Sorry, one more thing - I can't get the wildcards to work. Can you provide
an example?
-Andy S.
On Sat, Jan 3, 2015 at 6:50 PM, Andrew Spielberg <aespielb...@gmail.com>
wrote:
> Hi Aaron,
>
> w.r.t. killing the Abs, that's not sufficient, because sometimes I need
> the Abs( ) to turn into -Id( ).
>
> One of those, exp, was created via simpify. The other, expr, was created
> from "the ground up" using Symbols. No assumptions are being made.
>
> -Andy S.
>
> On Sat, Jan 3, 2015 at 2:28 PM, Aaron Meurer <asmeu...@gmail.com> wrote:
>
>>
>>
>> On Fri, Jan 2, 2015 at 9:50 PM, Andrew Spielberg <aespielb...@gmail.com>
>> wrote:
>>
>>> Sorry for the double post. It seems replace is very weak as well, not
>>> being able to detect multiples :-/
>>>
>>> In [60]: expr.replace(math.Abs(guardlength - 0.5*length), guardlength -
>>> 0.5*length)
>>> Out[60]: width*(-2*guardlength + length + Abs(2*guardlength -
>>> length))/Abs(2*guardlength - length)
>>>
>>> In [61]: expr.replace(math.Abs(2*guardlength - length), 2*guardlength -
>>> length)
>>> Out[61]: 0
>>>
>>
>> You can use Wild symbols to match against coefficients.
>>
>> But in your case, if all you want to do is kill all the Abs in the
>> expression, use expr.replace(Abs, Id).
>>
>> Aaron Meurer
>>
>>
>>>
>>>
>>> On Fri, Jan 2, 2015 at 11:47 PM, Andrew Spielberg <aespielb...@gmail.com
>>> > wrote:
>>>
>>>> This may be a dumb question, but can you please explain what is going
>>>> on here...? exp was made using simpify, expr was created from scratch.
>>>> Replace operates on them differently.
>>>>
>>>> In [48]: exp
>>>> Out[48]: width*(-2*guardlength + length + Abs(2*guardlength -
>>>> length))/Abs(2*guardlength - length)
>>>>
>>>> In [49]: expr
>>>> Out[49]: width*(-2*guardlength + length + Abs(2*guardlength -
>>>> length))/Abs(2*guardlength - length)
>>>>
>>>> In [50]: exp.replace(math.Abs(2*guardlength - length), 2*guardlength -
>>>> length)
>>>> Out[50]: width*(-2*guardlength + length + Abs(2*guardlength -
>>>> length))/Abs(2*guardlength - length)
>>>>
>>>> In [51]: expr.replace(math.Abs(2*guardlength - length), 2*guardlength -
>>>> length)
>>>> Out[51]: 0
>>>>
>>>> In [52]: exp == expr
>>>> Out[52]: False
>>>>
>>>
>> I can't say. According to this, exp and expr (without replace) are
>> different. I can't say why, though, without seeing how you made them, as
>> the string forms are identical. Are you using assumptions on your symbols?
>>
>> Aaron Meurer
>>
>>
>>>
>>>> -Andy S.
>>>>
>>>> On Fri, Jan 2, 2015 at 10:06 PM, Aaron Meurer <asmeu...@gmail.com>
>>>> wrote:
>>>>
>>>>>
>>>>>
>>>>> On Fri, Jan 2, 2015 at 12:13 PM, Andrew Spielberg <
>>>>> aespielb...@gmail.com> wrote:
>>>>>
>>>>>> Hi guys,
>>>>>>
>>>>>> Thanks for your help so far. I am revisiting this after ignoring
>>>>>> this issue for a while.
>>>>>>
>>>>>> I'm still trying to come up with a good way to use this. I've
>>>>>> noticed the following:
>>>>>>
>>>>>> Say:
>>>>>> a = Symbol('a')
>>>>>> b = Symbol('b')
>>>>>> assumptions = Q.positive(a - b)
>>>>>> expr = 1/Abs(a - b)
>>>>>>
>>>>>> If I try:
>>>>>>
>>>>>> refine(expr, assumptions)
>>>>>>
>>>>>> it returns:
>>>>>>
>>>>>> 1/(a - b)
>>>>>>
>>>>>> as desired. But, if I try:
>>>>>>
>>>>>> expr = Abs(b - a)/Abs(a - b)
>>>>>>
>>>>>> it returns:
>>>>>>
>>>>>> │-b + a│
>>>>>> ────────
>>>>>> a - b
>>>>>>
>>>>>> I can add an assumption that:
>>>>>>
>>>>>> assumptions = assumptions & Q.negative(b - a)
>>>>>>
>>>>>> And then refining returns 1. But then I can do something like:
>>>>>>
>>>>>> expr = Abs(0.5*b - 0.5*a)/Abs(a - b)
>>>>>>
>>>>>> And it fails again. Is the pattern matcher this weak? Is there any
>>>>>> way to get what I want that doesn't require refine, or is there a better
>>>>>> way to use refine to get what I want? My assumptions are simple - they
>>>>>> will all be linear equations of variables.
