Maple 2018 Questions and Posts

These are Posts and Questions associated with the product, Maple 2018


I am a student of economics writing my thesis. I have an inverse demand function defined:


where α,β are scalars, i{1,2,}, j {1,2,3}, h/=i and k/=j.

I wanted to know how do i input this kind of function in the program and how do i calculate the function of q[i,j] (the inverse)

Thank you!

Good day.

My question involves a set of prescribed points in the Cartesian plane. The x and y ranges are fixed. The points are connected by (imaginary) horizontal and vertical lines to produce a fixed number of blocks / grids.

An example is given in the attached file.

Now, I wish to reduce the intervals between these points by a scaling factor, n, so as to generate more blocks within the plane that is constrained by the x and y-ranges.

In doing so, I need to find the (x,y)-location of these points in the plane and it would also be great if I could obtain a simple plot.  

As I have several scaling factors to investigate, I was hoping someone may be able to guide me towards a simple routine to help obtain these solutions.

Once again, thanks for taking the time to read this.


ModularSquareRoot can't handle a really big n because of the factorization problem. But I would like to know if there is any other function than can use as parameters the factorization of n.

I already have an algorithm that does that for n=pq with p, q primers, and could generalize it, but I was wondering whether there was a built-in function that does that.

I want to find coodinates of the point A, B, C, D and X of a problem 6 at IMO 2018

I tried 


 A := [0, 0]; 
B := [5, 0]; 
C := [3, 4]; 
DD := [a, 2]; 
solve([Distance(B, A)*Distance(C, DD) = Distance(B, C)*Distance(A, DD)], [a]);

How can I get coordinate X lies inside life request?


I'm trying to implement Kernal PCA, I've got a large kernal matrix for which I have checked the elements are of floating point type, however when I try to run the Determinant operation on the matrix all of the coefficients say float(undefined).

In the same worksheet, there I have implemented the standard PCA routine, for which the determinant operation works fine. You can see this operation functioning corrrectly in it's testing section.

If anyone has any idea why this might be occuring I'd be really grateful for some advice.



Can anyone explain the reasoning that went into the programming decisions that led Maple to give these results?

is(-infinity, complex); #expected: false
is(-infinity-I*infinity, complex); #expected: false
exp(-infinity - I) = limit(exp(x-I), x= -infinity); #expected: 0=0
                         infinity*I = 0
is(exp(x)<>0) assuming x::complex; #expected: true
is(exp(x)<>0) assuming x::real; #expected: true
coulditbe(exp(x)=0) assuming x::complex; #expected: false



I need to solve or reduce (similar to the command Reduce in Mathematica) sets of nonlinear equations.  One such example is shown below:

eqns := {-1+theta[3, 6] = 0, 1-theta[3, 6] = 0, alpha+rho-theta[2, 2]+theta[3, 3] = 0, -theta[3, 6]^2+1 = 0, theta[2, 2]*theta[3, 6]-alpha = 0, theta[2, 2]*theta[3, 6]^2-alpha = 0, -2*theta[3, 3]*theta[3, 6]-2*rho = 0, theta[1, 2]*theta[2, 1]*theta[3, 6]^2+1 = 0, -alpha^2+rho^2+theta[2, 2]^2-theta[3, 3]^2 = 0, -theta[2, 2]^2*theta[3, 6]+2*theta[2, 2]*theta[3, 3]*theta[3, 6]+alpha^2+2*alpha*rho = 0, -theta[1, 3]*theta[2, 2]^2*theta[3, 0]+theta[1, 3]*theta[2, 2]*theta[3, 0]*theta[3, 3]-alpha^2*beta-alpha*beta*rho = 0, -theta[1, 2]*theta[2, 1]*theta[2, 2]*theta[3, 6]+2*theta[1, 2]*theta[2, 1]*theta[3, 3]*theta[3, 6]-alpha-2*rho = 0, -theta[1, 2]*theta[2, 1]*theta[2, 2]*theta[3, 3]+theta[1, 2]*theta[2, 1]*theta[3, 3]^2+theta[1, 3]*theta[2, 2]*theta[3, 0]*theta[3, 6]+alpha*beta+alpha*rho+rho^2 = 0, -alpha^2*rho-alpha*rho^2+theta[1, 2]*theta[2, 1]*theta[2, 2]-theta[1, 2]*theta[2, 1]*theta[3, 3]+theta[1, 3]*theta[3, 0]*theta[3, 6]-theta[2, 2]^2*theta[3, 3]+theta[2, 2]*theta[3, 3]^2+alpha+beta+rho = 0}

 and the indeterminates are:

fc := {theta[1, 2], theta[1, 3], theta[2, 1], theta[2, 2], theta[3, 0], theta[3, 3], theta[3, 6]}

Since I do know the solution, I issued the following command to check for typos.


and the outcome is zero for all equations.

