Lets say I want to find the intersection point between the line l in parametric form and plane p, both mentioned in the Maple code below. Is there smarter way than using the solve method that I use the two final lines? 

with(geom3d);
plane(p, 2*x+y-3*z-3 = 0, [x, y, z]);
                               p
line(l, [-1+3*t, 1+t, 2-t], t);
                               l
intersection(I, p, l);
                               I
solve({x = -1+3*t, y = 1+t, z = 2-t, 2*x+y-3*z-3 = 0}, {t, x, y, z});
                  {t = 1, x = 2, y = 2, z = 1}
 

Hello.

I'd like to plot two coupled functions x=x(t) and y=y(t) given by expression R0 and R1 (see below) for the interval t=0.001..0.999 and then after that extract tha data from the graphs for functions x(t) and y(t).

How can I do that in easiest way?

I will appreciate you.

The procedure "ContractIndices" seems to produce wrong results. This is proved by the following source code, comparing the result of this procedure and a simple direct calculation:

with(DifferentialGeometry):with(Tensor):with(Tools):

DGsetup([x,y],P);
m:=nops(DGinfo("FrameBaseVectors"));
g:=evalDG(1/y^2*dx &t dx+1/y^2*dy &t dy);
CS:=Christoffel(g,"SecondKind");
R0:=CurvatureTensor(CS);
RFc:=ContractIndices(R0,g,[[1,1]]); # Maple Version 2015

# Out of the Help Page: ?Tensor[ContractIndices]
# Form the tensor product T ⊗ S and contract 
# the 1st index of T against the 1st index of S. 
# ContractIndices(T, S, [[1, 1]]);

# Only for comparison: g:= 
# _DG([["tensor", P, [["cov_bas", "cov_bas"], []]], [[
# [1, 1], 1/y^2], 
# [[2, 2], 1/y^2]]]);

# g in table form with all indices, including the zeros: 
g1t:=
table([(1, 1) = 1/y^2, (2, 1) = 0, (1, 2) = 0, (2, 2) = 1/y^2]);

# Only fpr comparison:
# R0:=
# _DG([["tensor", P, [["con_bas", "cov_bas", "cov_bas", "cov_bas"], 
# []]], 
# [
# [[1, 2, 1, 2], -1/y^2], 
# [[1, 2, 2, 1], 1/y^2], 
# [[2, 1, 1, 2], 1/y^2], 
# [[2, 1, 2, 1], -1/y^2]]
# ]);

# R0 in table form with all indices, including the zeros:
R01t:=
table([
(2, 1, 1, 2) = 1/y^2, 
(2, 1, 1, 1) = 0, 
(2, 2, 2, 1) = 0, 
(2, 1, 2, 1) = -1/y^2, 
(1, 1, 1, 2) = 0, 
(1, 2, 2, 2) = 0, 
(1, 2, 2, 1) = 1/y^2, 
(2, 1, 2, 2) = 0, 
(2, 2, 1, 2) = 0, 
(2, 2, 2, 2) = 0, 
(1, 1, 2, 1) = 0, 
(1, 2, 1, 2) = -1/y^2, 
(2, 2, 1, 1) = 0, 
(1, 1, 2, 2) = 0, 
(1, 1, 1, 1) = 0, 
(1, 2, 1, 1) = 0
]);

# Only fpr comparison:
# RFc := 
# _DG([["tensor", P, [["cov_bas", "cov_bas", "cov_bas", "cov_bas"], 
# []]], 
# [
# [[1, 1, 2, 2], 1/y^4], 
# [[1, 2, 1, 2], -1/y^4], 
# [[2, 1, 2, 1], -1/y^4], 
# [[2, 2, 1, 1], 1/y^4]]
# ]);

# RFc in table form with all indices, including the zeros:
RFc1t:=
table(
[(2, 1, 1, 2) = 0, 
(2, 1, 1, 1) = 0, 
(2, 2, 2, 1) = 0, 
(2, 1, 2, 1) = -1/y^4, 
(1, 1, 1, 2) = 0, 
(1, 2, 2, 2) = 0, 
(1, 2, 2, 1) = 0, 
(2, 1, 2, 2) = 0, 
(2, 2, 1, 2) = 0, 
(2, 2, 2, 2) = 0, 
(1, 1, 2, 1) = 0, 
(1, 2, 1, 2) = -1/y^4, 
(2, 2, 1, 1) = 1/y^4, 
(1, 1, 2, 2) = 1/y^4, 
(1, 1, 1, 1) = 0, 
(1, 2, 1, 1) = 0
]);

