Thanks Matt, I've successfully tested the merged functionality. Once I have
some time on my hands, I'll try adding related functionality, such as
semi-orthogonal matrices.
Cheers,
Chris
On Tuesday, April 1, 2014 1:27:26 PM UTC-7, Matthew wrote:
>
> This has been added to SymPy and merged.
>
> In [1]: X = MatrixSymbol('X', n, n)
>
> In [2]: with assuming(Q.orthogonal(X)):
> ...: print refine(X * X.T)
> ...:
> I # identity matrix
>
>
>
> On Tue, Mar 18, 2014 at 4:32 PM, Chris <[email protected] <javascript:>>wrote:
>
>> Hi Matt,
>>
>>
>> awesome, I'll take a look and see how far I get.
>>
>> Thanks for your help!
>> Chris
>>
>> On Monday, March 17, 2014 8:41:21 PM UTC-7, Matthew wrote:
>>
>>> I added a bunch more refine handlers.
>>>
>>> Chris, if you wanted to play around with this branch and see if it does
>>> what you need that'd be helpful. Even better, maybe after looking at the
>>> diff in the PR you could add some logic yourself? The pattern of how to do
>>> this should be pretty easy to pick out.
>>>
>>>
>>> On Mon, Mar 17, 2014 at 7:37 PM, Matthew Rocklin <[email protected]>wrote:
>>>
>>>> Well, on the simplify/refine side I think we only need to call ask. At
>>>> some stage this might be wired back into `is_foo`
>>>>
>>>> I implemented this particular refinement in https://github.com/sympy/
>>>> sympy/pull/7296 just to see how it felt.
>>>>
>>>> BTW, refine could totally use a better dispatching system. If only,
>>>> ahem, someone had built such a thing....
>>>>
>>>>
>>>> On Mon, Mar 17, 2014 at 6:16 PM, Aaron Meurer <[email protected]>wrote:
>>>>
>>>>> I'm not clear what the plan should be regarding auto-evaluation and
>>>>> refine and the new assumptions. I feel that it hasn't been heavily
>>>>> thought out yet. We have to somehow balance the pain of having to call
>>>>> all sorts of with assuming() and refine() just to get things to
>>>>> simplify and the performance issues if they do it automatically (and
>>>>> also the issues of potentially not wanting it to always happen
>>>>> automatically).
>>>>>
>>>>> Aaron Meurer
>>>>>
>>>>> On Mon, Mar 17, 2014 at 7:12 PM, Matthew Rocklin <[email protected]>
>>>>> wrote:
>>>>> > Hi Chris,
>>>>> >
>>>>> > Thanks for the kind words.
>>>>> >
>>>>> > At the moment Matrix Expressions in the main branch do not use
>>>>> assumptions
>>>>> > while simplifying. IIRC they actually used to but I removed it so
>>>>> that I
>>>>> > could approach this more cleanly. One lofty reason for this was so
>>>>> that
>>>>> > this could be used as a model for the rest of sympy when it
>>>>> eventually jumps
>>>>> > over to the new assumptions system.
>>>>> >
>>>>> > If other devs see this e-mail - what are your thoughts on `refine`,
>>>>> the
>>>>> > simplify API suggested (but rarely used) by new assumptions? Should
>>>>> we
>>>>> > start using this? Should we roll it into simplify? In general at
>>>>> what
>>>>> > point should we appeal to new assumptions? At expression creation
>>>>> time? At
>>>>> > simplify time? At another simplify-like api time (e.g. refine
>>>>> time)? I
>>>>> > decided not to call upon new assumptions while creating expressions
>>>>> (e.g.
>>>>> > X.T creates a Transpose(X) even if X is symmetric). I think that my
>>>>> > reasoning at the time was performance.
>>>>> >
>>>>> > Chris, in general what you're asking for is easy for us to add. I
>>>>> would
>>>>> > like to make sure that we add it correctly.
>>>>> >
>>>>> > Also, it's been some time since this was all in my head. I may have
>>>>> said
>>>>> > some untrue things.
>>>>> >
>>>>> > Best,
>>>>> > -Matthew
>>>>> >
>>>>> >
>>>>> >
>>>>> >
>>>>> > On Mon, Mar 17, 2014 at 4:57 PM, Chris <[email protected]> wrote:
>>>>> >>
>>>>> >> Hi all,
>>>>> >>
>>>>> >>
>>>>> >> I stumbled upon the discussion on matrix assumptions and the bit of
>>>>> >> history behind this sympy module:
>>>>> >>
>>>>> >> http://scicomp.stackexchange.com/questions/74/symbolic-
>>>>> software-packages-for-matrix-expressions
>>>>> >>
>>>>> >> First off all, thank you Matt, this is incredibly cool stuff!
>>>>> >>
>>>>> >> Now, I'm trying to do some matrix algebra while encoding knowledge
>>>>> about
>>>>> >> the matrices involved. For instance, say my matrix U is unitary,
>>>>> i.e. U *
>>>>> >> U.T = I. I've looked around in the documentation and source code,
>>>>> but
>>>>> >> couldn't figure out, if the new assumption system can be used to
>>>>> simplify
>>>>> >> matrix expressions.
>>>>> >>
>>>>> >> I was trying to exploit this using sympy as follows:
>>>>> >>
>>>>> >> from sympy import Q, symbols, MatrixSymbol, ask, simplify
>>>>> >> from sympy.assumptions.assume import global_assumptions
>>>>> >>
>>>>> >> n = symbols('n', integer=True)
>>>>> >> U = MatrixSymbol('U', n, n)
>>>>> >>
>>>>> >> global_assumptions.add(Q.unitary(U))
>>>>> >>
>>>>> >> UU = U * U.T
>>>>> >>
>>>>> >> print UU
>>>>> >>
>>>>> >> simpleUU = simplify(UU)
>>>>> >> print simpleUU
>>>>> >>
>>>>> >>
>>>>> >> I was hoping that the second print would output the Identity, but
>>>>> somehow
>>>>> >> this didn't work. Any suggestions, pointers, hints?
>>>>> >>
>>>>> >>
>>>>> >> Cheers,
>>>>> >> Chris
>>>>> >>
>>>>> >> --
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