Advanced Search

MaplePrimes Questions

Maple gives trivial solution to linear system with...

Asked by: zenterix 405
linear-algebra parametric
October 06 2023
1  1

Consider the following. 

We have a matrix A with five parameters in it.

If we tell Maple to solve Ax=0, it gives us the trivial solution.

Then, if I make a matrix B where I choose specific values for those five parameters and I tell Maple to solve Bx=0 I get a non-trivial solution.

Why doesn't Maple give me a more informative result in the Ax=0 case? 

A := Matrix(5, 5, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (1, 5) = a__1, (2, 1) = 0, (2, 2) = 1, (2, 3) = 0, (2, 4) = 0, (2, 5) = b__1, (3, 1) = -216, (3, 2) = -18, (3, 3) = 0, (3, 4) = 0, (3, 5) = c__1, (4, 1) = 0, (4, 2) = 0, (4, 3) = 1, (4, 4) = 0, (4, 5) = d__1, (5, 1) = 0, (5, 2) = 0, (5, 3) = 0, (5, 4) = 1, (5, 5) = e__1}) = Matrix(%id = 36893488151959194068)NULL

with(LinearAlgebra)

GaussianElimination(A)

Matrix(%id = 36893488151959184316)

 (1)

LinearSolve(A, `<,>`(0, 0, 0, 0, 0))

Vector[column](%id = 36893488151959183100)

 (2)

B := Matrix(5, 5, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (1, 5) = 0, (2, 1) = 0, (2, 2) = 1, (2, 3) = 0, (2, 4) = 0, (2, 5) = 0, (3, 1) = -216, (3, 2) = -18, (3, 3) = 0, (3, 4) = 0, (3, 5) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 1, (4, 4) = 0, (4, 5) = 1, (5, 1) = 0, (5, 2) = 0, (5, 3) = 0, (5, 4) = 1, (5, 5) = 4}) = Matrix([[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [-216, -18, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 4]])NULL

GaussianElimination(B) = Matrix(%id = 36893488151959174788)NULL

LinearSolve(B, `<,>`(0, 0, 0, 0, 0))

Vector[column](%id = 36893488151959164916)

 (3)

``

NULL

An even easier way to show a non-trivial solution is to just make the entire last column zero.

Download polyn_matrix.mw

simplify piecewise function ...

Asked by: Zeineb 540
simplify piecewise incomplete-question
October 06 2023
0  2

Dear all 

I have a function defined on many sub-intervals, how can I simplify this the funciton obtained at each iteration. I hope obatin B_{i,1}, B_{i,2}, and B_{i,3} 

B_Spline.mw

Thank you 

Extract vectors from a vector...

Asked by: Muhammad Usman 240
vector
October 06 2023
0  2

Dear Users!

I hope everyone is fine here. I have three vectors say V[1], V[2] and V[3] as:

restart; with(LinearAlgebra); with(linalg);
V[1] := Vector([3, 2, -4]);
V[2] := Vector([1, 2/3, 7]);
V[3] := Vector([-9, 0, 1/2]);

I can define a Vector V have V[1], V[2] and V[3] using blockmatrix command as:

C := blockmatrix(3, 1, [V[1], V[2], V[3]]);

My question is that how I can extract vectors V[1], V[2] and V[3] from C? Thanks in advance

Four-vectors in Maple...

Asked by: Traruh Synred 55
vector physics duplicate-question
October 05 2023
1  19

Is there a simple 4-vector package available for Maple? Yes, I know about using Tensors, but don't want to fool with metrics and raising and lowering operators.

I have written my  own, but it seems buggy. I generate some vectors in in CM that should add up to a massless neutrino, but some times when I boost them to the 'lab' and do the addition there the neutrion acquires a substantial mass. It's not a merely numerical issue. It's weird because most of the time the neutrion mass is 0 or close to it.

My homemade boost proc 'boostTo' is attached.

Error, (in minimize) unexpected options: {x}...

Asked by: Missis 15
extrema minimize
October 05 2023
1  5

Привет. У меня проблема с пестремой, помогите пожалуйста:

restart;
y:=sqrt((x^2*(x^2-4))/(x^2-1));
readlib(extrema): readlib(maximize): readlib(minimize):
extrema(y,{},x,'s');s;
ymax:=maximize(y,{x});
Error, (in maximization) unexpected parameters: {x}
ymin:=minimize(y,{x});
Error, (in minimization) unexpected parameters: {x}

unable to plot 3d and 2d plots...

