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I have been working on a general solution to motion analysis and seem to be going backwards.  I have an numerical solution in Octave I use for comparison.  I have reduced the problem to a small example that exhibits the problem.

I posted a question similar to this, but, without a set of known values.

I am doing something wrong, but, what?

Tom Dean

## bearing.mpl, solve the target motion problem with bearings only.
##
## Consider a sensor platform moving through points (x,y) at times
## t[1..4] with the target bearings, Brg[1..4] taken at times t[1..4]
## with the target proceeding along a constant course and speed.
##
## time t, bearing line slope m, sensor position (x,y) are known
## values.
##
## Since this is a generated problem the target position at time t is
## provided to compare with the results.
##
#########################################################################
##
restart;
##
genKnownValues := proc()
    description "set the known values",
    "t - relative time",
    "x - sensor x location at time t[i]",
    "y - sensor y location at time t[i]",
    "m - slope of the bearing lines at time t[i]",
    "tgtPosit - target position at time t[i]";
    global t, m, x, y, tgtPosit;
    local dt, Cse, Spd, Brg, A, B, C, R, X;
    local tgtX, tgtY, tgtRange, tgtCse, tgtSpd;
## relative and delta time
    t := [0, 1+1/2, 3, 3+1/2];
    dt := [0, seq(t[idx]-t[idx-1],idx=2..4)];
## sensor motion
    Cse := [90, 90, 90, 50] *~ Pi/180; ## true heading
    Spd := [15, 15, 15, 22];  ## knots
## bearings to the target at time t
    Brg := [10, 358, 340, 330] *~ (Pi/180);
## slope of the bearing lines
    m:=map(tan,Brg);
## calculate the sensor position vs time
    x := ListTools[PartialSums](dt *~ Spd *~ map(cos, Cse));
    y := ListTools[PartialSums](dt *~ Spd *~ map(sin, Cse));
## target values  start the target at a known (x,y) position at a
## constant course and speed
    tgtRange := 95+25/32; ## miles at t1, match octave value...
    tgtCse := 170 * Pi/180; ## course
    tgtSpd := 10; ## knots
    tgtX := tgtRange*cos(Brg[1]);
    tgtX := tgtX +~ ListTools[PartialSums](dt *~ tgtSpd *~ cos(tgtCse));
    tgtY := tgtRange*sin(Brg[1]);
    tgtY := tgtY +~ ListTools[PartialSums](dt *~ tgtSpd *~ sin(tgtCse));
## return target position vs time as a matrix
    tgtPosit:=Matrix(4,2,[seq([tgtX[idx],tgtY[idx]],idx=1..4)]);
end proc:
##
#########################################################################
## t[], m[], x[], and y[] are known values
##
## equation of the bearing lines
eq1 := tgtY[1] - y[1]    = m[1]*(tgtX[1]-x[1]):
eq2 := tgtY[2] - y[2]    = m[2]*(tgtX[2]-x[2]):
eq3 := tgtY[3] - y[3]    = m[3]*(tgtX[3]-x[3]):
eq4 := tgtY[4] - y[4]    = m[4]*(tgtX[4]-x[4]):
## target X motion along the target line
eq5 := tgtX[2] - tgtX[1] = tgtVx*(t[2]-t[1]):
eq6 := tgtX[3] - tgtX[2] = tgtVx*(t[3]-t[2]):
eq7 := tgtX[4] - tgtX[3] = tgtVx*(t[4]-t[3]):
## target Y motion along the target line
eq8 := tgtY[2] - tgtY[1] = tgtVy*(t[2]-t[1]):
eq9 := tgtY[3] - tgtY[2] = tgtVy*(t[3]-t[2]):
eq10:= tgtY[4] - tgtY[3] = tgtVy*(t[4]-t[3]):
##
#########################################################################
##
## solve the equations
eqs  := {eq1,eq2,eq3,eq4,eq5,eq6,eq7,eq8,eq9,eq10}:

Sol:= solve(eqs, {tgtVx, tgtVy, seq([tgtX[k], tgtY[k]][], k= 1..4)}):
##

genKnownValues():
## these values are very close to Octave
evalf(t);evalf(m);evalf(x);evalf(y);evalf(tgtPosit);
## The value of tgtX[] and tgtY[] should equal the respective tgtPosit values
seq(evalf(eval([tgtX[idx],tgtY[idx]], Sol)),idx=1..4);

 

I accidentally came across a nice Mma animation. Unfortunately, I am able to present only few frames of it in MaplePrimes. See two inconsecutive frames below

 

