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Is there a way to simplify_full and trig_reduce a matrix?

asked 2010-11-25 10:54:20 -0500

Shashank gravatar image

updated 2010-11-28 07:27:26 -0500

niles gravatar image

I know I can do it component by component and then construct a matrix out of the output. But it would be nice if I could just say matrix.trig_reduce() and get a matrix with all the components trig_reduced. Thanks in advance

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kcrisman gravatar imagekcrisman ( 2011-01-03 15:01:50 -0500 )edit

3 answers

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answered 2010-11-25 14:25:22 -0500

Mike Hansen gravatar image

You can use the apply_map method which applies a function to each of the elements of the matrix. For example,

sage: m = matrix([[sin(x), cos(x)], [sin(x), cos(x)]]); m
[sin(x) cos(x)]
[sin(x) cos(x)]
sage: o = m*m.transpose(); o
[sin(x)^2 + cos(x)^2 sin(x)^2 + cos(x)^2]
[sin(x)^2 + cos(x)^2 sin(x)^2 + cos(x)^2]
sage: o.apply_map(lambda x: x.trig_reduce())
[1 1]
[1 1]

You could equivalently use attrcall

sage: o.apply_map(attrcall('trig_reduce'))
[1 1]
[1 1]
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The apply_map method is a great trick! Thanks for sharing.

cswiercz gravatar imagecswiercz ( 2010-11-30 09:33:47 -0500 )edit

That solves my problem I have a small function written which does, but would it be very difficult to define trig_reduce(), full_simplify() etc for matrices in sage. I don't know of any sage webpage for feature requests. But this is a feature that would make things a lot easier and user friendly.

Shashank gravatar imageShashank ( 2010-12-03 08:26:56 -0500 )edit
1

answered 2010-12-01 04:15:57 -0500

tcfisher gravatar image

I have to do this often, so I wrote a function:

def matrix_full_simplify(mat,m,n):
    matsimp=mat;
    for i in range(m):
        for j in range(n):
             matsimp[i,j]=mat[i,j].full_simplify();
    return matsimp;

Use:

amat = matrix_full_simplify(amat)

You could easily adapt this to be better or require fewer arguments and can create a similar function for vectors.

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answered 2011-05-16 09:21:54 -0500

kcrisman gravatar image

The trig one is possible, the other one is in the ticket. For posterity: As it turns out, we already have it, just not with all possible aliases! I didn't even know this.

sage: m = matrix([[sin(x), cos(x)], [sin(x), cos(x)]]); m
[sin(x) cos(x)]
[sin(x) cos(x)]
sage: o = m*m.transpose()
sage: o.simplify_trig()
[1 1]
[1 1]
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Asked: 2010-11-25 10:54:20 -0500

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Last updated: May 16 '11