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Having solution of an inequations system, is there a way/function/algorithm to find a particular numeric solution (as simplex[minimize] can do) ?

ex:

Q := {1 < x - y, x + y < 1};

R := solve(Q);

      { x < 1 - y, y < 0, y + 1 < x }

manually it's easy to find some numeric solutions:


      y = -1, x = 1
      y = -2, x = 0

but I need an automatic way.

Thank you for your help
s.py

 

a+a*c

a+a*b

a+b+c

assume system of polynomials are above, how to test whether inverse exist

and find inverse of them

 

I have a set "EQ" containing N linear equations in N unknowns. The only symbolic variables in each "EQ[i]" are the unknowns. I want to write a procedure that derives the matrices "A" and "b" where A.x=b is the same linear system stored in "EQ". In other words, I want to write the linear system in the matrix form.

Can anyone guide me through writting such a procedure?
As an example do it with the system written in the following file.

Note: This procedure will be used for large linear systems (e.g. 2000 Equations, 2000 Unknowns) so it will be important that the procedure uses the least operations required.

LinearSystem.mw

Thanks in advance.

I have a large system of linear algebraic equations that I want to solve (2005 Unknowns, 2005 Equations). I was wondering that what are the proper commands to use in maple for solving the system as fast as possible. Take a look at the files in the download link if you want to see the system of linear algebraic equations.

http://pc.cd/h79

Please provide me any suggesitons that you may think will be helpful like using other sofwares that are good in doing this work such as MATLAB or something else.


Thanks in Advance




I'm trying to solve this system of ODEs by Laplace transform. 

> de1 := d^2*y(t)/dt^2 = y(t)+3*x(t)

> de2 := d^2*x(t)/dt^2 = 4*y(t)-4*exp(t)

with initial conditions 

> ICs := y(0) = 2, (D(y))(0) = 3, x(0) = 1, (D(x))(0) = 2

 

Using 

> deqns := de1, de2

and

> var := y(t), x(t)

 

I need to solve it for both y(t) and x(t), I have tried this by:

> dsolve({ICs, deqns}, var, method = laplace)

And

> dsolve({ICs, deqns}, y(t), method = laplace)

> dsolve({ICs, deqns}, x(t), method = laplace)

 

However I get this error message:

Error, (in dsolve/process_input) invalid initial condition

 

Any help is appreciated

Hello i want to sort according to u derivatives (k) system.  And finding determining equations system and solving this system. Thank you very much.  

restart

with(PDEtools)

[CanonicalCoordinates, ChangeSymmetry, CharacteristicQ, CharacteristicQInvariants, ConservedCurrentTest, ConservedCurrents, ConsistencyTest, D_Dx, DeterminingPDE, Eta_k, Euler, FromJet, InfinitesimalGenerator, Infinitesimals, IntegratingFactorTest, IntegratingFactors, InvariantEquation, InvariantSolutions, InvariantTransformation, Invariants, Laplace, Library, PDEplot, PolynomialSolutions, ReducedForm, SimilaritySolutions, SimilarityTransformation, Solve, SymmetrySolutions, SymmetryTest, SymmetryTransformation, TWSolutions, ToJet, build, casesplit, charstrip, dchange, dcoeffs, declare, diff_table, difforder, dpolyform, dsubs, mapde, separability, splitstrip, splitsys, undeclare]

(1)

U := diff_table(u(x, y, t))

table( [(  ) = u(x, y, t) ] )

(2)

declare(U[])

u(x, y, t)*`will now be displayed as`*u

(3)

pde := diff(U[t]-(3/2)*U[x]-6*U[]^2*U[x]+U[x, x, x], x)+U[y, y] = 0

diff(diff(u(x, y, t), t), x)-(3/2)*(diff(diff(u(x, y, t), x), x))-12*u(x, y, t)*(diff(u(x, y, t), x))^2-6*u(x, y, t)^2*(diff(diff(u(x, y, t), x), x))+diff(diff(diff(diff(u(x, y, t), x), x), x), x)+diff(diff(u(x, y, t), y), y) = 0

