On Wed, 26 Mar 2008 17:04:10 -0700, Hector Villafuerte <[EMAIL PROTECTED]>
wrote:
>
> Hi,
> While trying to compute the Golden ratio using SAGE I noticed the
> following strange (to me) behavior in solve().
>
> * This fails:
>
> sage: var('a b phi')
> (a, b, phi)
> sage: solve([phi==a/b, phi==(a+b)/a], phi)
> ---------------------------------------------------------------------------
> <type 'exceptions.ValueError'> Traceback (most recent call last)
>
> /Users/hector/sage/<ipython console> in <module>()
>
> /Users/hector/sage/local/lib/python2.5/site-packages/sage/calculus/equations.py
> in solve(f, *args, **kwds)
> 1215 s = m.solve(args)
> 1216 except:
> -> 1217 raise ValueError, "Unable to solve %s for %s"%(f, args)
> 1218 a = repr(s)
> 1219 sol_list = string_to_list_of_solutions(a)
>
> <type 'exceptions.ValueError'>: Unable to solve [phi == a/b, phi == (b
> + a)/a] for (phi,)
>
>
> * This succeeds (note the (unnecessary?) need to also solve for 'a')
>
> sage: solve([phi==a/b, phi==(a+b)/a], phi,a)
> [[phi == (1 - sqrt(5))/2, a == -2*b/(sqrt(5) + 1)], [phi == (sqrt(5) +
> 1)/2, a == 2*b/(sqrt(5) - 1)]]
>
>
> Where the Golden ratio is phi == (sqrt(5) + 1)/2. So, am I missing
> something fundamental in the way solve() works or is this a bug?
> Thanks!
Some comments:
(1) A simpler way to use solve to find the golden ratio is:
sage: var('phi')
phi
sage: solve(phi==1+1/phi, phi)
[phi == (1 - sqrt(5))/2, phi == (sqrt(5) + 1)/2]
(2) If it's a bug, then it's a bug in Maxima. You may want to look at the
Maxima docs for solve. Here's what happens doing things like the above directly
in Maxima:
(%i4) solve([phi=a+b,phi=a+b], phi);
Dependent equations eliminated: (2)
(%o4) [[phi = b + a]]
(%i1) solve([phi=a/b,phi=a+b], phi)
;
Maxima encountered a Lisp error:
CAR: 2 is not a list
Automatically continuing.
To reenable the Lisp debugger set *debugger-hook* to nil.
(%i2) solve([phi=a*b,phi=a+b], phi);
Maxima encountered a Lisp error:
CAR: 2 is not a list
Automatically continuing.
To reenable the Lisp debugger set *debugger-hook* to nil.
(%i3) solve([phi=a-b,phi=a+b], phi);
Maxima encountered a Lisp error:
CAR: 2 is not a list
Automatically continuing.
To reenable the Lisp debugger set *debugger-hook* to nil.
--
William Stein
Associate Professor of Mathematics
University of Washington
http://wstein.org
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