Ticket #4948: trac-4948-mathematica_lists.patch

sage/interfaces/expect.py

@@ -11 +11 @@
 
 - William Stein (2006-03-01): got rid of infinite loop on startup if
   client system missing
+
+- Felix Lawrence (2009-08-21): edited ._sage_() to support lists and float exponents in foreign notation.
 """
 
 #*****************************************************************************
@@ -1137 +1139 @@
                      (operator.lt, self._lessthan_symbol()), (operator.le, "<="),
                      (operator.gt, self._greaterthan_symbol()), (operator.ge, ">=")])
 
+    def _exponent_symbol(self):
+        """
+        Return the symbol used to denote *10^ in floats, e.g 'e' in 1.5e6
+        """
+        return 'e'
+
     ############################################################
     #         Functions for working with variables.
     #  The first three must be overloaded by derived classes,
@@ -1443 +1451 @@
             yield self[i]
 
     def __len__(self):
-        raise NotImplementedError
+        """
+        Call self.sage() and return the length of that sage object.
+        
+        This approach is inefficient - each interface should override
+        this method with one that calls the external program's length
+        function.
+        
+        EXAMPLES::
+        
+            sage: len(gp([1,2,3]))
+            3
+        
+        AUTHORS:
+        
+        - Felix Lawrence (2009-08-21)
+        """
+        return len(self.sage())
 
     def __reduce__(self):
         return reduce_load, (self.parent(), self._reduce())
@@ -1536 +1560 @@
             #print msg
             pass
 
+    def _sage_repr(self):
+        """
+        Return a sage-friendly string representation of the object.
+        
+        Some programs use different notation to Sage, e.g. Mathematica 
+        writes lists with {} instead of [].  This method calls repr(self) 
+        then converts the foreign notation into Sage's notation.
+        
+        OUTPUT:
+        
+        A string representation of the object that is ready for
+        sage_eval().
+        
+        EXAMPLES::
+        
+            sage: repr(mathematica([1,2,3]))    # optional - mathematica
+            '{1, 2, 3}'
+            sage: mathematica([1,2,3])._sage_repr() # optional - mathematica
+            '[1, 2, 3]'
+        
+        ::
+        
+            sage: gp(10.^80)._sage_repr()
+            '1.0000000000000000000000000000000000000e80'    # 64-bit
+            sage: mathematica('10.^80')._sage_repr()  # optional - mathematica
+            '1.e80'
+        
+        AUTHORS:
+        
+        - Felix Lawrence (2009-08-21)
+        """
+        #TO DO: this could use file transfers when self.is_remote()
+        
+        string = repr(self).replace('\n',' ').replace('\r', '')
+        # Translate the external program's list formatting to Sage's
+        lld = self.parent()._left_list_delim()
+        if '[' != lld:      string = string.replace(lld, '[')
+        rld = self.parent()._right_list_delim()
+        if ']' != rld:      string = string.replace(rld, ']')
+        # Translate the external program's exponent formatting
+        expl = self.parent()._exponent_symbol()
+        if 'e' != expl: string = string.replace(expl, 'e')
+        return string
+
     def _sage_(self):
         """
         Attempt to return a Sage version of this object.
@@ -1548 +1616 @@
             1/2
             sage: _.parent()
             Rational Field
+        
+        AUTHORS:
+        
+        - William Stein
+        
+        - Felix Lawrence (2009-08-21)
         """
-        #TO DO: this could use file transfers when self.is_remote()
         try:
-            return sage.misc.sage_eval.sage_eval(repr(self).replace('\n',''))
+            return sage.misc.sage_eval.sage_eval(self._sage_repr())
         except:
             raise NotImplementedError
         

sage/interfaces/gp.py

@@ -553 +553 @@
         """
         return '=='
 
+    def _exponent_symbol(self):
+        """
+        Returns the symbol to denote the exponent of a number in GP.
+        
+        EXAMPLES::
+        
+            sage: gp._exponent_symbol()
+            ' E'
+        
+        ::
+        
+            sage: repr(gp(10.^80)).replace(gp._exponent_symbol(), 'e')
+            '1.0000000000000000000000000000000000000e80'    # 64-bit
+        """
+        return ' E'
+
     def help(self, command):
         r"""
         Returns GP's help for ``command``.

sage/interfaces/mathematica.py

@@ -179 +179 @@
 
     sage: n = mathematica(2434500)           # optional - mathematica
     sage: n.FactorInteger()                  # optional - mathematica
-    {{2, 2}, {3, 2}, {5, 3}, {541, 1}}       # optional - mathematica
+    {{2, 2}, {3, 2}, {5, 3}, {541, 1}}
     sage: n = mathematica(2434500)           # optional - mathematica
     sage: F = n.FactorInteger(); F           # optional - mathematica
     {{2, 2}, {3, 2}, {5, 3}, {541, 1}}
@@ -234 +234 @@
     ...       return mathematica(nu).BesselK(x).N(20).sage()
     ...
     sage: math_bessel_K(2,I)                      # optional - mathematica
-    0.180489972066962*I - 2.592886175491197
+    0.180489972066962*I - 2.592886175491197         # 32-bit
+    -2.592886175491196978 + 0.1804899720669620266*I # 64-bit
+
+::
+
+    sage: slist = [[1, 2], 3., 4 + I]
+    sage: mlist = mathematica(slist); mlist     # optional - mathematica
+    {{1, 2}, 3., 4 + I}
+    sage: slist2 = list(mlist); slist2          # optional - mathematica
+    [{1, 2}, 3., 4 + I]  
+    sage: slist2[0]                             # optional - mathematica
+    {1, 2}
+    sage: slist2[0].parent()                    # optional - mathematica
+    Mathematica
+    sage: slist3 = mlist.sage(); slist3         # optional - mathematica
+    [[1, 2], 3.00000000000000, I + 4]
+
+::
+
+    sage: mathematica('10.^80')     # optional - mathematica
+    1.*^80
+    sage: mathematica('10.^80').sage()  # optional - mathematica
+    1.00000000000000e80
 
 AUTHORS:
 
 - William Stein (2005): first version
 
 - Doug Cutrell (2006-03-01): Instructions for use under Cygwin/Windows.
+
+- Felix Lawrence (2009-08-21): Added support for importing Mathematica lists and floats with exponents.
 """
 
 #*****************************************************************************
@@ -460 +484 @@
     def _assign_symbol(self):
         return ":="
 
+    def _exponent_symbol(self):
+        """
+        Returns the symbol used to denote the exponent of a number in
+        Mathematica.
+        
+        EXAMPLES::
+        
+            sage: mathematica._exponent_symbol()        # optional - mathematica
+            '*^'
+        
+        ::
+        
+            sage: bignum = mathematica('10.^80')  # optional - mathematica
+            sage: repr(bignum)                          # optional - mathematica
+            '1.*^80'
+            sage: repr(bignum).replace(mathematica._exponent_symbol(), 'e').strip() # optional - mathematica
+            '1.e80'
+        """
+        return "*^"
+
     def _object_class(self):
         return MathematicaElement
 
@@ -513 +557 @@
         P = self._check_valid()
         return P.get(self._name, ascii_art=True)
 
+    def __len__(self):
+        """
+        Return the object's length, evaluated by mathematica.
+        
+        EXAMPLES::
+        
+            sage: len(mathematica([1,1.,2]))    # optional - mathematica
+            3
+        
+        AUTHORS:
+        - Felix Lawrence (2009-08-21)
+        """
+        return self.Length()
+
     def show(self, filename=None, ImageSize=600):
         r"""
         Show a mathematica expression or plot in the Sage notebook.