(4)

NULL

w := phi(x, y, t, U[])

phi(x, y, t, u(x, y, t))

(5)

w*(-12*U[x]^2-12*U[]*U[x, x])+12*w*U[x]^2+12*U[]*w*U[x, x]+(diff(w, x, x))*(-3/2-6*U[]^2)+diff(diff(w, t), x)+diff(w, y, y)+diff(w, x, x, x, x)-lambda*(diff(U[t]-(3/2)*U[x]-6*U[]^2*U[x]+U[x, x, x], x)+U[y, y])

-lambda*(diff(diff(u(x, y, t), t), x)-(3/2)*(diff(diff(u(x, y, t), x), x))-12*u(x, y, t)*(diff(u(x, y, t), x))^2-6*u(x, y, t)^2*(diff(diff(u(x, y, t), x), x))+diff(diff(diff(diff(u(x, y, t), x), x), x), x)+diff(diff(u(x, y, t), y), y))+(D[1, 1, 1, 1](phi))(x, y, t, u(x, y, t))+(D[1, 1, 1, 4](phi))(x, y, t, u(x, y, t))*(diff(u(x, y, t), x))+((D[1, 1, 1, 4](phi))(x, y, t, u(x, y, t))+(D[1, 1, 4, 4](phi))(x, y, t, u(x, y, t))*(diff(u(x, y, t), x)))*(diff(u(x, y, t), x))+(D[1, 1, 4](phi))(x, y, t, u(x, y, t))*(diff(diff(u(x, y, t), x), x))+((D[1, 1, 1, 4](phi))(x, y, t, u(x, y, t))+(D[1, 1, 4, 4](phi))(x, y, t, u(x, y, t))*(diff(u(x, y, t), x))+((D[1, 1, 4, 4](phi))(x, y, t, u(x, y, t))+(D[1, 4, 4, 4](phi))(x, y, t, u(x, y, t))*(diff(u(x, y, t), x)))*(diff(u(x, y, t), x))+(D[1, 4, 4](phi))(x, y, t, u(x, y, t))*(diff(diff(u(x, y, t), x), x)))*(diff(u(x, y, t), x))+2*((D[1, 1, 4](phi))(x, y, t, u(x, y, t))+(D[1, 4, 4](phi))(x, y, t, u(x, y, t))*(diff(u(x, y, t), x)))*(diff(diff(u(x, y, t), x), x))+(D[1, 4](phi))(x, y, t, u(x, y, t))*(diff(diff(diff(u(x, y, t), x), x), x))+((D[1, 1, 1, 4](phi))(x, y, t, u(x, y, t))+(D[1, 1, 4, 4](phi))(x, y, t, u(x, y, t))*(diff(u(x, y, t), x))+((D[1, 1, 4, 4](phi))(x, y, t, u(x, y, t))+(D[1, 4, 4, 4](phi))(x, y, t, u(x, y, t))*(diff(u(x, y, t), x)))*(diff(u(x, y, t), x))+(D[1, 4, 4](phi))(x, y, t, u(x, y, t))*(diff(diff(u(x, y, t), x), x))+((D[1, 1, 4, 4](phi))(x, y, t, u(x, y, t))+(D[1, 4, 4, 4](phi))(x, y, t, u(x, y, t))*(diff(u(x, y, t), x))+((D[1, 4, 4, 4](phi))(x, y, t, u(x, y, t))+(D[4, 4, 4, 4](phi))(x, y, t, u(x, y, t))*(diff(u(x, y, t), x)))*(diff(u(x, y, t), x))+(D[4, 4, 