On Tue, 05 Dec 2006 08:56:22 -0800, Joel B. Mohler
<[EMAIL PROTECTED]> wrote:
> William, thanks for your kind hint for me to be quiet a bit. I believe
> you are
> right that I should be so. After this e-mail and a few additions to the
> wiki, I
> will be quiet on this topic.
No, don't be quiet!!
> However, I don't agree that the suggestion of using variables from the
> polynomial ring is doing what mathematica does. Some Examples:
>
> Exhibit 1: My understanding is that you want f(1) to be 1 in sage, but
> mathematica is not so.
> In[1]:= f=x
> Out[1]= x
> In[2]:= f(1)
> Out[2]= x
>
> Exhibit 2: Mathematica has a dummy variable.
> In[12]:= f[x_]:=Sin[x]
> In[13]:= f'[x]
> Out[13]= Cos[x]
> In[14]:= f'[y]
> Out[14]= Cos[y]
>
> Exhibit 3: Part of the expected second variable is the name of the
> independent
> variable.
> In[6]:= Plot[Sin[x]]
> Plot::argmu: Plot called with 1 argument; 2 or more arguments are
> expected.
I was also confused about this.
Maple and Mathematica have symbolic expressions, like Sin[x] * Cos[y],
(or sin(x)*cos(y)), which you *can not* evalaute in those systems!
You can only do a variant of "substitution". This is what we should
do too, and doesn't require the preprocessor. In order to define
a function to be evaluated, one should just use Python's def or lambda.
Example in Maple:
auth2-213:~/s/spkg/standard was$ maple
|\^/| Maple 10 (APPLE PPC OSX)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc.
2005
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
| Type ? for help.
> f = sin(x);
f = sin(x)
> f(2);
f(2)
> f;
f
> f := sin(x);
f := sin(x)
> f;
sin(x)
> integrate(f, x);
-cos(x)
> f(2);
sin(x)(2)
> subs(x=2,f);
sin(2)
Example in Mathematica:
auth2-213:~/s/spkg/standard was$ math
Mathematica 5.2 for Mac OS X
Copyright 1988-2005 Wolfram Research, Inc.
-- Terminal graphics initialized --
In[1]:= f := Sin[x];
In[2]:= f[2];
In[3]:= f[2]
Out[3]= Sin[x][2]
In[4]:= Integrate[f, x];
In[5]:= Integrate[f,x]
Out[5]= -Cos[x]
OK, I forget how to subst in mathematica, but I have to go now.
Also, PARI has this same distinction too.
? f = x*y
%2 = y*x
? f(2,3)
*** unused characters: f(2,3)
^-----
? subst(f,x,2)
%3
= 2*y
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