Hello all, 

I am trying to compute the Groebner basis for a set of 3 coupled nonlinear equations. The variables I wish to solve for are A0,B0, and B1; however, my equations also have the variables DC, a, nu, q, and t. I wish to solve the 3 equations in terms of these other 5 variables such that I can substitute in any values I desire and obtain a result. When attempting to put the three equations into the PolynomialIdeal command from the PolynomialIdeals package, Maple gives me an error stating that the inputs must be polynomials with respect to all 8 variables. How would I go about declaring the other 5 variables such that they are considered arbitrary constants? 

I was able to get around the errors by assigning values to these 5 variables, though this is not what I am trying to accomplish. I need these 5 values to remain arbitrary.

I am very new to the concept of Groebner Bases and these commands so any help would be appreciated. I have attached my worksheet for reference. I am also happy to supply any additional information that may be needed to assist with this issue.

Thanks!
 

Download Groebner_Basis_Work.mw

Hello,

i have a vector-valued function mapping from R^n  -> R^m
I  compute its Jacobian Matrix as well as the Hessian Matrix of each output with regard to the inputs, which works so far.
Now I would like to use the CodeGeneration package to generate optimized C Code to compute these matrices numerically. This is, where i encounter a Problem:

I would like to optimize Code for all matrixes at once, because they contain common subexpressions. However CodeGeneration::C tells me it is unable to optimize the given input and generates unoptimized code.

I appended an exemplary file to illustrate the problem: Jacobian_Hessian_codeGeneration_tryout.mw

short version:

C(Jac, optimize = tryhard, resultname = JacobianMatrix);
C(H1, optimize = tryhard, resultname = Hessian1); 
C(H2, optimize = tryhard, resultname = Hessian2); 
C(H3, optimize = tryhard, resultname = Hessian3)

works, but is suboptimal.

C([JacobianMatrix = Jac, Hessian1 = H1, Hessian2 = H2, Hessian3 = H3], optimize)

fails to optimize and

C([Jac, H1, H2, H3], optimize)

fails completely.

(With Jac beeing a m by n matrix and H1-3 beeing n by n matrices)

If anyone can tell me what I'm missing here I'd really appreciate the help.

Dear friend,

please suggest a way for manipulation of derivative of a function symbolically. Assume

Typesetting[Suppress]([f(x)]);
Ex1 :=expand(diff(f(x+y)+x*f(x-y), x)^2)+expand(diff(f(x-y)-y*f(x+y), x)^2);

Result is as needed:

Ex1 := (D(f))(x+y)^2+2*(D(f))(x+y)*f(x-y)+2*(D(f))(x+y)*x*(D(f))(x-y)+f(x-y)^2+2*f(x-y)*x*(D(f))(x-y)+x^2*(D(f))(x-y)^2+(D(f))(x-y)^2-2*(D(f))(x-y)*y*(D(f))(x+y)+y^2*(D(f))(x+y)^2

But later I cannot use D(f) as a function. Expressions

subs((D(f)) = (t -> 1-t), Ex1);
subs(diff(f(x),x) = (t -> 1-t), Ex1);

do not handle it as a function.

Hello.

I am asked to find all the candidate points to absolute maximum or minimum in a domain delimited by several lines or curves.

Let me show you an example:

I am having trouble trying to find the candidate points on the boundary of the domain with LagrangeMultipliers.

How should I express the line or curve equations so that I can use them as constraints of LagrangeMultipliers? Should I use another method?

Thanks a lot.

HOW to dsolve fractional differential boundary conditions?

FRACTION.mw
 

Download FRACTION.mw

I want to solve the system of differential equations
sys :=
  diff(x(t,s),t) = y(t,s),
  diff(y(t,s),t) + x(t,s) = 0;
subject to the initial condition
ic := x(0,s) = a(s),
      y(0,s) = b(s);
where a(s) and b(s) are given.

This looks like a system of PDEs but actually it is a system
of ODEs because there are no derivatives with respect to s.
It is easy to obtain the solution by hand:

x(t,s) = b(s)*sin(t) + a(s)*cos(t)
y(t,s) = b(s)*cos(t) - a(s)*sin(t)

I don't know how to get this in Maple, either through dsolve()
or pdsolve().

Actually both dsolve({sys}) and pdsolve({sys}) do return
the correct general solution, however dsolve({sys, ic})
or pdsolve({sys, ic}) produce no output.  Is there a trick
to make the latter work?

hey is there a easy way to make maple solve an equation with similar different variables,

for eksample 

defining the different variables

x_0:=1       x_1:=4           x_2:=10

setting up and equation

solve x * 5

recieving answers for all defined x variables

= [5,20,50]

 The font plot option has no color parameter. 

Dear all,

I use the following statment (without numerical values)

if        IT<20     then        IT:=IT+1            

 if    ZUM<(0.1)^(8);    IT=20;         else;    

for i from 1 to 10   do                               YU[i]:=U[i];                  od;    

for i from 2 to 9 do                           DU1:=YU[i+1]- YU[i-1];        od:      

end if;    

ZUM:=U[1]-YU[1];  

end if;  

the following error occur

where is the problem.

i want to solve this equation,

y''(x)=5*exp(-10/y'(x)) on ]0,15[ with y(0)=0,y(15)=2 

can any one help me ? thank you

Hello

I have question. How can I rotate this 2-D plot and create 3-D plot?

plot(exp(-(x-3)^2*cos(4*(x-3))),x=1..5)

Thank you.

Respected member!

Please help me in finding the solution of this problem....
 

Download mplprimes.mw

Dear community, 

I'm new to maple and was wondering if you could help me out.

I have this curve where I want to make a line that goes from x=0.5 up to its value on the curve in this case 1.60 and then all the way to the y-axis so there is an area under the curve which I can color if that's even possible?

I have the following in maple:

k := 2.5;
                              2.5
Ca0 := 1;
                               1
v := 20;
                               20
Ca := Ca0*(1-x);
                             1 - x
Fa0 := Ca0*v;
                               20
Cb := Ca0*x;
                               x
ra := k*Ca*Cb;
                         2.5 (1 - x) x
plot(1/ra, x = 0 .. 1);
 

thank you for your help

Best Regards

Saad

I recently encontered a very strange result.

Lets define the procedure:

Fg := proc(x0,y0)
if (x0>=0)and(x0<=3) and (y0<=x0+2) and (y0>=x0-1) and (y0>=0) and (y0 <=3) then
return y0*(3-y0)*x0*(3-x0)*(x0+2-y0)*(y0-x0+1);
else
return 0;
end if:
end proc:

The plot looks like needed:

plot3d('Fg'(x,y), x=0..3, y=0..3);

But integration returns weird result:

evalf(Int('Fg'(x,y), [x=0..1, y=0..2.1]));

7.888753239

evalf(Int('Fg'(x,y), [x=0..1, y=0..2.2]));

Error, (in evalf/int) when calling 'Fg'. Received: 'cannot determine if this expression is true or false: 0 <= x and x <= 3 and y <= x+2 and x-1 <= y and 0 <= y and y <= 3'

hi...i have a problem with pdsolve this equations?

please help me.

thanks

mt.mw

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/mt.mw .
 

Download mt.mw