i use a not good example's polynomials to illustrate the idea

u1:=3*a*c+b^2+c;
u2:=7*a^5*b*c^3;
u3:=a+3*b^2;
T := lexdeg([a,b,c],[e1,e2, e3]);
GB := Basis([e1-u1, e2-u2, e3-u3],T);
result := NormalForm(a*b+b*c, GB, T);

now result is to express a*b+b*c in terms of e1, e2, e3 which represent u1, u2, u3.

is it possible to use preimage to find possible u1,u2,u3 if unknown u1,u2,u3 and given known eqx?

How to use preimage to find possible eqx if given known u1,u2,u3 to find eqx in NormalForm(eqx, GB, T)?

what i confused in code below is that if i know it in terms of -1*e1+2*e2+*e3

it already can be used to find eqx, it seems reasonable to put source1list as unknown to find eqx  or find unknown eq1, eq2, eq3 if given known eqx.

with(RegularChains):
with(ConstructibleSetTools):
source1 := PolynomialRing([e1, e2, e3]);
target1 := PolynomialRing([a, b, c]);
source1list := [...];
target1list := [eq1, eq2, eq3];
cs := PolynomialMapPreimage(target1list, source1list, source1, target1);
Info(cs, source1);
[[e1-e2-e3], [1]]
-1*eq1+2*eq2+*eq3;

Hi, I am using Maple 18 and struggling with plotting Newton's Method.

I am wanting use the function f(x)=x^3 +cx + 1 where c is a parameter and uses 100 parameter values between -2 and 0, with 100 iterations of each parameter.

Any help would be brilliant.

Thanks in advance,

Neil

deqn4 := {4*eta^4*(diff(f(eta), eta, eta, eta))*(diff(f(eta), eta))-12*eta^3*(diff(f(eta), eta, eta, eta))*f(eta)+12*eta^4*(diff(f(eta), eta, eta))*(diff(f(eta), eta))-36*eta^3*(diff(f(eta), eta, eta))*f(eta)-24*eta^3*(diff(f(eta), eta))^2+12*eta^2*(diff(f(eta), eta))*f(eta)-36*eta*f(eta)^2-4*eta^3*(diff(f(eta), eta, eta))*(diff(f(eta), eta))-12*eta^2*(diff(f(eta), eta, eta))*f(eta)+12*eta^3*f(eta)*(diff(f(eta), eta))+36*eta^2*f(eta)^2-4*eta^3*(diff(f(eta), eta, eta, eta, eta))-12*eta^3*(diff(f(eta), eta, eta, eta))+12*eta^2*(diff(f(eta), eta, eta))-12*eta*(diff(f(eta), eta))+24*f(eta) = 0};
/
| 4 / d / d / d \\\ / d \
< 4 eta |----- |----- |----- f(eta)||| |----- f(eta)|
| \ deta \ deta \ deta /// \ deta /
\

3 / d / d / d \\\
- 12 eta |----- |----- |----- f(eta)||| f(eta)
\ deta \ deta \ deta ///

4 / d / d \\ / d \
+ 12 eta |----- |----- f(eta)|| |----- f(eta)|
\ deta \ deta // \ deta /

3 / d / d \\
- 36 eta |----- |----- f(eta)|| f(eta)
\ deta \ deta //

2
3 / d \ 2 / d \
- 24 eta |----- f(eta)| + 12 eta |----- f(eta)| f(eta)
\ deta / \ deta /

2
- 36 eta f(eta)

3 / d / d \\ / d \
- 4 eta |----- |----- f(eta)|| |----- f(eta)|
\ deta \ deta // \ deta /

2 / d / d \\
- 12 eta |----- |----- f(eta)|| f(eta)
\ deta \ deta //

3 / d \ 2 2
+ 12 eta f(eta) |----- f(eta)| + 36 eta f(eta)
\ deta /

3 / d / d / d / d \\\\
- 4 eta |----- |----- |----- |----- f(eta)||||
\ deta \ deta \ deta \ deta ////

3 / d / d / d \\\
- 12 eta |----- |----- |----- f(eta)|||
\ deta \ deta \ deta ///

2 / d / d \\ / d \
+ 12 eta |----- |----- f(eta)|| - 12 eta |----- f(eta)|
\ deta \ deta // \ deta /

\
|
+ 24 f(eta) = 0 >
|
/
init4 := { {f(0) = 1, (D(f))(0) = 0, ((D@@2)(f))(0) = 0, ((D@@3)(f))(0.1e-2) = 0} };
{{f(0) = 1, D(f)(0) = 0, @@(D, 2)(f)(0) = 0,

@@(D, 3)(f)(0.001) = 0}}
dsol4 := dsolve(deqn4 union init4, numeric, method=rkf45);

Error, (in dsolve/numeric/process_input) system must be entered as a set/list of expressions/equations

Hi,

I have a eight different size lists.

