Aaron,
Thanks for the clarification. I think I get the idea, but I'm
having trouble matching expressions of the following form:
a = Wild('a')
b = Wild('b')
x = Symbol('x')
e1 = pi + x
e2 = pi - x
e3 = -pi + x
e4 = -pi - x
I would think that for e{1,2,3,4} that I could get the following
behavior:
>>> e1.match(a*pi + b)
{a: 1, b: x}
>>> e2.match(a*pi + b)
{a: 1, b: -x}
>>> e3.match(a*pi + b)
{a: -1, b: x}
e4.match(a*pi + b)
{a: -1, b: -x}
But instead, I get:
In [61]: e1.match(a*pi + b)
Out[61]:
⎧ x ⎫
⎨a: ─, b: π⎬
⎩ π ⎭
In [65]: e2.match(a*pi+b)
Out[65]: {a: 1, b: -x}
In [66]: e3.match(a*pi+b)
Out[66]:
⎧ x ⎫
⎨a: ─, b: -π⎬
⎩ π ⎭
In [67]: e4.match(a*pi+b)
Out[67]: {a: -1, b: -x}
The results for e2 and e4 makes sense to me, but I don't understand
the behavior for e1 and e3. Is there another simpler approach, or am
I missing something fundamental here?
Thanks,
~Luke
On May 25, 4:07 pm, "Aaron S. Meurer" <[email protected]> wrote:
> On May 25, 2009, at 11:56 AM, Luke wrote:
>
>
>
>
>
> > Here is the link for the Maxima trigsimp() code. It was written in
> > 1981, according to the comments!!!
> >http://maxima.cvs.sourceforge.net/viewvc/maxima/maxima/share/trigonom...
>
> > I emailed the authors of the Fu et al. paper to see if they would be
> > willing to share their implementation of the algorithm -- maybe we can
> > save ourselves some work this way.
>
> > I want to start coding for this, because much of the stuff I am doing
> > in PyDy is heavy on kinematics and the expressions become excessively
> > long unless intelligent trigsimplification is possible. Many of my
> > unittests simply will not work because some results I know to be true
> > cannot be achieved with the current state of trigsimp, so this has
> > become a significant limitation for me.
>
> > What should be the general framework for implementing the 'rules' that
> > are laid out in the Fu paper? There are certainly other rules we
> > could find, either on Wikipedia, Mathworld, or in a engineering/
> > mathematics reference manual.
>
> > I have read over how trigsimp() and trigsimp_nonrecursive() are
> > currently implemented, and I think I get the gyst of what the approach
> > is. Can somebody explain what this is doing exactly:
> > for pattern, simp in matchers:
> > res = result.match(pattern)
> > ....
>
> > I'm not 100% clear on the use of the .match() method, does somebody
> > have a quick example of use?
>
> This should be res = ret.match(pattern).
>
> match() takes a wildcard expression and matches it into a dictionary.
> In the code above, pattern is each of the items in the list
> ((a*sin(b)**2, a - a*cos(b)**2),(a*tan(b)**2, a*(1/cos(b))**2 - a),
> (a*cot(b)**2, a*(1/sin(b))**2 - a)) (it runs a for loop). a, b and c
> are wild cards, to it will try to take the expression result and find
> what a, b, and c are equal to.
>
> For example, consider the first one: a*sin(b)**2. If your ret ==
> 4*x*sin(x**2)**2, then running res = ret.match(a*sin(b)**2) will
> return the dictionary {a: 4*x, b: x**2}. You can then access a and b
> from res[a] and res[b].
>
> You should also probably be aware of the exclude option on Wild. If
> you do a = Wild('a', exclude=[sin(x)]), then a will not match anything
> with sin(x) in it. Do help(x.matches) for another example.
>
> > It seems like the flow of trigsimp (in the case of recursive==False
> > and deep==False):
> > 1) call trigsimp_nonrecursive(expr, deep==False), store the result in
> > 'result'
> > 2) do some final pattern matching on 'result', currently this will
> > only simplify a*sin(b)**c/cos(b)**c --> a*tan(b)**c
>
> > So, should all the rules in Fu et al. be implemented as a tuple of
> > length 2 tuples, similar to the existing matchers tuple?
>
> > I'm kind of thinking out loud right now and trying to figure out the
> > next step to take....
>
> > ~Luke
>
> > On May 21, 7:42 am, Akshay Srinivasan <[email protected]>
>
>
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