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Hello,

How can I pde with maple?please explain completely,and other question :How can I solve pde with plot in maple because some questions dont have exact answer?

with(PolynomialIdeals):

quotientlist := Quotient(GB, varj[j]);
finallist2 := [];
for z from 1 to nops(quotientlist) do
if
finallist2 := [op(finallist2), op(z,quotientlist)];
od:

there are only 3 monomials in quotientlist, but nops return 6

 

Let a finite set of closed intervals in the plane be given.
How to find all the intersections of these, outputing the intersection points together with the intersecting intervals?
This is a problem of computational geometry
(see http://en.wikipedia.org/wiki/Line_segment_intersection).
In other words, how to realize the sweep line algorithm to this end in Maple?

PS. I'd like to add that computional geometry has serious applications, in particular, in robotics.

Good afternoon.

 

I request your kind suggestion to my above cited query.

 

 

With thanks & Regards

 

M.Anand

Assistant Professor in Mathematics

SR International Institute of Technology,

Hyderabad, Andhra Pradesh, INDIA.

 

I want to solve system of equation but it has unknow parameter.

Then I test system of equation. It hasn't unknowparameter.

eq1 := x^2+y^2 = 4

eq2 := y-x^2 = 0

fsolve({eq1, eq2}, {x, y})

{x = -1.249621068, y = 1.561552813}

So I get answer by using fsolve.

 

Then I try to put unknow parameter in system of equation.

eq3 := x^2+ky^2 = 4

eq4 := ay-hx^2 = 0

fsolve({eq3, eq4}, {x, y})

Error, (in fsolve) {ay, hx, ky} are in the equation, and are not solved for

I don't get answer and open link. The link hasn't similar this problem.

To motivate some ideas in my research, I've been looking at the expected number of real roots of random polynomials (and their derivatives).  In doing so I have noticed an issue/bug with fsolve and RootFinding[Isolate].  One of the polynomials I came upon was

f(x) = -32829/50000-(9277/50000)*x-(37251/20000)*x^2-(6101/6250)*x^3-(47777/20000)*x^4+(291213/50000)*x^5.

We know that f(x) has at least 1 real root and, in fact, graphing shows that f(x) has exactly 1 real root (~1.018).  However, fsolve(f) and Isolate(f) both return no real roots.  On the other hand, Isolate(f,method=RC) correctly returns the root near 1.018.  I know that fsolve's details page says "It may not return all roots for exceptionally ill-conditioned polynomials", though this system does not seem especially ill-conditioned.  Moreover, Isolate's help page says confidently "All significant digits returned by the program are correct, and unlike purely numerical methods no roots are ever lost, although repeated roots are discarded" which is clearly not the case here.  It also seems interesting that the RealSolving package used by Isolate(f,method=RS) (default method) misses the root while the RegularChains package used by Isolate(f,method=RC) correctly finds the root.

 All-in-all, I am not sure what to make of this.  Is this an issue which has been fixed in more recent incarnations of fsolve or Isolate?  Is this a persistent problem?  Is there a theoretical reason why the root is being missed, particularly for Isolate?

Any help or insight would be greatly appreciated.

How do I calculate run of 0s or run of 1s using maple?


Q[1] := (e^(-n*T*s)-e^(-(n+1)*T*s)+(-exp(-Z[1]*n*T)*(s-Z[1])*exp(-n*T*(s-Z[1]))+exp(-Z[2]*n*T)*(s-Z[2])*exp(-n*T*(s-Z[2])))/(Z[1]-Z[2])+2*exp(-n*T*s)*(-1+Heaviside(-n*T)))/c+Z[1]*Z[2]*exp(-n*T*(s-Z[1]))/((s-Z[1])*exp(Z[1]*n*T)*(Z[1]-Z[2])*c)-Z[2]*Z[1]*exp(-n*T*(s-Z[2]))/((s-Z[2])*exp(Z[2]*n*T)*(Z[1]-Z[2])*c); 1; Q[2] := ((s-Z[1])*exp(-n*T*(s-Z[1]))*exp(-Z[1]*n*T)/(Z[2]-Z[1])+exp(-n*T*s)*(-1+Heaviside(-n*T)))/c+Z[1]*Z[2]*exp(-n*T*(s-Z[1]))/((s-Z[1])*exp(Z[1]*n*T)*(Z[1]-Z[2])*c)+(exp(-Z[2]*n*T)*(s-Z[2])*exp(-n*T*(s-Z[2]))/(Z[1]-Z[2])+exp(-n*T*s)*(-1+Heaviside(-n*T)))/c-Z[2]*Z[1]*exp(-n*T*(s-Z[2]))/((s-Z[2])*exp(Z[2]*n*T)*(Z[1]-Z[2])*c)+(e^(-n*T*s)-e^(-(n+1)*T*s))/c

