Here is a somewhat different solution that you might like more:
sage: var('x,a,b')
sage: def f(x):
return 2*x^a + b
sage: f(x)
2*x^a + b
sage: a = 2; f(x)
2*x^2 + b
sage: b = 1; f(x)
2*x^2 + 1
The fact that f is a python function instead of a SymbolicArithmetic
object has both advantages and disadvantages. I prefer it because I
have a better understanding of the basic python objects.
Cheers,
Marshall Hampton
On Jun 5, 5:36 am, Stan <[EMAIL PROTECTED]> wrote:
> Dear Robert,
>
> Thanks a lot for the quick solution. That's a whole new support
> experience!
>
> I was hoping I could define
> z=y.subs(locals())
> so that z would automatically adapt if the local variables change, but
> it does not. Every time I change the local variables, I have to
> redefine z=y.subs(locals())
> to update it. Whereas this is better than writing y(a=3,b=4), it would
> be even more convenient if I could define a function that
> automatically takes the actual local variables.
> Almost there...
>
> Thanks again,
> Stan
>
> On Jun 5, 11:47 am, Robert Bradshaw <[EMAIL PROTECTED]>
> wrote:
>
> > On Jun 5, 2008, at 2:34 AM, Stan wrote:
>
> > > Dear all,
>
> > > I would like to use Sage as an alternative to Mathematica and I am
> > > quite amazed about the demonstrated functionality of Sage. I just have
> > > a very basic problem with the way I am used to do calculations. Often,
> > > I define a set of equations with different variables in them, then I
> > > solve the equations for example for y, set some of the variables to
> > > prescribed values and plot y as a function of the free variable. In
> > > Sage, a symbolic function does not replace the variables by numbers if
> > > the variables have values assigned to them.
>
> > > Example:
>
> > > sage: var ('x a b')
> > > (x, a, b)
> > > sage: y=2*x^a+b
> > > sage: a=3;b=4
> > > sage: y
> > > 2*x^a + b
> > > sage: y(a=3,b=4)
> > > 2*x^3 + 4
>
> > > In the above example, y only uses the values of a and b if they are
> > > explicitly included in the call. This would become very tedious for a
> > > system of equations if I want to plot several of them with the same
> > > parameter values.
>
> > > Is there a way of formulating equations that will automatically
> > > evaluate if their variables have values assigned to them?
>
> > I would try something like
>
> > sage: var ('x a b')
> > (x, a, b)
> > sage: y=2*x^a+b
> > sage: a=3;b=4
> > sage: y
> > 2*x^a + b
> > sage: y.subs(locals())
> > 2*x^3 + 4
>
> > This will take all the local variables (with their names) and plug
> > their values in.
>
> > > Same example in Mathematica:
>
> > > In[282]:=
> > > y=2*x^a+b
>
> > > Out[282]=
> > > b + 2 x^a
>
> > > In[283]:=
> > > a=3;b=4;
> > > y
>
> > > Out[284]=
> > > 4 + 2 x^3
>
> > > Thanks for your help!
>
> > > Stan
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