I want to put it into the Array with simplest and clear way as possible respect to first column and containg symbols.
I enclose workseet.

Could you help somone?.
Thank you in advanced

wzel

fill_the_array.mw

i find maple help using regular chain library, but it has ideal source and ideal target,

when compare with singular, seems different, i am not sure singular code whether correct or not.

so, would like to ask how to do this in maple

if you know singular, i would like to know too.

ring r = 32003, (x,y), lp;
setring r;
ideal Z;
ideal i = x-x2-2*x*y+2*x2*y-2*x*y2+y+y2, 1-x2-2*x*y+2*x2*y-2*x*y2+y2;
map phi = r, i;
ideal i1 = preimage(r,phi,Z);
i1;
ideal i2 = preimage(r,i,i);
i2;
ideal i3 = preimage(r,i,Z);
i3;
ideal i4 = preimage(r,Z,i);
i4;

would like to apply to find Cohen Maculay

While(NewKer <> 0)

Mapping = Basis(M – N) ^ K[M]

NewKer = ker(Mapping, M, N)

N = M

M = NewKer

If IsCM(NewKer) = true then

    NewKer

End if

Do

Dear All,

I need your help to plot the phase portrait using DEtools[DEplot]  these are the lines of the code. But when I make RUN, there is an error. I need your help to fix the error. Many thinks.

r1:=1; r2:=1; q2:=2; q1=0.5;  a1:=1;

Sys1 := {diff(N(t),t) = r1*N*(1-N/q1)-P*N/(1+N), diff(P(t),t) = r2*P*(exp(-a1*P)-q2)+P*N/(1+N)};

DEtools[DEplot](Sys1,[N(t),P(t)],t=-10..10,N=0..2,P=0..2);

Many thinks

Hello, Maple wizards.

I have a problem with Tasks for parallel computations. In each task my programm should execute this command:

>B:=SignalProcessing:-DFT(A)

"A" and "B" are Arrays (1..m). "m" is integer. I have 8 tasks. Each task is a loop ("for i from 1 to n do..." n is integer), where my command is executing. "A" and "B" are local for each task. In this case each task should execute my command n times.

So, I obtain this:

"Error, (in SignalProcessing:-Engine:-DFT) attempting to assign to `FwdDFT` which is protected"

What is it? In Maple Help I read that ">SignalProcessing:-DFT" is Thread-Safe Function.

I have a characteristic equation. some times It has polar roots . sometimes It has real roots and sometimes both of them.

I want to extract real roots and extract polar roots if they are.

for instance:

q:=m3*r^3+m2*r^2+m1*r+m0:

rot:=solve(q=0,r);

I want to know how can I use if in this part ?

Can maple solve maximization problem like

q := proc (a, b, c) options operator, arrow; .2*b+.1*c end proc;
print(`output redirected...`); # input placeholder
(a, b, c) -> 0.2 b + 0.1 c
w := proc (a, b, c) options operator, arrow; .7*a+.1*c end proc;
print(`output redirected...`); # input placeholder
(a, b, c) -> 0.7 ab + 0.1 c
e := proc (a, b, c) options operator, arrow; .7*a+.2*b*c end proc;
print(`output redirected...`); # input placeholder
(a, b, c) -> 0.7 a + 0.2 b c

with(Optimization)

Maxmize(int(min(100+(.7*a+q)*(1/2), a), q)+int(min(100+(.2*b+w)*(1/2), b), w)+int(min(100+(.1*c+e)*(1/2), c), e)-a-b-c-ab-ac-bc)

Error, (in Optimization:-NLPSolve) cannot convert procedures to piecewise

Thanks alot if you can help me.Urgent! Really appreciate.