Asked by: KIRAN SAJJAN 40
ode numeric differential-equations
October 05 2023
0  3

  I am unable to draw both 3d plots sowing error please help me to solve

> 

restart:NULLNULL
> 

p1 := 0.1e-1; p2 := 0.2e-1; p3 := 0.1e-1; Px := p1+p2+p3
> 

rf := 1050; kf := .52; cpf := 3617; sigmaf := .8
> 

sigma1 := 25000; rs1 := 5200; ks1 := 6; cps1 := 670
> 

sigma2 := 59.7*10^6; rs2 := 8933; ks2 := 400; cps2 := 385
> 

sigma3 := 2380000; rs3 := 4250; ks3 := 8.9538; cps3 := 686.2
> 

NULL
> 

B1 := 1+2.5*Px+6.2*Px^2; B2 := 1+13.5*Px+904.4*Px^2; B3 := 1+37.1*Px+612.6*Px^2; B4 := (ks1+2*kf-2*Px*(kf-ks1))/(ks1+2*kf+Px*(kf-ks1)); B5 := (ks2+3.9*kf-3.9*Px*(kf-ks2))/(ks2+3.9*kf+Px*(kf-ks2)); B6 := (ks3+4.7*kf-4.7*Px*(kf-ks3))/(ks3+4.7*kf+Px*(kf-ks3))
> 

a2 := B1*p1+B2*p2+B3*p3
> 

a1 := 1-p1-p2-p3+p1*rs1/rf+p2*rs2/rf+p3*rs3/rf
> 

a3 := 1-p1-p2-p3+p1*rs1*cps1/(rf*cpf)+p2*rs2*cps2/(rf*cpf)+p3*rs3*cps3/(rf*cpf)
> 

a4 := B4*p1+B5*p2+B6*p3
> 

NULL
> 

a5 := 1+3*((p1*sigma1+p2*sigma2+p3*sigma3)/sigmaf-p1-p2-p3)/(2+(p1*sigma1+p2*sigma2+p3*sigma3)/((p1+p2+p3)*sigmaf)-((p1*sigma1+p2*sigma2+p3*sigma3)/sigmaf-p1-p2-p3))

``

``

> 



NULL
> 

ODE:=[(a2+K)*(diff(U0(eta), eta, eta))/a1-Ra*(diff(U0(eta), eta))+lambda0/a1-a5*M1^2*U0(eta)/a1+K*(diff(N0(eta), eta))/a1+la*Ra*Theta0(eta)*(1+Qc*Theta0(eta)), (a2+K)*(diff(U1(eta), eta, eta))/a1-H^2*l1*U1(eta)-Ra*(diff(U1(eta), eta))+lambda1/a1-a5*M1^2*U1(eta)/a1+K*(diff(N1(eta), eta))/a1+la*Ra*(Theta1(eta))(1+2*Qc*Theta0(eta)), diff(N0(eta), eta, eta)-Ra*a1*Pj*(diff(N0(eta), eta))-2*n1*N0(eta)-n1*(diff(U0(eta), eta)), diff(N1(eta), eta, eta)-Ra*a1*Pj*(diff(N1(eta), eta))-2*n1*N1(eta)-n1*(diff(U1(eta), eta))-H^2*a1*Pj*l1*N1(eta), (a4/(a3*Pr)-delta*Ra^2/H^2+4*Rd*(1+(Tp-1)^3*Theta0(eta)^3+3*(Tp-1)^2*Theta0(eta)^2+(3*(Tp-1))*Theta0(eta))/(3*a3*Pr))*(diff(Theta0(eta), eta, eta))-Ra*(diff(Theta0(eta), eta))+a5*Ec*M1^2*U0(eta)^2/a3+(a2+K)*Ec*(diff(U0(eta), eta))^2/a1+Q*Theta0(eta)/a3+4*(diff(Theta0(eta), eta))^2*Rd*(3*(Tp-1)+6*(Tp-1)^2*Theta0(eta)+3*(Tp-1)^3*Theta0(eta)^2)/(3*a3*Pr), (a4/(a3*Pr)-delta*Ra^2/H^2+4*Rd*(1+(Tp-1)^3*Theta0(eta)^3+3*(Tp-1)^2*Theta0(eta)^2+(3*(Tp-1))*Theta0(eta))/(3*a3*Pr))*(diff(Theta1(eta), eta, eta))-(H^2*l1+2*Ra*delta*l1+Ra)*(diff(Theta1(eta), eta))+(Q/a3-delta*H^2*l1^2)*Theta1(eta)+2*(a2+K)*Ec*(diff(U0(eta), eta))*(diff(U1(eta), eta))/a1+2*a5*Ec*M^2*U0(eta)*U1(eta)/a3+4*(diff(Theta0(eta), eta, eta))*Theta1(eta)*Rd*(3*(Tp-1)+6*(Tp-1)^2*Theta0(eta)+3*(Tp-1)^3*Theta0(eta)^2)/(3*a3*Pr)+4*Rd*(diff(Theta0(eta), eta))^2*(6*(Tp-1)^2*Theta1(eta)+6*(Tp-1)^3*Theta0(eta)*Theta1(eta))/(3*a3*Pr)+4*Rd*(diff(Theta1(eta), eta))*(diff(Theta0(eta), eta))*(6*(Tp-1)+6*(Tp-1)^3*Theta0(eta)^2+12*(Tp-1)^2*Theta0(eta))/(3*a3*Pr)]:
> 


