*x1[1]+0.8499818772e-4*x1[2]-0.3399927509e-3*x1[3]+0.1274972816e-2*x1[4]-0.4759898512e-2*x1[5]+0.1776462123e-1*x1[6]-0.6629858642e-1*x1[7]+.2474297245*x1[8]-.9234203114*x1[9]+3.446251521*x1[10]-12.86158577*x1[11]+0.9157263318e-4*x1[12]+12.86121948*x1[13]-3.444969504*x1[14]+.9186585345*x1[15]-.2296646336*x1[16]+0.3827743894e-1*x1[17]-1.00000000*x2[12] = 0

eq2[12] := -0.1416636462e-4*x2[1]+0.8499818772e-4*x2[2]-0.3399927509e-3*x2[3]+0.1274972816e-2*x2[4]-0.4759898512e-2*x2[5]+0.1776462123e-1*x2[6]-0.6629858642e-1*x2[7]+.2474297245*x2[8]-.9234203114*x2[9]+3.446251521*x2[10]-12.86158577*x2[11]+0.9157263318e-4*x2[12]+12.86121948*x2[13]-3.444969504*x2[14]+.9186585345*x2[15]-.2296646336*x2[16]+0.3827743894e-1*x2[17]-1.00000000*u[12] = 0

eq1[13] := 3.795959581*10^(-6)*x1[1]-0.2277575748e-4*x1[2]+0.9110302994e-4*x1[3]-0.3416363623e-3*x1[4]+0.1275442419e-2*x1[5]-0.4760133314e-2*x1[6]+0.1776509084e-1*x1[7]-0.6630023004e-1*x1[8]+.2474358293*x1[9]-.9234430872*x1[10]+3.446336519*x1[11]-12.86190299*x1[12]+0.1275442419e-2*x1[13]+12.85680122*x1[14]-3.428480326*x1[15]+.8571200814*x1[16]-.1428533469*x1[17]-1.00000000*x2[13] = 0

eq2[13] := 3.795959581*10^(-6)*x2[1]-0.2277575748e-4*x2[2]+0.9110302994e-4*x2[3]-0.3416363623e-3*x2[4]+0.1275442419e-2*x2[5]-0.4760133314e-2*x2[6]+0.1776509084e-1*x2[7]-0.6630023004e-1*x2[8]+.2474358293*x2[9]-.9234430872*x2[10]+3.446336519*x2[11]-12.86190299*x2[12]+0.1275442419e-2*x2[13]+12.85680122*x2[14]-3.428480326*x2[15]+.8571200814*x2[16]-.1428533469*x2[17]-1.00000000*u[13] = 0

eq1[14] := -1.017473702*10^(-6)*x1[1]+6.104842212*10^(-6)*x1[2]-0.2441936885e-4*x1[3]+0.9157263318e-4*x1[4]-0.3418711639e-3*x1[5]+0.1275912022e-2*x1[6]-0.4761776926e-2*x1[7]+0.1777119568e-1*x1[8]-0.6632300579e-1*x1[9]+.2475208275*x1[10]-.9237603042*x1[11]+3.447520389*x1[12]-12.86632125*x1[13]+0.1776462123e-1*x1[14]+12.79526277*x1[15]-3.198815692*x1[16]+.5331359486*x1[17]-1.00000000*x2[14] = 0

eq2[14] := -1.017473702*10^(-6)*x2[1]+6.104842212*10^(-6)*x2[2]-0.2441936885e-4*x2[3]+0.9157263318e-4*x2[4]-0.3418711639e-3*x2[5]+0.1275912022e-2*x2[6]-0.4761776926e-2*x2[7]+0.1777119568e-1*x2[8]-0.6632300579e-1*x2[9]+.2475208275*x2[10]-.9237603042*x2[11]+3.447520389*x2[12]-12.86632125*x2[13]+0.1776462123e-1*x2[14]+12.79526277*x2[15]-3.198815692*x2[16]+.5331359486*x2[17]-1.00000000*u[14] = 0

eq1[15] := 2.739352275*10^(-7)*x1[1]-1.643611365*10^(-6)*x1[2]+6.574445459*10^(-6)*x1[3]-0.2465417047e-4*x1[4]+0.9204223643e-4*x1[5]-0.3435147752e-3*x1[6]+0.1282016864e-2*x1[7]-0.4784552683e-2*x1[8]+0.1785619387e-1*x1[9]-0.6664022279e-1*x1[10]+.2487046973*x1[11]-.9281785663*x1[12]+3.464009568*x1[13]-12.92785971*x1[14]+.2474292549*x1[15]+11.93814269*x1[16]-1.989690448*x1[17]-1.00000000*x2[15] = 0

