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Is there a way to directly code a complex conjugat...

Asked by: Earl 985
October 23 2023
1  4

Is there a way to directly code a complex conjugate such as z with overbar without using the verbose conjugate(z)?

Comment compléter ce tableau et ainsi que les autr...

Asked by: Diadjé Sacko 0
orthonormal bijection
October 23 2023
0  1

Soit h : [1 ; + ∞[ℝ

1.a°) Complète le tableau ci-dessus et trace la courbe ( Ch) de h dans un repére orthonormé ( O,I,j )

 𝑥 1 2 3 4 5

h(𝑥 )

b°) Montre que h est une bijection

c°) Détermine la bijection réciproque h-¹ de h

d°) Calcule hoh-¹ et h-¹oh ( 𝑥 )

2.) Trace la courbe ( Ch-¹) dans le même repére que ( Ch)

Different answer of same expression...

Asked by: AHSAN 160
rootfinding numeric
October 23 2023
0  3

I have solved a simple expression with different built-in methods.... I received differents answers ...What is the exact way to get the same answers by all methods

help_roots.mw.

simple code to generate random magic squares...

Asked by: jalal 435
integer arithmetic randomtools
October 23 2023
0  3

Hi,

I am looking for a simple code to generate random magic squares (with the sum of integers) of dimensions 4x4 or 5x5.

Thank you

find an index in a list...

Asked by: 2cUniverse 115
list index
October 23 2023
2  11

I have a very simple question:

How do I find the index of an list element.

For example to find 96 in the following list which is the 25th element.

R := [1, 2, 4, 8, 16, 32, 64, 31, 62, 27, 54, 11, 22, 44, 88, 79, 61, 25, 50, 3, 6, 12, 24, 48, 96, 95, 93, 89, 81, 65, 33, 66, 35, 70, 43, 86, 75, 53, 9, 18, 36, 72, 47, 94, 91, 85, 73, 49];
max(R);
                               96

So how to find 25 ?

How can I add a parameter type that is Matrix or l...

Asked by: zenterix 405
parameters procedure type
October 22 2023
1  3

I have the following procedure

export exportCsvMatrix := proc(m:: Matrix, fileName: string)

  ExportMatrix(fileName, m, target=csv):

end:

However, I would like to be able to pass a list of matrices as well.

How can I add a parameter type that is Matrix or list of Matrix?

solution of differential equations...

Asked by: emersondiaz 60
ode syntax dsolve
October 22 2023
2  5

Good day to all the members who read this question.
I ask for your help to find the right way to solve this two differential equations (is attached the file). Used the common code "dsolve" but is not working on this problem. Doesn't matter if the solution is numeric or algebraic.
I will thaks a lot your kind help.
Best regards to all of you

DIFFERENTIAL_EQUATION.mw

restart

with(PDEtools)

First Part

The differential equation to solve:

(Delta*LinearAlgebra:-Transpose(D[1/2])*D__0-I*`μ__e`*D__0/(lambda+I*`μ__e`*r)-2*(`μ__e`^2*r^2+lambda^2))*R(r)

Definitions

D__n = `∂__r`+I*omega(a^2+r^2)/Delta+I*a*m/Delta+2*n*(r-M)/Delta

LinearAlgebra:-Transpose(D[n]) = `∂__r`-I*omega(a^2+r^2)/Delta-I*a*m/Delta+2*n*(r-M)/Delta

a := 1; M := 1; omega := 1; m := 1; `μ__e` := 1; lambda := 1

Delta := -2*M*r+a^2+r^2

I divided the differential equation in 3 parts (A, B, C).

A := (-I*omega(a^2+r^2)-I*a*m+r-M)*(diff(R(r), r)+I*omega(a^2+r^2)*R(r)/Delta+I*a*m*R(r)/Delta)+Delta*(diff(R(r), r, r))+I*omega(a^2+r^2)*(diff(R(r), r))+I*a*m*(diff(R(r), r))

B := -I*`μ__e`*(diff(R(r), r)+I*omega(a^2+r^2)*R(r)/Delta+I*a*m*R(r)/Delta)/(lambda+I*`μ__e`*r)

C := -(2*(`μ__e`^2*r^2+lambda^2))*R(r)

DE := A+B+C

E := dsolve(DE)