4](phi))(x, y, t, u(x, y, t))*(diff(diff(u(x, y, t), x), x)))*(diff(u(x, y, t), x))+2*((D[1, 4, 4](phi))(x, y, t, u(x, y, t))+(D[4, 4, 4](phi))(x, y, t, u(x, y, t))*(diff(u(x, y, t), x)))*(diff(diff(u(x, y, t), x), x))+(D[4, 4](phi))(x, y, t, u(x, y, t))*(diff(diff(diff(u(x, y, t), x), x), x)))*(diff(u(x, y, t), x))+3*((D[1, 1, 4](phi))(x, y, t, u(x, y, t))+(D[1, 4, 4](phi))(x, y, t, u(x, y, t))*(diff(u(x, y, t), x))+((D[1, 4, 4](phi))(x, y, t, u(x, y, t))+(D[4, 4, 4](phi))(x, y, t, u(x, y, t))*(diff(u(x, y, t), x)))*(diff(u(x, y, t), x))+(D[4, 4](phi))(x, y, t, u(x, y, t))*(diff(diff(u(x, y, t), x), x)))*(diff(diff(u(x, y, t), x), x))+3*((D[1, 4](phi))(x, y, t, u(x, y, t))+(D[4, 4](phi))(x, y, t, u(x, y, t))*(diff(u(x, y, t), x)))*(diff(diff(diff(u(x, y, t), x), x), x))+(D[4](phi))(x, y, t, u(x, y, t))*(diff(diff(diff(diff(u(x, y, t), x), x), x), x))+(D[2, 2](phi))(x, y, t, u(x, y, t))+(D[2, 4](phi))(x, y, t, u(x, y, t))*(diff(u(x, y, t), y))+((D[2, 4](phi))(x, y, t, u(x, y, t))+(D[4, 4](phi))(x, y, t, u(x, y, t))*(diff(u(x, y, t), y)))*(diff(u(x, y, t), y))+(D[4](phi))(x, y, t, u(x, y, t))*(diff(diff(u(x, y, t), y), y))+(D[1, 3](phi))(x, y, t, u(x, y, t))+(D[3, 4](phi))(x, y, t, u(x, y, t))*(diff(u(x, y, t), x))+((D[1, 4](phi))(x, y, t, u(x, y, t))+(D[4, 4](phi))(x, y, t, u(x, y, t))*(diff(u(x, y, t), x)))*(diff(u(x, y, t), t))+(D[4](phi))(x, y, t, u(x, y, t))*(diff(diff(u(x, y, t), t), x))+((D[1, 1](phi))(x, y, t, u(x, y, t))+(D[1, 4](phi))(x, y, t, u(x, y, t))*(diff(u(x, y, t), x))+((D[1, 4](phi))(x, y, t, u(x, y, t))+(D[4, 4](phi))(x, y, t, u(x, y, t))*(diff(u(x, y, t), x)))*(diff(u(x, y, t), x))+(D[4](phi))(x, y, t, u(x, y, t))*(diff(diff(u(x, y, t), x), x)))*(-3/2-6*u(x, y, t)^2)+12*u(x, y, t)*phi(x, y, t, u(x, y, t))*(diff(diff(u(x, y, t), x), x))+12*phi(x, y, t, u(x, y, t))*(diff(u(x, y, t), x))^2+phi(x, y, t, u(x, y, t))*(-12*(diff(u(x, y, t), x))^2-12*u(x, y, t)*(diff(diff(u(x, y, t), x), x)))

