Subject: Implicit: Taylor, Poiseux and Newton's diagram
From: Stavros Macrakis
Date: Fri, 1 Jun 2012 12:54:56 -0400
Correction:
(%o28) true <<< "is" performs "mathematical" equality, not
formal equality
should read:
(%o28) true <<< is/equal performs "mathematical" equality, not
formal equality
On Fri, Jun 1, 2012 at 12:50 PM, Stavros Macrakis <macrakis at alum.mit.edu>wrote:
> On Fri, Jun 1, 2012 at 3:29 AM, Oliver Kullmann <O.Kullmann at swansea.ac.uk>wrote:
>
>> By the way, how would one actually check in Maxima for identity, so that
>> "1+1" is only identical to "1+1" and nothing else? It seems the evaluation
>> (rewriting) of 1+1 to 2 is hard to avoid?
>>
>
> In Maxima, it is important to distinguish between "evaluation"
> (substitution of values, calling of imperative routines) and
> "simplification" (rewriting).
>
> Almost every part of Maxima dealing with mathematical objects depends on
> its input being in simplified form. For example, almost nothing in Maxima
> recognizes the unsimplified quotient a/b -- internally, it is always
> handled as a*b^-1. So for instance with simp=false, diff(x/x,x) =>
> 'diff(x/x,x), though diff(x*x^-1,x) => x^-1*(x^-1*(-1)+log(x)*0)*x+1*x^-1
> (which simplifies to 0).
>
> Normally, simplification is on or off globally, so it is not easy to avoid
> simplification (rewriting) while also dealing with normal (simplifying)
> operations. However, it is possible to construct unsimplified
> expressions and force Maxima to treat them as if they were simplified --
> see simpfunmake in my package simplifying.lisp (cf.
> http://www.ma.utexas.edu/pipermail/maxima/2011/024588.html). Some
> operations on these pseudo-simplified expressions will force
> simplification, and what exactly other operations perform on them is not
> easy to guess:
>
> (%i19) load("simplifying.lisp")$
> (%i20) foo: simpfunmake(verbify("*"),[2,3,a,a]);
> (%o20) 2*3*a*a
> (%i21) ?print(%);
> ((MTIMES SIMP) 2 3 $A $A)
> (%o21) 2*3*a*a
> (%i22) foo/2;
> (%o22) 3*a*a <<< the 2 is cancelled
> (%i23) foo/3;
> (%o23) 2*3*a*a/3 <<< the 3 is not...
> (%i24) foo/a;
> (%o24) 2*3*a <<< the a is cancelled
> (%i25) foo/a^2;
> (%o25) 2*3*a/a <<< one a is cancelled, but not the other...
> (%i26) is(foo=foo);
> (%o26) true
> (%i27) is(foo=6*a^2);
> (%o27) false
> (%i28) is(equal(foo,6*a^2));
> (%o28) true <<< "is" performs "mathematical" equality, not
> formal equality
>
> Order matters:
>
> (%i31) bar: simpfunmake(verbify("*"),[a,2,a]);
> (%o31) a*2*a
> (%i32) bar/2;
> (%o32) a*2*a/2
> (%i33) bar/a;
> (%o33) 2*a
> (%i34) bar/a^2;
> (%o34) 2*a/a
>
> (%i43) bqz: simpfunmake(verbify("*"),[b,a,2,a,b]);
> (%o43) b*a*2*a*b
> (%i44) bqz/a;
> (%o44) b*a*2*a*b/a
>
> It's not clear to me exactly what problem you're trying to solve, but
> perhaps that helps?
>
> Of course, another approach is simply to use your own functions/operators.
> Maxima is perfectly happy to deal with undefined functions in prefix or
> infix form:
>
> (%i46) infix("%%");
> (%o46) "%%"
> (%i47) a %% b;
> (%o47) a %% b
>
> for which you can define your own rewrite rules (?? patterns) to apply
> automatically or only on demand.
>
> -s
>
>