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How to create a matrix in sage that expands with a variable number of rows and columns and in each row the values are squared?

asked 2017-12-06 20:28:33 -0600

sageAmateur345 gravatar image

I need to make a code that takes takes two inputs: n and d and creates a matrix of the values of a list P.

'n' will be the number of columns and 'd' the number of rows.

In each row, I need the values of the following row to be raised to an incrementally rising power.

This is what I have so far:

define inputs

n=5 d=5 f=x^2

define a list of size n

P=[(i,f(i)) for i in range(n)]

define a matrix

C=matrix([(P[i][0]) for i in range(n)]) show(C)

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Please mark the python and sage code as such, just mark it and pres Control+K. (Or hit that button with the two rows 101 and 010 in the header of the question area.

The above looks (slightly changed) like:

# define inputs
n, d, f = 5, 5, x^2

# define a list of size n
P = [ (j, f(j)) for j in range(n) ]

# define a matrix
C = ???

Please describe mathematically which is the matrix that should be defined.

Try ?matrix in the sage interpreter to see more examples.

dan_fulea gravatar imagedan_fulea ( 2017-12-07 13:31:54 -0600 )edit

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answered 2017-12-07 04:16:32 -0600

tmonteil gravatar image

updated 2017-12-07 04:18:07 -0600

To get some documentation on how to create custom matrices, you can do:

sage: matrix?

You will see some examples using a function taking a pair (i,j) and returning some f(i,j) to be placed in the entry [i,j] of the constructed matrix.

For example, if you want that the entry [i,j] has value i*j^2 (say), you can do:

sage: m = 4 ; n = 5
sage: matrix(QQ, m, n, lambda i, j: i*j^2)
[ 0  0  0  0  0]
[ 0  1  4  9 16]
[ 0  2  8 18 32]
[ 0  3 12 27 48]
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Asked: 2017-12-06 20:28:33 -0600

Seen: 28 times

Last updated: Dec 07