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Hi tcfisher,

Here's one less-tedious way, using Python's list comprehension, string formatting, and an alternate format for the matrix command:

sage: plist = ['p%s%s'%(i,j) for i in range(4) for j in range(4)]
sage: m = matrix(SR,4,4,plist); m
[p00 p01 p02 p03]
[p10 p11 p12 p13]
[p20 p21 p22 p23]
[p30 p31 p32 p33]

Note that this does not inject the variables 'pij' into the global namespace, so trying to write them directly will result in an error:

sage: p00
Traceback (most recent call last):
...
NameError: name 'p00' is not defined

But if all you want to do is manipulate these matrices, that will work fine:

sage: m^2
[  p00^2 + p01*p10 + p02*p20 + p03*p30 p00*p01 + p01*p11 + p02*p21 + p03*p31 p00*p02 + p01*p12 + p02*p22 + p03*p32 p00*p03 + p01*p13 + p02*p23 + p03*p33]
[p00*p10 + p10*p11 + p12*p20 + p13*p30   p01*p10 + p11^2 + p12*p21 + p13*p31 p02*p10 + p11*p12 + p12*p22 + p13*p32 p03*p10 + p11*p13 + p12*p23 + p13*p33]
[p00*p20 + p10*p21 + p20*p22 + p23*p30 p01*p20 + p11*p21 + p21*p22 + p23*p31   p02*p20 + p12*p21 + p22^2 + p23*p32 p03*p20 + p13*p21 + p22*p23 + p23*p33]
[p00*p30 + p10*p31 + p20*p32 + p30*p33 p01*p30 + p11*p31 + p21*p32 + p31*p33 p02*p30 + p12*p31 + p22*p32 + p32*p33   p03*p30 + p13*p31 + p23*p32 + p33^2]

And of course if you need the 'pij' in the global namespace, you can always declare the variables by looping over plist (or maybe something more clever, if you give it some thought, but I haven't really :)

sage: for p in plist:
....:     var(p)
....:     
p00
p01
p02
p03
p10
p11
p12
p13
p20
p21
p22
p23
p30
p31
p32
p33
sage: p00
p00
sage: p00 + 2*p13
p00 + 2*p13

Hi tcfisher,

Here's one less-tedious way, using Python's list comprehension, string formatting, and an alternate format for the matrix command:

sage: plist = ['p%s%s'%(i,j) for i in range(4) for j in range(4)]
sage: plist
['p00', 'p01', 'p02', 'p03', 'p10', 'p11', 'p12', 'p13', 'p20', 'p21', 'p22', 'p23', 'p30', 'p31', 'p32', 'p33']

sage: m = matrix(SR,4,4,plist); m
[p00 p01 p02 p03]
[p10 p11 p12 p13]
[p20 p21 p22 p23]
[p30 p31 p32 p33]

Note that this does not inject the variables 'pij' into the global namespace, so trying to write them directly will result in an error:

sage: p00
Traceback (most recent call last):
...
NameError: name 'p00' is not defined

But if all you want to do is manipulate these matrices, that will work fine:

sage: m^2
[  p00^2 + p01*p10 + p02*p20 + p03*p30 p00*p01 + p01*p11 + p02*p21 + p03*p31 p00*p02 + p01*p12 + p02*p22 + p03*p32 p00*p03 + p01*p13 + p02*p23 + p03*p33]
[p00*p10 + p10*p11 + p12*p20 + p13*p30   p01*p10 + p11^2 + p12*p21 + p13*p31 p02*p10 + p11*p12 + p12*p22 + p13*p32 p03*p10 + p11*p13 + p12*p23 + p13*p33]
[p00*p20 + p10*p21 + p20*p22 + p23*p30 p01*p20 + p11*p21 + p21*p22 + p23*p31   p02*p20 + p12*p21 + p22^2 + p23*p32 p03*p20 + p13*p21 + p22*p23 + p23*p33]
[p00*p30 + p10*p31 + p20*p32 + p30*p33 p01*p30 + p11*p31 + p21*p32 + p31*p33 p02*p30 + p12*p31 + p22*p32 + p32*p33   p03*p30 + p13*p31 + p23*p32 + p33^2]

And of course if you need the 'pij' in the global namespace, you can always declare the variables by looping over plist (or maybe something more clever, if you give it some thought, but I haven't really :)

sage: for p in plist:
....:     var(p)
....:     
p00
p01
p02
p03
p10
p11
p12
p13
p20
p21
p22
p23
p30
p31
p32
p33
sage: p00
p00
sage: p00 + 2*p13
p00 + 2*p13