Unanswered Questions

This page lists MaplePrimes questions that have not yet received an answer

Dear all 
I need the sign of eigenvalue of the given marrix.
Note that it is not essay to compute the eigenvalues but we can use  ROUTH Hurwitz criterion that give the sign of eigenvalues without computing them


Thank you 

How can I draw Steiner trees of hypercubes in graph theory? 

With the following steps

S1: Open Help pressing F1

S2: enter `if in the search field

S3: click a topic in the result list

S4: search within the topic with find/replace (Crtl f) the term `if 

I get plenty of results where I cannot find the search term in the help topic. Why is that?

Is help ignoring the left single quotes ` ?

I don't think so: I get usefull results for `` and `i, which in the later case also lists the topic "ifelse" that contains `if in the textbody.

So, why does advanced searching with the exact phrase "`if" not list the "ifelse" topic?

Realted question:

Why does the search term "(* " not list the relevant help topic help(comment)?

Somehow related in the context of getting more specific results:



Can anyone help me with the following technique?



Are there any restrictions regarding path and filename length in Maple?

I am experiencing problems working with a file on a server, path and file length is 207 characters.

Maple 2022.2

> restart
> expr = x^4-10*x^2+1
> plot(expr)

produces an error message:
com.maplesoft.maplets.ComponentAccessException: not a valid plot structure

plot(expr, x) works Ok.

Tom Dean

How I can solve a PDE on two regions with matching conditions at the common boundary?  


Can MapleSim simulate a situation where a cable passes through a hole in an object, where the cable is constrained by the hole and the object also experiences forces from the cable because of the hole?


What would be the procedure to find the eigenvalues for a coupled harmonic oscillators characterized by eigenvalue E1 and E2? Are they treated as parameters in the numerical solution of the system of ode?

thanks in advance 

How to plot this equation



A := Matrix([[1, -1, 1, -1], [1, 1, -1, -1], [-1, 1, 1, -1], [1, 1, 1, 1]]);
B := Matrix([[1], [0], [1], [0]])

As a part of my learning curve, I am trying to play with extending Maple's BernsteinBasis, which has only a limited support right now (BernsteinBasis - Maple Help (maplesoft.com)).

My goal is to implement basis operation on polynomials in Bernstein basis, so that derivatives, integrals and products of polynomials in  BernsteinBasis would be again expressed in BernsteinBasis.

While it looks like it is relatively easy to extend diff procedure, by using `diff/BernsteinBasis`, I didn't find anything similar for the int. Is there something like `int/BernsteinBasis`?

The problem is that when I am trying to implement my own int procedure in a module that  would extend standard int, it seems I need to manually implement logic for (at very least) linearity, so that int(p(x) + q(x), x) would decay into int(p(x), x) + int(q(x), x ) (I probably don't need more complex rewriting rules). So before trying this approach, is there any easy way such as with diff?





# General formula
diff(BernsteinBasis(k, n, a, b, x), x);

n*BernsteinBasis(k-1, n-1, a, b, x)/(b-a)-n*BernsteinBasis(k, n-1, a, b, x)/(b-a)


# In expressions
diff(2*x*BernsteinBasis(1, 2, 0, 1, x) + BernsteinBasis(2, 2, 0, 1, x), x);

2*BernsteinBasis(1, 2, 0, 1, x)+2*x*(2*BernsteinBasis(0, 1, 0, 1, x)-2*BernsteinBasis(1, 1, 0, 1, x))+2*BernsteinBasis(1, 1, 0, 1, x)


# Convertion to MatrixPolynomialObject works
p := diff(BernsteinBasis(1, 2, 0, 1, x) + BernsteinBasis(2, 2, 0, 1, x), x);
P := convert(p, MatrixPolynomialObject, x);

p := 2*BernsteinBasis(0, 1, 0, 1, x)


P := Record(Value = Default[value], Variable = x, Degree = 1, Coefficient = coe, Dimension = [1, 1], Basis = BernsteinBasis, BasisParameters = [1, 0, 1], IsMonic = mon, OutputOptions = [shape = [], storage = rectangular, order = Fortran_order, fill = 0, attributes = []])


Matrix(%id = 36893490288797933188)


# Now, integrataion



# Still works
int(x^2, x);



# Not implemented but will be added later...
int(BernsteinBasis(1, 2, 0, 1, x), x);

"Will be implemented here..."


