What is equivalent to applyrule in Maple

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You can use the method subs:

sage: e1 = cos(x) + sin(x) - exp(x) + x^2/3
sage: e2 = sin(x)
sage: e3 = 1/x + 1/x^2
sage: e1.subs({e2:e3})
1/3*x^2 + 1/x + 1/x^2 + cos(x) - e^x

Note though that it won't work with too complicated expressions for e2. For more on this, you may have a look to the documentation of subs in the reference manual.

You can try:

sage: e1.substitute({e2:e3})

or even

sage: e1.substitute({e2:e3, 1/e2:1/e3})

if it can help.

If this does not work, please do not hesitate to provide a way to construct e1, e2 and e3 so that we can think about it.