Trac #20040: Merge #19944

src/sage/rings/asymptotic/growth_group.py

@@ -1414,7 +1414,8 @@ def _singularity_analysis_(self, var, zeta, precision):
 
         An asymptotic expansion for `[z^n] f` where `n` is ``var``
         and `f` has this growth element as a singular expansion
-        in `(1-z\zeta)\to 0`.
+        in `T=\frac{1}{1-\frac{z}{\zeta}}\to \infty` where this element
+        is a growth element in `T`.
 
         TESTS::
 
@@ -2872,7 +2873,8 @@ def _singularity_analysis_(self, var, zeta, precision):
 
         An asymptotic expansion for `[z^n] f` where `n` is ``var``
         and `f` has this growth element as a singular expansion
-        in `(1-z\zeta)\to 0`.
+        in `T=\frac{1}{1-\frac{z}{\zeta}}\to \infty` where this element
+        is a growth element in `T`.
 
         EXAMPLE::
 

src/sage/rings/asymptotic/term_monoid.py

@@ -1252,7 +1252,8 @@ def _singularity_analysis_(self, var, zeta, precision):
 
         An asymptotic expansion for `[z^n] f` where `n` is ``var``
         and `f` has this term as a singular expansion
-        in `(1-z\zeta)\to 0`.
+        in `T=\frac{1}{1-\frac{z}{\zeta}}\to \infty` where this element
+        is a monomial in `T`.
 
         TESTS::
 
@@ -2403,7 +2404,8 @@ def _singularity_analysis_(self, var, zeta, precision):
 
         An asymptotic expansion for `[z^n] f` where `n` is ``var``
         and `f` has this term as a singular expansion
-        in `(1-z\zeta)\to 0`.
+        in `T=\frac{1}{1-\frac{z}{\zeta}}\to \infty` where this element
+        is a monomial in `T`.
 
         EXAMPLES::
 
@@ -3594,7 +3596,8 @@ def _singularity_analysis_(self, var, zeta, precision):
 
         An asymptotic expansion for `[z^n] f` where `n` is ``var``
         and `f` has this term as a singular expansion
-        in `(1-z\zeta)\to 0`.
+        in `T=\frac{1}{1-\frac{z}{\zeta}}\to \infty` where this element
+        is a monomial in `T`.
 
         EXAMPLES::