Maple 2020 Questions and Posts

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

Asked by: Earl 955

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 955

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 6740

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.

Help with assumptions and complex numbers...

Asked by: jrive 195

April 11 2022

1 2

I'm trying to solve a coupled inductor problem. All I'm trying to do is solve for the currents (which I could do), then solve for resonance by setting the imaginary part of I1 to 0 and solving for omega. I then want to plug this resonant frequency back into I1 and evaluate it for some component values and coupling coefficient.

The problem is that even though I define the various variables as real, Maple doesn't seem to recognize them as such. I suspect I've failed to define one of them, and that is why it is responding like it is, but I can't find it.

I'm also getting some weird behavior.....for example if I type : wres0, I get the value I assigned to it --that's fine. But then, when I type : wres0/(2*pi), I get an error, "Error, unable to parse 'mverbatim" --- what does this mean?

This should be a pretty straight forward calculation on Maple, but at this point, I think I may be better off doing it by hand! I appreciate any help you can provide. Thank you.

reflected_load.mw

Two questions regarding a sliding ladder...

Asked by: Earl 955

April 09 2022

0 0

This worksheet animates part of the motion of the classic ladder sliding down a wall.

Please answer the two questions posed in the opening text.

Respondents will need to establish their own link to the DirectSearch package

Slide_Ladder.mw

Re: How to treat differentiaion operator as a coef...

Asked by: pik1432 245

April 04 2022

3 15

Hello all,

Would you allow me to ask this one question?
[moderator: See also this previous question]

Is there any possible way to treat the differentiation operator (e.g., 'D') as an ordinary coefficient of a polynomial?

For example, as described in the attached worksheet, I was wondering if there is a way to re-write the LHS of the expression 'eq_e5_9b' as the expression 'desired'.

In Kwon Park

>

restart;

>	with(DEtools):

>	eq_e5_9b := psi__d0Delta__delta(t) + psi__q0 D(Delta__delta(t))/omega__0 = p_(Delta__psi__d(t))/omega__0 - Delta__psi__q(t);

psi__d0*Delta__delta(t)+psi__q0*D(Delta__delta(t))/omega__0 = p_(Delta__psi__d(t))/omega__0-Delta__psi__q(t)

(1)

>	collect(lhs(eq_e5_9b), Delta__delta(t));

psi__d0*Delta__delta(t)+psi__q0*D(Delta__delta(t))/omega__0

(2)

>	desired := Delta__delta(t) * (psi__d0 + psi__q0 * D/omega__0);

Delta__delta(t)*(psi__d0+psi__q0*D/omega__0)

(3)

>

Download Q20220404.mw

Is this O(N^8)?...

Asked by: Thomas Dean 327

April 03 2022

2 6

I am trying to decide O of times fo a computer process. I thought it was n^2*log(N) or something like that.

With 12 points, it may be hard to determine if O(N^4), etc.

See big-o.mw

Why do these integration results differ?...

Asked by: Earl 955

March 28 2022

2 6

The uploaded worksheet attempts to determine arc lengths of an ellipse by two methods. Why do their results differ?

ArcLength_of_Ellipse.mw

Integrating int(1/(A^2 - B^2*cos(t))^(1/2), t = 0 ...

Asked by: CatherineKamal 10

March 23 2022

2 1

I want to integrate the function int(1/(A^2 - B^2*cos(t))^(1/2), t = 0 .. 2*Pi), I get the correct solution, but I want to prevent all the "if" statements from appearing. I have tried to use "assume" but the if statement still does not disappear.

How to save explore plot ?...

Asked by: priya_priti 35

March 21 2022

1 1

Download Plot.mw

Is there any way to save "explore plot" in such a way that the slider of constants should appear in the extension file?

So that I can see the constant changing in the extension file too.

How do I find the center of mass and moment of ine...

Asked by: Earl 955

March 17 2022

2 7

For example for an ellipsoid with principal axes 3, 2 and 1 along the x, y and z coordinate axes respectively, with center at the origin and truncated at x equals 1.

What math will reveal its center of mass and its moment of inertia for an axis of revolution through the center of mass and parallel to the y axis?

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