R(r) = DESol({diff(diff(_Y(r), r), r)-(1-r+I/(1+I*r))*(diff(_Y(r), r))/(r^2-2*r+1)-(-(2*I)*((-1-2*I)+r)/(r^2-2*r+1)-2/((1+I*r)*(r^2-2*r+1))+2*r^2+2)*_Y(r)/(r^2-2*r+1)}, {_Y(r)})

 (1)

dsolve({DE, DE(0) = 1}, numeric, range = 0 .. 20)

Error, (in dsolve/numeric/type_check) insufficient initial/boundary value information for procedure defined problem

  

Second Part

The differential equation to solve:

[`#msub(mi("L",fontweight = "bold"),mfrac(mn("1",fontweight = "bold"),mn("2",fontweight = "bold"),linethickness = "1"))`*LinearAlgebra:-Transpose(L[1/2])+a*`μ__e`*sin(theta)*LinearAlgebra:-Transpose(L[1/2])/(lambda+a*`μ__e`*cos(theta))+2*(lambda^2+a^2*`μ__e`*cos(theta)^2)]*S(theta) = 0

Definitions:

L__n = a*omega*`sinθ`+m*`cosecθ`+n*`cotθ`+`∂__θ`

LinearAlgebra:-Transpose(L[n]) = -a*omega*`sinθ`-m*`cosecθ`+n*`cotθ`+`∂__θ`

Also I divided the differential equation in 3 parts (A, B, C).

F := (omega*a*sin(theta)+m/sin(theta)+1/(2*tan(theta)))(diff(S(theta), theta)-omega*a*sin(theta)*S(theta)-m*S(theta)/sin(theta)+S(theta)/(2*tan(theta)))+diff(S(theta), theta, theta)-omega*a*sin(theta)*(diff(S(theta), theta))-m*(diff(S(theta), theta))/sin(theta)+(diff(S(theta), theta))/(2*tan(theta))

G := a*`μ__e`*sin(theta)*(diff(S(theta), theta)-omega*a*sin(theta)*S(theta)-m*S(theta)/sin(theta)+S(theta)/(2*tan(theta)))/(lambda+a*`μ__e`*cos(theta))

H := (2*(lambda^2+a^2*`μ__e`*cos(theta)^2))*S(theta)

DF := F+G+H

dsolve(DF)

dsolve({DF, DF(0) = 1}, numeric, range = 0 .. 20)

Error, (in dsolve/numeric/type_check) insufficient initial/boundary value information for procedure defined problem

  

NULL

Download DIFFERENTIAL_EQUATION.mw

Where is documentation for `<,>`?...

Asked by: zenterix 405
matrix vector operator
October 22 2023
1  7

I have a very difficult time finding things in the documentation.

I would like to see documentation for `<,>` and `<|>`, as in `<,>`(1,2,3,4).

If I write ?<|> in Maple I get

If I do ?<,> I get

However, there is no mention of the usage of the backticks.

Finally, if I do ?`<,>` I get

No mention of the use of `<,>`. I only know about this from a previous reply to one of my questions and now I have forgotten the details so I am trying to look it up but it's hard to find.

Why does this worksheet calculates for ever?...

Asked by: FDS 190
procedure
October 22 2023
0  18

Dear Power Users, I tried to make a model in Maple but after several hours of struggling I need some help. Can someone tell me what I did wrong or explain to me what is the meaning of the maplemint comment on procedure (optimalisatie)? Thank you in advance.

DiLeoCasper.mw 

Determining Elements of the Span of a Set of Vecto...

Asked by: DJJerome1976 540
linear-algebra
October 22 2023
1  4

Suppose I have a set of vectors, say S = {x+4, 3x-7}, a specific vector f = -5x + 10 and I would like to determine if f is an element of Span(S). By hand it's a rather simple process, check the consistency of the corresponding linear system. Is there a way to automate this in Maple? That is, define a vector space (using any finite vectors: polynomials, matrices, etc.) with some basis and check to see if a given element belongs to that space? Moreover, if it does belong, could we get the linear combination of the elements of the basis that produces the desired vector?

How do I program Maple to display consective numbe...

Asked by: Carolyn Davis 15
seq printf
October 21 2023
0  2

For the t output I need to show 1, 1.2, 1.4....2, my attempt is highlighted in green below

Can anyone assist please?