Hi there,

I used the following plot command in maple13.

with(plots):

implicitplot(abs(x)+abs(y)=2, x=-2..2, y=-2..2, scaling=constrained)

But the output(square) is not complete at vertices.In fact at the vertex the graph is like a trapezoid.

Any help will be appreciated.

Yegan

> restart;
> with(plots);
> Eq1 := diff(f(eta), eta, eta, eta)+f(eta)*(diff(f(eta), eta, eta))-2*(diff(f(eta), eta))^2-M^2*(diff(f(eta), eta)) = 0;
/ d / d / d \\\ / d / d \\
|----- |----- |----- f(eta)||| + f(eta) |----- |----- f(eta)||
\ deta \ deta \ deta /// \ deta \ deta //

2
/ d \ 2 / d \
- 2 |----- f(eta)| - M |----- f(eta)| = 0
\ deta / \ deta /
> Eq2 := 1+(4/3)*R*(diff(theta(eta), eta, eta))+Pr*(f(eta)*(diff(theta(eta), eta))-(diff(f(eta), eta))*theta(eta)) = 0;
4 / d / d \\
1 + - R |----- |----- theta(eta)||
3 \ deta \ deta //

/ / d \ / d \ \
+ Pr |f(eta) |----- theta(eta)| - |----- f(eta)| theta(eta)| = 0
\ \ deta / \ deta / /
> bcs1 := f(0) = S, (D(f))(0) = 1+L*G, (D(D(f)))(0) = .1, f(6) = 0;
f(0) = S, D(f)(0) = 1 + L G, @@(D, 2)(f)(0) = 0.1, f(6) = 0
> fixedparameter := [S = .1, M = .1];
[S = 0.1, M = 0.1]
> Eq3 := eval(Eq1, fixedparameter);
/ d / d / d \\\ / d / d \\
|----- |----- |----- f(eta)||| + f(eta) |----- |----- f(eta)||
\ deta \ deta \ deta /// \ deta \ deta //

2
/ d \ / d \
- 2 |----- f(eta)| - 0.01 |----- f(eta)| = 0
\ deta / \ deta /
> fixedparameter := [R = .1, Pr = .7];
[R = 0.1, Pr = 0.7]
> Eq4 := eval(Eq2, fixedparameter);
/ d / d \\ / d \
1 + 0.1333333333 |----- |----- theta(eta)|| + 0.7 f(eta) |----- theta(eta)|
\ deta \ deta // \ deta /

/ d \
- 0.7 |----- f(eta)| theta(eta) = 0
\ deta /
> bcs2 := theta(0) = 1+T*B, (D(theta))(6) = B, theta(6) = 0;
theta(0) = 1 + T B, D(theta)(6) = B, theta(6) = 0

> T := .1; B := .1;
0.1
0.1
> L := [0., .1, .2, .3];
[0., 0.1, 0.2, 0.3]
> for k to 4 do R := dsolve(eval({Eq3, Eq4, bcs1, bcs2}, L = L[k]), [f(eta), theta(eta)], numeric, output = listprocedure); Y || k := rhs(R[2]); YL || k := rhs(R[3]) end do;
Error, (in dsolve/numeric/bvp/convertsys) too many boundary conditions: expected 6, got 7
> plot([YL || (1 .. 4)], 0 .. 6, 1 .. -.2, labels = [eta, diff(f(eta), eta)]);

Dear all;

I need your help to get all the solution of this nonlinear  system  with four parameters: r1, r2, q1, q2  assumed to be positives. Let the system:

the first equation is: r1*x*(1-x/q1)=x*y/(1+x)

the second equation: r2*y*(exp(-y)-q2)=-x*y/(1+x)

How can get the positive solution ( x, y) of the previous system.

Thank you for your help.

Consider the function

The above definition may result in four cases depening on r and x.

Can Maple calculate automatically all possible cases and the corresponding Maxima, Minima and Values at intervals limits?

I have an ode in the form:

diff(u(x),x)-f(x)=u(x)^3+B(X)*u(x)+g(x)

how to extaract and name the different coefficients of the equation?

Thanks 

Hamada

Having a little trouble getting data from openstreetmap from export here

http://www.openstreetmap.org/export#map=17/43.4763/-80.5459