lower-right convex hull of a set of points in the ...

Hi!,

Assume that we hace a set points in the plane, put X:=[a1,a2,...,aN] where each ai is given by its coordinates [x,y]. The commnad "convexhull(X)" give us the points of the convex hull of X, but how I can find to "lower-right" of these points? Please, see the attached image. I need to findo the points A,C,E and F, marked with a solid circle.

What causes an unsolvable Tarjan form?...

I am working on a model in MapleSim which is giving me the error "DSN/RunSimulation: internal error: condition iteration failure: unable to solve Tarjan form at initial point."

Are there any general tips on what in a model could cause this error?

How do i get a envolope plot base on odeplot graph...

Hello,

I am so happy that this is my first time to ask a quension here.

Like the graph pasted down, i can get a graph of a ode with the odeplot in time domain.

Furthermore, i just want to get a envelope plot based on the time domain graph, just like showed in

the example graph here,

i have no way to plot it in maple,

Does anyone know a method to plot it in maple?

Linear solve command with multiple core (Maple 18,...

Daer maple useres,

I am solving around 170 linear algebraic equations (symbolic) using linearalgebra " solve" command. I see the cpu usage is only 15%; as I the cpu is  i-7, octacore ,15% means around 1 core is in use. With time (12 hours)  cpu usage goes down to 0% showing free memory approx 0.

Why  is it happening? Is it due to high memory usage in storing large symobic expressions? Is there a way to engage all the cores( 100% Cpu)?

Thanks and regards.

modify an expression, fraction...

Hello People in mapleprimes,

a^k*k/(a*a__0^k)

would not be simplifyed to k*a^(k-1)/a__0^k

with

symplify(a^k*k/(a*a__0^k)) assuming(k>1);

or other commands including expand.

Is there any way other than simplify(numer(..)/a)/simplify(denom(..)/a); ?

free variables in solve...

Hi!

I am trying to solve a large system using solve(). Fortunately, my system is linear and it does have solutions. Actually, the system has free variables that gives multiple solutions.

However, I have hundreds of variables with different names and subscripts, and I only need one solution of the system. I noticed that solve() actually output the solution with the free variables on the right. So, is there a way that I can find all the free variables and give them 0, to get only one set of solution?

Thanks!

William

What's the best way to search inserted table and r...

Using Insert->Table... and inserting information in the cells.

So I've created Table1 but I can't seem to call any row/column cell information using that name.  How do we do that?  Also, what is the best way to search for information in those cells and return information in adjacent cells?

Intersection of plane and line ?...

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}

Plot of coupled functions and extraction of the da...

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.

Is there a strong mistake in the DifferentialGeom...

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 &otimes; 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
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!

ImprovementsInPdsolve.mw...

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 plot phase portrait on a cylinder?...

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

Error in DEplot3D...

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.

maximize equation subject to constraints...

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?