MaplePrimes Questions

How can an equation containing a logarithmic function be converted into a polynomial?

In the metric search command in the differential gometry package, you can use the petrov type of the Plebanski Tensor as a selection criteria.

But if you had a form of a metric tensor, how do you go about finding the petrov type of the Plebanski Tensor?

Is there a way in the physics package to get my index to run from 0 to 3 instead of 1 to 4/0?

Hi,

I have a data structure/plotting question. How do I plot the 3 lambdas (singleaxis) and the 6 betas (dualaxis) for 12 calibrations (1000 runs each)? All the details are in the script 230523_different-calibrations.mw. Thank you!

For the beta plots and subplots, please follow the dualaxis example output format at the bottom of my script for each of the 12 calibrations.

For the lambda plots, I'd like to combine a few of them as follows (each plot with lambda_1 subplot, lambda_2 subplot, and lambda_3 subplot - note that the lambda plot example at the bottom of the script is dualaxis but I just need singleaxis):

PLOT 1 (singleaxis): lambda_1, _2, _3 for ncal2 and ncal3 (superimposed, 2 data series for each subplot)

PLOT 2 (singleaxis):  lambda_1, _2, _3 for ncal7 and ncal8 (superimposed, 2 data series for each subplot)

PLOT 3 (singleaxis):  lambda_1, _2, _3 for ncal4, ncal5, ncal6 (superimposed, 3 data series for each subplot)

PLOT 4 (singleaxis):  lambda_1, _2, _3 for ncal9, ncal10, ncal11 (superimposed, 3 data series for each subplot)

Hello,

I want to animate a ball rolling on the surface cos(abs(x)+abs(y)).  The ball mass m is 1kg, radius r is 0.1meters starts at (0.5,0.5,cos(abs(5)+abs(5))) meters using g=9.8. 

If we say the initial velocity of the ball is pushed in some random direction. 

How do I show the path of the ball and animate?

Thanks,

Arthur


there’s few redundant values. I just want the positive values. How it can be done?

restart

NULL

n := [80, 79, 83, 84, 83, 83, 81, 85, 86, 86, 83, 82, 83, 84, 81, 80, 83, 79, 82, 81, 85]

[80, 79, 83, 84, 83, 83, 81, 85, 86, 86, 83, 82, 83, 84, 81, 80, 83, 79, 82, 81, 85]

(1)

``

nops(n)

21

(2)

for i from 3 to 17 do f[i] := n[i-2]-3*n[i-1]+3*n[i]; i = i+1; f[i+1] := n[i-2]+4*n[i-1]-6*n[i]+n[i+1] end do

92

 

3 = 4

 

-18

 

82

 

4 = 5

 

-10

 

80

 

5 = 6

 

4

 

84

 

6 = 7

 

-1

 

77

 

7 = 8

 

14

 

95

 

8 = 9

 

-17

 

84

 

9 = 10

 

-9

 

85

 

10 = 11

 

-4

 

77

 

11 = 12

 

14

 

83

 

12 = 13

 

9

 

86

 

13 = 14

 

-3

 

85

 

14 = 15

 

-9

 

74

 

15 = 16

 

13

 

81

 

16 = 17

 

11

 

90

 

17 = 18

 

-18

(3)

``

NULL


 

Download fyp_2.mw

Hi,

I am exploring the Grading package in Maple, and I want to create a random question about limits. (Question 9). Any ideas for the correct code? Thank you

QUIZZTestMaple.mw

I learned about Dodgson calculation of the determinant only recently (https://en.m.wikipedia.org/wiki/Dodgson_condensation).
I am only interested in symbolic expressions of the determinant.
Furthermore, I compared several methods. Not surprisingly, the build in method is the fastest. But why is the seq method slower than the proc method for the Dodgson method? Is there anything I could do to program it more efficiently?
 

restart; with(LinearAlgebra)

with(combinat); with(GroupTheory)

DetDef := proc (A) local i, n, sigma; description "Jeremy Johnson. Downloaded from https://www.cs.drexel.edu/~jjohnson/2016-17/winter/cs300/lectures/determinant.mw"; n := RowDimension(A); add(PermParity(Perm(sigma))*mul(A[i, sigma[i]], i = 1 .. n), `in`(sigma, permute([`$`(1 .. n)]))) end proc

InnerMatrix := proc (M::Matrix) SubMatrix(M, 2 .. RowDimension(M)-1, 2 .. ColumnDimension(M)-1) end proc