((s-Z[1])*exp(-n*T*(s-Z[1]))*exp(-Z[1]*n*T)/(Z[2]-Z[1])+exp(-n*T*s)*(-1+Heaviside(-n*T)))/c+Z[1]*Z[2]*exp(-n*T*(s-Z[1]))/((s-Z[1])*exp(Z[1]*n*T)*(Z[1]-Z[2])*c)+(exp(-Z[2]*n*T)*(s-Z[2])*exp(-n*T*(s-Z[2]))/(Z[1]-Z[2])+exp(-n*T*s)*(-1+Heaviside(-n*T)))/c-Z[2]*Z[1]*exp(-n*T*(s-Z[2]))/((s-Z[2])*exp(Z[2]*n*T)*(Z[1]-Z[2])*c)+(e^(-n*T*s)-e^(-(n+1)*T*s))/c

(1)

Q[1] = Q[2]"(->)"true"(->)"true"(->)"true"(->)"true

Q[2] = ((s-Z[1])*exp(-n*T*(s-Z[1]))*exp(-Z[1]*n*T)/(Z[2]-Z[1])+exp(-n*T*s)*(-1+Heaviside(-n*T)))/c+Z[1]*Z[2]*exp(-n*T*s)/((s-Z[1])*(Z[1]-Z[2])*c)+(exp(-Z[2]*n*T)*(s-Z[2])*exp(-n*T*(s-Z[2]))/(Z[1]-Z[2])+exp(-n*T*s)*(-1+Heaviside(-n*T)))/c-Z[2]*Z[1]*exp(-n*T*s)/((s-Z[2])*(Z[1]-Z[2])*c)+(e^(-n*T*s)-e^(-T*s)*e^(-n*T*s))/c
"(->)"true
Q[2] = ((s-Z[1])*exp(-n*T*(s-Z[1]))*exp(-Z[1]*n*T)/(Z[2]-Z[1])+exp(-n*T*s)*(-1+Heaviside(-n*T)))/c+(exp(-Z[2]*n*T)*(s-Z[2])*exp(-n*T*(s-Z[2]))/(Z[1]-Z[2])+exp(-n*T*s)*(-1+Heaviside(-n*T)))/c+Z[1]*Z[2]*exp(-n*T*s)/((s-Z[1])*(Z[1]-Z[2])*c)-Z[2]*Z[1]*exp(-n*T*s)/((s-Z[2])*(Z[1]-Z[2])*c)+(e^(-n*T*s)-e^(-T*s)*e^(-n*T*s))/c
"(->)"true"(->)"true``

((s-Z[1])*exp(-n*T*(s-Z[1]))*exp(-Z[1]*n*T)/(Z[2]-Z[1])+exp(-n*T*s)*(-1+Heaviside(-n*T)))/c+(exp(-Z[2]*n*T)*(s-Z[2])*exp(-n*T*(s-Z[2]))/(Z[1]-Z[2])+exp(-n*T*s)*(-1+Heaviside(-n*T)))/c = (2*Heaviside(-n*T)-1)*exp(-n*T*s)/c
"(->)"true"(->)"true"(->)"true

Q[2] = (2*Heaviside(-n*T)-1)*exp(-n*T*s)/c+Z[1]*Z[2]*exp(-n*T*s)/((s-Z[1])*(Z[1]-Z[2])*c)-Z[2]*Z[1]*exp(-n*T*s)/((s-Z[2])*(Z[1]-Z[2])*c)+(e^(-n*T*s)-e^(-T*s)*e^(-n*T*s))/c
"(->)"false"(->)"false"(->)"false

``


Download inexplicable.mw

Can anyone explain the false return on the last line?  MAPLE seems to recognize the simplified expression on the next to last line, but when substituted into the expression for Q2 MAPLE does not seem to recognize the simplification.

How can I plot a volume (many surfaces) in X,Y, Z axis where X,Y,Z are functions in 4 variables (a,b,c,d), and the domain for the 4 variables are 

-90<=a>=90, -10<=b>=10, -12<=c>=12, -90<=d>=0,

 

X := proc (a, b, c, d) options operator, arrow; 324.*cos(b)*sin(c)*cos(d)+324.*sin(b)*sin(d)+323.5*cos(b)*sin(c) end procX := proc (a, b, c, d) options operator, arrow; 324.*cos(b)*sin(c)*cos(d)+324.*sin(b)*sin(d)+323.5*cos(b)*sin(c) end proc

