I understand that symbols are assumed complex by default. But when I tell
sympy the symbol is real, it does not make the appropriate simplification.
Here is what the dev branch produces for me right now:
>>> from sympy import *
>>> x = Symbol('x',real=True)
>>> simplify(abs(cosh(x)))
Abs(cosh(x))
Is it not possible to assess the 'realness' of the variable within the
simplify function?
Nolan
On Tuesday, February 23, 2016 at 7:43:34 AM UTC-5, brombo wrote:
>
> Sympy assumes symbols to be complex. For a real symbol you need
>
> x = Symbol('x',real=True)
>
> On Mon, Feb 22, 2016 at 9:44 PM, Nolan Dyck <[email protected]
> <javascript:>> wrote:
>
>> Hi Everyone,
>>
>> I've been poking around in the sympy source, and I've noticed that the `
>> simplify` command does not deal with expressions like the following:
>>
>> >>> from sympy import *
>> >>> from sympy.abc import x
>> >>> simplify(abs(cosh(x)))
>> Abs(cosh(x))
>>
>> A simple glance at the graph of cosh(x) reveals that Abs(cosh(x)) ==
>> cosh(x). So, in case it's not obvious the above expression should return:
>>
>> cosh(x)
>>
>> I'd like to take a stab at implementing this but I need some direction. I
>> hope this isn't duplicating something I have stupidly missed (the
>> inequality solvers don't seem to identify cases where absolute value
>> brackets are unnecessary. There are three key cases (as far as I can see):
>>
>> 1. The argument within the abs brackets is non-negative over all
>> combinations of all independent variables. Therefore, the absolute value
>> brackets redundant / unnecessary and may be removed.
>> 2. The argument within the abs brackets is non-positive over all
>> combinations of all independent variables. Therefore, the absolute value
>> brackets may be removed and the expression may be multiplied by -1 for
>> the
>> same effect.
>> 3. The argument within the abs brackets contains both positive and
>> negative values depending on the values of the independent variables.
>>
>> Ok, so to implement the above rules in the general sense it makes sense
>> to me to perform the following steps given the expression
>> Abs(f(x_1,x_2,...x_n)):
>>
>> 1. Determine the number of real roots of f(x).
>> 1. If there are one or more real roots then for each root:
>> 1. Determine whether the gradient of f(x) is zero:
>> 1. If non-zero slope at root, then argument expression
>> obtains opposite signed value at some point, so return Abs(f(x))
>> 2. Slope of f(x) at root is 0.
>> 3. Determine if the root is an inflection point (need to figure
>> out exactly how to test for this over multiple variables in the
>> expression)
>> 1. If at inflection point then the expression will still
>> become opposite signed on either side of the root, so return
>> Abs(f(x))
>> 2. Any and all roots coincide with extrema values of f(x).
>> Therefore f(x) may be represented without absolute value brackets.
>> 2. If f(x) >= 0 remove the absolute value brackets and return the
>> argument expression.
>> 3. If f(x) < 0 remove the absolute value brackets, multiply the
>> expression by -1 and return it.
>>
>> There are a few things which I'm not sure how it will work out:
>>
>> - Imaginary numbers. Does anyone know if I will need to write special
>> code for this, or should the above procedure work out anyway?
>> - The case where a symbol in the expression has been defined with the
>> positive flag:
>>
>> >>> y = Symbol('y')
>> >>> simplify(abs(sinh(y)))
>> Abs(sinh(y))
>>
>> >>> y = Symbol('y',positive=True)
>> >>> simplify(abs(sinh(y)))
>> sinh(y)
>>
>> - Are there sneaky ways of determining in a precise manner whether a
>> function which cannot be reduced (e.g. cosh(x)+cos(x)) has real roots,
>> even
>> if finding those roots would only be possible numerically? Is there
>> another
>> sympy module which can help with this?
>> - What about variables which produce no real roots over a given
>> range? Is there a way to handle those? E.g.
>>
>> >>> y = Symbol('y',range=[0,pi])
>> >>> simplify(abs(sin(y)))
>> sin(y)
>>
>> - Redundant absolute value brackets are removed somewhere. Can anyone
>> tell me where exactly in the code this happens in the simplify function?
>> I
>> can't seem to find it:
>>
>> >>> from sympy.abc import x
>> >>> simplify(abs(abs(x)+1))
>> Abs(x) + 1
>> >>> simplify(abs(x+1))
>> Abs(x + 1)
>>
>> So, right now I have forked the sympy repo (see here
>> <https://github.com/NauticalMile64/sympy>) and set up my own little
>> function in sympy.symplify called abssimp.py (just copied combsimp.py and
>> started from there), and added an appropriate if-absolute check in the main
>> simplify function. Is this the right way to go about adding such a feature?
>> Would the code that I write here also be used in solve or something?
>>
>> Any guidance / advice would be appreciated.
>>
>> Thanks!
>> Nolan Dyck
>>
>> --
>> You received this message because you are subscribed to the Google Groups
>> "sympy" group.
>> To unsubscribe from this group and stop receiving emails from it, send an
>> email to [email protected] <javascript:>.
>> To post to this group, send email to [email protected] <javascript:>
>> .
>> Visit this group at https://groups.google.com/group/sympy.
>> To view this discussion on the web visit
>> https://groups.google.com/d/msgid/sympy/aeb34566-d4b8-46f4-8eb5-f7acabbd12f4%40googlegroups.com
>>
>> <https://groups.google.com/d/msgid/sympy/aeb34566-d4b8-46f4-8eb5-f7acabbd12f4%40googlegroups.com?utm_medium=email&utm_source=footer>
>> .
>> For more options, visit https://groups.google.com/d/optout.
>>
>
>
--
You received this message because you are subscribed to the Google Groups
"sympy" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at https://groups.google.com/group/sympy.
To view this discussion on the web visit
https://groups.google.com/d/msgid/sympy/9128b7db-cb5b-4551-81fb-d7eb3b8195f4%40googlegroups.com.
For more options, visit https://groups.google.com/d/optout.
