Sage Developer's Guide - Mirrors

Sage Developer’s Guide, Release 6.1.1return self.am()else:return self.am().change_ring(R)def adjacency_matrix(self, sparse=None, boundary_first=False):...Similarly, provide a _vector_ method for an object that can be coerced to a vector over a ringR. Then the Sage function vector will work for this object. The following is from the fileSAGE_ROOT/sage/sage/modules/free_module_element.pyx:cdef class FreeModuleElement(element_Vector):...def _vector_(self, R):return self.change_ring(R)# abstract base class4.2.3 Sage PreparsingTo make Python even more usable interactively, there are a number of tweaks to the syntax made when you useSage from the commandline or via the notebook (but not for Python code in the Sage library). Technically, this isimplemented by a preparse() function that rewrites the input string. Most notably, the following replacements aremade:• Sage supports a special syntax for generating rings or, more generally, parents with named generators:sage: R. = QQ[]sage: preparse(’R. = QQ[]’)"R = QQ[’x, y’]; (x, y,) = R._first_ngens(2)"• Integer and real literals are Sage integers and Sage floating point numbers. For example, in pure Python thesewould be an attribute error:sage: 16.sqrt()4sage: 87.factor()3 * 29• Raw literals are not preparsed, which can be useful from an efficiency point of view. Just like Python ints aredenoted by an L, in Sage raw integer and floating literals are followed by an “r” (or “R”) for raw, meaning notpreparsed. For example:sage: a = 393939rsage: a393939sage: type(a)sage: b = 393939sage: type(b)sage: a == bTrue• Raw literals can be very useful in certain cases. For instance, Python integers can be more efficient than Sageintegers when they are very small. Large Sage integers are much more efficient than Python integers since theyare implemented using the GMP C library.Consult the file preparser.py for more details about Sage preparsing, more examples involving raw literals, etc.4.2. Coding in Python for Sage 35