How do I get a numeric approximation for symbolic expressions that have
variables? I want to leave the variables alone, but get numeric
approximations for all constants. For example, here's how it works in
mathematica:
In[1]:= a:=1+Sqrt[2]*x
In[2]:= a
Out[2]= 1 + Sqrt[2] x
In[3]:= N[a]
Out[3]= 1. + 1.41421 x
However, the corresponding thing does not work in Sage:
sage: a=1+sqrt(2)*x
sage: a
sqrt(2)*x + 1
sage: n(a)
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
/home/grout/<ipython console> in <module>()
/home/grout/downloads/sage-3.1.3.alpha1/local/lib/python2.5/site-packages/sage/misc/functional.py
in numerical_approx(x, prec, digits)
/home/grout/sage/local/lib/python2.5/site-packages/sage/calculus/calculus.py
in numerical_approx(self, prec, digits)
1300 except TypeError:
1301 # try to return a complex result
-> 1302 approx = self._complex_mpfr_field_(ComplexField(prec))
1303
1304 return approx
/home/grout/sage/local/lib/python2.5/site-packages/sage/calculus/calculus.py
in _complex_mpfr_field_(self, field)
4852 0
4853 """
-> 4854 return self._convert(field)
4855
4856 def _complex_double_(self, field):
/home/grout/sage/local/lib/python2.5/site-packages/sage/calculus/calculus.py
in _convert(self, typ)
4786 raise
4787 else:
-> 4788 return typ(g)
4789 return self._operator(*fops)
4790
/home/grout/downloads/sage-3.1.3.alpha1/local/lib/python2.5/site-packages/sage/rings/complex_field.py
in __call__(self, x, im)
/home/grout/sage/local/lib/python2.5/site-packages/sage/calculus/calculus.py
in _complex_mpfr_field_(self, field)
4852 0
4853 """
-> 4854 return self._convert(field)
4855
4856 def _complex_double_(self, field):
/home/grout/sage/local/lib/python2.5/site-packages/sage/calculus/calculus.py
in _convert(self, typ)
4780 """
4781 try:
-> 4782 fops = [typ(op) for op in self._operands]
4783 except TypeError:
4784 g = self.simplify()
/home/grout/downloads/sage-3.1.3.alpha1/local/lib/python2.5/site-packages/sage/rings/complex_field.py
in __call__(self, x, im)
/home/grout/sage/local/lib/python2.5/site-packages/sage/calculus/calculus.py
in _complex_mpfr_field_(self, field)
4852 0
4853 """
-> 4854 return self._convert(field)
4855
4856 def _complex_double_(self, field):
/home/grout/sage/local/lib/python2.5/site-packages/sage/calculus/calculus.py
in _convert(self, typ)
4780 """
4781 try:
-> 4782 fops = [typ(op) for op in self._operands]
4783 except TypeError:
4784 g = self.simplify()
/home/grout/downloads/sage-3.1.3.alpha1/local/lib/python2.5/site-packages/sage/rings/complex_field.py
in __call__(self, x, im)
/home/grout/sage/local/lib/python2.5/site-packages/sage/calculus/calculus.py
in _complex_mpfr_field_(self, field)
1453
1454 def _complex_mpfr_field_(self, field):
-> 1455 raise TypeError
1456
1457 def _complex_double_(self, C):
TypeError:
This came up today when I was trying to convince the class that a rather
complicated looking taylor polynomial was really just a nice polynomial,
even though the coefficients looked really complicated.
Thanks,
Jason
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