int(BernsteinBasis(1, 2, 0, 1, x), x)


# This is the problem: how to implement basis properties such as linearity?
int(2 * BernsteinBasis(1, 2, 0, 1, x), x);

int(2*BernsteinBasis(1, 2, 0, 1, x), x)




BernsteinPolynomials := module()
    description "Basic operations in Bernstein basis";
	option package;
	global BernsteinBasis, `diff/BernsteinBasis`;
	export int;

	BernsteinBasis := proc(k, n, a, b, x)
		description "Bernstein basis polynomial";
		if k::numeric then
			if k < 0 then 
				return 0;
			end if
		end if;
		if n::numeric then
			if n < 0 then 
				return 0; 
			end if;
			if k::numeric then
				if k > n then
					return 0;
				end if;
			end if;
		end if;
	end proc;

	`diff/BernsteinBasis` := proc()
		description "Derivative of the Bernstein basis polynomial in the Bernstein basis";
		if _npassed = 6 then
			if _passed[-1] = _passed[-2] then
				_passed[2] * BernsteinBasis(_passed[1] - 1, _passed[2] - 1, _passed[3], _passed[4], _passed[5]) / (_passed[4] - _passed[3]) -
				_passed[2] * BernsteinBasis(_passed[1], _passed[2] - 1, _passed[3], _passed[4], _passed[5]) / (_passed[4] - _passed[3]);
			end if;
		end if;
	end proc;
	int := proc()
		description "Integral of the Bernstein basis polynomial in the Bernstein basis";
		if type(_passed[1], 'specfunc'(anything, BernsteinBasis)) then
		    print("Will be implemented here...");
		end if;
	end proc;

end module;

Download bernstein.mw

In my code, without knowing what the expression is, other than it has RootOf, the code called allvalues and got internal error 

Error, (in SolveTools:-Basis) invalid input: igcd received 5/7, which is not valid for its 2nd argument

Is this to be expected depending on the input, or is this some internal problem I need to report?



Error, (in SolveTools:-Basis) invalid input: igcd received 5/7, which is not valid for its 2nd argument

Maple 2023.2 on windows 10

ps.  Reported to Maplesoft


V := m^4*(1-(varphi/mu)^p);



V1 := diff(V, varphi);



V2 := diff(V1, varphi);



f := Zeta * (varphi^2);



f1 := diff(f, varphi);



f2 := diff(f1, varphi);



R:= simplify(((V/3-f1*V1/(3*V))/((1-kappa^2*f)/(12*kappa^2)+f1/V)));



N:=evalf(int((3*V1*kappa^2*((2*V*V1)/3 - f1^2*V1*R/(3*V) - f1*V1^2/(3*V))/(V*(-f*kappa^2 + 1)*(-R*f1 - 2*V1))),varphi=varphi__hc..varphi__end)assuming varphi__hc > 0, varphi__hc > varphi__end);

-1.*(int(-3.*(varphi/mu)^p*p*kappa^2*(-.6666666667*m^8*(1.-1.*(varphi/mu)^p)*(varphi/mu)^p*p/varphi+5.333333333*Zeta^2*varphi*m^4*(varphi/mu)^p*p*kappa^2*(-3.*(varphi/mu)^(2.*p)*m^4+(varphi/mu)^(3.*p)*m^4+3.*(varphi/mu)^p*m^4-1.*m^4-2.*Zeta*(varphi/mu)^p*p+2.*Zeta*(varphi/mu)^(2.*p)*p)/((m^4*(Zeta*kappa^2*varphi^2-1.)*(varphi/mu)^p+(-1.*Zeta*kappa^2*varphi^2+1.)*m^4+24.*Zeta*varphi*kappa^2)*(-1.+(varphi/mu)^p)*(1.-1.*(varphi/mu)^p))-.6666666667*Zeta*m^4*((varphi/mu)^p)^2*p^2/(varphi*(1.-1.*(varphi/mu)^p)))/(varphi*(1.-1.*(varphi/mu)^p)*(-1.*Zeta*kappa^2*varphi^2+1.)*(-8.*kappa^2*m^4*(-3.*(varphi/mu)^(2.*p)*m^4+(varphi/mu)^(3.*p)*m^4+3.*(varphi/mu)^p*m^4-1.*m^4-2.*Zeta*(varphi/mu)^p*p+2.*Zeta*(varphi/mu)^(2.*p)*p)*Zeta*varphi/((m^4*(Zeta*kappa^2*varphi^2-1.)*(varphi/mu)^p+(-1.*Zeta*kappa^2*varphi^2+1.)*m^4+24.*Zeta*varphi*kappa^2)*(-1.+(varphi/mu)^p))+2.*m^4*(varphi/mu)^p*p/varphi)), varphi = varphi__end .. varphi__hc))


