I have a code that outputs a long string of mathematics after various string replacements which I save into a file in the format of a Python function. Here is the code (for a 1 x 1 matrix):

restart:
Size:=1:
## This is the matrix which is generated in a string format
mat1:="Matrix(1, 1, [[-1/2*(A^8*hh*m3+6*A^7*B*hh*m3-2*A^7*hh*m3*z3+16*A^6*B^2*hh*m3-14*A^6*B]])":
## Open up file
filename2:=fopen(cat("Matrix", Size, "x", Size,"HH.py"),WRITE,TEXT): 

## Format file
fprintf(filename2,"import numpy as np\ndef myfuncHH(A,B):\n    z3 = 2\n    m3 = float('inf')\n    Mat_size = %a", Size): 
fprintf(filename2,"\n    arr = np.array([%a",mat1): 
fprintf(filename2,"],dtype=np.float64)"): 
fprintf(filename2,"\n    shape = ( Mat_size, Mat_size )\n    HH=arr.reshape( shape )\n    return HH"):
fclose(filename2):

This generates almost the exact output that is required:

import numpy as np
def myfuncHH(A,B):
    z3 = 2
    m3 = float('inf')
    Mat_size = 1
    arr = np.array(["Matrix(1, 1, [[-1/2*(A^8*hh*m3+6*A^7*B*hh*m3-2*A^7*hh*m3*z3+16*A^6*B^2*hh*m3-14*A^6*B]])"],dtype=np.float64)
    shape = ( Mat_size, Mat_size )
    HH=arr.reshape( shape )
    return HH

The part I want to remove is the "Matrix(1, 1, [   "Maths in here"   ])"]

I can use stringtools to tidy up most of this, but I am having trouble getting rid of the quotes of the string itself. I have tried escaping them and that does nothing. Is there a simple way to do this or will a regex have to be made?

- Yeti

I wrote some procedures in an older version of Maple to sort through a matrix and find repeated elements, and then set the matrix elements equal to one another. As an example, consider the matrix:

Due to its symmetric nature the upper triangular matrix is just the same as the lower triangular. i.e. the elements are equal: (2,1)=(1,2), (3,1)=(1,3) etc...

I have attached a minimal working example Maple script, which processes an input matrix, finds repeats and sets the elements equal to one another (e.g. [1,2]=[2,1], literally printing this) and saves the output to a file using a specific format for processing by another program. The matrix in the file is numeric but the actual matrices contain a lot of algebraic terms and can get quite large. This is where my procedures struggle as they take a very, very long time to process larger algebraic matrices to group the repeats. Is there a more Maple friendly way of going about this problem rather than these "archaic" procedures?

Here is the script:

duplicates_matrix_.mw

Thank you in advance

-Yeti

I have a Maple code which generates a matrix, saves it to a .txt file and this is then read in to a C++ program. I have hit a snag with these matrices, in that they are generating absolutely enourmous .txt files. I need to get to a 5000*5000 matrix yet a 200*200 is generating a 100MB file.

The matrix elements contain a lot of algebraic terms which I would like to keep general as these are defined in the C++ code. They also contain hypergeometric functions which in the example below I have left unsimplified (although they are simplified before reaching C++). I have tried various operations/combinations to simplify, but the file sizes still come out very large.

From previous experience expanding the expressions and then simplifying allows Maple to "do more" with it, but it does not seem to work in this instance. I have tried map(options,expr), simplify(expr,options), combine(expr,options), convert (expr,options) etc... The script attached only contains a small example 10*10 matrix on its own without the code which generates it due to the size of the code. What is the best way to simplify these matrices to generate the smallest .txt file?

Large_Matrix.mw

Any help is appreciated.

-Yeti
 

I have a list of functions which looks like this:

RR:={F[l, m-2, n-1], F[l, m+2, n], F[l, m+2, n-1], F[l-1, m+1, n-2], ...}

I wish to remove the first and second arguments from the functions, so only leaving the third argument containing the n's. I then wish to group these remaining terms together to shorten the list. i.e.

RR:={F[n-1], F[n], F[n-2]}

I have used the 'subsop' command with 1 and 2 specified as NULL in a loop, but I was wondering if there is a better way to do it? I like to avoid loops where possible and use some inbuilt Maple magic to make it tidier and (usually) more efficient.

-Yeti

I have a list of coefficients each assigned a triple of indices. E.g. CF_{x,y,z}. These indicies are also able to take other values between +-2. E.g. CF_{x+2,y-1,z} or CF_{x,y-2,z+1} as examples. I have a working loop that cycles through the list of these coefficients and I am able to call a particular one by specifying the triple of indicies. This script has been attached:

triple_index_script.mw

I would like to modify this script to have more control over single indexes. As an example, say I want to add up all the coefficients which have z as a subscript (so not z+1,z-2 etc...) and I don't care what the x and y subscripts are; I want to be able to call that sum using the same notation in the script but with a single index. e.g. (using a new example function called RR_MapZ):

RR_MapZ[0]; ## This would return the sum of all coefficients that had z in their subscript

and this would return the sum of all the coefficients which have subscript Z. If I wanted to add up all the coefficients which had index Z+1 I would do:

RR_MapN[1]; ## This would return the sum of all coefficients that had z+1 in their subscript

What would be the most efficient way to do this?

-Yeti