When I try the command solve as follows:


the result is

{theta[1, 2] = theta[1, 2], theta[1, 3] = theta[1, 3], theta[2, 1] = -1/theta[1, 2], theta[2, 2] = alpha, theta[3, 0] = -beta/theta[1, 3], theta[3, 3] = -rho, theta[3, 6] = 1}

that should be right but it is not what I am expecting.  

How can maple return the solution needed?


Some sets of solutions do not have a solution as the one above.  Some indeterminates cannot be found, is there a way maple returns the solution of the ones that can be solved and reduced the set of equations into two parts, solved ones e non solved ones?  I can provide an example if needed.


Many thanks.




I have written a module M which contains some procedures P1, P2, ...
This module contains the statement option package.

In a separate worksheet I type the command L := with(M) to load this module and stack in the list L the names of all the procedures M contains.
I would like now to use showstat to display the content of all these procedures..

I thus typed:
for p in L do  showstat(p) end do;

I got an error saying that showstat expects a name as argument.
In the command above p is not a name but a symbol.

Is there a possibility to "showstat" all the procedures M contains ?

Motivation:I'd like to count the number of command lines in module M (showstat removes the lines of comments) ... maybe there exist an other way than using showstat ?

Thanks in advance


What is the derivative of the composed Bessel function BesselJ(alpha, sqrt(u^2+v^2-2*uv*cos(phi))) with respect to u?

BesselJ(alpha, sqrt(u^2+v^2-2*uv*cos(phi))) is a composed function of the form f(g(u)) with f=BesselJ(u) and g=sqrt(u^2+v^2-2*uv*cos(phi)).

Best regards

In Maple outputs, long fraction bars occur quite frequently. A common example is of the type A(x)/x, where A(x) may be a complicated expression made up by standard functions, derivatives, integrals etc. in terms of x and some constants, denoted by names. Maple displays such an expression in terms of a long solidus and x as the denominator. This looks rather weird. A preferable display would be of the form x^-1 A(x) or A(x) multiplied by 1/x. I have unsuccessfully tried to achieve this but failed. Can this be done?



For given positive integers 𝑎 and 𝑏, there exist positive integers 𝑟 and 𝑠 (the so-called Bezout’s coefficients) so that 𝑔𝑐𝑑(𝑎,𝑏)=𝑟 𝑎+𝑠 𝑏. Using Euclidean algorithm, one can find these coefficients by using a forward and a backward substitution. Surf the web, let say this one, or use any Discreet Mathematics textbook to find out how these coefficient can be computed using Euclidean algorithm. Now, write a code in Maple to compute Bezout’s coefficients for the numbers 18344 and 65208. 

Application developed using Maple and MapleSim. You can observe the vector analysis using Maple and the simulation using MapleSim. Also included a video of the result. It is a simple structure. A pole fastened by two cables and a force applied to the top. The results are to calculate tensions one and two. Consider the mass of each rope. In spanish.

Lenin Araujo Castillo

Ambassador of Maple


I have two input variables namely torque and speed. I need to find the input current for the given induction motor. I have written down the required equations in math mode. So, when I give a specific input i.e. torque is 30 Nm and speed is 2000 rpm i get the input current. Now I need to put in a for loop for the math mode i.e. i need output current dataset for 10% increment in torque from zero to full torque and 10% increment in speed from 0 to full load speed. I cant seem to find any resource to do that in maple. Could anyone help me out?

  Dear sir, I request to provide the inequalities or constraints for the uploaded Linear Programing Problem to plot the graph and solve by simplex method.