Y := proc (a, b, c, d) options operator, arrow; (324*1.*sin(a)*sin(b)*sin(c)+324*1.*cos(a)*cos(c))*cos(d)+(-1)*324.*sin(a)*cos(b)*sin(d)+323.5*sin(a)*sin(b)*sin(c)+323.5*cos(a)*cos(c)-100 end proc

Y := proc (a, b, c, d) options operator, arrow; (324*1.*sin(a)*sin(b)*sin(c)+324*1.*cos(a)*cos(c))*cos(d)+(-1)*324.*sin(a)*cos(b)*sin(d)+323.5*sin(a)*sin(b)*sin(c)+323.5*cos(a)*cos(c)-100 end proc

Z := proc (a, b, c, d) options operator, arrow; (324*cos(a)*sin(b)*sin(c)-324*sin(a)*cos(c))*cos(d)-324*cos(a)*cos(b)*sin(d)+323.5*cos(a)*sin(b)*sin(c)+(-1)*323.5*sin(a)*cos(c)+150 end proc

Z := proc (a, b, c, d) options operator, arrow; (324*cos(a)*sin(b)*sin(c)-324*sin(a)*cos(c))*cos(d)-324*cos(a)*cos(b)*sin(d)+323.5*cos(a)*sin(b)*sin(c)+(-1)*323.5*sin(a)*cos(c)+150 end proc

Let Poly2 denote the vector space of polynomials

(with real coefficients) of degree less than 3.

Poly2 = {a1t^2+ a2 t+ a3 |a1; a2; a3 €R}

You may assume that {1,t; t^2}is a basis for Poly2.

(1) Show that L1 = {t^2 + 1; t-2 ; t + 3}and L2 = {2 t^2 + t; t^2 + 3; t}

are bases for Poly2.

(2) Let = 8t^2- 4+ 6 and = 7t^2- t + 9. Find the coordinates for

and with respect to the basis L1 and with respect to the basis L2

(3) find the coordinate change matrix P from the basis L1 to the basis L2.find P^-1

Just I answer part (1) can you help me to answer 2 and 3 

I'm working on a complex problem in Composite Materials. I've gotten to a near-result 6x6 matrix, with several cells containing polynomial denominators. I have an equation for simplifying these, which boils the polynomials down to a single variable, but I can't seem to get it to substitute in. Can anyone help me solve this? The problem is also time-sensitive.

 

I would like to plot this :

yz(x+y+2z)^3-8=0 such as x^2+x(y+2z)-1<0 and y^2+y(x+2z)-3<0

The difficulty is that bounds depend on other variables. I was trying to use Maple implicitplot3d function, but I don't see a way.

Is it possible to use Maple for such plot ? If so, how ?

 

Thank you for your answer

I am considering to write a wrapper for plot and related commands (could redefine the commands or introduce a new name) which facilitates export of Maple plots to postscript. The command should interpret some of the options and remove them from the options sequence before submitting the remaining ones to the original plot().
E.g. it should recognize a title="TITLE" parameter and process TITLE (e.g. write it to a specific file). Similarly I would want to be able to pass additional parameters, e.g. filename="FILE" in order to specify how the output file name should be set. Is this a sensible approach. How can I realize this detailed option 'parsing' in Maple?

Hi all,

I created a package and saved it already. I checked and found it at D:/CaoHoc/LuanVan/Code/workspace/HINHHOC9.m but when I load it using with command, it has error.

[.............Code to create package..............]

>url := currentdir();
                   url := "D:\CaoHoc\LuanVan\Code\workspace"

>
>save HINHHOC9, cat(url, "/HINHHOC9.m");
>
>libname := libname, url;
libname := "C:\Program Files\Maple 18\lib",

    "D:\CaoHoc\LuanVan\Code\workspace\LuanVan\binaries",

    "C:\Program Files\Maple 18\lib", "D:\CaoHoc\LuanVan\Code\workspace"

>
>         with(HINHHOC9);
Error, (in with) user level initialization for package `HINHHOC9' failed: file
or directory does not exist

Please help me to identify the problem. Thanks

eq1a := Homogenize(eq1, h);
eq2a := Homogenize(eq2, h);
eq3a := Homogenize(eq3, h);
David Cox using Algebraic Geometry page 82 use resultant to eliminate variable h
eq1b := eq1a - x;
eq2b := eq2a - y;
eq3b := eq3a - z;
T2:=lexdeg([a,b,c],[x,y,z]);
GB := Basis([eq1b,eq2b,eq3b], T2);
r1 := resultant(eq1b, eq2b, h);
r2 := resultant(eq1b, eq3b, h);
r1 = r2

page 82 teach how to eliminate, after do question 2, discover r1 and r2 are the same.

how to eliminate the variable h with resultant after homogenize ideal with variable h

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