Im trying to create a groebner basis to solve a series of equations to make a basis. The values can only be 1 to 4 for a..p which im also unsure if/how to define which may be causing the problem.

 My equations are as follows:

e1 := (((a-1)(a-2))(a-3))(a-4) = 0;
e2 := (((b-1)(b-2))(b-3))(b-4) = 0;
e3 := (((c-1)(c-2))(c-3))(c-4) = 0;
e4 := (((d-1)(d-2))(d-3))(d-4) = 0;
e5 := (((e-1)(e-2))(e-3))(e-4) = 0;
e6 := (((f-1)(f-2))(f-3))(f-4) = 0;
e7 := (((g-1)(g-2))(g-3))(g-4) = 0;
e8 := (((h-1)(h-2))(h-3))(h-4) = 0;
e9 := (((i-1)(i-2))(i-3))(i-4) = 0;
e10 := (((j-1)(j-2))(j-3))(j-4) = 0;
e11 := (((k-1)(k-2))(k-3))(k-4) = 0;
e12 := (((l-1)(l-2))(l-3))(l-4) = 0;
e13 := (((m-1)(m-2))(m-3))(m-4) = 0;
e14 := (((-1+n)(n-2))(n-3))(n-4) = 0;
e15 := (((-1+o)(o-2))(o-3))(o-4) = 0;
e16 := (((p-1)(p-2))(p-3))(p-4) = 0;
e17 := a+b+c+d-10 = 0;
e18 := a*b*c*d-24 = 0;
e19 := e+f+g+h-10 = 0;
e20 := e*f*g*h-24 = 0;
e21 := i+j+k+l-10 = 0;
e22 := i*j*k*l = 24;
e23 := m+n+o+p-10 = 0;
e24 := m*n*o*p-24 = 0;
e25 := a+b+e+f-10 = 0;
e26 := a*b*e*f-24 = 0;
e27 := c+d+g+h-10 = 0;
e28 := c*d*g*h-24 = 0;
e29 := i+j+m+n-10 = 0;
e30 := i*j*m*n-24 = 0;
e31 := k+l+o+p-10 = 0;
e32 := k*l*o*p-24 = 0;
e33 := a+e+i+m-10 = 0;
e34 := a*e*i*m-24 = 0;
e35 := b+f+j+n-10 = 0;
e36 := b*f*j*n-24 = 0;
e37 := c+g+k+o-10 = 0;
e38 := c*g*k*o-24 = 0;
e39 := d+h+l+p-10 = 0;
e40 := d*h*l*p-24 = 0;
e41 := c = 4;
e42 := e = 1;
e43 := j = 2;                  
e44 := p = 3;
 

Hi

This question may have been asked before but I cannot find it!

I am currently have 3 lists:

L:= [1,3,5,2,3]

M:=[4,2,4,6,2]

R:= [5,3,2,1,4]

I would like to be able to come up with a way (I assume a procedure) where I can order L and M based on the numerical order of R. So in this case that would be:

R:=[1,2,3,4,5]

L:=[2,5,3,3,1]

M:=[6,4,2,2,4]

I hope this makes sense? Any help would be greatly appreciated!

Hi All,

I am ploting with the command of:

logplot([1-R(Pp, tp, tf, 'qN(Pp, tp, tf)'), 1/(1+1+tp), .5/(.5+.5+tp), (1-Pp)*Beta(2, 1+tp)/(Pp*Beta(1, 1)+(1-Pp)*Beta(1, 1+tp))], Pp = 0 .. 1, style = pointline, numpoints = 1, gridlines = true, symbolsize = 10, legend = ["Our worst-case prior with Pp", "Flat prior Beta (1,1)", "Jeffrey's prior Beta (0.5,0.5)", "Normalised flat prior Beta (1,1) with Pp"], labels = ["Pp", "Posterior expected pfd"], symbol = [asterisk, diagonalcross, box, circle], title = "Given fixed t_past=100")

and get:

which is ok but the legends are wrong. where are the symbols in the legends? Am I missing something....

how to solve differential equations with dependent functions in maple? 

with(PDEtools):
V:=-exp(I*(k*x+omega*t+theta))*sqrt((k^2+omega)/(k*sigma))*sech(sqrt(k^2+omega)*(-2*k*t+x));
pde[1] := simplify(I*(diff(V, t, t))+diff(V, x, x)-I*sigma*V*(conjugate(V)*(diff(V, x))-V*(diff(conjugate(V), x)))) = 0;

Dear sir, can we get a plot of graph with line style like  line+symbol so on.. 

I am attaching codes and sample graph .

h:=z->1-(delta2/2)*(1 + cos(2*(Pi/L1)*(z - d1 - L1))):
K1:=(4/h(z)^4)-(sin(alpha)/F)-h(z)^2+Nb*h(z)^4:
lambda:=(F,Nb,delta2)->Int(K1,z=0..1):

L1:=0.2:
d1:=0.2:
alpha:=Pi/6:
A:=plot( [seq(seq(lambda(F,Nb,delta2), Nb=[0.1,0.2,0.3]), F=[0.1,0.2,0.5])],
          delta2=0.02..0.1, linestyle = [solid,longdash,dashdot],'
          thickness = 2',color=[red$3,blue$3,black$3],
          legend=["Nb=0.1","Nb=0.2","Nb=0.3",""$6]):
B:=plots:-textplot([[0.05,-1,F=0.1],[0.05,1.5,F=0.2], [0.05,3,F=0.5]], font=[times, 14]):

plots:-display(A, B);

Hi, I want to convert differential operator (D) to diff in below file, but "convert" doesn't work properly. I think beacuse both "D" and "diff" exist in the answer or mabey there is an other reason. what should I do?

