[Maxima] Representing the case "no result"
drdieterkaiser at web.de
Mon Jun 8 17:57:02 CDT 2009
Am Montag, den 08.06.2009, 15:24 -0700 schrieb Richard Fateman:
> can you deal with inf*%i ? Check on what mathematica does -- I think it
> allows for a unit vector in any direction in the complex plane.
> adding all this to the simplifier is risky, e.g. inf+inf=inf,
> inf-inf=undefined or perhaps .
> It would be hard to convince Robert D that this is a good idea if it
> slows things down.
> (Hard to convince me and others, too. But possible)
As a guide I have chosen the definitions on functions.wolfram.com and
For the following I used the definitions:
directed_infinity(1) ---> '$inf
directed_infinity(-1) ---> '$minf
directed_infinity(0) ---> '$infinity
directed_infinity(false) ---> '$und or '$ind
I have not distinguished beetween '$und and '$ind and call both cases
indeterminate. This can be changed.
Next I have implemented the arithmetic (addition, multiplication,
exponentiation) for directed infinities. In a first try I have implemented
the code directly into the simplifying functions for add, mul and power.
I have tried to be complete. These are examples:
Numbers and symbols are absorbed from the directed infinity:
The addition of inf and inf gives inf:
The addition of inf and minf gives indeterminate:
But subtraction of inf and minf gives again inf:
Multiplication with Zero gives indeterminate:
Expressions in a multiplication are absorbed as an argument of the directed
infinity. The argument is simplified to the complex signum value:
The general case which simplifies to the correct expressions:
Division of Zero through infinities:
Zero and a directed infinity as a power:
Nested directed infinities are simplified:
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