special case for principal specialization of order 1

src/sage/combinat/sf/elementary.py

@@ -394,6 +394,12 @@
                 sage: e.zero().principal_specialization(3)
                 0
             """
+            if n == 1:
+                R = self.base_ring()
+                mc = self.monomial_coefficients(copy=False).items()
+                return R.sum(c for partition, c in mc
+                             if not partition or partition[0] == 1)
+
             from sage.combinat.q_analogues import q_binomial
 
             def get_variable(ring, name):

src/sage/combinat/sf/homogeneous.py

@@ -304,6 +304,9 @@
                 sage: s = x.principal_specialization(3); s
                 0
             """
+            if n == 1:
+                return self.base_ring().sum(self.coefficients(sort=False))
+
             from sage.combinat.q_analogues import q_binomial
 
             def get_variable(ring, name):

src/sage/combinat/sf/monomial.py

@@ -398,6 +398,12 @@
                 sage: m.zero().principal_specialization(3)
                 0
             """
+            if n == 1:
+                R = self.base_ring()
+                mc = self.monomial_coefficients(copy=False).items()
+                return R.sum(c for partition, c in mc
+                             if len(partition) <= 1)
+
             if q == 1:
                 if n == infinity:
                     raise ValueError("the stable principal specialization at q=1 is not defined")

src/sage/combinat/sf/powersum.py

@@ -797,6 +797,9 @@
                 sage: p.zero().principal_specialization(3)
                 0
             """
+            if n == 1:
+                return self.base_ring().sum(self.coefficients(sort=False))
+
             def get_variable(ring, name):
                 try:
                     ring(name)
@@ -926,12 +929,9 @@
                     t = get_variable(self.base_ring(), 't')
 
                 def f(partition):
-                    n = 0
-                    for part in partition:
-                        if part != 1:
-                            return 0
-                        n += 1
-                    return t**n
+                    if partition and partition[0] != 1:
+                        return 0
+                    return t**len(partition)
 
                 return self.parent()._apply_module_morphism(self, f, t.parent())
 

src/sage/combinat/sf/schur.py

@@ -685,6 +685,12 @@
                 sage: s.zero().principal_specialization(3)
                 0
             """
+            if n == 1:
+                R = self.base_ring()
+                mc = self.monomial_coefficients(copy=False).items()
+                return R.sum(c for partition, c in mc
+                             if len(partition) <= 1)
+
             def get_variable(ring, name):
                 try:
                     ring(name)