I am trying to check if the inputs are a pair of row or column matrices. How should I do that? I have tried type but no success.

Download 2024-08-18_Test_Matrix_Dimension.mw

Why doesn't evalf work on the data structures below?
 

Download evalf.mw

Suppose we have the following simple Matrix

T := <1,2;3,4>;

How do we replace an entry with another expression?

I know that for a list L := [1,2,3] we can do, for example subsop(2=500,L) to replace the entry at index 2.

This creates a new list since lists are immutable.

As far as I can tell, a Matrix is mutable.

However, I wish to change an entry in a Matrix without mutating it.

My actual use case is the following.

I use LinearAlgebra:-Eigenvectors to obtain a Matrix of eigenvectors. Some of the entries are huge expressions with many variables. I would like to sub in placeholders where these huge expressions are so I can visualize the Matrix better, but without modifying the original Matrix.

Dear all, in the example below I create a matrix(3x2) and each element contains a vector. How can I avoid the double brackets of the matrix elements or eliminate the double brackets?

Thanks for help

Hi

 I know that (G, A)=Basis(F,output=extended) computes reduced Groebner basis for polynomial ideal F, while  A is a list of lists.  If A is converted to a matrix, we get G=FA. Is there a command to compute matrix B such that F=GB?

Thank you. 

For the legend in the image below I would have expected a black image and not a white

Hi everyone ...

How can I define the below Matrix with for command: (A[n] is n*n and n=1...i)

Tnx...

Should not  print("my matrix is ",A) at least print "my matrix is " even if A is not correctly filled/setup?

Notice that nothing shows on screen when using print (but lprint does)

Is this expected? If it makes any difference, I am using worksheet and this is my display options

Download why_print_empty_june_7_2024.mw

Let M a matrix of zeros and ones for instance.

N := 10^5:  # This is the order of magnitude I have to consider (10^4 may be enough if L is "small")
L := 5:     # L is between 3 and 8 in practice (see context at the end of this post)
M := LinearAlgebra:-RandomMatrix(N, L, generator=0..1):

Let C a set of colums of M and |C| the number of elements of C.
Let P a list of length |C| of  zeros and ones.

I want to count al the rows in M such that 

`and`( seq( M[n, C[k]] = P[k], k = 1.. |C| ) )

For instance

pattern := n -> `if`(evalb(`and`(seq(S[n, C[k]]=P[k], k=1..3))), 1, 0):
t0 := time():
add(pattern(n), n=1..N);
time()-t0
                             12351
                             0.431  # seconds

This code appears to be quite slow when one consider that I have to run it for all the possible choices of C and P (the contect is detailed below).

Do you have any some ideas to improve the efficiency (in terms of computational time) of this counting operation?
Thanks in advance

The context:
Let A = {1, 2, .., L} and P(A) the power set of A.
I set Q(A) = P(A) \ ( { } union A}.
Let C and C'  two disjoint subsets of Q(A).
Example

# With L=3

Q(A) = { {1},  {2},  {3},  {1, 2},  {1, 3},  {2, 3} }

# if A chose C = 
C = {2}

# Then C' is member of 
C' in { {1}, {3}, {1, 3}

For any couple (C, C')  I want to do this

1. Let |C| (|C'|) cardinal of C (resp C').
    
2. Let us consider that members of C (resp C') "point to" the corresponding columns of M.
   for instance C = {2, 3} refers to columns 2 and 3 of M.
   As C and C' are ordered iI will write them indistinctely as lists (for instance C = [2, 3] in example above) when necessary.
    
3. To a given |C| (|C'|) one may associate 2^|C| (resp 2^|C'|) sequences of 0 and 1.
   For instance,  to C = {2, 3} are associated sequences [0, 0], [0, 1], [1, 0], [1, 1].
   Let s(C) (s(C')) the list, or set, of 0-1 sequences associated to C (resp C')..
    
4. For any couple (C, C') and any of the 2^|C|+|C'| combinations (p, p') where p belongs to s(C) and p' belongs to s(C') I want to count the number of occurrences defined by: 

   seq( M[n, C[k]] = p[k], k=1..|C|) and seq( M[n, C'[k]] = p'[k], k=1..|C'|) 

   For instance, if C={2} and C={1, 3} I want to count the number M rows M such that 

   p = [0], p'=[1, 0]
   M[n, 2]=0 and M[n, 1]=1 and M[n, 3]=0;
   
   p = [1], p'=[1, 1] 
   M[n, 2]=1 and M[n, 1]=1 and M[n, 3]=1
   
   ... and so on

The computational time may ne quite large because of the number of possible couples (C, C') when L is large ( there exists  Stirling2(L+1, 3) such couples: already 90 couples for L=5  ... and 28501 for L=10).