I find this animation very deep. I don't remember something similar. It looks like an iterative
map shown in its dynamics. Not being an expert in Mathematica, I don't understand the machinery of the generating code.
n = 1000;
r := RandomInteger[{1, n}];
f := (#/(.01 + Sqrt[#.#])) & /@ (x[[#]] - x) &;
s := With[{r1 = r}, p[[r1]] = r; q[[r1]] = r];
x = RandomReal[{-1, 1}, {n, 2}];
{p, q} = RandomInteger[{1, n}, {2, n}];
Graphics[{PointSize[0.007], Dynamic[If[r < 100, s];
Point[x = 0.995 x + 0.02 f[p] - 0.01 f[q]]]}, PlotRange -> 2]
Here is its fragment translated into Maple:
>with(MmaTranslator):
>FromMma(" (#/(.01 + Sqrt[#.#])) & /@ (x[[#]] - x) &;");
map(unapply(_Z1/(0.1e-1+sqrt(_Z1 . _Z1)), _Z1), unapply(x(_Z1)-x, _Z1))
To my regret,
>FromMma(" n = 1000;
r := RandomInteger[{1, n}];
f := (#/(.01 + Sqrt[#.#])) & /@ (x[[#]] - x) &;
s := With[{r1 = r}, p[[r1]] = r; q[[r1]] = r];
x = RandomReal[{-1, 1}, {n, 2}];
{p, q} = RandomInteger[{1, n}, {2, n}];
Graphics[{PointSize[0.007], Dynamic[If[r < 100, s];
Point[x = 0.995 x + 0.02 f[p] - 0.01 f[q]]]}, PlotRange -> 2]");
Error, (in MmaTranslator:-FromMma) incorrect syntax (at position 11) in last character of "...0)
r"

Hello Dear!

I want to solve the system of linear equation but facing some problem please see the attachmen. I am waiting your positive response 

1_(1).mw

Hi everyone.

I'm going to solve a problem with HPM in Maple. I wrote some initial codes but now I'm confused becouse of P^0 coefficients in A1 and B1. I mean I can't reach to f0 and g0.

I upload that file. these are codes that i typed. could you please help me how can I reach to them(f0 & g0)?

http://www.filehosting.org/file/details/573095/Maple%20Project+.mw

Hi all,

Using the Physics package, I have defined a density operator, shown in the image below:

Definition of Density Operator

(I did assume(s ≠i), assume(v≠h).

I then operate on it with the Bracket as shown in the next image:

Bracket on Density Operator

 

I think this should evaluate to (|Y,s,h><Y,s,h|)/2; or at least that's the result I want. However, Maple evaluates this to zero.

Is there a where to convince Maple to evaluate this to what I want/expect?

Thanks in advance,

Kevin

Circuit problem...

Yesterday at 2:37 AM lucaud 5

why the current luca_amplificatore_retroazione.msimand voltage is egual to zero?

I don't know the use to me of having PDF exports having animations requiring huge emails since I don't own website. Yet, I've been fooling with Apple textbook maker app that has movie imort to PDFs. Someday, I'll use google drive links...

So, action item, maybe Maple would like to have a worksheet drop in to this apple textbook app Like movies. I hope it's easy from Apple taunting html5.

Hi,

 

I am trying to solve a simple system of the form AX=0, where A is a N*N matrix, X is an N*1 vector (and the right-hand side of the equation is an N*1 vector of zeros, I apologize for the inexact notation). The difficulty comes from the fact that the values of A are parameterized by 2*N parameters (that I will write as the 2*N vector P), and I would like to get a solution in the form X=f(P).

 

One solution is to try to use LinearAlgebra[LinearSolve], but it only returns the trivial solution X=0, which I am not interested in.

Another solution is to compute analytically the Moore-Penrose pseudoinverse Ag of A, as the general solution is of the form

(I - Ag A)f ;

where f is a vector of free parameters. However, even for a small matrix size (N=4), Maple is still computing after 3 hours on my (fairly powerful) machine, and it is taking more and more memory over time. As the results are polynomial/rational equations in the parameters P, I was actually expecting Maple to be more powerful than other softwares, but for this particular problem, Matlab's symbolic toolbox (muPAD) gives quick solutions until N=6. I need, in the end, to solve additional polynomial/rational equations that are derived from the solutions X=f(P), where Matlab fails. This is why I would really like to be able to solve the above-mentioned problem AX=0 with Maple in order to try to solve the subsequent step of the problem (polynomial system) with Maple.

 

Any suggestions on how to do this would be highly appreciated! Thank you very much for your time and help.

 

Laureline

I would prefer that all the polynomials generated in my workbook by MAPLE were in expanded form.  For instance, it the elements of a matrix are polynomials, I want to see the expanded form for all of them.  What do I type into a workbook to make this happen.  (I am a new user of MAPLE.) 

12pt type is difficult for me to read.  I would like to fix a workbook so that everything yet to appear will be in 18pt type, without my having to enlarge things one at a time.   (I am a new MAPLE user.)  

When I print 2 matrix it always try to multiply them. How to force just to show?

Hi

Given two lists I and J of the same size, how can we find all perfect mathings of two lists? 

In other way, how can we find all pairing of elements of I and J? 

For exapmle, given I = [1,2,3] and J = [4,5,6], i would like to get 

[[1,4],[2,5],[3,6]], [[1,4], [2,6],[3,5]], [[1,5],[2,4],[3,6]], [[1,5],[2,6],[3,4]], [[1,6],[2,4],[3,5]], [[1,6],[2,5],[3,4]]

I can see how I can use the permutation of one list and match component-wise in order will do it, but would there be more efficient way to complete  the task? 

Ultimately, I would like do this for a list of lists, that is, for example,

I = [[3,5],[6,7,9,12]] and J = [[8,10], [1,2,4,11]] then I would like to get 

[[3,8],[5,10],[6,1],[7,2],[9,4],[12,11]] and by the above example, get 24 of product of disjoint cycles like such.

Thanks

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