Maple 15 Questions and Posts

These are Posts and Questions associated with the product, Maple 15

Hello,

Questions

1)  Can we compute the error  ( x(t-2*Pi) - x(t) )  without plotting  abs(  x( t-2*Pi ) - x(t) ) ?

     i.e. using norm 1, 2 or infinity  ?

 

2)  what is op( [ a, b, c] , F ),  where F is a piecewise function ?


Download example.mw

 

how to use python to call maple and scroll up or down scrollbar

Hi, I have this procedure (from Maple 5) but I am using it in Maple 15. My problem is this program can not run. I think there is some commond incorrect, but not sure which ones. Please help me in this problem. Thanks a lot.

cocycle.mw

NULL

Cocycle := proc (L, n) local i, j, k, h, v, u, w, C, eqns, e, f, g; v := vector(n); eqns := {}; u := vector(n); w := vector(n); C := array(antisymmetric, 1 .. n, 1 .. n, []); for i to n do for j from i+1 to n do for k from j+1 to n do for h to n do v[h] := L[i, j, h]; u[h] := L[j, k, h]; w[h] := L[k, i, h] end do; e := array(sparse, 1 .. n, [k = 1]); f := array(sparse, 1 .. n, [i = 1]); g := array(sparse, 1 .. n, [j = 1]); eqns := `union`(eqns, multiply(transpose(e), multiply(C, v)))+multiply(transpose(f), multiply(C, u))+multiply(transpose(g), multiply(C, w)) end do end do end do; print('The*cocycles*are', eqns) end proc

proc (L, n) local i, j, k, h, v, u, w, C, eqns, e, f, g; v := vector(n); eqns := {}; u := vector(n); w := vector(n); C := array(antisymmetric, 1 .. n, 1 .. n, []); for i to n do for j from i+1 to n do for k from j+1 to n do for h to n do v[h] := L[i, j, h]; u[h] := L[j, k, h]; w[h] := L[k, i, h] end do; e := array(sparse, 1 .. n, [k = 1]); f := array(sparse, 1 .. n, [i = 1]); g := array(sparse, 1 .. n, [j = 1]); eqns := `union`(eqns, multiply(transpose(e), multiply(C, v)))+multiply(transpose(f), multiply(C, u))+multiply(transpose(g), multiply(C, w)) end do end do end do; print('The*cocycles*are', eqns) end proc

(1)

NULL

NULL


Download cocycle.m

>
>
> w0 := 2*pi*sqrt(5)*10^9;
>
> mu0 := 4*pi*10^(-7); pi := 3.14; wepnorm := 4*pi*sqrt(3)*10^9; wmpnorm := 2*pi*sqrt(6)*10^9; wmpz := 4*pi*10^9; w := 10;
> k0 := w0/c; d := 10^(-9);
> enorm := e0*(1-wepnorm^2/w^2); munorm := mu0*(1-wmpnorm^2/w^2); mz := mu0*(1-wmpz^2/w^2); c := 3*10^8; e0 := 8.85*10^(-12);
> t1 := enorm*mz/(e0*mu0)-1; t2 := mz/munorm;
> eq1 := alpha0^2+t2*k1z^2-t1*k0^2;
>
>
>
>
>
>
>
t:=0:
for alpha0 from 0 to 25 by 5 do
t:=t+1:
>
k1z[t]:=fsolve(eq1,k1z,complex):

od:
Eff:=[seq([k1z[i],alpha0[i]],i=1..t)]:

with(plots):
display(plot(Eff,color=red));

Error, (in plot) found points with fewer or more than 2 components

 

how we can solve an ode with boundaries by using RK4 and any other technique??

how we can solve an ode with exat soltuion n calculate the unknw constant which aries after solving an ode.???

     Parallel curves on surfaces. The distance between the points of the curves is measured along the curves of intersection of the surface and perpendicular planes.
     (According to tradition, it also does not make sense.)

equidistant_curve_surface_MP.mw

 









 

 

I'm running into a very simple problem with the way that Maple integrates Heaviside functions. Naively, it should act like a step function, but it is not integrating properly. See the attached document.

int(int(Heaviside(-x^2-y^2+1), x = -1 .. 1), y = -1 .. 1)

0

(1)

evalf(Int(Heaviside(-x^2-y^2+1), [x = -1 .. 1, y = -1 .. 1]))

3.141592654

(2)

int(piecewise(-x^2-y^2+1 > 0, 1, 0), [x = -1 .. 1, y = -1 .. 1])

Pi

(3)

``


Note that the symbolic integration of the Heaviside function (defined to be 1 inside the unit circle and 0 outside) gives zero, whereas it should clearly give the area of the unit circle, which the numerical integration does. I even checked that the (suposedly equivalent) piecewise definition symbolically evaluates to the area, and it, too, gets the right answer.

Anyone have any clue as to why the symbolic integration of this Heaviside function is so wrong? My understanding is that if we do the integral as two nested 1D integrals, the returned function (as a function of y) is zero everywhere except at y=0, but that result cannot be right either.

Thoughts?