> 

#Clear memory and load packages.
restart;
with(plots):
with(Statistics):

#Define vectors and variables.
actual:=<2,3.5136,5.8016,9.1136,13.7376,20>:
t:=<1,1.2,1.4,1.6,1.8,2>:
n:=6:
RMSE:=0:

#Perform a simple linear regression on the data.
P:=LinearFit([1,x],t,actual,x);

#Display the model errors.
printf("t    Actual P  Model P  Error\n");
for i from 1 to n do
   model:=subs(x=t[i],P):
   err:=actual[i]-model:
   RMSE:=RMSE+err^2:
   printf("%2d %7.4f% 10.4f% 9.4f\n",(i+(1/5)),actual[i],model,err);
end do:

#Display the root mean square error.
RMSE:=sqrt(RMSE/n);

#Plot the points and the model.
p1:=plot(t,actual,style=point,view=[0..7,8..26]):
p2:=plot(P,view=[0..7,8..26]):
display(p1,p2);

-HFloat(17.540266666666668)+HFloat(17.712)*x

  

t    Actual P  Model P  Error

  

Error, (in fprintf) integer expected for integer format

  

HFloat(0.7463867411787324)

  

 
> 

NULL

Download Asst_4_Question_1f.mw

Help with searching elements on list....

Asked by: Jamie128 165
list select
October 21 2023
0  3

I have a lists within lists.  I needed to search for a specific element in the sub-list and need to extract each such sublist that has an element.

I am only familiar with the search tool. Could someone suggest a simple way to do this.

For example, I have the following.

s := [{f0(t, r) = 0, n(t) = n(t)}, {f0(t, r) = 0, n(t) = 0}, {f0(t, r) = 0, n(t) = 0}]

I need to extract the sublist that has n(t)=n(t) so only the first element of the list s.

Error, (in convert/ratpoly) invalid subscript sele...

Asked by: Essam 20
numapprox pade
October 21 2023
2  2

 

How to create orthonormal triads with "Physics:-Ve...

Asked by: olivier107 10
basis orthonormal physics
October 21 2023
2  0

Hello,
I recently discovered the "Physics" package wich provides tools for manipulating abstract vectors (non-component).
In the "Physics:-Vectors", an orthonormal basis (i,j,k) is available and my main concern is how to generate arbitrary other 3D orthonormal bases to be able to calculate results in "vectorial form" without manipulating vectors' components.

To better explain my needs I have setup a kind of minimal example in the attached file where some questions are asked.

Thanks in advance for any feedback.

orthonormal-triads.mw

NULL

restart

with(Physics)

with(Physics[Vectors])

Creation of 2 rotation matrices

dir1 := `<,>`(0, 0, 1)

dir2 := `<,>`(0, 1, 0)

seq(assign(cat(R, i), Student:-LinearAlgebra:-RotationMatrix(theta[i], eval(cat(dir, i)))), i = 1 .. 2)

print(R1, R2)

Matrix(%id = 36893490614987576012), Matrix(%id = 36893490614987577572)

 (1)

whattype(R1)

Creation of  orthogonal unit "Physics:-Vectors" from previous matrices

x1_ := _i*R1[1, 1]+_j*R1[2, 1]+_k*R1[3, 1]``

y1_ := _i*R1[1, 2]+_j*R1[2, 2]+_k*R1[3, 2]

z1_ := _i*R1[1, 3]+_j*R1[2, 3]+_k*R1[3, 3]NULL

NULL

x2_ := _i*R2[1, 1]+_j*R2[2, 1]+_k*R2[3, 1]NULL

y2_ := _i*R2[1, 2]+_j*R2[2, 2]+_k*R2[3, 2]

z2_ := _i*R2[1, 3]+_j*R2[2, 3]+_k*R2[3, 3]

Q1: Is there a more elegant way of creating "Physics:-Vectors" from matrices ?