>>>>>>
>>>>>
>>>>> I don't think refine is even using a pattern matcher. It really isn't
>>>>> very powerful yet, as I noted earlier in this thread.
>>>>>
>>>>> replace() has a better pattern matching abilities if that's all you're
>>>>> going for.
>>>>>
>>>>> Aaron Meurer
>>>>>
>>>>>
>>>>>> -Andy S.
>>>>>>
>>>>>> On Fri, Nov 14, 2014 at 6:03 PM, Aaron Meurer <asmeu...@gmail.com>
>>>>>> wrote:
>>>>>>
>>>>>>> Note that if you want to kill all abs in your expression, there's an
>>>>>>> easier way. expr.replace(Abs, Id)
>>>>>>>
>>>>>>> Aaron Meurer
>>>>>>>
>>>>>>> On Fri, Nov 14, 2014 at 5:02 PM, Aaron Meurer <asmeu...@gmail.com>
>>>>>>> wrote:
>>>>>>>
>>>>>>>> As I said, it's *very* proof of concept. Many advanced things don't
>>>>>>>> work.
>>>>>>>>
>>>>>>>> In this case, I think the issue is with the assumptions in general.
>>>>>>>> They can't deduce from the facts And(Q.positive(-beamwidth),
>>>>>>>> Q.positive(-length), Q.positive(0.9*beamwidth - length))
>>>>>>>> that 0.866025403784438*beamwidth - length is positive. I'm not
>>>>>>>> even sure what algorithms need to be implemented to make this work.
>>>>>>>>
>>>>>>>> Why are your beamwidth and length variables negative? From the
>>>>>>>> variable names, they sound like they should be positive?
>>>>>>>>
>>>>>>>> Aaron Meurer
>>>>>>>>
>>>>>>>> On Wed, Nov 12, 2014 at 9:44 PM, Andrew Spielberg <
>>>>>>>> aespielb...@gmail.com> wrote:
>>>>>>>>
>>>>>>>>> refine_abs isn't doing the trick here either. Am I using this
>>>>>>>>> module incorrectly?
>>>>>>>>>
>>>>>>>>> On Tue, Nov 11, 2014 at 6:09 PM, Andrew Spielberg <
>>>>>>>>> aespielb...@gmail.com> wrote:
>>>>>>>>>
>>>>>>>>>> Thanks guys. This seems to be mostly working so far.
>>>>>>>>>>
>>>>>>>>>> Any idea why this wouldn't be, though?
>>>>>>>>>>
>>>>>>>>>> In [1]: assumptions
>>>>>>>>>> Out[1]: And(Q.positive(-beamwidth), Q.positive(-length),
>>>>>>>>>> Q.positive(0.9*beamwidth - length))
>>>>>>>>>>
>>>>>>>>>> In [2]: exp
>>>>>>>>>> Out[2]: 0.866025403784439*beamwidth*(0.866025403784438*beamwidth
>>>>>>>>>> - length)/Abs(0.866025403784438*beamwidth - length)
>>>>>>>>>>
>>>>>>>>>> In [3]: math.refine(exp, assumptions)
>>>>>>>>>> Out[3]: 0.866025403784439*beamwidth*(0.866025403784438*beamwidth
>>>>>>>>>> - length)/Abs(0.866025403784438*beamwidth - length)
>>>>>>>>>>
>>>>>>>>>> (math is my sympy module)
>>>>>>>>>>
>>>>>>>>>> A little confused here as to why the fraction wouldn't simplify
>>>>>>>>>> out. (0.866025403784438*beamwidth -
>>>>>>>>>> length)/Abs(0.866025403784438*beamwidth - length) should be 1.
>>>>>>>>>>
>>>>>>>>>> -Andy S.
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> On Tue, Nov 11, 2014 at 3:16 AM, Mateusz Paprocki <
>>>>>>>>>> matt...@gmail.com> wrote:
>>>>>>>>>>
>>>>>>>>>>> Hi,
>>>>>>>>>>>
>>>>>>>>>>> On 11 November 2014 01:13, Aaron Meurer <asmeu...@gmail.com>
>>>>>>>>>>> wrote:
>>>>>>>>>>> > Q is just a namespace for the assumptions, like Q.positive or
>>>>>>>>>>> Q.real.
>>>>>>>>>>> >
>>>>>>>>>>> > refine() simplifies things based on assumptions.
>>>>>>>>>>>
>>>>>>>>>>> I think we shouldn't use "refine()" and "simplifies" together as
>>>>>>>>>>> this
>>>>>>>>>>> only can increase confusion. Simplification implies that there
>>>>>>>>>>> is an
>>>>>>>>>>> optimisation procedure applied. refine() just transforms an
>>>>>>>>>>> expression
>>>>>>>>>>> given some facts about it.