 

Download Heaviside-error.mw

        General description of the method of solving underdetermined systems of equations. As a particular application of the idea proposed a universal method  kinematic analysis for all kinds of  spatial and planar link mechanisms with any number degrees of freedom.  The method can be used for powerful CAD linkages.   
         http://www.maplesoft.com/applications/view.aspx?SID=154228

       


      Some examples of a much larger number calculated by the proposed method. Examples gathered here not to look for them on the forum and opportunity to demonstrate the method.  Among the examples, I think, there are very complicated.

https://vk.com/doc242471809_408704758
https://vk.com/doc242471809_408704572
https://vk.com/doc242471809_376439263
https://vk.com/doc242471809_402619761
https://vk.com/doc242471809_402610228
https://vk.com/doc242471809_401188803
https://vk.com/doc242471809_400465891
https://vk.com/doc242471809_400711315
https://vk.com/doc242471809_387358164
https://vk.com/doc242471809_380837279
https://vk.com/doc242471809_379935473
https://vk.com/doc242471809_380217387
https://vk.com/doc242471809_363266817
https://vk.com/doc242471809_353980472
https://vk.com/doc242471809_375452868
https://vk.com/doc242471809_353988163 
https://vk.com/doc242471809_353986884 
https://vk.com/doc242471809_353987119
https://vk.com/doc242471809_324249241
https://vk.com/doc242471809_324102889
https://vk.com/doc242471809_322219275
https://vk.com/doc242471809_437298137
https://vk.com/doc242471809_437308238
https://vk.com/doc242471809_437308241
https://vk.com/doc242471809_437308243
https://vk.com/doc242471809_437308245
https://vk.com/doc242471809_437308246
https://vk.com/doc242471809_437401651
https://vk.com/doc242471809_437664558

 

 

Round := proc(x,n::integer:=1)
parse(sprintf(cat("%.",n,"f"),x));
end proc:

roundcoeffs1:=proc(p,x,n:=1) local t,c;
c:=map(Round, [coeffs(p,x,t)],n);
add(i, i = zip(`*`, c, [t]));
end:

ggg:=.9940413618*y^3-1.785839107*c*A*y^3-2.357517322*c*A*y^2+.375393240*c*y*B-.3575173222*c*A*y-.2082022533*c*B-0.1787591445e-1*y^2-0.1787591445e-1*y-0.5958638151e-2+.2141608926*c*A+.7917977467*c*B*y^3+2.375393240*c*B*y^2;

roundcoeffs1(ggg, [y^3, c*A*y^3, c*A*y^2, c*y*B, c*A*y, c*B, y^2, y, c*A, c*B*y^3, c*B*y^2], 4);


Error, (in sprintf) number expected for floating point format

with(Optimization):

theta := Complex(1,1);
Minimize(theta^3-3*(A*theta^2+B), {0 <= theta^3-3*(A*theta^2+B)}, assume = nonnegative)

Error, (in Optimization:-NLPSolve) complex value encountered

from mathematica,

 

n = 5;
CalabiYau[z_, k1_, k2_] := Module[{z1 = Exp[2Pi I k1/n]Cosh[z]^(2/n), z2 = Exp[2Pi I k2/n]Sinh[z]^(2/n)}, {Re[z1], Re[z2], Cos[alpha]Im[z1] + Sin[alpha]Im[z2]}];
Do[alpha = (0.25 + t)Pi; Show[Graphics3D[Table[ParametricPlot3D[CalabiYau[x + I y, k1, k2], {x, -1, 1}, {y, 0, Pi/2}, DisplayFunction -> Identity, Compiled ->False][[1]], {k1, 0, n - 1}, {k2, 0, n - 1}], PlotRange -> 1.5{{-1, 1}, {-1, 1}, {-1, 1}}, ViewPoint -> {1, 1, 0}]], {t, 0, 1, 0.1}];

 

n := 5;

z1 := exp(2*3.14*I*k1/n)*cosh(z)^(2/n);
z2 := exp(2*3.14*I*k2/n)*sinh(z)^(2/n);

alpha = (0.25 + t)Pi;

xx := Re(z1);
yy := Re(z2);
uu := cos(alpha)*Im(z1) + sin(alpha)*Im(z2);

 

where k1, k2, alpha are variables

print([xx,yy,uu]);

i find algcurve has implicitize

how to use this implicitize to find 3d surface?

is there any other method to find?

 

i searched groebner basis can do this, but in mathematica is different from maple example

i got this error in window 8 in surface 2  then follow this post and install again still error

https://www.maplesoft.com/support/faqs/detail.aspx?sid=139020

then follow

http://www.maplesoft.com/support/faqs/detail.aspx?sid=32607

then follow and install again same error

http://www.maplesoft.com/support/faqs/detail.aspx?sid=32631

and install again same eror

then i add option -f c:\Program File (x86)\MapleXX in cmd and then no error any more 

but no install succeed 

where it go, it still not install

then i try again, there is no room enough to install,  hard disk do not have enough space, then i go to c:\Windows\Temp, after deleted file in it, still not enough space

 

i find 

https://www.maplesoft.com/support/install/maple15_install.html

but template do not state how to activate later

how to write this template and how to clear the temp file created by previous failed cmd install method

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