Here is an example from the `lts` branch computing the product of two
functions
that have different ranges in each:
>>> p = Piecewise((a,abs(x-1)<1),(b,abs(x-2)<2),(c,True))*Piecewise((d,x>1
),(e,True))
>>> piecewise_fold(p)
Piecewise(
(a*d, (x > 1) & (x < 2)),
(b*d, (x > 1) & (x < 4)),
(c*d, x > 1),
(a*e, Abs(x - 1) < 1),
(b*e, Abs(x - 2) < 2),
(c*e, True))
>>> _.integrate(x).diff(x)
Piecewise(
(c*e, x <= 0),
(a*e, x <= 1),
(a*d, x <= 2),
(b*d, x <= 4),
(c*d, True))
[Note that value `b*e` does not appear in the final result because it has
been determined to not appear because higher priority expression are
defined on the range in which `b*e` is defined.]
I like the idea of range_function. Here are two ways it might be done:
>>> def range_function(x, *args):
... return Piecewise(*[
... (a[0], And(x>=a[1],x<=a[2])) for a in args])
...
>>> range_function(x, (a,1,2),(b,3,4),(c,0,6))
Piecewise((a, (x >= 1) & (x <= 2)), (b, (x >= 3) & (x <= 4)), (c, (x >= 0) &
(x <= 6)))
>>> def interval_function(x, *args):
... return Piecewise(*[
... (a[0], a[1].contains(x)) for a in args])
...
>>> interval_function(x, (a,Interval(1,2)),(b,Interval.Lopen(0,4)))
Piecewise((a, (x >= 1) & (x <= 2)), (b, (x <= 4) & (x > 0)))
On Sunday, June 11, 2017 at 4:33:28 PM UTC-5, [email protected] wrote:
>
>
>
> On Wednesday, June 7, 2017 at 5:49:34 PM UTC-4, Aaron Meurer wrote:
>>
>>
>>
>> >
>> > My thoughts on Piecewise is that it's trying to do too many things.
>> There's
>> > a difference between representing a function whose form changes
>> depending on
>> > the value of its argument (in my case, t) and an answer that depends on
>> > parameter values (a and b). The latter distinction is best described
>> with a
>> > cases statement. I.e., t is different from a and b.
>>
>> I'm not sure I follow here. Are you suggesting to use a separate
>> object. What would it look like?
>>
>> I'm thinking of a "range" object (I wish the name "Piecewise" was still
> available). Something like this:
>
> f = range_function([(f1,t1,t2),(f2,t3,t4),...],t)
>
> The first argument is a list of functions with the range of the arguments
> for that function. The final argument is the variable. The notation mimics
> the integrate function.
>
> I've written a partially completed convolution function for these range
> functions. Convolution requires knowing the range of each function. But I
> got stuck when I ran the example before whose answer depends on parameter
> values. That the answer depends on parameter values is the job for a
> "cases" function (like the Latex cases function).
>
> The last step (which I haven't finished, but it's straightforward) is to
> combine the outputs of the various convolutions into a range function.
>
> I haven't given much thought how to extend the range function to multiple
> variables. It's probably straightforward when the ranges are rectangles,
> but maybe less for other shapes (e.g., circles).
>
>
>
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