(6)

k := simplify(%)

-(3/2)*(D[1, 1](phi))(x, y, t, u(x, y, t))+(D[1, 3](phi))(x, y, t, u(x, y, t))+(D[2, 2](phi))(x, y, t, u(x, y, t))+(D[1, 1, 1, 1](phi))(x, y, t, u(x, y, t))+4*(D[1, 1, 1, 4](phi))(x, y, t, u(x, y, t))*(D[1](u))(x, y, t)+6*(D[1, 1, 4](phi))(x, y, t, u(x, y, t))*(D[1, 1](u))(x, y, t)+4*(D[1, 4](phi))(x, y, t, u(x, y, t))*(D[1, 1, 1](u))(x, y, t)+(D[4](phi))(x, y, t, u(x, y, t))*(D[1, 1, 1, 1](u))(x, y, t)+2*(D[2, 4](phi))(x, y, t, u(x, y, t))*(D[2](u))(x, y, t)+(D[4](phi))(x, y, t, u(x, y, t))*(D[2, 2](u))(x, y, t)+(D[3, 4](phi))(x, y, t, u(x, y, t))*(D[1](u))(x, y, t)+(D[4](phi))(x, y, t, u(x, y, t))*(D[1, 3](u))(x, y, t)-3*(D[1, 4](phi))(x, y, t, u(x, y, t))*(D[1](u))(x, y, t)-(3/2)*(D[4](phi))(x, y, t, u(x, y, t))*(D[1, 1](u))(x, y, t)-lambda*(D[1, 3](u))(x, y, t)+(3/2)*lambda*(D[1, 1](u))(x, y, t)-lambda*(D[1, 1, 1, 1](u))(x, y, t)-lambda*(D[2, 2](u))(x, y, t)+6*(D[1, 1, 4, 4](phi))(x, y, t, u(x, y, t))*(D[1](u))(x, y, t)^2+4*(D[1, 4, 4, 4](phi))(x, y, t, u(x, y, t))*(D[1](u))(x, y, t)^3+(D[4, 4, 4, 4](phi))(x, y, t, u(x, y, t))*(D[1](u))(x, y, t)^4+3*(D[4, 4](phi))(x, y, t, u(x, y, t))*(D[1, 1](u))(x, y, t)^2+(D[4, 4](phi))(x, y, t, u(x, y, t))*(D[2](u))(x, y, t)^2+(D[3](u))(x, y, t)*(D[1, 4](phi))(x, y, t, u(x, y, t))-(3/2)*(D[4, 4](phi))(x, y, t, u(x, y, t))*(D[1](u))(x, y, t)^2-6*(D[1, 1](phi))(x, y, t, u(x, y, t))*u(x, y, t)^2+12*lambda*u(x, y, t)*(D[1](u))(x, y, t)^2+6*lambda*u(x, y, t)^2*(D[1, 1](u))(x, y, t)+12*(D[1](u))(x, y, t)*(D[1, 4, 4](phi))(x, y, t, u(x, y, t))*(D[1, 1](u))(x, y, t)+6*(D[1](u))(x, y, t)^2*(D[4, 4, 4](phi))(x, y, t, u(x, y, t))*(D[1, 1](u))(x, y, t)+4*(D[1](u))(x, y, t)*(D[4, 4](phi))(x, y, t, u(x, y, t))*(D[1, 1, 1](u))(x, y, t)+(D[3](u))(x, y, t)*(D[4, 4](phi))(x, y, t, u(x, y, t))*(D[1](u))(x, y, t)-12*(D[1, 4](phi))(x, y, t, u(x, y, t))*(D[1](u))(x, y, t)*u(x, y, t)^2-6*(D[4, 4](phi))(x, y, t, u(x, y, t))*(D[1](u))(x, y, t)^2*u(x, y, t)^2-6*(D[4](phi))(x, y, t, u(x, y, t))*(D[1, 1](u))(x, y, t)*u(x, y, t)^2

(7)

frontend(coeff, [k, U[x]^2]);

0

(8)

frontend(coeff, [k, U[x]*U[x, x]])

Error, invalid input: coeff received O*O, which is not valid for its 2nd argument, x

 

NULL


Download det.eq..mw

 

bifurcation diagram...

September 29 2014 sarra 195

Hi,

I have a non linear ode with sinosoial term, (sin(x)).

How can we Analyse the system and plot the bifurcation diagram:

x'=r*x-sin(x);

Thank you very much for your help.

 

Hi

I have three system of ODE and i would like to solve it using Homotopy perturbation method. Could you please provide to me the code in Maple or the Maple pachage that used to solve it by Homotopy perturbation method ?

I hope to hear you soon

Sara

 

Hi there. 

