MaplePrimes Questions

Hi everyone,

I am using Maple for quite a while, now I would like to do something new.

I am a teacher at a german highschool and I would like to generate class tests with maple. Say for an example, I need 30 tests,  where the first task is calculating the first derivative of a function. This function should be different for every person, for example f(x)=a*x^3+3x^2, where the value of a is different in every test (probably random).

So what I need is a way to generate nice looking sheets in Maple (including page breaks, titles and so on). Is there a way to generate such a thing in maple or do I have to export to TeX and adjust there quite a bit?

Maybe someone has done a similar thing. Actually I am looking for something like serial letters in Maple.

Any idea, how I could do such a thing?

Thanx for your help,

Axel

GraphTheory:-GraphEqual says that G1 and G2 are equal, but GraphTheory:-AllPairsDistance gives different results instead: 

restart;

with(GraphTheory)

M := `<|>`(`<,>`(0, 0, 0), `<,>`(1, 0, 0), `<,>`(1, 1, 0))

G__1 := Graph(convert(-M, Matrix, datatype = integer[8]))

G__2 := Graph(convert(-M, Matrix, datatype = integer))

GraphEqual(G__1, G__2)

true

(1)

AllPairsDistance(G__1)

AllPairsDistance(G__2)

Matrix(%id = 36893491227039185244)

 

Error, (in GraphTheory:-AllPairsDistanceExt) negative cycle detected

 

 

Download allpairs.mw

So, which one is incorrect? Any reasons?

restart

with(PolynomialIdeals):

``

``

randomzero := proc (ListVar) local A, G, i, lm, B, f, g; option trace; A := ListVar; G := NULL; for i to nops(A) do f := A[i]^(i+1)+randpoly([op(`minus`({op(A)}, {A[i]}))], terms = 1, coeffs = rand(-4 .. -1), degree = i); G := G, f end do; print(IsZeroDimensional(`<,>`(G))); RETURN([G]) end proc:

randomzero([x, y])

{--> enter randomzero, args = [x, y]

 

[x, y]

 

"G:="

 

x^2-y-4

 

x^2-y-4

 

y^3-3*x

 

x^2-y-4, y^3-3*x

 

true

 

<-- exit randomzero (now at top level) = [x^2-y-4, y^3-3*x]}

 

[x^2-y-4, y^3-3*x]

(1)

``

Download bug.mw

Hi

I think there is a bug in the "randpoly" command. please see the attached file line 7 of my procedure "randomzero". Why x^2-y-4 is created while terms=1 is considered and the outputs must contain binomial?

Some work, while others don't work. 
 

restart;

`assuming`([is(1/(sqrt(n*(n+1))*(sqrt(n)+sqrt(n+1))) = 1/sqrt(n)-1/sqrt(n+1))], [n::posint])

true

(1)

sum(1/sqrt(n)-1/sqrt(n+1), n = 1 .. infinity)

1

(2)

sum(1/(sqrt(n*(n+1))*(sqrt(n)+sqrt(n+1))), n = 1 .. infinity)

sum(1/((n*(n+1))^(1/2)*(n^(1/2)+(n+1)^(1/2))), n = 1 .. infinity)

(3)

`assuming`([sum(binomial(3*n, n)*x^n/(2*n+1), n = 0 .. infinity)], [abs(x) <= 4/27])

(2/3)*3^(1/2)*sin((1/3)*arcsin((3/2)*3^(1/2)*x^(1/2)))/x^(1/2)

(4)

`assuming`([eval(binomial(3*n, n)*x^n/(2*n+1), n = 0)+sum(binomial(3*n, n)*x^n/(2*n+1), n = 1 .. infinity, parametric)], [abs(x) <= 4/27])

1+x*hypergeom([1, 4/3, 5/3], [2, 5/2], (27/4)*x)

(5)

simplify(convert(1+x*hypergeom([1, 4/3, 5/3], [2, 5/2], (27/4)*x)-hypergeom([1/3, 2/3], [3/2], (27/4)*x), elementary), symbolic)

(1/3)*(3*x^(1/2)+3*x^(3/2)*hypergeom([1, 4/3, 5/3], [2, 5/2], (27/4)*x)-2*3^(1/2)*sin((1/3)*arcsin((3/2)*3^(1/2)*x^(1/2))))/x^(1/2)

(6)

plot((1/3)*(3*x^(1/2)+3*x^(3/2)*hypergeom([1, 4/3, 5/3], [2, 5/2], (27/4)*x)-2*3^(1/2)*sin((1/3)*arcsin((3/2)*3^(1/2)*x^(1/2))))/x^(1/2), x = -4/27 .. 4/27)

 

verify(0, (1/3)*(3*x^(1/2)+3*x^(3/2)*hypergeom([1, 4/3, 5/3], [2, 5/2], (27/4)*x)-2*3^(1/2)*sin((1/3)*arcsin((3/2)*3^(1/2)*x^(1/2))))/x^(1/2), 'equal')

FAIL

(7)

NULL


 

Download unable_to_sum.mw

How to explain this behavior?
I have read the help page, but I can not get the point.

