## Maple 15 Questions and Posts

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

I have tried everything to find out how to customise the header and footer for my tutor marked assignments.

I want to have a heading on the top of the page which has a continuous line running underneath the text of the heading. And I want to have a footing on the bottom of each page which has a continuous line running above the text of the footing text.

I noticed that the 2015 Maple user manual has this feature so it must be possible.

I cannot see how to do this using the standard customise header and footer menu.

Thanks in anticipation of an answer.

DLW

## compute the error and op function...

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 ?

## how to use python to call maple and scroll up or d...

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

## The procedure can not run...

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.

 >
 (1)

 >

## I want to know why is this error message keeps ap...

>
>
> 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

 (1)

 (2)

## how we can solve an ode with boundaries by using R...

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

## solution for ode and how to tackle constant ...

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

## Parallel curves on surfaces

by: Maple 15

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

## Error in Integrating Heaviside Function...

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.

 (1)

 (2)

 (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?

by: Maple 15

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

## Error, (in sprintf) number expected for floating p...

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

## how to use optimization with complex number?...

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

## how to calculate implicit Cartesian equation from ...

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

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