>>>>>>>>>>>
>>>>>>>>>>> Mateusz
>>>>>>>>>>>
>>>>>>>>>>> This example returns x - y,
>>>>>>>>>>> > because sqrt((x - y)**2) is equal to x - y if x - y is
>>>>>>>>>>> positive (but not in
>>>>>>>>>>> > general).
>>>>>>>>>>> >
>>>>>>>>>>> > What kinds of simplifications are you expecting to get out of
>>>>>>>>>>> your
>>>>>>>>>>> > constraints?
>>>>>>>>>>> >
>>>>>>>>>>> > Aaron Meurer
>>>>>>>>>>> >
>>>>>>>>>>> >
>>>>>>>>>>> > On Mon, Nov 10, 2014 at 5:42 PM, Andrew Spielberg <
>>>>>>>>>>> aespielb...@gmail.com>
>>>>>>>>>>> > wrote:
>>>>>>>>>>> >>
>>>>>>>>>>> >> Hi Aaron,
>>>>>>>>>>> >>
>>>>>>>>>>> >> Thanks for the speedy reply. I'm not sure I fully understand
>>>>>>>>>>> what this
>>>>>>>>>>> >> example does, or how. Could you perhaps elaborate? What is
>>>>>>>>>>> Q? What is the
>>>>>>>>>>> >> difference between refine and simplify?
>>>>>>>>>>> >>
>>>>>>>>>>> >> I should note that the entirety of my constraints will be
>>>>>>>>>>> linear, so if
>>>>>>>>>>> >> the current functionality can do that, that's enough.
>>>>>>>>>>> >>
>>>>>>>>>>> >> -Andy S.
>>>>>>>>>>> >>
>>>>>>>>>>> >> On Mon, Nov 10, 2014 at 5:06 PM, Aaron Meurer <
>>>>>>>>>>> asmeu...@gmail.com> wrote:
>>>>>>>>>>> >>>
>>>>>>>>>>> >>> There is a framework to do this with refine, like
>>>>>>>>>>> refine(sqrt((x -
>>>>>>>>>>> >>> y)**2), Q.positive(x - y)), but not much is implemented yet,
>>>>>>>>>>> so the
>>>>>>>>>>> >>> simplifications possible are quite limited (in fact, there's
>>>>>>>>>>> not much more
>>>>>>>>>>> >>> than the one that I just showed that is implemented).
>>>>>>>>>>> >>>
>>>>>>>>>>> >>> Aaron Meurer
>>>>>>>>>>> >>>
>>>>>>>>>>> >>> On Mon, Nov 10, 2014 at 3:58 PM, Andrew Spielberg <
>>>>>>>>>>> aespielb...@gmail.com>
>>>>>>>>>>> >>> wrote:
>>>>>>>>>>> >>>>
>>>>>>>>>>> >>>> Hi all,
>>>>>>>>>>> >>>>
>>>>>>>>>>> >>>> When creating variables, I know you can provide certain
>>>>>>>>>>> constraints on
>>>>>>>>>>> >>>> the domain of that variable. For instance, one could say
>>>>>>>>>>> that a certain
>>>>>>>>>>> >>>> variable, x, is positive, real, rational, etc. These
>>>>>>>>>>> constraints affect the
>>>>>>>>>>> >>>> way the simplify function behaves.
>>>>>>>>>>> >>>>
>>>>>>>>>>> >>>> I am wondering, without creating auxiliary variables, can
>>>>>>>>>>> add other
>>>>>>>>>>> >>>> constraints? For example, if I have a variable x that
>>>>>>>>>>> always must be
>>>>>>>>>>> >>>> greater than another variable y, can I specify:
>>>>>>>>>>> >>>>
>>>>>>>>>>> >>>> x > y
>>>>>>>>>>> >>>>
>>>>>>>>>>> >>>> in some way, and have the simplifier intelligently know how
>>>>>>>>>>> to handle
>>>>>>>>>>> >>>> it? I know I could change my representation to be a = (x -
>>>>>>>>>>> y) and do
>>>>>>>>>>> >>>> everything in terms of my variable a, and set a positive,
>>>>>>>>>>> but this is less
>>>>>>>>>>> >>>> than ideal and will not work in a lot of my cases.
>>>>>>>>>>> >>>>
>>>>>>>>>>> >>>> If there is no way to set these assumptions, is there some
>>>>>>>>>>> other
>>>>>>>>>>> >>>> recommended way to do intelligent simplification in some
>>>>>>>>>>> way?
>>>>>>>>>>> >>>>
>>>>>>>>>>> >>>> -Andy S.
>>>>>>>>>>> >>>>
>>>>>>>>>>> >>>> --
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