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Symbolic linear algebra

Most of my research is in numerical methods/numerical analysis. I need to perform derivations using arbitrary matrices. Currently, when using sage, I have to declare all the elements of a symbolic matrix:

var('p00 p01 p02 p03 p10 p11 p12 p13 p20 p21 p22 p23 p30 p31 p32 p33') Pmat=matrix([[p00,p01,p02,p03],[p10,p11,p12,p13],[p20,p21,p22,p23],[p30,p31,p32,p33]])

Clearly for large matrices this is prohibitively tedious. In Mathematica, I simply use:


I am then able to put constraints on the elements of p and solve for the values for the given method I am trying to derive. I prefer to use sage over Mathematica, so if someone can enlighten me how to accomplish this task in sage, I would appreciate it.