(LB,UB):= (0,1):


BCs:= [
  
  U0(0) = 0, U1(0) = 0, N0(0) = 0, N1(0) = 0, Theta0(0) = 0, Theta1(0) = 0, U0(1) = 0, U1(1) = 0, N0(1) = 0, N1(1) = 0, Theta0(1) = 1, Theta1(1) = 0
]:
> 

NULL
> 


Params:= Record(
   
   M1=  1.2, Rd=0.8,la=0.8,n1=1.2,Q=0.2,Pj=0.001,Ra=0.8,Ec=1,    Pr= 21,   delta= 0.2,    t1= (1/4)*Pi, lambda0=2,lambda1=3,   Qc= 0.1,    l1= 1,K=0.4,H=3 ,deltat=0.05  ):
   
> 

NBVs:= [   
 
a1**D(U0)(0) = `C*__f` , # Skin friction coefficient
 (a4+(4*Rd*(1/3))*(1+(Tp-1)*(Theta0(0)+0.1e-2*exp(l1*t1)*Theta1(0)))^3)*((D(Theta0))(0)+0.1e-2*exp(l1*t1)*(D(Theta1))(0)) = `Nu*`    # Nusselt number     
]:
Nu:= `Nu*`:
Cf:= `C*__f`:

 
> 

Solve:= module()
local
   nbvs_rhs:= rhs~(:-NBVs), #just the names
   Sol, #numeric dsolve BVP solution of any 'output' form
   ModuleApply:= subs(
      _Sys= {:-ODEs[], :-BCs[], :-NBVs[]},
      proc({
          M1::realcons:=  Params:-M1,
         Pr::realcons:= Params:-Pr,
         Rd::realcons:= Params:-Rd,
         la::realcons:= Params:-la,
         Tp::realcons:= Params:-Tp,
         n1::realcons:= Params:-n1,
         Q::realcons:= Params:-Q,
         Pj::realcons:= Params:-Pj,
         Ra::realcons:= Params:-Ra,
         Ec::realcons:= Params:-Ec,
         t1::realcons:=  Params:-t1,
         delta::realcons:= Params:-delta,
         lambda0::realcons:= Params:-lambda0,
         lambda1::realcons:= Params:-lambda1,
         Qc::realcons:= Params:-Qc,
         K::realcons:= Params:-K,
         l1::realcons:= Params:-l1,
         H::realcons:= Params:-H
      })
         Sol:= dsolve(_Sys, _rest, numeric);
         AccumData(Sol, {_options});
         Sol
      end proc
   ),
   AccumData:= proc(
      Sol::{Matrix, procedure, list({name, function}= procedure)},
      params::set(name= realcons)
   )
   local n, nbvs;
      if Sol::Matrix then
         nbvs:= seq(n = Sol[2,1][1,Pos(n)], n= nbvs_rhs)
      else
         nbvs:= (nbvs_rhs =~ eval(nbvs_rhs, Sol(:-LB)))[]
      fi;
      SavedData[params]:= Record[packed](params[], nbvs)
   end proc,
   ModuleLoad:= eval(Init);
export
   SavedData, #table of Records
   Pos, #Matrix column indices of nbvs
   Init:= proc()
      Pos:= proc(n::name) option remember; local p; member(n, Sol[1,1], 'p'); p end proc;
      SavedData:= table();
      return
   end proc ;
   ModuleLoad()
end module:
 
> 


 
> 

 

> 

#procedure that generates 3-D plots (dropped-shadow contour + surface) of an expression


