exponential matrix exp(A)

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I don't think there are any hard-coded size limits.

At the same time, experimentation with random_matrix(ZZ,i,i) suggests that Maxima hits a wall with this already when i=4. RR doesn't look much better, and

sage: m = random_matrix(RDF,4,4)
sage: m.exp?

basically says as much. But

sage: m = random_matrix(RDF,4,4)
sage: exp(m)
[ 0.360479628838 -0.145794589097    1.4781378783  0.316593839994]
[ 0.317770329736 0.0984841855079 -0.733966866354 -0.820812967827]
[ -1.58402218787  0.783288361066  0.965206766202  0.919221986577]
[-0.254553742946  0.837705408602  -2.47262343564   1.63085510321]
sage: m = random_matrix(RDF,10,10)
sage: exp(m)

looks much better. So the answer to your question depends on what you are exactly looking for.