Maple 2016 Questions and Posts

These are Posts and Questions associated with the product, Maple 2016

In the below calculations, I get some solutions after solving the system. I am not sure if this is done assuming that all the values that are under the radicals are positive or indeed they are positive without further assumptions. I mean can I be sure that each given set of solution is a feasible solution? I suspect that Maple may ignore the assumptions sometimes.  

The following are the equation and plot3d of the minimal surface named Catalan:

Catalan := [alpha-sin(alpha)*cosh(beta), 1-cos(alpha)*cosh(beta), 4*sin((1/2)*alpha)*sinh((1/2)*beta)]
plot3d(Catalan, alpha = 0 .. 2*Pi, beta = -3 .. 3, scaling = constrained, title = "Catalan's surface", titlefont = [Courier, bold, 14])

I would like to color and thicken the edge of this surface to emphasize what I presume is the wire which frames the soap film which forms the surface.

Contourplot3d only shows contours at constant values of the z coordinate, however the plot3d display with style option "surface with line" clearly shows the surface's edge contour, among others.

Given the surface equation, is there any way to display the surface edge programmatically e.g. as a spacecurve? 

Without my knowingly changing any Maple parameters, the execution time values of variables appearing in the window displayed when a DEBUG statement is executed have recently started to be listed at the end of my worksheet.

If I have been doing extensive debugging this list can be quite lengthy and a nuisance to erase.

Why did this listing suddenly begin and how can I stop it?

 I'm thinking upload a technical paper into maple cloud, and i would like to keep the intellectual property of this paper or have a mention from the reader if they use it. Is it possible?. Thanks!

Suppose Delta:=f(a,b)x^2+g(a,b)x+h(a,b), where f,g,h are functions of a and b. Is there a way to find conditions on a,b such that Delta is positive?

i want to solve this DAE system usin Dsolve , but i obtain this error message (cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up), if anyone can help me ,

Hello all, 

I am trying to compute the Groebner basis for a set of 3 coupled nonlinear equations. The variables I wish to solve for are A0,B0, and B1; however, my equations also have the variables DC, a, nu, q, and t. I wish to solve the 3 equations in terms of these other 5 variables such that I can substitute in any values I desire and obtain a result. When attempting to put the three equations into the PolynomialIdeal command from the PolynomialIdeals package, Maple gives me an error stating that the inputs must be polynomials with respect to all 8 variables. How would I go about declaring the other 5 variables such that they are considered arbitrary constants? 

I was able to get around the errors by assigning values to these 5 variables, though this is not what I am trying to accomplish. I need these 5 values to remain arbitrary.

I am very new to the concept of Groebner Bases and these commands so any help would be appreciated. I have attached my worksheet for reference. I am also happy to supply any additional information that may be needed to assist with this issue.

Thanks!
 

restart

NULL

``

SED2 := proc (A0, B0, B1) options operator, arrow; (32/3)*(nu+7)*A0^2*Pi*DC/(a^2*(1+nu))+3*DC*Pi*((1+nu)^4*(B0^2+(13/42)*B1^2+(4/5)*B0*B1)*a^2+(328/315)*A0^2*(1+nu)^2*((B0+(142/451)*B1)*nu^3+((323/41)*B0+(1490/451)*B1)*nu^2+(11*B0+(3874/451)*B1)*nu-(1847/41)*B0-(8034/451)*B1)*a+(128/105)*A0^4*(nu^4+18*nu^3+132*nu^2+494*nu+939))/(t^2*a^2*(1+nu)^4)-(1/6)*q*a^2*A0-(-(1/4)/a^2-(1/4)*(5+nu)/(a^2*(1+nu)))*A0*q*a^4-(1/2)*(5+nu)*A0*q*a^2/(1+nu) end proc;

proc (A0, B0, B1) options operator, arrow; (32/3)*(nu+7)*A0^2*Pi*DC/(a^2*(1+nu))+3*DC*Pi*((1+nu)^4*(B0^2+(13/42)*B1^2+(4/5)*B0*B1)*a^2+(328/315)*A0^2*(1+nu)^2*((B0+(142/451)*B1)*nu^3+((323/41)*B0+(1490/451)*B1)*nu^2+(11*B0+(3874/451)*B1)*nu-(1847/41)*B0-(8034/451)*B1)*a+(128/105)*A0^4*(nu^4+18*nu^3+132*nu^2+494*nu+939))/(t^2*a^2*(1+nu)^4)-(1/6)*q*a^2*A0-(-(1/4)/a^2-(1/4)*(5+nu)/(a^2*(1+nu)))*A0*q*a^4-(1/2)*(5+nu)*A0*q*a^2/(1+nu) end proc

(1)

NULL

``

eqA0 := proc (A0, B0, B1) options operator, arrow; diff(SED2(A0, B0, B1), A0) end proc:

eqB0 := proc (A0, B0, B1) options operator, arrow; diff(SED2(A0, B0, B1), B0) end proc:

eqB1 := proc (A0, B0, B1) options operator, arrow; diff(SED2(A0, B0, B1), B1) end proc:

NULL

``

type(SED2, polynom);

true

(2)

type(eqA0, polynom);

true

(3)

type(eqB0, polynom);

true

(4)

type(eqB1, polynom);

true

(5)

NULL

``

with(Groebner):

with(PolynomialIdeals):

