Trac #20040: exchange order of parameters var and zeta in _singularit…

…y_analysis_

src/sage/rings/asymptotic/growth_group.py

@@ -2882,9 +2882,9 @@ def _singularity_analysis_(self, var, zeta, precision):
             1/sqrt(pi)*(1/2)^n*n^(-1/2) - 1/8/sqrt(pi)*(1/2)^n*n^(-3/2)
             + O((1/2)^n*n^(-5/2))
             sage: G = GrowthGroup('log(x)^QQ')
-            sage: G(log(x))._singularity_analysis_(1, 'n', 5)
+            sage: G(log(x))._singularity_analysis_('n', 1, precision=5)
             n^(-1) + O(n^(-3))
-            sage: G(log(x)^2)._singularity_analysis_(2, 'n', 3)
+            sage: G(log(x)^2)._singularity_analysis_('n', 2, precision=3)
             8*(1/2)^n*n^(-1)*log(n) + 8*euler_gamma*(1/2)^n*n^(-1)
             + O((1/2)^n*n^(-2)*log(n)^2)
 
@@ -2896,7 +2896,7 @@ def _singularity_analysis_(self, var, zeta, precision):
             NotImplementedError: singularity analysis not implemented
             for non-integer exponent 1/2 of log(x)
             sage: G = GrowthGroup('log(log(x))^QQ')
-            sage: G(log(log(x))^(1/2))._singularity_analysis_('n', 3)
+            sage: G(log(log(x))^(1/2))._singularity_analysis_('n', 2, precision=3)
             Traceback (most recent call last):
             ...
             NotImplementedError: singularity analysis not implemented

src/sage/rings/asymptotic/growth_group_cartesian.py

@@ -1190,16 +1190,16 @@ def _substitute_(self, rules):
                 from misc import substitute_raise_exception
                 substitute_raise_exception(self, e)
 
-        def _singularity_analysis_(self, zeta, var, precision):
+        def _singularity_analysis_(self, var, zeta, precision):
             r"""
             Perform singularity analysis on this growth element.
 
             INPUT:
 
-            - ``zeta`` -- a number
-
             - ``var`` -- a string denoting the variable
 
+            - ``zeta`` -- a number
+
             - ``precision`` -- an integer
 
             OUTPUT:
@@ -1212,32 +1212,32 @@ def _singularity_analysis_(self, zeta, var, precision):
 
                 sage: from sage.rings.asymptotic.growth_group import GrowthGroup
                 sage: G = GrowthGroup('exp(x)^QQ * x^QQ * log(x)^QQ')
-                sage: G(x^(1/2))._singularity_analysis_(2, 'n', 2)
+                sage: G(x^(1/2))._singularity_analysis_('n', 2, precision=2)
                 1/sqrt(pi)*(1/2)^n*n^(-1/2) - 1/8/sqrt(pi)*(1/2)^n*n^(-3/2)
                 + O((1/2)^n*n^(-5/2))
-                sage: G(log(x))._singularity_analysis_(1, 'n', 5)
+                sage: G(log(x))._singularity_analysis_('n', 1, precision=5)
                 n^(-1) + O(n^(-3))
-                sage: G(x*log(x))._singularity_analysis_(1, 'n', 5)
+                sage: G(x*log(x))._singularity_analysis_('n', 1, precision=5)
                 log(n) + euler_gamma + 1/2*n^(-1) + O(n^(-2))
 
             TESTS::
 
-                sage: G('exp(x)*log(x)')._singularity_analysis_(1, 'n', 5)
+                sage: G('exp(x)*log(x)')._singularity_analysis_('n', 1, precision=5)
                 Traceback (most recent call last):
                 ...
                 NotImplementedError: singularity analysis of
                 exp(x)*log(x) not implemented
-                sage: G('exp(x)*x*log(x)')._singularity_analysis_(1, 'n', 5)
+                sage: G('exp(x)*x*log(x)')._singularity_analysis_('n', 1, precision=5)
                 Traceback (most recent call last):
                 ...
                 NotImplementedError: singularity analysis for more
                 than two factors not yet implemented
-                sage: G(1)._singularity_analysis_(2, 'n', 3)
+                sage: G(1)._singularity_analysis_('n', 2, precision=3)
                 Traceback (most recent call last):
                 ...
                 NotImplementedOZero: The error term in the result is O(0)
                 which means 0 for sufficiently large n.
-                sage: G('exp(x)')._singularity_analysis_(2, 'n', 3)
+                sage: G('exp(x)')._singularity_analysis_('n', 2, precision=3)
                 Traceback (most recent call last):
                 ...
                 NotImplementedError: singularity analysis not implemented
@@ -1250,7 +1250,7 @@ def _singularity_analysis_(self, zeta, var, precision):
                 raise NotImplementedOZero(var=var)
             elif len(factors) == 1:
                 return factors[0]._singularity_analysis_(
-                    zeta=zeta, var=var, precision=precision)
+                    var=var, zeta=zeta, precision=precision)
             elif len(factors) == 2:
                 from growth_group import MonomialGrowthGroup
                 from sage.rings.integer_ring import ZZ