I attached file here.1.mw

thanks in advance.

I wish to model the motion of a ball that bounces up and down in a vertical line, and whenever it hits the ground, it bounces back with only a fraction of the collision speed.

We expect that the amplitude of the consecutive bounces to diminish and for all practical purposes the ball to come to a standstill.  It's not difficult to calculate the motion analytically by hand.

However, when I attempted to solve the equation of motion numerically with Maple's dsolve()  and event handling, I ran into a problem.  As the amplitude of the bounces approaches zero, numerical noise sets in and the ball tunnels itself underground!  See the worksheet below.

I don't know how to prevent the ball from going underground.  Any ideas?

Download bouncing_ball.mw

How can I Plot exact solution, numeric solution and error function in one graph?

Please find attached code.

Thanks.

question.mw

Hi guys, 

I need help with differentiating a function I have defined. Here is the function I have:

The right hand side of this expression is a solution I have previously found via Maple, I know that this is correct. Basically I have a function a that is dependent on the another functon u(x,y,t).

Now the way I have defined this gives me the RHS of the above equation which is what I want. However, what I now need to do is to show that this constant function _F1(x,y,t) is equal to zero. I know this to be true via hand calcuations, but to do so I need to sub it into another equation where it has the derivatives of a. The way the derivatives are defined is through the D function. But this doesn't seem to work with how I have defined the function previously.

D[1](a)(x, y, t, u(x, y, t), diff(u(x, y, t), x), diff(u(x, y, t), y), diff(u(x, y, t), t), diff(u(x, y, t), x, x), diff(u(x, y, t), y, x), diff(u(x, y, t), x, t), diff(u(x, y, t), y, t), diff(u(x, y, t), t, t)) 

This should give me 

-4*diff(u(x,y,t),x,x,x)+diff(_F1(x,y,t),x)
However it just repeats what I input. I have tried defining the function in a different way,

a:=(x, y, t, u(x, y, t), diff(u(x, y, t), x), diff(u(x, y, t), y), diff(u(x, y, t), t), diff(u(x, y, t), x, x), diff(u(x, y, t), y, x), diff(u(x, y, t), x, t), diff(u(x, y, t), y, t), diff(u(x, y, t), t, t)) ->-4*diff(u(x,y,t),x,x)+_F1(x,y,t)

However this returns an error where I am not allowed to define this.

Can anyone help, would be a massive help. Thanks in advance.

What wouldn't work in Maple 2018 if I removed the Microsoft Visual C++ 2015 redistributable?  I have older versions of the C++ redistributable packages (ie 2013).  I hadn't noticed anything unusual when I initially removed it but maybe there's something that's affected in Maple?  Code generation package routines maybe?  What commands in Maple would be affected?

Reason is, I'm getting errors with another software and re-installing the 2015 C++ redistributable isn't installing properly.  So I'm just hoping there's no issues using Maple without the C++ 2015 redistributable being installed properly. 

Dear sir i want to display only three curves 1, curve 2 curve 3  in legends but in the plot it should be nine curve a sampe codes and a sample graph is attaching , please give suggestions. Here is my codes 

h:=z->1-(delta2/2)*(1 + cos(2*(Pi/L1)*(z - d1 - L1))):
K1:=(4/h(z)^4)-(sin(alpha)/F)-h(z)^2+Nb*h(z)^4:
lambda:=(F,Nb,delta2)->Int(K1,z=0..1):

L1:=0.2:
d1:=0.2:
alpha:=Pi/6:
A:=plot( [seq(seq(lambda(F,Nb,delta2), Nb=[0.1,0.2,0.3]), F=[0.1,0.2,0.5])], delta2=0.02..0.1, linestyle = [solid,longdash,dashdot],'thickness = 2',color=[red$3,blue$3,black$3]):

B:=plots:-textplot([[0.05,-1,F=0.1],[0.05,1.5,F=0.2], [0.05,3,F=0.5]], font=[times, 14]):

plots:-display(A, B);
 sample graphs 

Is it possible to split an execution group containing 2D input?
(without conversion to 1D which destroys the format).
Using F3 or the menu seems to work only for lines with a prompt.
But usually an execution group has a single prompt; lines with prompts appear e.g. when two execution groups are joined (with F4).
Is copy&paste the only solution?

Hi All,

I am thinking is there any simple function that could extract part of the points that have been ploted by plot() or plot3d(). And more ideally, we can specify some constraints such that the points being extracted must satisfy.

I guess Maple must stored the points somewhere in the memory in some kinds of data structure....

thanks.

I am seeking the limit of a series representation of a waveform to within so many significant figures.  Unfortunately, as the series contains more & more terms the demands on computation memory become a problem.  Perhaps there is a method within MAPLE I am not familiar with that can possibly circumvent this problem?

Below is the link to my worksheet.  The presumed theoretical limit is supposed to be 0.0894945 (this is based on what I have read)  (perhaps it may be wrong).  So far I have 3 of the sig figs agree, but would like to take it further.  Is this possible with different MAPLE commands than what I am currently employing?  Currently, MAPLE crashes if I venture beyond 100000 terms in the series.

seeking_the_limit.mw