eq2[15] := 2.739352275*10^(-7)*x2[1]-1.643611365*10^(-6)*x2[2]+6.574445459*10^(-6)*x2[3]-0.2465417047e-4*x2[4]+0.9204223643e-4*x2[5]-0.3435147752e-3*x2[6]+0.1282016864e-2*x2[7]-0.4784552683e-2*x2[8]+0.1785619387e-1*x2[9]-0.6664022279e-1*x2[10]+.2487046973*x2[11]-.9281785663*x2[12]+3.464009568*x2[13]-12.92785971*x2[14]+.2474292549*x2[15]+11.93814269*x2[16]-1.989690448*x2[17]-1.00000000*u[15] = 0

eq1[17] := 3.913360392*10^(-8)*x1[1]-2.348016235*10^(-7)*x1[2]+9.392064942*10^(-7)*x1[3]-3.522024353*10^(-6)*x1[4]+0.1314889092e-4*x1[5]-0.4907353932e-4*x1[6]+0.1831452664e-3*x1[7]-0.6835075261e-3*x1[8]+0.2550884838e-2*x1[9]-0.9520031827e-2*x1[10]+0.3552924247e-1*x1[11]-.1325969380*x1[12]+.4948585097*x1[13]-1.846837101*x1[14]+6.892489894*x1[15]-25.72312247*x1[16]+20.28718708*x1[17]-1.*x2[17] = 0

eq2[17] := 3.913360392*10^(-8)*x2[1]-2.348016235*10^(-7)*x2[2]+9.392064942*10^(-7)*x2[3]-3.522024353*10^(-6)*x2[4]+0.1314889092e-4*x2[5]-0.4907353932e-4*x2[6]+0.1831452664e-3*x2[7]-0.6835075261e-3*x2[8]+0.2550884838e-2*x2[9]-0.9520031827e-2*x2[10]+0.3552924247e-1*x2[11]-.1325969380*x2[12]+.4948585097*x2[13]-1.846837101*x2[14]+6.892489894*x2[15]-25.72312247*x2[16]+20.28718708*x2[17]-1.*u[17] = 0

$eqq1 := {-7.425625842*x1[1]-3.446244947*x1[2]+13.78497979*x1[3]-3.693674202*x1[4]+.9897170194*x1[5]-.2651938761*x1[6]+0.7105848494e-1*x1[7]-0.1904006365e-1*x1[8]+0.5101769676e-2*x1[9]-0.1367015052e-2*x1[10]+0.3662905327e-3*x1[11]-0.9814707864e-4*x1[12]+0.2629778184e-4*x1[13]-7.044048706*10^(-6)*x1[14]+1.878412988*10^(-6)*x1[15]-4.696032471*10^(-7)*x1[16]+7.826720785*10^(-8)*x1[17]-1.000000000*x2[2] = 0}$

$eqq2 := {-7.425625842*x2[1]-3.446244947*x2[2]+13.78497979*x2[3]-3.693674202*x2[4]+.9897170194*x2[5]-.2651938761*x2[6]+0.7105848494e-1*x2[7]-0.1904006365e-1*x2[8]+0.5101769676e-2*x2[9]-0.1367015052e-2*x2[10]+0.3662905327e-3*x2[11]-0.9814707864e-4*x2[12]+0.2629778184e-4*x2[13]-7.044048706*10^(-6)*x2[14]+1.878412988*10^(-6)*x2[15]-4.696032471*10^(-7)*x2[16]+7.826720785*10^(-8)*x2[17]-1.000000000*u[2] = 0}$

$eq := {0, 1.*x1[17]-.1, -7.425625842*x1[1]-3.446244947*x1[2]+13.78497979*x1[3]-3.693674202*x1[4]+.9897170194*x1[5]-.2651938761*x1[6]+0.7105848494e-1*x1[7]-0.1904006365e-1*x1[8]+0.5101769676e-2*x1[9]-0.1367015052e-2*x1[10]+0.3662905327e-3*x1[11]-0.9814707864e-4*x1[12]+0.2629778184e-4*x1[13]-7.044048706*10^(-6)*x1[14]+1.878412988*10^(-6)*x1[15]-4.696032471*10^(-7)*x1[16]+7.826720785*10^(-8)*x1[17]-1.000000000*x2[2] = 0, -7.425625842*x2[1]-3.446244947*x2[2]+13.78497979*x2[3]-3.693674202*x2[4]+.9897170194*x2[5]-.2651938761*x2[6]+0.7105848494e-1*x2[7]-0.1904006365e-1*x2[8]+0.5101769676e-2*x2[9]-0.1367015052e-2*x2[10]+0.3662905327e-3*x2[11]-0.9814707864e-4*x2[12]+0.2629778184e-4*x2[13]-7.044048706*10^(-6)*x2[14]+1.878412988*10^(-6)*x2[15]-4.696032471*10^(-7)*x2[16]+7.826720785*10^(-8)*x2[17]-1.000000000*u[2] = 0}$

