how about we use same method for invert(A) as for A^^-1 ?

I'd think  that the general rule should be that functions which aren't
specifically CRE or specifically rational shouldn't convert to CREs or
rational numbers.  If the input is in bfloats, the output should be in
bfloats.  Though CRE does make a lot of matrix calculations more efficient,
it can also change the form of the entries quite a bit.

            -s

On Tue, Dec 11, 2012 at 2:11 PM, Robert Dodier <robert.dodier at gmail.com>wrote:

> At this point I'd like to propose that invert be renamed to
> invert_by_adjoint and the hitherto-undocumented invertmx (which is
> called by A^^-1 to do the work) be renamed to invert.
>
> On 2012-12-10, Barton Willis <willisb at unk.edu> wrote:
>
> > Algorithmically, I don't feel the love for the adjoint method for
> > matrix inversion.  Is there a difference between invert and ^^-1 when
> > modulus # false?
>
> The only different between invert(A) and A^^-1 that I can see is that
> invert(A) doesn't convert elements to CRE while A^^-1 does.
> E.g. if A has bigfloat elements, A^^-1 converts them to rationals while
> invert(A) leaves them be.
>
> invert(A) also honors some flags (e.g. detout) which, I suppose, some
> user might possibly want.
>
> > This works the way I expect:
> >
> > (%i6) m . invert_by_lu(m, noncommutingring);
> > (%o6)
> matrix([matrix([1,0],[0,1]),matrix([0,0],[0,0])],[matrix([0,0],[0,0]),matrix([1,0],[0,1])])
>
> That's good, although invert_by_lu isn't entirely successful with
> nonscalar elements. E.g.:
>
>   declare ([a, b, c, d], nonscalar);
>   matrix_element_mult : ".";
>   matrix_element_transpose : 'transpose;
>   A : matrix ([a, b], [c, d]);
>   A1 : invert_by_lu (A, noncommutingring);
>    => matrix([a^^(-1) . (b . (d-c . a^^(-1) . b)^^(-1) . c . a^^(-1)+1),
>               -a^^(-1) . b . (d-c . a^^(-1) . b)^^(-1)],
>              [-(d-c . a^^(-1) . b)^^(-1) . c . a^^(-1),
>               (d-c . a^^(-1) . b)^^(-1)])
>
>   expand (A . A1);
>    => matrix([1,0],
>              [-d . (d-c . a^^(-1) . b)^^(-1) . c . a^^(-1)
>                +c . a^^(-1) . b . (d-c . a^^(-1) . b)^^(-1) . c .  a^^(-1)
>                +c . a^^(-1),
>               d . (d-c . a^^(-1) . b)^^(-1)
>                -c . a^^(-1) . b . (d-c . a^^(-1) . b)^^(-1)])
>
>   expand (A1 . A);
>    => matrix([1,
>               -a^^(-1) . b . (d-c . a^^(-1) . b)^^(-1) . d
>                +a^^(-1) . b . (d-c . a^^(-1) . b)^^(-1) . c . a^^(-1) .  b
>                +a^^(-1) . b],
>              [0,
>               (d-c . a^^(-1) . b)^^(-1) . d
>                -(d-c . a^^(-1) . b)^^(-1) . c . a^^(-1) . b])
>
> When the elements are in a noncommutative ring, is the matrix inverse
> well-defined? Maybe there is only a left or right inverse? I don't know.
>
> Maybe A . A1 and A1 . A could be reduced to 1's and 0's by enabling some
> flags? Dunno.
>
> best
>
> Robert Dodier
>
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