I'm kind of new to Maple and i'm trying to solve a Linear Algebra problem for my class of Linear Algebra of the course of Physics. Also, my first language is portuguese so forgive for my not-so-perfect english.

I have a (solved) linear system of 7 equations and 12 variables (A, B, C, D, E, F, G, H, I, J, K, L) that is the following:

  • A = 33 - K - L
  • B = 1 + F - J
  • C = -15 - F + J + K + L
  • D = 15 + H - K
  • E = 16 - F - H + J + K
  • G = 34 - H - J - L
  • I = 18 - J - K

Note: I'm using letters (A, B, ..., L) instead of X1X2, ..., X12 because it's easier to write it like this here and because I don't know if the Xn notation is allowed on Maple (i don't think so).

So, the system is possible but undetermined (with 5 degrees of freedom), being F, H, J, K and L the free variables.

Until here, everything's fine. The problem arises when the professor asks us for every solution of the system that satisfies the condition that all the variables (form A to L) are positive integers (A, B, C, D, E, F, G, H, I, J, K, L ϵ IN → natural numbers).

From my understanding, that gives rise to a system of linear inequalities with 12 variables and the following inequalities:

  • A = 33 - K - L > 0
  • B = 1 + F - J > 0
  • C = -15 - F + J + K + L > 0
  • D = 15 + H - K > 0
  • E = 16 - F - H + J + K > 0
  • G = 34 - H - J - L > 0
  • I = 18 - J - K > 0
  • > 0
  • > 0
  • > 0
  • > 0
  • > 0                            (and A,B,C,D,E,F,G,H,I,J,K,L ϵ IN)



After some research, i found that a possible way to solve this type of system of linear inequalities is trough a method of elimination (analog to Gauss-Jordan's elimination method for systems of linear equations) named Fourier-Motzkin. But it's hardwork and i wanted to do it on the computer. After some research, i came across with the following Maple command:

SolveTools[Inequality][LinearMultivariateSystem]

http://www.maplesoft.com/support/help/Maple/view.aspx?path=SolveTools%2fInequality%2fLinearMultivariateSystem

So, I tried to use that command to solve my system, with the following result (or non-result):

with(SolveTools[Inequality]);
LinearMultivariateSystem({F > 0, H > 0, J > 0, K > 0, L > 0, 1+F-J > 0, 15+H-K > 0, 18-J-K > 0, 33-K-L > 0, 34-H-J-L > 0, -15-F+J+K+L > 0, 16-F-H+J+K > 0}, [F, H, J, K, L]);

Error, (in SolveTools:-Inequality:-Piecewise) piecewise takes at least 2 parameters


So, i really need help solving this as the professor told us that the first one to solve would win a book, eheh. I don't know what I'm doing wrong. Maybe this Maple command is not made for 12 variables? Or maybe i'm just writing something on a wrong form. I've never used Maple before so i can be doing something really stupid without knowing it.

I would really apreciate an answer, as my only goal as a future physicist is to unveil the secrets of the Cosmos to us all.

Thank you again.

Miguel Jesus





how to convert between (system of polynomials or module) and rational function which is a four dimensional space

For two angles a and b, and functions f and g, I have a system of two equations,

diff(a(t),t$2) = f(a(t), b(t), diff(a(t),t), diff(b(t),t)) and diff(b(t),t$2) = g(a(t), b(t), diff(a(t),t), diff(b(t),t)).

The actual equations (i.e. not in terms of f and g) are known but are ommitted because they are very long.

 

I need not the solutions but simply the time t at which a(t) = b(t). While I have inputted the full equations into Maple, I do not know how to ask it to find an expression for t in terms of the constants of the equation.

How would I ask Maple to find this time?

A linear system with three variables has augmented matrix that is row-equivalent to the 
following matrix: 

k + 3 2 k − 4 = 3 
0 2 −9 = 5 
0 0 k^2 + k − 2 = k − 1 
Determine the values of k for which the system has: 
(a) exactly one solution, 
(b) infinitely many solutions, 
(c) no solutions.

Hi.