TestContr:=proc()
    description "Simple contraction";
    local i,j,k,l;
    global RR;
    for i from 1 to m do
        for j from 1 to m do
            for k from 1 to m do
                for l from 1 to m do
                    RR[i,j,k,l]:=add(R01t[r,j,k,l]*g1t[i,r],r=1..m)
                od;
            od;
        od;
    od;
    print(`OK`)
end;

TestContr();

# Result of this:
# RR:=
# table(
# [(2, 1, 1, 2) = 1/y^4, 
# (2, 1, 1, 1) = 0, 
# (2, 2, 2, 1) = 0, 
# (2, 1, 2, 1) = -1/y^4, 
# (1, 1, 1, 2) = 0, 
# (1, 2, 2, 2) = 0, 
# (1, 2, 2, 1) = 1/y^4, 
# (2, 1, 2, 2) = 0, 
# (2, 2, 1, 2) = 0, 
# (2, 2, 2, 2) = 0, 
# (1, 1, 2, 1) = 0, 
# (1, 2, 1, 2) = -1/y^4, 
# (2, 2, 1, 1) = 0, 
# (1, 1, 2, 2) = 0, 
# (1, 1, 1, 1) = 0, 
# (1, 2, 1, 1) = 0
# ]);

Testeq:=proc()
    local i,j,k,l;
    # global
    for i from 1 to m do
        for j from 1 to m do
            for k from 1 to m do
                for l from 1 to m do
    if not (RFc1t[i,j,k,l] = RR[i,j,k,l]) then 
     print([i,j,k,l]) fi;
                od;
            od;
        od;
    od;
end;

Testeq();
# Result of this:
#                          [1, 1, 2, 2]
#                          [1, 2, 2, 1]
#                          [2, 1, 1, 2]
#                          [2, 2, 1, 1]

# No equality for these indices!

Hello,

I have tryed, to run the file ImprovementsInPdsolve.mw with the Mapleversion 2017.3 but in the first example pde[1] I got this error:

Error, (in assuming) when calling 'dsolve'. Received: 'cannot determine if this expression is true or false: not 0 <= -(1/2)*Pi'

 pde[2],  pde[3] and others are o.k. but pde[4] to pde[6] not. Can You give me a hint what's wrong?

With kindly regards

Wolfgang Gellien

How to plot phase portrait on a cylinder for The Lotka–Volterra equations (for some definite α, β, γ, δ):

I have a ploblem here:

plots[changecoords](subs(CURVELIST = CURVES, DEplot3d({(diff(rho(t), t))*(cos(varphi))(t)+rho(t)*(diff((cos(varphi))(t), t)) = 0.1*rho(t)*(cos(varphi))(t)-0.8e-4*rho(t)^2*(cos(varphi))(t)*(sin(varphi))(t), (diff(rho(t), t))*(sin(varphi))(t)+rho(t)*(diff((sin(varphi))(t), t)) = 0.4e-4*rho(t)^2*(cos(varphi))(t)*(sin(varphi))(t)-0.4e-1*rho(t)*(sin(varphi))(t)}, [rho(t), varphi(t)], t = 0 .. 2*Pi, [[rho(0) = 1, varphi(0) = 0]], scene = [rho, varphi, t])), cylindrical);
Error, (in DEtools/DEplot/CheckDE) only derivatives of dependent variables can be present
 

Thank you for the help.

hi everybody i am beginner in maple, i want to maximize this equation:

(k[m]*a-(a*r*k[m]-a*k[m]-b*c-b*c[m])/(2*(-1+r)))*((1-r)*(a*r*k[m]-a*k[m]-b*c-b*c[m])/(2*b*(-1+r))-c-c[m])

subject to constraints:

a > 0, b > 0, c > 0, r > 0, k[m] > 1, k[m]*a > (a*k[m]*(-1+r)-b*(c+c[m]))/(2*(-1+r)), a >= b*c, r < 1, a/b < (c[m]+c[r])/(k[m]*(-1+r)-r+1), a/b < (c+c[m])/(k[m]*(-1+r)), (c+cm)*b+a*k[m]*(-1+r) < 0

is it possible? if it is not, i want to know that equation could be positive or not and in what range of variables it could be positive?

if S:=V*t then find the filling time for decreasing in velocity ?? distanc2 = 200 mm  decrease velosity 0.58 to 0.06nmm/s find time ?

This is my first post here, and any help is really appreciated.