Please, is there anyway I can solve this problem with a nice output? The solution I got is complicated. Please, helper is need

f := exp(-beta*x)*x^(5-alpha)

int(f, x)

beta^(alpha-6)*(-x^(-alpha)*beta^(-alpha)*(alpha^4-14*alpha^3+71*alpha^2-154*alpha+120)*(alpha-6)*(beta*x)^((1/2)*alpha)*exp(-(1/2)*beta*x)*WhittakerM(-(1/2)*alpha, -(1/2)*alpha+1/2, beta*x)/(-alpha+6)+x^(-alpha)*beta^(-alpha)*(beta^4*x^4-alpha*beta^3*x^3+alpha^2*beta^2*x^2+5*beta^3*x^3-alpha^3*beta*x-9*alpha*beta^2*x^2+alpha^4+12*alpha^2*beta*x+20*beta^2*x^2-14*alpha^3-47*alpha*beta*x+71*alpha^2+60*beta*x-154*alpha+120)*(alpha-6)*(beta*x)^((1/2)*alpha)*exp(-(1/2)*beta*x)*WhittakerM(-(1/2)*alpha+1, -(1/2)*alpha+1/2, beta*x)/(-alpha+6))

How to write a program that obtains the value of the function by giving different values
Like the example below:

 

I rephrased my previous question in a more synthetic form
(there was probably a lot in it that I thought was important for understanding the problem, but I realized afterwards that it only added confusion).

The true question is yellow-highlighted in the code below

restart

# The result below seems natural: we were taught in school that exp 
# being a bijective function we can get rid of it in the equality to
# solve and write simply x=Pi.

x = solve(exp(x)=exp(Pi), x)

x = Pi

(1)

# But the solution method solve uses is not that natural (and I
# don't really understand it).
# infolevel[solve] := 10:
# x = solve(exp(x)=exp(Pi), x);

# Replacing now exp by some undefined function f produces a
# kind of "no-solution" answer: this seems quite normal because
# not knowing the properties of f one cannot simply get rid of it.

infolevel[solve] := 0:
x = solve(f(x)=f(Pi), x)

x = RootOf(f(_Z)-f(Pi))

(2)

# Finally replace f by a bijective function with no analytic expression.

s = solve(erf(x)=erf(Pi), x) assuming x::real

s = RootOf(erf(_Z)-erf(Pi))

(3)

# It would have seem reasonable for Maple to answer x=Pi, or
# at least it is what I would have done given the properties
# of the erf function.
#
# How can I "force" Maple to "simplify" it's RootOf result to get
# x=Pi?


Download solve_erf.mw

For those interested in the motivations of this quastion, see here Where_does_the_question_come_from.mw

The original question is here Original_question.pdf

How is the expansion of trigonometric functions in Maple like the following function?

Hi!

I'm trying to recreate a Mathcad sheet in Maple Flow

I could use some help figuring out how elementwise operations are made:

From mathcad, what i want to reproduce:

What I have in Maple Flow so far:

1) How do i get MF to output numerical valus in sigma_t ?

2) How would H look in MF? 

Thank you!

Ragards
Siggi

 

that in Kip Thorne's book Maple is mentioned through out ?

Kip Thorne and Roger Blandford : "Modern Classical Physics: Optics, Fluids, Plasmas, Elasticity, Relativity, and Statistical Physics"

also, courtesy of Caltech in Chapter 24

restart;
alias(u = u(x, z, t), f = f(x, z, t));
                              u, f
u := (f+sqrt(R))*exp(I*R*x);
                    /     (1/2)\           
                    \f + R     / exp(I R x)
pde1 := I*(diff(u, z))+diff(u, x, x)+diff(u, t, t)+u*abs(u)*abs(u)-(u*abs(u)*abs(u))*abs(u)*abs(u);
    / d   \              / d  / d   \\           
  I |--- f| exp(I R x) + |--- |--- f|| exp(I R x)
    \ dz  /              \ dx \ dx  //           

