Two questions:

The algortihms that Groebner[Basis] uses at each step computes some "tentative" or "pseudo-basis". The "tentative" basis is not a Groebner basis but it is in the ideal generated by the original system of polynomial eq.

1) Is this correct ? Provided this is correct, then

2) How can one retrive the last "tentative" basis?
 If I just use timelimit I can abort the computations but how can one retrive the last computation?

Please respond me by email, thanks.

wingwatson7@gmail.com

Good evening, dear experts. 

I want to solve the system of PDEs, but i get a mistake:

"Error, (in pdsolve/numeric/xprofile) unable to compute solution for t>HFloat(0.0):

solution becomes undefined, problem may be ill posed or method may be ill suited to solution"

How  can I determine the method for pdsolve?
Thanks for answers.

It's my file with the functions:
restart;
alias(X = x(t, tau), Y = y(t, tau));
xt, yt := map(diff, [X, Y], t)[];
xtau, ytau := map(diff, [X, Y], tau)[];
M := (xtau*(-Y+.1*X)+ytau*X)/(xtau^2+ytau^2);
pde1 := xt = -Y+.1*X-xtau*M;
pde2 := yt = -M*ytau+X;

cond := {x(0, tau) = 1, x(t, 0) = 1, y(0, tau) = 1, y(t, 0) = 1};
Sol := pdsolve({pde1, pde2}, cond, numeric, time = t, range = 0 .. 1);
Sol:-value(t = 1);
%;
Error, (in pdsolve/numeric/xprofile) unable to compute solution for t>HFloat(0.0):
solution becomes undefined, problem may be ill posed or method may be ill suited to solution

I was answering this question on another platform, and wanted to compare with Maple. On Matlab, this is the result

format long
916.536 + 3.3

      9.198359999999999e+02

When using Maple I get

evalhf(916.536 + 3.3);
     919.836000000000013

I am on a 64 bit intel PC, and the OS is windows 7, 64 bit, and I my Maple is 64 bit version also.

Using Mathematica on my PC, which is 64 bit also, I get same as Matlab:

FullForm[916.536 + 3.3]
    919.8359999999999`

and help on evalhf says:
"A call to evalhf evaluates an expression to a numerical value using the floating-point 
hardware of the underlying system. The evaluation is done in double precision."

So, the question is, why I am not gettting the same result as those others shown above?
May be it has to do with this:

"The evalhf function converts all its arguments to hardware floats, computes the answer 
and converts the answer to a Maple float result."

?

Here is the original question http://www.mapleprimes.com/ViewTemp.ashx?f=21095_1386318320/screen06.12.13.docx , replaced by the questioner.  She/he must not do such things.

The differential equation dy/dt = t / (2-y), y(0)=1 fails the tests in section 5.1 at y=2. [ f(t,y) is undefined at y=2 and the y-partial derivative of f(t,y) is also undefined there. ] If a solution stays away from y=2, there is no problem at all. Try a few different initial conditions and summarize your findings. Use the Runge-Kutta order 4 method with a fixed step size.

Hint: You may find Maple's solution of the differential equation helpful:

s1 := dsolve({diff(y(t),t)= t/(2-y(t))}, y(t)); 

In the solution _C1 is a constant to be determined using the initial conditions.

Is the output of >polarplot command in maple12 is always in circular pattern, we cann't have rectangular boxed plot?

I have  AX=B , I want to find X , A is 3*3 matrix  <.9,-.3,-.6>|<-.2,.6,-.4>|<-.4,-.4,.8>   B=matrix(3, 1, [600, 600, 600]) ? I using  linearslove, but it is not work.

Download question_13.12.06.mw

I have following expression

f:=t->((1/8)*s^2*sinh(4*t)+t+(1/2)*s^2*t+s*sinh(2*t))/(1+s*cosh(2*t))

which is 1 solution of the ODE

ode2 := -(diff(y(t), t, t))+(4-12/(1+s*cosh(2*t))+(8*(-s^2+1))/(1+s*cosh(2*t))^2)*y(t) = 0

Now I wanted to construct 2 linear independent solutions via:

f1:=f(t_b-t)

f2:=f(t-t_a)

and calculate the Wronskian:

with(LinearAlgebra); with(VectorCalculus)

Determinant(Wronskian([f(t_b-t), f(t-t_a)], t))

Since I know these functions are solutions of the second order ODE which does not contain any first order derivative the Wronskian should be a constant. Unfortunately Maple has a hard time to simplify it since the epxression is a little big. Is it my fault or has anyone an idea what to do?

An economy consists of service and food sectors. Assume that to produce $1 worth of service consumes 50 cents worth of service and 20 cents worth of food,and to produce $1 worth of food consumes 40 cents worth of serives and 20 cents worth of food. Assume that there is an external demand for $2 million worth of serices and $12 million worth of food.

a)Determine the comsumption matrix C for this economy.

b)In order to satisfy the demand, how much of each must be produce?(Find the production vector that will satisfy the demand.)

c)For this production vector, what is the value of serices that is consumed internally by the food industry ?

Hello, I am trying to do a fourier transfrom using the package < DiscreteTransfroms >.

The function is an gaussian function for now,

Here is the code I tried

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

restart

with(DiscreteTransform):

> X := Vector(1000, proc (k) options operator, arrow; (1/200)*k-5/2 end proc);
> Y := Vector(1000, proc (k) options operator, arrow; evalf(exp(-10*((1/100)*k-5)^2)) end proc);

> X2, Y2 := FourierTransform(X, Y);
Vector[column](%id = 18446744080244879358),

Vector[column](%id = 18446744080244879478)
> plot(X2, Re(Y2));

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

The program returns two vector, X2 and Y2 who are supposed to be the fourier transforme of a gaussian so.. a gausian but when I plot the result X2 on the horizontal and Y2 on vertical, the graph doesn't resemble a gaussian function or any function at all.

Please help!!

Alex

4th_order.mw How can one solve this problem with maple?

> restart;
> Digits := 10;
> m := 11;
> P := 100;
> alpha := 1;
> F[0] := 0;
> F[1] := epsilon;
> epsilon := 0;
> F[2] := A;
> T[0] := -T[1]/alpha-1;
> T[1] := B;
> for k from 0 to m do F[k+3] := (-(sum(F[k-r+2]*F[r]*(k-r+2)*(k-r+1), r = 0 .. k))-1+sum(F[r+1]*F[k-r+1]*(r+1)*(k-r+1), r = 0 .. k))*factorial(k)/factorial(k+3); T[k+2] := -P*(sum(F[r]*T[k-r+1]*(k-r+1), r = 0 .. k))*factorial(k)/factorial(k+2) end do;
> f := 0;
> t := 0;
>
> for k from 0 to m do f := f+F[k]*eta^k; t := t+T[k]*eta^k end do;
> print(f);
> print(t)

> with(numapprox);
> pade(f, eta, [4, 4]);

>pade(t, eta, [4, 4])

>solve({limit(pade(f, eta, [4, 4]), eta = infinity) = 0., limit(pade(t, eta, [4, 4]), eta = infinity) = 0.}, [A, B])

Hi!

Say, I got an expression that depends on two variables, x and y. How can I tell Maple, that y is actually just a (real) constant, so y does not depend on x?

Because when I apply a differentiation with the "D" - command, it would always also write out expressions, where y is differentiated w.r.t. x.

Thanks!

Hi There,

Can any one correct me the mistake in the following differentiation:

Above command gives the following error:

Error, (in simpl/abs) abs is not differentiable at non-real arguments