Hi,
there is an inconsistency problem with subs:
sage: e = x**2 + 1
sage: e
x^2 + 1
sage: e.subs(x= x**2)
x^4 + 1
sage: e.subs(x**2= x)
------------------------------------------------------------
File "<ipython console>", line 1
<type 'exceptions.SyntaxError'>: keyword can't be an expression
(<ipython console>, line 1)
sage: e.subs(x**2, x)
---------------------------------------------------------------------------
<type 'exceptions.TypeError'> Traceback (most recent call last)
/home/ondra/ext/sage-2.8.13-i686-Linux/<ipython console> in <module>()
/home/ondra/ext/sage/local/lib/python2.5/site-packages/sage/calculus/calculus.py
in subs(self, *args, **kwds)
2506
2507 def subs(self, *args, **kwds):
-> 2508 return self.substitute(*args, **kwds)
2509
2510 def _recursive_sub(self, kwds):
<type 'exceptions.TypeError'>: substitute() takes at most 2 arguments (3 given)
Clearly, there is no way how to substitute for x**2 with the current
syntax, since we are abusing Python keywords arguments. I propose not
to use .subs(x=1), but only .subs(x, 1), because it's clean and it
will work when we implement substituting for x**2 (not yet in Sage). I
think you will disagree with an argument, that mathematicians are used
to writing .subs(x=1), well, I disagree with that,
I think mathematicians are very clever people and they will be able to
handle that, but as a compromise, .subs() should be able to accept
both.
BTW, this is how this works in SymPy:
In [1]: e = x**2 + 1
In [2]: e
Out[2]:
2
1 + x
In [3]: e.subs(x, x**2)
Out[3]:
4
1 + x
In [4]: e.subs(x**2, x)
Out[4]: 1 + x
Ondrej
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