NULL

NULL

WL := PolynomialIdeal({eqA0(A0, B0, B1), eqB0(A0, B0, B1), eqB1(A0, B0, B1)})

Error, (in PolynomialIdeals:-PolynomialIdeal) generators must be polynomials with respect to, {A0, B0, B1, DC, a, nu, q, t}

 

NULL

type(WL, PolynomialIdeals:-PolynomialIdeal);

false

(6)

``

NULL

GB := Basis(WL, lexdeg([B0, B1], [A0]))

Error, (in Groebner:-Basis) the first argument must be a list or set of polynomials or a PolynomialIdeal

 

NULL

``

GB[1];

GB[1]

(7)

GB[2];

GB[2]

(8)

GB[3];

GB[3]

(9)

``

``

A00 := solve(GB[1], A0):

A00 := simplify(remove(has, [A00], I)):

A0 := A00[1]

Error, invalid subscript selector

 

B10 := solve(GB[2], B1):

B10 := simplify(remove(has, [B10], I)):

B1 := B10[1]

Error, invalid subscript selector

 

B00 := solve(GB[3], B0):

B00 := simplify(remove(has, [B00], I)):

B0 := B00[1]

Error, invalid subscript selector

 

NULL

``


 

Download Groebner_Basis_Work.mw

 

Hello,

i have a vector-valued function mapping from R^n  -> R^m
I  compute its Jacobian Matrix as well as the Hessian Matrix of each output with regard to the inputs, which works so far.
Now I would like to use the CodeGeneration package to generate optimized C Code to compute these matrices numerically. This is, where i encounter a Problem:

I would like to optimize Code for all matrixes at once, because they contain common subexpressions. However CodeGeneration::C tells me it is unable to optimize the given input and generates unoptimized code.


I appended an exemplary file to illustrate the problem: Jacobian_Hessian_codeGeneration_tryout.mw

short version:

C(Jac, optimize = tryhard, resultname = JacobianMatrix);
C(H1, optimize = tryhard, resultname = Hessian1); 
C(H2, optimize = tryhard, resultname = Hessian2); 
C(H3, optimize = tryhard, resultname = Hessian3)

works, but is suboptimal.

C([JacobianMatrix = Jac, Hessian1 = H1, Hessian2 = H2, Hessian3 = H3], optimize)

fails to optimize and

C([Jac, H1, H2, H3], optimize)

fails completely.

(With Jac beeing a m by n matrix and H1-3 beeing n by n matrices)

If anyone can tell me what I'm missing here I'd really appreciate the help.

Dear friend,

please suggest a way for manipulation of derivative of a function symbolically. Assume

Typesetting[Suppress]([f(x)]);
Ex1 :=expand(diff(f(x+y)+x*f(x-y), x)^2)+expand(diff(f(x-y)-y*f(x+y), x)^2);

Result is as needed:

Ex1 := (D(f))(x+y)^2+2*(D(f))(x+y)*f(x-y)+2*(D(f))(x+y)*x*(D(f))(x-y)+f(x-y)^2+2*f(x-y)*x*(D(f))(x-y)+x^2*(D(f))(x-y)^2+(D(f))(x-y)^2-2*(D(f))(x-y)*y*(D(f))(x+y)+y^2*(D(f))(x+y)^2

But later I cannot use D(f) as a function. Expressions

subs((D(f)) = (t -> 1-t), Ex1);
subs(diff(f(x),x) = (t -> 1-t), Ex1);

do not handle it as a function.

Hello.

I am asked to find all the candidate points to absolute maximum or minimum in a domain delimited by several lines or curves.

Let me show you an example:

I am having trouble trying to find the candidate points on the boundary of the domain with LagrangeMultipliers.

How should I express the line or curve equations so that I can use them as constraints of LagrangeMultipliers? Should I use another method?

Thanks a lot.

I want to solve the system of differential equations
sys :=
  diff(x(t,s),t) = y(t,s),
  diff(y(t,s),t) + x(t,s) = 0;

subject to the initial condition
ic := x(0,s) = a(s),
      y(0,s) = b(s);

where a(s) and b(s) are given.

This looks like a system of PDEs but actually it is a system
of ODEs because there are no derivatives with respect to s.
It is easy to obtain the solution by hand:

x(t,s) = b(s)*sin(t) + a(s)*cos(t)
y(t,s) = b(s)*cos(t) - a(s)*sin(t)

I don't know how to get this in Maple, either through dsolve()
or pdsolve().

Actually both dsolve({sys}) and pdsolve({sys}) do return
the correct general solution, however dsolve({sys, ic})
or pdsolve({sys, ic}) produce no output.  Is there a trick
to make the latter work?

 

hey is there a easy way to make maple solve an equation with similar different variables,

for eksample 

defining the different variables

x_0:=1       x_1:=4           x_2:=10

setting up and equation

solve x * 5

recieving answers for all defined x variables

= [5,20,50]

 

 

 The font plot option has no color parameter. 

Dear all,

I use the following statment (without numerical values)

if        IT<20     then        IT:=IT+1            

 if    ZUM<(0.1)^(8);    IT=20;         else;    

for i from 1 to 10   do                               YU[i]:=U[i];                  od;    

for i from 2 to 9 do                           DU1:=YU[i+1]- YU[i-1];        od:      

end if;    

ZUM:=U[1]-YU[1];  

end if;  

the following error occur

where is the problem.

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