ParamPlot3d:= proc(
   Z::{procedure, `module`}, #procedure that extracts z-value from Solve's dsolve solution
   X::name= range(realcons), #x-axis-parameter range
   Y::name= range(realcons), #y-axis-parameter range
   FP::list(name= realcons), #fixed values of other parameters
   {
      #fraction of empty space above and below plot (larger "below"
      #value improves view of dropped-shadow contourplot):
      zmargin::[realcons,realcons]:= [.05,0.15],
      eta::realcons:= :-LB, #independent variable value
      dsolveopts::list({name, name= anything}):= [],
      contouropts::list({name, name= anything}):= [],
      surfaceopts::list({name, name= anything}):=[]    
   }
)
local
   LX:= lhs(X), RX:= rhs(X), LY:= lhs(Y), RY:= rhs(Y),
   Zremember:= proc(x,y)
   option remember; #Used because 'grid' should be the same for both plots.
      Z(
         Solve(
            LX= x, LY= y, FP[],
            #Default dsolve options can be changed by setting 'dsolveopts':
            'abserr'= 0.5e-7, 'interpolant'= false, 'output'= Array([eta]),  
            dsolveopts[]
         )
      )
   end proc,
   plotspec:= (Zremember, RX, RY),
   C:= plots:-contourplot(
      plotspec,
      #These default plot options can be changed by setting 'contouropts':
      'grid'= [25,25], 'contours'= 5, 'filled',
      'coloring'= ['yellow', 'orange'], 'color'= 'green',
      contouropts[]
   ),
   P:= plot3d(
      plotspec,
      #These default plot options can be changed by setting 'surfaceopts':
      'grid'= [25,25], 'style'= 'surfacecontour', 'contours'= 6,
      surfaceopts[]
   ),
   U, L #z-axis endpoints after margin adjustment
;
   #Stretch z-axis to include margins:
   (U,L):= ((Um,Lm,M,m)-> (M*(Lm-1)+m*Um, M*Lm+m*(Um-1)) /~ (Um+Lm-1))(
      zmargin[],
      (max,min)(op(3, indets(P, 'specfunc'('GRID'))[])) #actual z-axis range
   );
   plots:-display(
      [
         plots:-spacecurve(
            {
               [[lhs(RX),rhs(RY),U],[rhs(RX),rhs(RY),U],[rhs(RX),rhs(RY),L]], #yz backwall
               [[rhs(RX),rhs(RY),U],[rhs(RX),lhs(RY),U],[rhs(RX),lhs(RY),L]]  #xz backwall
            },
            'color'= 'grey', 'thickness'= 0
         ),
         plottools:-transform((x,y)-> [x,y,L])(C), #dropped-shadow contours
         P
      ],
      #These default plot options can be changed simply by putting the option in the
      #ParamPlot3d call:
      'view'= ['DEFAULT', 'DEFAULT', L..U], 'orientation'= [-135, 75], 'axes'= 'frame',
      'labels'= [lhs(X), lhs(Y), Z], 'labelfont'= ['TIMES', 'BOLDOBLIQUE', 16],
      'caption'= nprintf(cat("%a = %4.2f, "$nops(FP)-1, "%a = %4.2f"), (lhs,rhs)~(FP)[]),
      'captionfont'= ['TIMES', 14],
      'projection'= 2/3,   
      _rest
   )
end proc:

> 

NULL
> 

NULL
> 

GetNu := proc (Sol::Matrix) options operator, arrow; Sol[2, 1][1, Solve:-Pos(:-Nu)] end proc
> 

ParamPlot3d(
   GetNu,Q= 0..5, Rd= 0..5, [
   
   Pr= 21   ],
   labels= [Q, gamma, Nu]
);

Error, (in plot/iplot2d/levelcurve) could not evaluate expression

  

``

Download P6_3D_plots.mw

Surface btw spacecurves in 3d......

Asked by: MarcinM 30
October 05 2023
1  9

Hi,

Anyone knows how to plot a surface btw 2 spacecurves in 3d? For example a flat curve x^2+y^2=1 which maybe a upper half of above circle for y=0 to 1 and a spacecurve which is a function for example 2+x^2*y. So second curve should be above the first and limit a surface From the top. 

Can't find a solution in help and parametric curves does not solve a problem.

In fact it would be enough to have a vertical surface starting on a xy plane and limited by Givenchy function. As it is in line integral calculations.

Regards

Marcin

How Do I enter this into Maple?...

Asked by: EdisonSu223 5
linearalgebra homework do-my-homework-for-me
October 04 2023
1  1

How to manually build a loglog plot (without using...

Asked by: zenterix 405
plot plotting loglogplot
October 04 2023
0  1

Consider the following worksheet (perhaps it is better to download the worksheet and execute since the contents below aren't showing the commands used to plot the last two plots).

