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By Stein W.A.

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Fortunately, all of the necessary cdef extern declarations needed to use MPIR are already declared in Sage. You can view all the declarations from the notebook by navigating to /src/libs/gmp. Let’s use MPIR directly to create two rational numbers and add them together. The code below is complicated and illustrates many issues and techniques, so we will explain it in great depth. Once you understand this, you can deal with many issues that will come up with Cython. % cython from sage .

1 We could make use of MPIR by reading the documentation for MPIR and using cdef extern as above. Fortunately, all of the necessary cdef extern declarations needed to use MPIR are already declared in Sage. You can view all the declarations from the notebook by navigating to /src/libs/gmp. Let’s use MPIR directly to create two rational numbers and add them together. The code below is complicated and illustrates many issues and techniques, so we will explain it in great depth.

Here is an example in which we create a Cython class that wraps a Python string, and provides the ability of changing the entries of the string: % cython cdef class StringMutator : cdef bytes s # cdef ’s attribute def __init__ ( self , bytes s ): self . s = s def __setitem__ ( self , int i , bytes a ): if i < 0 or i >= len ( self . = 1: raise ValueError ( < char * > self . s )[ i ] = ( < char * > a )[0] def __repr__ ( self ): return self . s def __str__ ( self ): return " % s " % self . s 61 sage : sage : sage : sage : HellX sage : HellX s = " Hello World " t = StringMutator ( s ) t [4] = ’X ’ print s World print t World Notice that setting an entry is fast: sage : timeit ( " t [4]= ’ X ’" , number =10^5) 100000 loops , best of 3: 226 ns per loop We did include some bounds checking to avoid crashes: sage : t [100] = ’x ’ Traceback ( most recent call last ): ...

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