Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

Apparently functions working on lines do not work on segments.

I can't see any logical explanation why that should be so.

Please consider expanding functionality in future Maple versions.

segprojection.mw

Hei

Vet noen om Windows 11 støtter Maple 2020? Eller støttes det bare av Windows 10.

If I understand right, the form  is equivalent to  (where the optional index variable is omitted), which produces a sequence of n occurrences of y. But how to explain the following output (of p1())? 

restart;

kernelopts(version)

`Maple 2023.0, X86 64 WINDOWS, Mar 06 2023, Build ID 1689885`

(1)

p0 := proc()
    local a := 1, b := 2;
    seq('assign(('a', 'b') = (a + 1, 2*b))', 1 .. 3);
    print(a, b)
end:

p1 := proc()
    local a := 1, b := 2;
    seq('assign(('a', 'b') = (a + 1, 2*b))', 3);
    print(a, b)
end:

p2 := proc()
    local a := 1, b := 2;
    'assign(('a', 'b') = (a + 1, 2*b))' $ 3;
    print(a, b)
end:

p3 := proc()
    local a := 1, b := 2;
    to 3 do
        assign(('a', 'b') = (a + 1, 2*b))
    od;
    print(a, b)
end:

p0()

p1()

p2()

p3()

4, 16

 

5, 32

 

4, 16

 

4, 16

(2)


Download singular_behaviour_of_`seq`.mw

Main code: 

p1 := proc()
    local a := 1, b := 2;
    seq('assign(('a', 'b') = (a + 1, 2*b))', 3);
    print(a, b)
end:
p1():

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

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)


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 been working in the building construction industry for more than 30 years, and one of the big things which has been coming up is parametric design.

While every major big software company has come up with its own package (Bentley with Generative Components, Autodesk with Dynamo), there is one software now that has won over all them - Grasshopper 3D.

Nowadays all major software products are trying to write bidirectional links to Grasshopper. Inhouse we do have Tekla on the BIM side and FEM-Design on the calculation side where both are capable to link to Grasshopper.

Grasshopper itself is also capable of running Python code, though in a reduced kind of way.

I would very much like to see Maple to have a Grasshopper link, probably achievable through Python.

At least Maplesoft should have a quick look at it, to see if this is possible or not.

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)

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