## Maple 15 Questions and Posts

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

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

## install error and no error when using cmd to insta...

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

## Functions defined by a procedure...

Hi,

Let, fixed an integer i and 1<=j<=2^{i}-1, for each x and y in [0,1] let the following mapping

Then, with the above procedure we can obtained, for a fixed i, all the mappings for j=1,...,2^{i}-1

However, How can I to evalute the "components" of the above procedure? For instance, I can not to compute CreaF(2)[1](0.35,0.465) (i.e., the first function in the "vector" CreaF(2), in x=0.35, y=0.465).

Thanks very much for your time.

## Saving the multiple output of an expression withou...

Hi, I am new to maple, but I think that my question should be simple.

I have a matrix where each element is an expression. I want to compute the matrix for different constant and to save it without crushing the previous matrix.

If the file that I joined, I have a first part where the constant are defined. In the second part the expression of the matrix is defined. Finally, I compute each matrix with different constant. Each results is called C_p0, C_s0, C_g0. When I called them back, only the last matrix computed remains.

I would like to be able to save each matrix to performed operation on them later.

Thank you.

Forum_Question1.mw

Homogénéisation

 Paramètre des matériaux

Tenseurs Élémentaires

Tenseur de rigidité

Matrice de rigidité

 (1.2.1.1.1)

 (1.2.1.1.2)

 (1.2.1.1.3)

 (1)

## Equidistant curves

by: Maple 15

equidistant_curve_MP.mw  Equidistant curves to the curves on the surface. (Without any sense, but real.)

## Does mtaylor ignore "assuming"?...

I have the following expression (generated by some other procedure):

This does not have a taylor expansion in pV[6] in the general case because the square roots can become negative:

taylor(xpr,pV[6]);
Error, does not have a taylor expansion, try series()

But I can get an expansion by restrictig the range of pV[6]:

taylor(xpr,pV[6]) assuming -0.01<pV[6],pV[6]<0.01;

So far things are perfectly fine. But when I try mtaylor:

mtaylor(xpr,pV[6]) assuming -0.01<pV[6],pV[6]<0.01;
Error, (in assuming) when calling 'mtaylor'. Received: 'does not have a taylor expansion, try series()'

So the assumption seems to be ignored. I can work around this by expanding in pV[6] first, using taylor, and then expanding the result from that using mtaylor (I really also want the expansions in the other pV components; 6 in total although in this example some do not show up). I'll have to convince myself that this work-around gives the correct result but I think it does. However, I don't particularly like it.

I consider this a bug and am tempted to submit an SCR. But before I do that; is there anything obvious I am missing here?

Thanks,

M.D.

PS: This was done using Maple 15. I'll check newer versions later.

mtaylor_assuming.mw

## Equidistant surface

by: Maple 15

Example of the equidistant surface at a distance of 0.25 to the surface
x3
-0.1 * (sin (4 * x1) + sin (3 * x2 + x3) + sin (2 * x2)) = 0
Constructed on the basis of universal parameterization of surfaces.

equidistant_surface.mw

## How Do I Separate Variables?...

When I was editing the head of the question (? instead of .), its body disappeared. Please, insert it again.

Regard,

Markiyan Hirnyk

## Problem with delta as parameter...

I want to ask., I put delta as my constant in maple program and I want the answer are in delta as well., but the thing is., when running., it let delta=0, delta=-1, and delta=delta.,
the condition is we cannot let delta=1 or delta=0 because it is just same for s5 and s7.,.(delta is refer to the s8). How can I get answer as delta? with the condition? here I attach my maple programme..

> derivation := proc (A, n)
local i, j, k, t, s5, s7, s8, m, D,
sols5, sols7, sols8, eqns5, eqns7, eqns8,
BChange5, BChange7, BChange8; eqns5 := {}; eqns7 := {}; eqns8 := {};
D := matrix(n, n);
BChange5 := matrix(n, n); BChange7 := matrix(n, n); BChange8 := matrix(n, n);
for i to n do for j to n do for m to n do
s5 := sum(0*A[i, j, k]*D[m, k], k = 1 .. n)-(sum(A[k, j, m]*D[k, i]+A[i, k, m]*D[k, j], k = 1 .. n));
s7 := sum(0*A[i, j, k]*D[m, k], k = 1 .. n)-(sum(A[k, j, m]*D[k, i]+0*A[i, k, m]*D[k, j], k = 1 .. n));
s8 := sum(0*A[i, j, k]*D[m, k], k = 1 .. n)-(sum(A[k, j, m]*D[k, i]+delta*A[i, k, m]*D[k, j], k = 1 .. n));
eqns5 := `union`(eqns5, {s5}); eqns7 := `union`(eqns7, {s7}); eqns8 := `union`(eqns8, {s8})
end do end do end do;
sols5 := [solve(eqns5)]; sols7 := [solve(eqns7)]; sols8 := [solve(eqns8)];
t := nops(sols5); t := nops(sols7); t := nops(sols8);
for i to t do for j to n do for k to n do
BChange5[k, j] := subs(sols5[i], D[k, j]);
BChange7[k, j] := subs(sols7[i], D[k, j]);
BChange8[k, j] := subs(sols8[i], D[k, j])
end do end do;
print("eqns&Assign;", eqns5); print("sols:=", sols5); print("BChange5:=", BChange5);
print("eqns&Assign;", eqns7); print("sols:=", sols7); print("BChange8:=", BChange7);
print("eqns&Assign;", eqns8); print("sols:=", sols8); print("BChange8:=", BChange8)
end do end proc;