I learnt that MapleFlow (MF) was a product similar (and better) than MathCad (MC). I have a old copy of MC, v.11 (with Maple symbolic engine) and I compared it with MF from my engineering dep. 

Can one kindly explain why Sum of a simple Matrix does not work, if the index is placed as exponent? Here what I did:

SI_MODEL.mw
I have tried the following code to simulate the following SI Model. But when I run it, it gives me several mistakes and most importantly does not calculate the Jacobian Matrix and the eigenvalues. 

Any help would be deeply appreciated

Download SI_MODEL.mw

Dear all,

the BlockCopy command is a miracle for me that I don't understand. Is there an easier command or an easy to understand documentation?

Thanks

Dear all, I'm new with maple. How can I extend an existing matrix?

XX := Matrix(2, 4, [[1, 1, 1, 1], [2, 2, 2, 2]])

extend(XX,1,0,0) # doesn't work

Thanks for help

How to show that any Pythagorean triplet can be obtained from <3,4,5> ? Thank you.
Can we simplify this program?

#Génération Géométrique et Algébrique des triplets Pythagoriciens
restart;
with(geometry);
with(LinearAlgebra);
_EnvHorizomtalName = 'x';
_EnvVerticalName = 'y';

with(plottools);
P := point([0, 0], color = black, symbol = cross, symbolsize = 25);
Oo := point([1/2, 1/2], color = black, symbol = cross, symbolsize = 25);
A := point([1, 1/2], color = black, symbol = cross, symbolsize = 25);
with(plots);
c1 := circle([1/2, 1/2], 1/2, color = blue);
NULL;
PA := line([0, 0], [1, 1/2], color = red);
eqC := (x - 1/2)^2 + (y - 1/2)^2 = 1/4;
eqPA := y = 1/2*x;
sol := solve({eqC, eqPA}, {x, y});

t1 := textplot([0, 0, 'typeset'("P"), font = [Times, Bold, 14]], 'align' = 'above');
t2 := textplot([1, 1/2, 'typeset'("A"), font = [Times, Bold, 14]], 'align' = 'right');
t3 := textplot([1/5, 1/10, 'typeset'("A'"), font = [Times, Bold, 14]], 'align' = 'above');
A1 := point([1 - 1/5, 1/10], color = black, symbol = cross, symbolsize = 25);
diff(A, x) := point([1/5, 1/10], color = black, symbol = cross, symbolsize = 25);
t4 := textplot([1 - 1/5, 1/10, 'typeset'("A1"), font = [Times, Bold, 14]], 'align' = 'right');
A2 := point([1 - 1/5, 1 - 1/10], color = black, symbol = cross, symbolsize = 25);
t5 := textplot([1 - 1/5, 1 - 1/10, 'typeset'("A2"), font = [Times, Bold, 14]], 'align' = 'right');
A3 := point([1/5, 1 - 1/10], color = black, symbol = cross, symbolsize = 25);
t6 := textplot([1/5, 1 - 1/10, 'typeset'("A3"), font = [Times, Bold, 14]], 'align' = 'right');

poly := Matrix([[1/5, 1/10], [1 - 1/5, 1/10], [1 - 1/5, 1 - 1/10], [1/5, 1 - 1/10]], datatype = float);
pol := polygonplot(poly, color = blue, transparency = 0.95);

display(c1, P, Oo, A, PA, seq(A || i, i = 1 .. 3), seq(t || i, i = 1 .. 6), pol, scaling = constrained, axes = none, size = [600, 600]);

R1 := Transpose(<<1, -2, 2> | <2, -1, 2> | <2, -2, 3>>);
R2 := Transpose(<<1, 2, 2> | <2, 1, 2> | <2, 2, 3>>);
R3 := Transpose(<<-1, 2, 2> | <-2, 1, 2> | <-2, 2, 3>>);
V := <3, 4, 5>;
MatrixVectorMultiply(R1, V);
MatrixVectorMultiply(R2, V);
MatrixVectorMultiply(R3, V);
t1 := <2225, 3648, 4273>;
t2 := MatrixVectorMultiply(1/R1, t1);
t3 := MatrixVectorMultiply(1/R3, t2);
t4 := MatrixVectorMultiply(1/R2, t3);
t5 := MatrixVectorMultiply(1/R1, t4);
t6 := MatrixVectorMultiply(1/R3, t5);
MatrixVectorMultiply(MatrixMatrixMultiply(MatrixMatrixMultiply(MatrixMatrixMultiply(MatrixMatrixMultiply(R1, R3), R2), R1), R3), V);
% - t1;
NULL;
 

ras5_v1.mw 

How can I  change eq13 to eq14 without using op command manually?

Thank you for your help in advance,