On Mon, Dec 07, 2020 at 02:06:22PM +0100, Waldek Hebisch wrote:
> On Mon, Dec 07, 2020 at 06:57:08PM +0800, Qian Yun wrote:
> >
> > To record the problem we encountered this time, it boils down to
> >
> > y :=
> > (complex(0,1)*x*exp((complex(0,2)*x)/complex(1,0))+complex(-1,0)*x)/(complex(1,1)*exp((complex(0,2)*x)/complex(1,0))+complex(1,1))
> >
> > a :=
> > (complex(0,-1)*exp((complex(0,1)*x)/complex(1,0))^2+complex(0,-1))/(complex(2,0)*exp((complex(0,1)*x)/complex(1,0)))
> >
> > b :=
> > (complex(-2,0)*exp((complex(0,1)*x)/complex(1,0)))/(complex(1,0)*exp((complex(0,1)*x)/complex(1,0))^2+complex(-1,0))
> >
> > And smaller?(y,a) smaller?(a,b) smaller?(b,y) are all true,
> > causing it impossible to order kernel exp(y),exp(a),exp(b).
>
> The expressions are transcendental and 'smaller?' should work
> for them. OTOH inside integrator 'exp(2*%i*x)' and 'exp(%i*x)'
> should not appear together, 'normalize' removes first one
> and no other routine should introduce new unnormalizes
> kernels. Unfortunaltely, some routines do this and
> we need to replace them by correct ones.
Oops, '%i' is algebraic. I was thinking that special
handling in Complex avoids the trouble and that one
can treat it as transcendentals, but unfortunately not.
Actually, already definiton of 'smaller?' in Fraction
is unsound...
We need some order for display purposes so probably need
to define 'smaller?' for kernels, but it must be done
in more ad-hoc way...
--
Waldek Hebisch
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