Expressions Involving Infinity

[Gaurav Dhingra]

>>> from sympy import Symbol, oo, simplify

>>> x = Symbol('x', real=True)

>>> simplify( x*oo )

oo*x

Do we use extended real number system(Affinely Extended Real Number System) in sympy ?

If we do use them, then why not expressions like these  "x*oo" evaluated to a Piecewise function like 

>>> Symbol('x')

>>> simplify( x*oo )

Piecewise( ( -oo, x< 0 ), ( oo, x > 0), (Nan, x==0 ))       # i expect this to happen.

Gaurav Dhingra

[Christophe Bal]

Hello.

I think that the 2nd writing will be hard to handle in more complex calculus. Maybe the three possibilities should be available if an assumption is made on x.

A simple user.

Christophe BAL

Enseignant de mathématiques en Lycée et développeur Python amateur

---

French math teacher in a "Lycée" and Python amateur developer

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[Gaurav Dhingra]

On Sunday, May 17, 2015 at 12:43:59 PM UTC+5:30, Gaurav Dhingra wrote:

>>> from sympy import Symbol, oo, simplify

>>> x = Symbol('x', real=True)

>>> simplify( x*oo )

oo*x

Do we use extended real number system(Affinely Extended Real Number System) in sympy ?

If we do use them, then why not expressions like these  "x*oo" evaluated to a Piecewise function like 

>>> Symbol('x', real=True)

>>> simplify( x*oo )

Piecewise( ( -oo, x< 0 ), ( oo, x > 0), (Nan, x==0 ))       # i expect this to happen.

 

Edit: I have  2nd writing of x to 'real=True'

Gaurav Dhingra

[Gaurav Dhingra]

Actually that was a mistake i made in writing the 2nd one.

[AMiT Kumar]

As far as I know, I don't think we deal with Extended

Real Number System, probably that's not documented

as well.

For instance:

In [4]: solve(x <= oo)

Out[4]: And(-oo < x, x < oo)

I think we need to wait for our assumption system to

become more mature before completely supporting

Extended Real system.

AMiT Kumar

Delhi Technological University

www.iamit.in

On Sunday, May 17, 2015 at 12:43:59 PM UTC+5:30, Gaurav Dhingra wrote:

[Aaron Meurer]

x is generally assumed to be complex (not real, so your Piecewise is
not really correct). Hence it could also be I*oo or -I*oo or even zoo.
x*oo is the simplest form of this. Plus, it's best to minimize
automatic simplification, and especially avoid automatic
"simplification" that actually makes the expression more complex (like
your Piecewise).

Aaron Meurer

[Gaurav Dhingra]

Sorry for late reply. However i had mentioned in my second post as an edit that 'x' is with assumption 'real=True'.

But i now understand that  "operation i suggested" makes the expression more of complex. Rather than simplifying it.