I am new in Maple and I'm trying to get functions from system of equations.

Constants are defined in line 4 and equations are:

eq1 := E2 = fE2(1+(KaE2+Ca)/(1+KaE2*fE2+KaT*fT+KaDHT*fDHT)+KsE2*Cshbg/(1+KsE2*fE2+KsT*fT+KsDHT*fDHT))

eq2 := T = fT(1+KaT*Ca/(1+KaE2*fE2+KaT*fT+KaDHT*fDHT)+KsT*Cshbg/(1+KsE2*fE2+KsT*fT+KsDHT*fDHT))

eq3 := DHT = fDHT(1+KaDHT*Ca/(1+KaE2*fE2+KaT*fT+KaDHT*fDHT)+KsDHT*Cshbg/(1+KsE2*fE2+KsT*fT+KsDHT*fDHT))

KsT = 0.10e11; KaT = 4.6*0.10e6; KsE2 = 3.14*0.10e10; KaE2 = 4.21*0.10e6; KsDHT = 3*0.10e6; KaDHT = 3.5*0.10e6;

fT, fE2 and fDHT are variables, not functions (i.e. fT is not f(T) ) and I am trying to get fT=f(E2,T,DHT,Ca,Cshbg), fE2=f(E2,T,DHT,Ca,Cshbg) and fDHT=f(E2,T,DHT,Ca,Cshbg).

When I type:

eliminate({eq1, eq2, eq3}, {fE2, fT, fDHT})

Maple gives me a blank field. No error, no other comment.

I have no idea where I'm making mistakes.

Any suggestion is appreciated.

 

Thanks in advance.

Hello everyone!

I'm working with Maple for 8 years and this is the first time I encounter such a problem:

I solve a linear ODE system for my quantum Mechanics research and i want to calculate a quantity formed by the solutions of the system. Everything is going fine with laplace transformation and the symbolic answer is very fast although extremely big (it uses RootOf simplification)

When i use evalf to take numerical approximations of the quantity, the answer is very fast. OK

When i leave unspecified two parameters in order to get a 3d plot the answer takes about 40mins to appear. I think it is too slow but anyway, i can live with it. OK

I want this 3d plot for different parameters of the ODE so i have to do the above process many times. But for some parameter values of the ODE, i get a 3dplot for which:

1) The display of numpoints (surface and line) is incorrect.

2) Plot gets deformed as long as i rotate it!!! The orientation angle changes the appearance of the plot, something obviously unacceptable. I have access to maple 17, 15, 14, and 12. Maple 17 and 15 exhibit this behavior (64 bit Maple editions). But when i tried with Maple 12-standard interface(64 bit) and Maple 14 -Classical interface (32bit) everything went fine, but at the cost of  300 extra secs. I got a solid 3d-plot that is invariant under rotations.

My video card is Ati radeon 6800 HD and i installed the latest drivers. I don't know why is this happening. I thought of putting the blame on me, but in maple 12 and maple 14 everything is fine. It is a pity, because Maple 17 gives very nice and smooth 3d plots.

The first plot is the correct one with maple 12. The second is produced with maple 14. All good.

The third and the second are produced with different orientations of the same plot (Maple 17). Wrong display of data and change of image after rotation. The final one is again from Maple 17 but with style=points. It is in is in full agreement with the first two plots. 

Conclusion: Style=surface and line doesnt produce the correct plot, while style=point does. As for hardware acceleration, i unticked it with no results.

Extra information: When i try to open the maple 12 worksheet which is correct, with Maple 17, again i take the wrong displayed and unstable picture. Moreover only maple 14 classical edition works well. Maple 14 standard interface is also pathological.

Heeeeelp guys!!!

 

 

Dear Maple Users,

I'm beginner in Maple.

I have this system of Pde:

with lambda experimental parameter and n,c,v dependent variables. I write this on Maple but I read on internet that the solution "float(undefined)" is an error.

I will insert this initial condition: c(x,0)=0,n(x,0)=0.4

Thanks everybody

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