## Groebner produces inconsistent result...

Hello,

Calculated a Grobasis basis. Used the 19 of the 29 equations to produce a Sylvester type matrix to get a univarite polynomial. The problem I am having is I can't produce a consistant matrix. I think the problem may lie in how I sort the equations. I have used this method once before and it worked to produce the result then. Run the worksheet and the run it again and most likely a different outcome occurs. I copy and pasted the polynmial list to make this worksheet. The coefficients are very long. Have annotated the worksheet to help explain.                                    ## A linear stochastic model?...

Hi,

I have a linear mathematical model that is in deterministic form, but actually one of the input parameters has a stochastic nature and follows a log normal distribution function. and I need to include this in the formulation. Please help me with this questions:

1) Do I need to use stochastic programming methods to solve it? if yes, how?

2) How can I include the distribution function in my model?

3) Can I solve the these kinds of problems using Maple?

## Problem with solve command...

Hi,

I am designing a power transformer using Maple, and I am trying to solve for the minimum number of turns around my core for the desired effect. The equations to solve include numbers of turns (must be positive integers) and other constraints (positive floats).

To validate my worksheet, I am beta-testing it on an existing transformer, so I know of at least one solution that works. But when I submit the equations to Maple, it can't find the solution I know with integer solutions.

The equation is :

SOL := `assuming`([solve({N__2/N__1 = m__t, k__c*L__L(g__ap*Unit('m'), N__1)*I__M__pk = (1/2)*V__sec*T__res/m__t, g__ap <= 2*10^(-3), B__max(g__ap*Unit('m'), N__1, I__M__pk) <= B__max__core}, {N__1, N__2, g__ap, I__M__pk}, UseAssumptions)], [N__1::posint, N__2::posint, g__ap::positive])

{N__1 = 7.701193685, N__2 = 12.50000000*N__1, I__M__pk = (-1.855203719*10^9*g__ap^2+1.523613883*10^11*g__ap+5.590656409*10^6)*Unit('A')/(5.000000*10^6+2.43902439*10^8*g__ap), I__M__pk = (-1.100291349*10^11*g__ap^2+9.036307746*10^12*g__ap+3.315727980*10^8)*Unit('A')/(N__1^2*(5.000000*10^6+2.43902439*10^8*g__ap)), g__ap <= 0.2000000000e-2, 0. < g__ap}

Except I know there is a solution with N__1 = 6 and N_82 = 75. If I force n__1:=75 and solve again for the other variables, the solution is OK :

X := `assuming`([solve({N__2/N__1 = m__t, k__c*L__L(g__ap*Unit('m'), N__1)*I__M__pk = (1/2)*V__sec*T__res/m__t, g__ap <= 2*10^(-3), B__max(g__ap*Unit('m'), N__1, I__M__pk) <= B__max__core}, {N__2, g__ap, I__M__pk}, UseAssumptions)], [N__2::posint, g__ap::positive])

X := {N__2 = 75., I__M__pk = -0.3759328777e-1*Unit('Wb')*(8.130081300*10^10*g__ap^2-6.676951220*10^12*g__ap-2.45000000*10^8)/(Unit('H')*(5.000000*10^6+2.43902439*10^8*g__ap)), g__ap <= 0.2000000000e-2, 0. < g__ap}

I am a bit puzzled about why Maple doesn't find this solution...

Thank you very much for your help.

## Maple 18 can't plot...

Hi everyone, I got a problem. I'm a new user and I'm getting to know this beautiful software.

The problem is that when I enter a function in math mode (the easyest with simple inputs I guess), once I right click and plot only the cartesian plot is shown, without the actual function.

What should I try? Math without plots is boring... :)

Thank you!

## XMaple Startup Extemely Slow for Specific User...

Hello All,

I am running Maple 18 on Ubuntu 14.04.4 with x86_64 architecture. When running the xmaple command for a specific user, the java loading window takes about 5-10 minutes to appear. With other users, it takes around 15 seconds. All users are running the same xmaple script, I did not see and conflicting environment variables.

I was wondering if the community had any other ideas as to what could be causing this slow response?

