I think you shouldn't blame it all on the user. I understand and
appreciate that Sage makes a clear distinction between different types
and handles them differently. But that doesn't explain the numerous
errors which are caused by SAGE's funtions which should work with a
specific type, but simply refuse to.

Here is another instance: http://alpha.sagenb.org/home/pub/701/

It does not work because "abs( )" returns an "Expression" which
will cause find_local_minimum to cause errors.

This is one instance of dozens I've encountered. Other examples include
functions returning floats while yet others cause errors when called
with floats instead of Reals, etc...

On Mon, May 13, 2013 at 05:22:07PM -0700, rjf wrote:
>    On Monday, May 13, 2013 2:11:59 PM UTC-7, ManDay wrote:
> 
>      Could anyone shed a bit of light on this?
> 
>      The more I try, the more SAGE's types get in my way.
> 
>    It is pretty much understood by some people in the computer algebra
>    system-building community
>    that "types" or "categories" or similar concepts imposed on users who
>    understand some mathematics (but maybe not much modern algebra)
>     and not much about programming language design and numerical computation,
>    will fall into holes.
> 
>    See what happened to Scratchpad / Axiom. It tries and maybe does as
>    good a job as we know how to do, but users don't go for it.
> 
>    It is not too surprising to find people falling into holes in the Sage
>    type system.
> 
>    Sorry, no easy solution to everything along these lines has emerged.  So
>    far
>    as I can tell, Python offers no step forward, and maybe a step backward.
> 
>    RJF
> 
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