gh-36773: Raise a power series to a power series
    
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This adds the functionality to compute the power series `f^g` when it is
well defined.

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This adds functionality that is useful for generating function
computations.

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Fixes #36772.

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URL: #36773
Reported by: trevorkarn
Reviewer(s): Frédéric Chapoton, Pietro-D, Travis Scrimshaw

Author: Release Manager

src/sage/rings/power_series_ring_element.pyx

@@ -104,6 +104,7 @@ from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 import sage.misc.misc
 import sage.arith.all as arith
 import sage.misc.latex
+from sage.structure.element import parent
 from sage.rings.integer import Integer
 from sage.rings.finite_rings.integer_mod_ring import IntegerModRing
 
@@ -1135,11 +1136,34 @@ cdef class PowerSeries(AlgebraElement):
             x + x^3
             sage: O(x^4)^(1/2)
             O(x^2)
+
+            sage: R.<x,t> = QQ[[]]
+            sage: f = (1+x)^(1+t)
+            sage: f.O(5)
+            1 + x + x*t + 1/2*x^2*t - 1/6*x^3*t + 1/2*x^2*t^2 + O(x, t)^5
+
+            sage: R.<x> = QQ[[]]
+            sage: (e^(e^x - 1)).O(5)
+            1 + x + x^2 + 5/6*x^3 + 5/8*x^4 + O(x^5)
+            sage: e^e^x
+            Traceback (most recent call last):
+            ...
+            ArithmeticError: constant term of power series does not support exponentiation
+
+            sage: R.<x> = QQ[[]]
+            sage: S.<t> = QQ[] # a polynomial ring
+            sage: (1+x)^(1+t)
+            Traceback (most recent call last):
+            ...
+            ValueError: exponent must be a rational number or power series
         """
         try:
             right = QQ.coerce(r)
-        except TypeError:
-            raise ValueError("exponent must be a rational number")
+        except (TypeError, ValueError):
+            if r.parent() is self.parent():
+                return (r * self.log()).exp()
+            else:
+                raise ValueError("exponent must be a rational number or power series")
 
         if right.denominator() == 1:
             right = right.numerator()