I have two complex polynomials 

f(w)= w^8+w^6+4*w^4+w^2+1 , and 

g(w)= w^16+2*w^14+9*w^12-2*w^10+44*w^8-2*w^6+9*w^4+2*w^2+1 .

I want to plot the roots of f in blue, roots of g in red and a unit circle in black at the same picture. 

Thanks in advance for your help.

There are two questions:

1. I have an ODE system solved numerically, but it has a singularity at Pi because of cot(x). I need to know whether the solution goes to infinity at this point or it has some value. I tried the limit operation, but it doesn't seem to work. Am I doing it wrong or is there no way to do such thing? See details in file 1 1.mw.

I know I can evaluate the function at point Pi - 10^(-10), Pi - 10^(-9) etc, and it has really close values there, but still I doubt it is a strong proof of the function not going to infinity.

Also the following "technical" question: why is Maple building the plot from 0 to Pi (or from -Pi to Pi symmetrically), even if I enter different range? For cot(x) it builds the plot normally, not just from -Pi to Pi, althouth cot(x) has singularity at Pi AND at 0, but my plots are somehow broken off at Pi.

2. I have 2 similar procedures and I need the plots of both of them. But first plot is built correctly and for the second there appears an error: "Error, (in plot) procedure expected, as range contains no plotting variable". I tried entering other ranges, including very small ones, but it didn't help. It calculates the values at points of range nicely though. See details in file 2 2.mw.

And one more time "technical" question about warnings in the procedures. I tried typing "local" or "global" before variables, but Maple gives me an error. How do I get rid of the warnings correctly?

I know it is difficult to see into those problems, but I strongly look for help! Thank you for your time!

As the title states, i want to have an automated logging occur of the details of the executions, including code content, origin worksheet,date the execution was attempted. I think i know a way to do it but id prefer if there was an option that already exists in the maple interface

Dear all

My goal us to show that equation (11) is exactly (q^n-1)/(q-1)*y^(n-1),   a  simplification must be introduced and so that we obtain the necessary (q^n-1)/(q-1)*y^(n-1). 
Note that the operators are not commutative.

Question.mw

Than you for your help

So I have recently finished up a project that took different sounds found in nature, and through the Spectrogram command, plotted the frequency of each sound over time with some really cool results!

https://www.maplesoft.com/applications/view.aspx?SID=154346 

The contrast between sounds produced by the weather such as tornadoes, thunder, and hail versus something as innocuous as a buzzing bee, a chorus of crickets, or a purring cat really shows the variance in the different sounds we hear in our day to day life, while also creating some very interesting imagery.

My personal favourite was the cricket chorus, producing a very ordered image with some really cool spikes through many different frequencies as the crickets chirped, as shown here:

Using this plot, we can do some interesting things, like count the number of chirps in 8 seconds, which turns out to be 18-18.5. Why Is this important? Well, there’s a law known as Dolbear’s Law(shown here: https://en.wikipedia.org/wiki/Dolbear%27s_law)  which uses the number of chirps in a minute for Fahrenheit, or 8 seconds for Celsius to calculate the temperature. Celsius is very simple, and just requires adding 5 to the number of chirps in 8 seconds, which gets us a temperature of 23C.

T_c= 5 + N₈

For Fahrenheit, it’s a bit more complicated, as we need the chirps in a minute. This is around 132 chirps in our case. Putting that into the formula:

T_F= 50 +((N₆₀ – 40)/4)

Which gets us 73F, or 22.7C, so you can see that it works pretty well! Pretty cool, huh?

There was also some really cool images that were produced, like the thunder plot:

Which I personally really like due to the contrasting black and yellow spike that occurs. Overall this was a very fun project to do, getting to tweak the different colours and scales of each spectrogram, creating a story out of a sound. Hope you all enjoy it!

In previous version of Maple (e.g. Maple 2015) I was able to copy
"2D Output" equations directly from a Maple Worksheet to MS Word.

These equations could be edited for fine element placement. In the 2017.3 version
it is does not seem to be possible anymore. When I copy the "2D Output" the image
is not copied only the text.

Is this a feature that was removed or a configuration problem ?

Thank you

LL 

Coding_Equilibria.mw

Hi, the coding answer I generate from maple is different from the real answer. Any solution?

The solution should be S=pi/mu*(mu-P*pi*mu+phi/mu+phi+vartheta) and V=pi/mu*(P*pi*mu+vartheta/mu+phi+vartheta)
 

Download Coding_Equilibria.m