> AS1 := array(sparse, 1 .. 2, 1 .. 2, 1 .. 2, [(1, 1, 2) = 1]);
> derivation(AS1, 2);

> AS2 := array(sparse, 1 .. 2, 1 .. 2, 1 .. 2, [(1, 1, 1) = 1, (1, 2, 2) = 1]);
> derivation(AS2, 2);

> AS3 := array(sparse, 1 .. 2, 1 .. 2, 1 .. 2, [(1, 1, 1) = 1, (2, 1, 2) = 1]);
> derivation(AS3, 2);

> AS4 := array(sparse, 1 .. 2, 1 .. 2, 1 .. 2, [(1, 1, 1) = 1, (2, 2, 2) = 1]);
> derivation(AS4, 2);

> AS5 := array(sparse, 1 .. 2, 1 .. 2, 1 .. 2, [(1, 1, 1) = 1, (1, 2, 2) = 1, (2, 1, 2) = 1]);
> derivation(AS5, 2);

> AS1 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(1, 3, 2) = 1, (3, 1, 2) = 1]);
> derivation(AS1, 3);

> AS2 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(1, 3, 2) = 1, (3, 1, 2) = alpha]);
> derivation(AS2, 3);

> AS3 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(1, 1, 2) = 1, (1, 2, 3) = 1, (2, 1, 3) = 1]);
> derivation(AS3, 3);

> AS4 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(1, 3, 2) = 1, (2, 3, 2) = 1, (3, 3, 3) = 1]);
> derivation(AS4, 3);

> AS5 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(2, 3, 2) = 1, (3, 1, 1) = 1, (3, 3, 3) = 1]);
> derivation(AS5, 3);

> AS6 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(3, 1, 2) = 1, (3, 2, 2) = 1, (3, 3, 3) = 1]);
> derivation(AS6, 3);

> AS7 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(1, 2, 1) = 1, (2, 2, 2) = 1, (3, 1, 1) = 1, (3, 3, 3) = 1]);
> derivation(AS7, 3);

> AS8 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(1, 3, 1) = 1, (2, 3, 2) = 1, (3, 1, 1) = 1, (3, 3, 3) = 1]);
> derivation(AS8, 3);

> AS9 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(2, 3, 2) = 1, (3, 1, 1) = 1, (3, 2, 2) = 1, (3, 3, 3) = 1]);
> derivation(AS9, 3);

> AS10 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(1, 3, 1) = 1, (2, 3, 2) = 1, (3, 1, 1) = 1, (3, 2, 2) = 1, (3, 3, 3) = 1]);
> derivation(AS10, 3);

> AS11 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(1, 3, 2) = 1, (2, 3, 2) = 1, (3, 1, 2) = 1, (3, 2, 2) = 1, (3, 3, 3) = 1]);
> derivation(AS11, 3);

> AS12 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(1, 1, 2) = 1, (1, 3, 1) = 1, (2, 3, 2) = 1, (3, 1, 1) = 1, (3, 2, 2) = 1, (3, 3, 3) = 1]);
> derivation(AS12, 3);

> AS13 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(1, 1, 1) = 1, (2, 2, 2) = 1, (3, 3, 3) = 1]);
> derivation(AS13, 3);

> AS14 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(1, 2, 1) = 1, (2, 1, 1) = 1, (2, 2, 2) = 1, (3, 3, 3) = 1]);
> derivation(AS14, 3);

> AS15 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(1, 2, 1) = 1, (2, 2, 2) = 1, (3, 3, 3) = 1]);
> derivation(AS15, 3);

> AS16 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(2, 1, 1) = 1, (2, 2, 2) = 1, (3, 3, 3) = 1]);
> derivation(AS16, 3);

> AS17 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(1, 1, 2) = 1, (3, 3, 3) = 1]);
> derivation(AS17, 3);
>

## Rotational motion mechanism

by: Maple 15

Rotational motion mechanism with quasi stops
02rep.pdf
DIMA.mw