; restart; with(plots); _local(O); P := b*x*cos(phi)+a*y*sin(phi)-a . b = 0; P := b x cos(phi) + a y sin(phi) - a . b = 0 Q := a*x*sin(phi)-b*y*cos(phi)-c^2*sin(phi)*cos(phi) = 0; 2 Q := a x sin(phi) - b y cos(phi) - c sin(phi) cos(phi) = 0 M := op(solve([P, Q], [x, y])); M := [subs(M, x), subs(M, y)]; X := `&-+`(P/sqrt(b^2*cos(phi)^2+a^2*sin(phi)^2)); Y := `&-+`(Q/sqrt(b^2*cos(phi)^2+a^2*sin(phi)^2)); #L'équation générale des coniques ayant pour axes MN et MT est, par rapport aux nouveaux axes de coordonnées X^2/A+Y^2/B-1 = (0*et)*par*rapport*aux*anciens; P^2/(A*(b^2*cos(phi)^2+a^2*sin(phi)^2))+Q^2/(B*(b^2*cos(phi)^2+a^2*sin(phi)^2))-1 = 0; 2 /b x cos(phi) + a y sin(phi) - a . b \ &-+|----------------------------------- = 0| | (1/2) | |/ 2 2 2 2\ | \\a sin(phi) + cos(phi) b / / --------------------------------------------- A 2 / 2 \ |a x sin(phi) - b y cos(phi) - c sin(phi) cos(phi) | &-+|-------------------------------------------------- = 0| | (1/2) | | / 2 2 2 2\ | \ \a sin(phi) + cos(phi) b / / + ------------------------------------------------------------ B - 1 = 0 #1.-Ecrivons que la conique (1) est tangente en O à Oy : il faut pour cela annuler le coefficient de y et le terme indépendant. #Nous obtenons 2 équations en A et B, d'où nous tirons : A=a² et B=c²cos(phi)² a := 10; b := 7; c := sqrt(a^2-b^2); phi := 4*Pi*(1/5); Ell := implicitplot(x^2/a^2+y^2/b^2-1 = 0, x = -11 .. 11, y = -8 .. 8, color = grey); O := [0, 0]; M := [a*cos(phi), b*sin(phi)]; vec := plot([O, M], color = black, thickness = 1); P := implicitplot(P, x = -20 .. 20, y = -20 .. 20, color = aquamarine); Q := implicitplot(Q, x = -20 .. 20, y = -20 .. 20); F1 := [(a+b)*cos(phi), (a+b)*sin(phi)]; F2 := [2*M[1]-F1[1], 2*M[2]-F1[2]]; F1F2 := plot([F1, F2], color = green, thickness = 3); ELL := implicitplot((b*x*cos(phi)+a*y*sin(phi)-a . b)^2/(a^2*(b^2*cos(phi)^2+a^2*sin(phi)^2))+(a*x*sin(phi)-b*y*cos(phi)-c^2*sin(phi)*cos(phi))^2/(c^2*cos(phi)^2*(b^2*cos(phi)^2+a^2*sin(phi)^2))-1 = 0, x = -20 .. 20, y = -20 .. 20, color = blue, thickness = 3); Hyp := implicitplot((b*x*cos(phi)+a*y*sin(phi)-a . b)^2/(b^2*(b^2*cos(phi)^2+a^2*sin(phi)^2))+(a*x*sin(phi)-b*y*cos(phi)-c^2*sin(phi)*cos(phi))^2/(-c^2*sin(phi)^2*(b^2*cos(phi)^2+a^2*sin(phi)^2))-1 = 0, x = -20 .. 20, y = -20 .. 20, color = black); dF1 := plottools[disk](F1, .3, color = red); dF2 := plottools[disk](F2, .3, color = red); cir1 := implicitplot(x^2+y^2 = (a+b)^2, x = -20 .. 20, y = -18 .. 18, color = pink); cir2 := implicitplot(x^2+y^2 = (a-b)^2, x = -10 .. 10, y = -4 .. 4, color = coral); asym1 := implicitplot((b*x*cos(phi)+a*y*sin(phi)-a . b)/b+(a*x*sin(phi)-b*y*cos(phi)-c^2*sin(phi)*cos(phi))/(c*sin(phi)) = 0, x = -20 .. 20, y = -18 .. 18, color = black, linestyle = DOT); asym2 := implicitplot((b*x*cos(phi)+a*y*sin(phi)-a . b)/b-(a*x*sin(phi)-b*y*cos(phi)-c^2*sin(phi)*cos(phi))/(c*sin(phi)) = 0, x = -20 .. 20, y = -18 .. 18, color = black, linestyle = DOT); tp := textplot([[M[1], M[2]+.8, "M"], [F1[1]-.8, F1[2], "F1"], [F2[1]+.8, F2[2]+.3, "F2"], [5, 15, "axe P"], [8, -10, "axe Q"]]); display([Ell, vec, P, Q, F1F2, cir1, cir2, ELL, Hyp, dF1, dF2, asym1, asym2, tp], scaling = constrained, axes = normal, axis = [gridlines = [1, color = blue]], xtickmarks = 0, ytickmarks = 0, view = [-20 .. 20, -20 .. 20], size = [500, 500]); #Eléments fixes : Ell, cir1, cir2, O #Parties mobiles : ELL, Hyp, P,Q, M,F1, F2, # FIGURE MOBILE n := 100; dt := 2*Pi/n; Phi := 0; P := b*x*cos(phi+dt)+a*y*sin(phi+dt)-a . b = 0; Q := a*x*sin(phi+dt)-b*y*cos(phi+dt)-c^2*sin(phi+dt)*cos(phi+dt) = 0; M := [cos(phi+dt)*(sin(phi+dt)^2*a*c^2+Typesetting[delayDotProduct](a . b, b, true))/(a^2*sin(phi+dt)^2+cos(phi+dt)^2*b^2), sin(phi+dt)*(-cos(phi+dt)^2*b*c^2+Typesetting[delayDotProduct](a . b, a, true))/(a^2*sin(phi+dt)^2+cos(phi+dt)^2*b^2)]; ELL := (b*x*cos(phi+dt)+a*y*sin(phi+dt)-a . b)^2/(a^2*(a^2*sin(phi+dt)^2+cos(phi+dt)^2*b^2))+(a*x*sin(phi+dt)-b*y*cos(phi+dt)-c^2*sin(phi+dt)*cos(phi+dt))^2/(c^2*cos(phi+dt)^2*(cos(phi+dt)^2*b^2+a^2))-1 = 0; NULL; display([Ell, cir1, cir2], scaling = constrained);
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