Error, (in Optimization:-NLPSolve) constraints must be specified as a set or list of equalities and inequalities

uexact := piecewise(0 <= x and x <= .3, 200*x*(1/9)-20/3, .3 <= x and x <= .7, 0, .7 <= x and x <= 1, -200*x*(1/9)+140/9)

x2exact := piecewise(0 <= x and x <= .3, (100/9)*x^2-(20/3)*x+1, .3 <= x and x <= .7, 0, .7 <= x and x <= 1, -(100/9)*x^2+(140/9)*x-49/9)

piecewise(0 <= x and x <= .3, (100/27)*x^3-(10/3)*x^2+x, .3 <= x and x <= .7, 1/10, .7 <= x and x <= 1, -(100/27)*x^3+(70/9)*x^2-(49/9)*x+37/27)

>

Download 1.mw

Can this apparent contradiction be explained?...

Asked by: Earl 980

May 03 2022

1 2

This worksheet displays an intersection between two spheres based on a test which seems unrelated to the display.

How can this be explained?

Intersecting_spheres.mw

evalf/Int issue with Maple 2020...

Asked by: mmcdara 7601

April 27 2022

1 5

Hi,

This chunk of code gives me almost instantly the desired result with Maple 2015 but fails returning a result after 5 minutes when ran from Maple 2020.
Changing the method or trying to tune their options doesn't fix the issue (for a larger value of the absolute tolerance the result, close to 1, is even obviously false).

Could you please help me to fix this?
TIA

>

restart;

>	interface(version)

(1)

>	with(Statistics):

>

Model_1 := (X, Y, Z) -> 1.3479120558270161+(-1)*.3390713110446567*X+1.0332964944900824*Y+(-1)*.8046331250569234*Z+0.9028899142595827e-1*X^2+(-1)*.28022910356641223*Y^2+1.3698461513469624*Z^2+0.6023630210658247e-1*Y*X+(-1)*.1988111077193626*Z*X+.6782902277463169*Z*Y+(-1)*0.7589729001497135e-1*X*Y*Z:

Model_2 := (X, Y, Z) -> .7215754021067852-.961682838202105*X+.4890842364596477*Y-.8214961524335734*Z+.15745942215497866*X^2-1.8023544416693338*Y^2+.36598799463016246*Z^2+1.3957614823018496*Y*X+.725398415577742*Z*X+1.9474707393604542*Z*Y-1.1780201448596594*X*Y*Z:

ExpMod_2 := unapply(expand(Model_2(Model_1(X1, Y1, Z1), Y2, Z2)), (X1, Y1, Z1, Y2, Z2)):

>

fy1 := PDF(Normal(0.1055, 0.0297), Y1):
fz1 := PDF(Normal(1, 0.2/3), Z1):
fy2 := PDF(Normal(0.17, 0.0476), Y2):
fz2 := PDF(Normal(1, 0.2/3), Z2):

C   := evalf(
         (1-eval(CDF(Normal(0.1055, 0.0297), Y), Y=0))
         *
         (1-eval(CDF(Normal(0.17, 0.0476), Y), Y=0))
         *
         (eval(CDF(Normal(1, 0.2/3), Z), Z=1.2)-eval(CDF(Normal(1, 0.2/3), Z), Z=0.8))^2
       ):

J := Int(
        fy1*fz1*fy2*fz2*(1+tanh(10^4*(ExpMod_2(2.14, Y1, Z1, Y2, Z2)-1.25)))/2,
        Y1=0..0.4,
        Z1=0.8..1.2,
        Y2=0..0.4817,
        Z2=0.8..1.2,
        method = _CubaDivonne, methodoptions=[absepsilon=1e-8]
      ):

Prob(X__2 > 1.25) = nprintf("%1.3e", evalf(J)/C);

(2)

>

Download 2020_issue.mw

"Error while printing" message when trying "Print ...

Asked by: PsiSquared 45

April 26 2022

2 1

When trying to print a Maple Document as a PDF on Mac, I am now getting an "Error while printing" message. A 1-page pdf is created that's empty. This is a new error, one that I've never seen when printing as PDF for any other Maple Document I've created.

I'm running Mac OS 12.3.1, the latest version of Mac OS and using Maple 2020.

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