Now, suppose that we want to compute `&x`(`#mover(mi("x1"),mo("&rarr;"))`, `#mover(mi("y2"),mo("&rarr;"))`) : since `#mover(mi("y2"),mo("&rarr;"))` = `#mover(mi("j"),mo("&and;"))` we have `&x`(`#mover(mi("x1"),mo("&rarr;"))`, `#mover(mi("y2"),mo("&rarr;"))`) = sin(`#mover(mi("x1"),mo("&rarr;"))`, `#mover(mi("j"),mo("&and;"))`)*`#mover(mi("z1"),mo("&rarr;"))` and sin(`#mover(mi("x1"),mo("&rarr;"))`, `#mover(mi("j"),mo("&and;"))`)*`#mover(mi("z1"),mo("&rarr;"))` = sin((1/2)*Pi-`&theta;__1`)*`#mover(mi("z1"),mo("&rarr;"))` and sin((1/2)*Pi-`&theta;__1`)*`#mover(mi("z1"),mo("&rarr;"))` = cos(theta[1])*`#mover(mi("z1"),mo("&rarr;"))`

The cross product operator  `&x`(x1_, y2_) yields

cos(theta[1])*_k

 (2)

(which is a correct answer) instead of cos(theta[1])*`#mover(mi("z1"),mo("&rarr;"))` because vector `#mover(mi("z1"),mo("&rarr;"))` has is not known as a unit basis vector.

Similarly, `&x`(z1_, x1_) yields -sin(theta[1])*`#mover(mi("i"),mo("&and;"))`+cos(theta[1])*`#mover(mi("j"),mo("&and;"))` instead of  `#mover(mi("y1"),mo("&rarr;"))` as it would be the case when computing `&x`(_k, _i) ?

Q2: Is there a way to declare new triads of "Physics:-Vectors" with properties similar to the provided triad _i, _j, _k ?

Q3: Is the code defining the canonical basis i, _j, _kavailable for inspection and inspiration to setup orthonormal triads ?

Q4: Is it possible to get a (column) matrix of the vector components ? The function Physics:-Vectors:-Component(y1_, n) can only get 1 component at a time and only in the canonical basis i, _j, _k.

NULL

restart

with(Physics)

with(Physics[Vectors])NULL

After a proper definition of 2 new vector bases `#mover(mi("x1"),mo("&rarr;"))`, `#mover(mi("y1"),mo("&rarr;"))`, `#mover(mi("z1"),mo("&rarr;"))` and `#mover(mi("x2"),mo("&rarr;"))`, `#mover(mi("y2"),mo("&rarr;"))`, `#mover(mi("z2"),mo("&rarr;"))`, the position vector OM_ := l__1*x1_+l__2*x2_NULLNULL

l__1*x1_+l__2*x2_

 (3)

NULL

projected on `#mover(mi("x2"),mo("&rarr;"))` would yield directly Typesetting[delayDotProduct](l__1, `#mover(mi("x2"),mo("&rarr;"))`.`#mover(mi("x1"),mo("&rarr;"))`, true)+l__2 instead of expand(OM_.x2_)

l__1*Physics:-Vectors:-`.`(x1_, x2_)+l__2*Physics:-Vectors:-Norm(x2_)^2

 (4)

because of the unit vectors.

Download orthonormal-triads.mw

Bug in simplify piecewise...

Asked by: Rouben Rostamian 8506
simplify piecewise physics
October 20 2023
1  2

This used to work in Maple 2022.  Something is broken in 2023. 

 

> 

restart;
> 

kernelopts(version);

`Maple 2023.1, X86 64 LINUX, Jul 07 2023, Build ID 1723669`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1561 and is the same as the version installed in this computer, created 2023, October 20, 22:58 hours Pacific Time.`

> 

U := Int(exp(-1/4*t - 1/4*x)*piecewise(x < -2, 1, x < -1, -x - 1, 0), x = -t .. 0);

Int(exp(-(1/4)*t-(1/4)*x)*piecewise(x < -2, 1, x < -1, -x-1, 0), x = -t .. 0)

> 

Uval := simplify(value(U));

Uval := `simplify/piecewise/unfactor`(4*piecewise(t < 1, 0, t < 2, t-5+4*exp(`&ndash;`((1/4)*t)+1/4), 2 <= t, 1+4*exp(`&ndash;`((1/4)*t)+1/4)-4*exp(`&ndash;`((1/4)*t)+1/2)))

> 

eval(Uval, {x=5, t=6});

`simplify/piecewise/unfactor`(4+16*exp(-5/4)-16*exp(-1))

> 

 
 

Download simplify-piecewise-bug.mw

 

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