NULL

T = log(R)/(a+b*log(R))^2

plot(log(R)/(-1.16+.675*log(R))^2, R = 1000 .. 30000)

  

NULL

10^log[10](T) = log(R)/(a+b*log(R))^2

NULL

log[10](T) = log[10](log(R)/(a+b*log(R))^2)

NULL

w = log[10](z/(b*z+a)^2)

w = ln(z/(b*z+a)^2)/ln(10)

 (1)

NULL

plot(log[10](z/(-1.16+.675*z)^2), z = log(1000) .. log(30000))

  

NULL

``

NULL

plots:-loglogplot(log(R)/(-1.16+.675*log(R))^2, R = 1000 .. 30000)

  

NULL

 

My question is about making a loglog plot of the equation

for R between 1000 and 30000.

 

The second to last plot is of w as a function of z, as in the last equation below

and the plot command is (where I have subbed in a=-1.16 and b=0.675)

In the second to last plot, of course we have negative values of w. If we were to consider the underlying values of T, they would never be negative of course.

The last plot is the command

I think this last plot is what I want (though I am not sure because I am not totally sure what plots:-loglogplot is doing).

 

My question is how to obtain this loglog plot manually. That is, I want the axes to show values of R on the x axis and T on the y axis (just like a usual loglog plot shows).

In other words, how to go from the second to last plot to the same plot but showing the corresponding R and T values instead of z and w.

Download loglog.mw

display solution pdesolve...

Asked by: Zeineb 540
pde differential-equations
October 04 2023
0  1

Dear all

I would like to get the solution of a system : pde with boundary and initial condition. Everything well coded, but the code does not return the solution 

sol_heat.mw

Thanks for your help 

How to get Maple to output result of solve using b...

Asked by: zenterix 405
log
October 04 2023
2  4


Here is a small worksheet to illustrate my question

Consider the expression

 

solve(sqrt(log[10](R)/T) = a+b*log[10](R), T) = ln(R)*ln(10)/(ln(10)^2*a^2+2*ln(10)*ln(R)*a*b+ln(R)^2*b^2)NULL

NULL

Can we somehow tell Maple to keep the logarithms in base 10?

 

NULL


I'd like for the final expression to have only base 10 logarithms.

 

When I do it with pen and paper, I get

 

It is this last expression that I would like Maple to output.

Download log10.mw

The issue with mtaylor for a function of 2 variabl...

Asked by: Vortex 65
series mtaylor
October 04 2023
0  3

Hello.

I want to check my analytical calculations and to compare my results with the series expansion for x=0 and y=0 of the function

R0 := -(1-tanh((1/2)*l*sqrt(k*y^2+x^2)*d)^2)*x/(k*y^2+x^2)+2*tanh((1/2)*l*sqrt(k*y^2+x^2)*d)*x/(l*(k*y^2+x^2)^(3/2)*d)

by means of the command 

mtaylor(R0, [x, y], 5);

 

However, I have a message from Maple 17

Error, (in mtaylor) does not have a taylor expansion, try series()

I read here a little bit about some bugs of mtaylor function, but how to resolve this issue?

introduce the cosine...

Asked by: jalal 435
embedded-components trigonometry
October 04 2023
0  0

Hi, I'm looking to create a discovery activity to introduce the cosine . Any ideas for using Maple components with a slider to vary the position of a point on a line while displaying distances and their ratios? Thank you

Doc2.pdf

principal measurement of an angle...

Asked by: jalal 435
radians mod
October 04 2023
0  1

Hi,

How can one obtain the principal measurement of an angle (which belongs to the interval ]-π;π]?

Thank you

QuestionMesPrincipale.mw

How does Maple arrive at an implicit solution to i...

Asked by: Joseph Poveromo 25
October 04 2023
0  3
Equation:=int(y'(x)*w(x)) = [int([y(x)^(1/2)]*w(x))]^(-2/3) When plugging this Equation into dsolve, Maple provides the following implicit solution: Solution:= [3*y(x)^(4/3)]/4 + int[(2*y(x)^(5/6)/[3*int([(y(x)^(1/2))*w(x)]/[3*int[(y(x)^(1/2))*w(x)]^(5/3) When going to odeadvisor, the suggestion was to first convert to the form y = G(x,y'(x) and then utilize the method of 'patterns', which I could not apply to this equation. If anyone can fill in the steps between 'Equation' and 'Solution', it would be greatly, appreciated. P.S.Sadly, I am unable to attach the actual Maplesoft worksheet.
First 163 164 165 166 167 168 169 Last Page 165 of 2427