very rough and sketchy tentative of Puiseux polynomials

src/module_list.py

@@ -1172,6 +1172,9 @@ def uname_specific(name, value, alternative):
     Extension('sage.rings.power_series_ring_element',
               sources = ['sage/rings/power_series_ring_element.pyx']),
 
+    Extension('sage.rings.polynomial.puiseux_polynomial',
+              sources = ['sage/rings/polynomial/puiseux_polynomial.pyx']),
+
     Extension('sage.rings.rational',
               sources = ['sage/rings/rational.pyx'],
               libraries=['ntl']),

src/sage/rings/polynomial/all.py

@@ -42,6 +42,9 @@
 from sage.rings.polynomial.laurent_polynomial_ring import LaurentPolynomialRing
 lazy_import('sage.rings.polynomial.omega', 'MacMahonOmega')
 
+# Puiseux Polynomial Rings
+lazy_import('sage.rings.polynomial.puiseux_polynomial_ring', 'PuiseuxPolynomialRing')
+
 # Infinite Polynomial Rings
 from sage.rings.polynomial.infinite_polynomial_ring import InfinitePolynomialRing
 

src/sage/rings/polynomial/puiseux_polynomial.pxd

@@ -0,0 +1,17 @@
+from sage.structure.element cimport CommutativeAlgebraElement, ModuleElement, RingElement, Element
+from sage.rings.polynomial.polydict cimport ETuple, PolyDict
+from sage.rings.polynomial.multi_polynomial cimport MPolynomial
+
+
+cdef class PuiseuxPolynomial(CommutativeAlgebraElement):
+    cdef PuiseuxPolynomial _new_c(self)
+    cpdef _add_(self, other)
+    cpdef _mul_(self, other)
+    cpdef _floordiv_(self, other)
+    cpdef long number_of_terms(self) except -1
+    cpdef dict dict(self)
+
+cdef class PuiseuxPolynomial_univariate(PuiseuxPolynomial):
+    cpdef ModuleElement __u
+    cdef long __n
+    cpdef _unsafe_mutate(self, i, value)