simplify(-1.*(int(-3.*(varphi/mu)^p*p*kappa^2*(-.6666666667*m^8*(1.-1.*(varphi/mu)^p)*(varphi/mu)^p*p/varphi+5.333333333*Zeta^2*varphi*m^4*(varphi/mu)^p*p*kappa^2*(-3.*(varphi/mu)^(2.*p)*m^4+(varphi/mu)^(3.*p)*m^4+3.*(varphi/mu)^p*m^4-1.*m^4-2.*Zeta*(varphi/mu)^p*p+2.*Zeta*(varphi/mu)^(2.*p)*p)/((m^4*(Zeta*kappa^2*varphi^2-1.)*(varphi/mu)^p+(-1.*Zeta*kappa^2*varphi^2+1.)*m^4+24.*Zeta*varphi*kappa^2)*(-1.+(varphi/mu)^p)*(1.-1.*(varphi/mu)^p))-.6666666667*Zeta*m^4*((varphi/mu)^p)^2*p^2/(varphi*(1.-1.*(varphi/mu)^p)))/(varphi*(1.-1.*(varphi/mu)^p)*(-1.*Zeta*kappa^2*varphi^2+1.)*(-8.*kappa^2*m^4*(-3.*(varphi/mu)^(2.*p)*m^4+(varphi/mu)^(3.*p)*m^4+3.*(varphi/mu)^p*m^4-1.*m^4-2.*Zeta*(varphi/mu)^p*p+2.*Zeta*(varphi/mu)^(2.*p)*p)*Zeta*varphi/((m^4*(Zeta*kappa^2*varphi^2-1.)*(varphi/mu)^p+(-1.*Zeta*kappa^2*varphi^2+1.)*m^4+24.*Zeta*varphi*kappa^2)*(-1.+(varphi/mu)^p))+2.*m^4*(varphi/mu)^p*p/varphi)), varphi = varphi__end .. varphi__hc)))

Error, (in content/content) invalid arguments



Download ex.mw

In an old question, @mbras asked for a "partial" `convert/elsymfun`. However, SymPy's sympy.polys.rings.PolyElement.symmetrize seems to provide more examples that cannot be handled by the program that appeared in that question.
For instance, 

>>> from sympy import var
>>> var('x:z,p:r')
(x, y, z, p, q, r)
>>> from sympy.polys.polyfuncs import symmetrize
>>> symmetrize(x**2-(y**2+2**z),[y,x],formal=True,symbols=[p+p,q*q])[0]
-2**z - 4*p**2 + 2*q**2
>>> symmetrize(x*x*y+y*y*z+z*z*x,[y,x,z],formal=True,symbols=[p,q,r])
(0, x**2*y + x*z**2 + y**2*z, [(p, x + y + z), (q, x*y + x*z + y*z), (r, x*y*z)])

Though I can , can't the built-in  be generalized to such expressions (in other words, write the polynomial part of input as a symmetric part and a remainder with (named, if need be) elementary symmetric polynomials)?

Besides, since any symmetric polynomial can also be expressed in terms of the complete symmetric polynomials, is there a similar  command in Maple?

The uploaded worksheet begins to uniformly tile the Poincare disk with pentagons using hyperbolic reflection .

Although relatively easy to create the central pentagon and the first adjacent pentagon, it becomes increasingly difficult to determine which lines to reflect to create the remaining pentagons in the first tier adjacent to the central pentagon and more so to create the pentagons of the second tier adjacent to those in the first tier and so on.

Is there a better technique for accomplishing this?

In particular can Mobius tranformations be employed to do this? If so, please replay with or point to a working example of this for me to follow.


Sorry, I forgot that respondents to this question must establich their own link to the DirectSearch package.

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