           / d   \                /     (1/2)\  2           
     + 2 I |--- f| R exp(I R x) - \f + R     / R  exp(I R x)
           \ dx  /                                          

       / d  / d   \\           
     + |--- |--- f|| exp(I R x)
       \ dt \ dt  //           

                                                            2
       /     (1/2)\                           2 |     (1/2)| 
     + \f + R     / exp(I R x) (exp(-Im(R x)))  |f + R     | 

                                                            4
       /     (1/2)\                           4 |     (1/2)| 
     - \f + R     / exp(I R x) (exp(-Im(R x)))  |f + R     | 

simplify(%);
         / d   \              / d  / d   \\           
       I |--- f| exp(I R x) + |--- |--- f|| exp(I R x)
         \ dz  /              \ dx \ dx  //           

                / d   \                 2             
          + 2 I |--- f| R exp(I R x) - R  exp(I R x) f
                \ dx  /                               

             (5/2)              / d  / d   \\           
          - R      exp(I R x) + |--- |--- f|| exp(I R x)
                                \ dt \ dt  //           

                                               2  
                                   |     (1/2)|   
          + exp(I R x - 2 Im(R x)) |f + R     |  f

                                               2       
                                   |     (1/2)|   (1/2)
          + exp(I R x - 2 Im(R x)) |f + R     |  R     

                                               4  
                                   |     (1/2)|   
          - exp(I R x - 4 Im(R x)) |f + R     |  f

                                               4       
                                   |     (1/2)|   (1/2)
          - exp(I R x - 4 Im(R x)) |f + R     |  R     
collect(%, exp(I*R*x));
  /  (5/2)       / d   \      2       / d   \   / d  / d   \\
  |-R      + 2 I |--- f| R - R  f + I |--- f| + |--- |--- f||
  \              \ dx  /              \ dz  /   \ dx \ dx  //

       / d  / d   \\\           
     + |--- |--- f||| exp(I R x)
       \ dt \ dt  ///           

                                          2  
                              |     (1/2)|   
     + exp(I R x - 2 Im(R x)) |f + R     |  f

                                          2       
                              |     (1/2)|   (1/2)
     + exp(I R x - 2 Im(R x)) |f + R     |  R     

                                          4  
                              |     (1/2)|   
     - exp(I R x - 4 Im(R x)) |f + R     |  f

                                          4       
                              |     (1/2)|   (1/2)
     - exp(I R x - 4 Im(R x)) |f + R     |  R     
 

Hi Dears

I need some random zero-dimensional binomial ideals (20 ideals or more) with two, three, or four ... generators with 4 variables atmost. Then I want to regenerate each of them such that some of their generators are not binomial and the obtained ideals are equal to the first corresponding original binomial ideals. How can do I this automatically?

As a simple example let I be an ideal generated by {x-1, y-1, z-1} which is zero-dim. We can obtain J=<x-z, x+z-2, y+z-2> that is equal to I.

Thank you in advance.

Dear all

I have the following code that  compute a parameter labeled by A. 

I used some input vectors and my aim is to get A <1 

A_less_than_one.mw

I tried to change some values of input vectors but unfortunattely I can not have A<1 

Maybe I have a mistake in the code or something else 

Thank you for your help 

I have a very simple procedure that I wrote to get information for an inequality using data from two lists, upon which I can create a pointplot . Now I know people will see what I have done and probably cringe, and believe me I do as well. I know it is not efficient and there is probably a numerous number of ways to do it better but my procedural skills for Maple are lacking. 

From my file you will see what I am attempting to do,nonetheless I will mention it here. I have two lists X,W. for each value in I want to fine the value in W that yields F(X,L)<G(X,L) where F(X,L) is a complicated integral that I have to evalute numerically, I have tried using unapply as outline in https://www.mapleprimes.com/questions/229070-How-Can-I-Speed-Up-This-Numerical-Integral it however only made my problem worse. For small lists it seems to be reasonable but for larger precision it is not the useful. I have looked through the ?do help page and some other resources but to no avail. From what I have seen though I believe I should be using the until command in do but I can't figure it out with having two lists. 

Any help,tips or tricks will be greatly appreciated.

NumericScale.mw

When I try to enter units using the units palette Maple Flow 2023.1 will erase the numerical value entered. That never happened before in previous releases of Maple Flow. No problem if you enter the units yourself, the problem is when you use the units palette. What is going on? A couple of weeks ago I also posted a question about not beeing able to enter an equal sign when entering a math expression in a text region. Agai, this never happened before in previous releases of Maple Flow. What is happening? Am I doing something wrong?

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