MatrixDet := proc (M::Matrix) local C, n, i, j; n := RowDimension(M)-1; C := Matrix(n, n); seq(seq(assign('C[i, j]', Determinant(M([i, i+1], [j, j+1]))), j = 1 .. n), i = 1 .. n); return C end proc

Dodgson := proc(M::Matrix)
 MatrixDet(M);
InnerMatrix(M) ^~ (-1) *~ MatrixDet(MatrixDet(M));
do if 1 < RowDimension(%) then InnerMatrix(`%%`) ^~ (-1) *~ MatrixDet(%);
end if;
until RowDimension(%) = 1;
Trace(%):
end proc:

Dodgsonseq := proc (E::Matrix) local w, dim, Z; dim := RowDimension(E); Z[dim] := E; Z[dim-1] := MatrixDet(E); Z[dim-2] := `~`[`*`](`~`[`^`](InnerMatrix(E), -1), MatrixDet(MatrixDet(E))); seq(assign('Z[w-1]', `~`[`*`](`~`[`^`](InnerMatrix(Z[w+1]), -1), MatrixDet(Z[w]))), w = dim-1 .. 1, -1); Trace(Z[1]) end proc

LaPlace := proc (M::Matrix) local c; add((-1)^(c+1)*M[1, c]*Minor(M, 1, c), c = 1 .. ColumnDimension(M)) end proc

dim := 7; A := Matrix(dim, dim, shape = symmetric, symbol = a)

7

(1)

start_time := time(); st := time[real](); Det1 := abs(A); CPUtime_used_Build_in_Determinant := time()-start_time; REALtime_used_Build_in_Determinant := time[real]()-st; start_time := time(); st := time[real](); Det2 := DetDef(A); CPUtime_used_Jeremy_Johnson_Determinant := time()-start_time; REALtime_used_Jeremy_Johnson_Determinant := time[real]()-st; start_time := time(); st := time[real](); Det3 := Dodgsonseq(A); CPUtime_usedDodgsonseq := time()-start_time; REALCPUtime_usedDodgsonseq := time[real]()-st; start_time := time(); st := time[real](); Det4 := Dodgson(A); CPUtime_usedDodgson := time()-start_time; REALtime_usedDodgson := time[real]()-st; start_time := time(); st := time[real](); Det5 := LaPlace(A); CPUtime_usedLaPlace := time()-start_time; REALtime_usedLaPlace := time[real]()-st; simplify(Det1-Det2); simplify(Det1-Det3); simplify(Det1-Det4); simplify(Det1-Det5)
``

0.32e-1

 

0.34e-1

 

0.93e-1

 

.108

 

47.094

 

41.295

 

40.766

 

38.158

 

0.31e-1

 

0.50e-1

 

0

 

0

 

0

 

0

(2)

Download test_Determinants_symbolic.mw

I had purchached reseach licience Maple 2022 towards the end of 2022 only and Quantum Chemistry Toolbox I purchased in Feb 2022 only.

Now i find significant update in toolbox in just 3 months. Now guide me how should i address this issuse.

I had to take loan in india to buy the toolbox.

It is only 3 months.

Can you suggest me how solve the problem to get the update without spending again.

What is the way guide someone.

I calculate the limit

Let me know if there are any errors in my calculations?


 

restart

assume(a > 0)

limit(int(sin(x)/x, x = n .. n+a), n = infinity)

0

(1)

int(sin(x)/x, x = n .. n+a)

-Si(n)+Si(n+a)

(2)

plot3d(-Si(n)+Si(n+a), a = -5 .. 5, n = -5 .. 5)

 

limit(-Si(n)+Si(n+a), n = infinity)

0

(3)

limit(-Si(n), n = infinity)

-(1/2)*Pi

(4)

limit(Si(n+a), n = infinity)

(1/2)*Pi

(5)

NULL


Thank you in advance.

Download limit_int.mw

I have a polyhedron with A(1,1,0), B(-1,1,0), C(-1,-1,0), H(-1/2,0,1), K(1/2,-1/2,0). How can I calculate volume of polyhedron ABCHK?
 

How can a horizontal axis be curved in a plot? like this

plot(F*r*sin(theta) - m, theta = 0 .. Pi)

When I am setting up the coordinates in the physics package, I use the following command. And it sets it to (r,theta,phi,t).

Setup(dimension = 4, mathematicalnotation = true, coordinates = spherical)

Is there a way to change it to (t,r,theta,phi)?

It gets a bit more confusing when we are looking at rank 2 objects.

Hi, I am working on an activity about conic sections, but I have a small issue with the display of the ellipse and the circle. My outlines are not complete. Any ideas on how to identify my error? Thanks  SectionsConiquesTest.mw

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