Michael

## Solutions for each value of omega...

I have an equation as shown below.  In this i need to get the value of 'a' for each 'omega'.  'omega' range from 0 to 2 with increment 0.01

And save all the values of 'a' as a column matrix named 'result'. ## How to make this DEplot3d?...

after solved,

diff(a(t), t) = diff(a(t), t)

diff(b(t), t) = 0

diff(c(t), t) = -b(t)/c(t)

there is a diff(a(t), t) term

how to plot this kind of system?

can diff(a(t), t) be ignore so that only consider two equations, diff(b(t),t) and diff(c(t),t) ?

if so, i use below to plot, it can not show the arrow clearing , i can only see arrow near origin, but not far point

with(plots):
fieldplot([0, y/x], x = -2 .. 2, y = -2 .. 2);
fieldplot([0, y/x], x = -2 .. 2, y = -2 .. 2, arrows = SLIM,grid = [1, 1]);
fieldplot([0, y/x], x = -10 .. 10, y = -10 .. 10);

## Is there an example...

about how to calculate vector field of system of 3 differential equations which in terms of a(t), b(t), c(t) , diff(a(t),t), diff(b(t),t), diff(c(t),t)?

is the only method is the express diff(a(t),t), diff(b(t),t), diff(c(t),t) in terms of a(t), b(t), c(t) ?

for example

<diff(a(t),t), diff(b(t),t), diff(c(t),t)>

if result is

diff(a(t),t) = a(t)*b(t)

diff(b(t),t) =b(t)*c(t)

diff(c(t),t) =c(t)*a(t)

<a(t)*b(t), b(t)*c(t), c(t)*a(t)>

then

is it the vector field <a*b, b*c, c*a> ?

## How to produce this DEplot?...

sys := {diff(b(t),t) = 0,diff(c(t),t) = -b(t)/a(t)};
DEplot(sys, [b(t),c(t)], t=0..5, x=-5..5, y=-5..5);
Error, (in DEtools/DEplot) Option keyword (x) was not in the allowed set of options, consisting of: iterations, arrows, dirgrid, obsrange, scene, colour, linecolour, stepsize, a dependent variable range, a list of initial conditions or one of the allowed plot options: {animate, axes, color, colour, coords, font, scaling, style, symbol, title, view, animatecurves, animatefield, axesfont, dirfield, labelfont, linestyle, numframes, resolution, thickness, tickmarks, titlefont, xtickmarks, ytickmarks}, or one of the allowed dsolve/numeric options: {abserr, control, ctrl, initial, itask, maxder, maxfun, maxkop, maxord, maxpts, maxstep, method, mi..

## How to find this gradient?...

diff(a(t), t) = diff(a(t), t);
diff(b(t),t) = 0;
diff(c(t),t) = -b(t)/a(t);

[diff(rhs(sol), a(t)),diff(rhs(sol), b(t)),diff(rhs(sol), c(t))];
Error, (in VectorCalculus:-diff) invalid input: diff received a(t), which is not valid for its 2nd argument

## How to produce dfieldplot?...

eq2 := b(t)*(diff(c(t), t))*(diff(a(t), t))+b(t)*(diff(a(t), t))+a(t)*(diff(c(t), t));
eq3 := a(t)*(diff(b(t), t))(diff(a(t), t))+b(t)*(diff(b(t), t))*(diff(c(t), t));
eq4 := b(t)*(diff(c(t), t))(diff(b(t), t))+a(t)*(diff(b(t), t))+b(t)*(diff(c(t), t));
dfieldplot([eq2,eq3,eq4],[t,x],t=0..5,a=-5..5,b=-5..5,c=-5..5);
dfieldplot([eq2,eq3],[t,x],t=0..5,a=-5..5,b=-5..5);
eq2a := eval(subs(c(t)=exp(t), eq2));
eq3a := eval(subs(c(t)=exp(t), eq3));
eq4a := eval(subs(c(t)=exp(t), eq4));
dfieldplot([eq2a,eq3a], [a(t), b(t)], t = -5 .. 5, a = -5 .. 5, b = -5 .. 5, arrows = SLIM, color = black, dirfield = [10, 10]);

## Possible Bug in Maple ...

Hey,

I think I found a bug concerning the useage of assume and alias:

 > restart:
 > alias(a=a(t),b=b(t)); (1)
 > assume(a(t),real);
 > getassumptions(a(t)); (2)
 > assume(b(t),real);
 > getassumptions(a(t)); (3)
 > getassumptions(b(t)); (4)
 >
 >
 >

Commenting out the alias command produces correct results. I am on linux with build 922027.

alias_bug.mw

## How to factorize to matrix ...

from determinant's polynomial?

## Problem with wave equation...

I am trying to find a general solution to the 1D-wave equation

Eq1:=diff(u(x,t),t\$2)=diff(u(x,t),x\$2);

pdsolve(Eq1,HINT=f(x)*g(t)); # Hinting pdsolve gives general solution using separation of variables

pdsolve({Eq1,u(x,0)=f(x),D(u)(x,0)=g(x)}); # without HINT and using intial conditions, I get travelling wave solution

pdsolve({Eq1,u(x,0)=f(x),D(u)(x,0)=g(x)},HINT=f(x)*g(t)); # Now when I try to use hint and ICs both, pdsolve return nothing.

I want to use separation of variables to find solution to the wave equation.

Any comment?

Thanks