# Can I express an abstract, symbolic range of reals?

Hello, I'm very new at sage. I'd like to express a range like range(-3.0,3.0,0.02) but with symbols for all the parameters, like range(a,b,delta), that displays nicely with show(). I would like to be able to substitute in floats at some later stage.

a. I'm not sure what a conventional symbolic expression for a range of floats is

b. Not sure how to express it in SageMath.

My goal is to be able to express constructing a chain rule over a finite input range. I seem to be able to express the chaining of functions ok, but am getting stuck with what i'm calling the constant function which is this range. If I use the range(-3.0,3.0,0.02) I get swamped by the output.

P.S. I don't want to use a built-in differentiate, I'm going to use finite differences.

Cheers...

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In Jupyter notebook I'm up to here, could be horribly unconventional:

from typing import List, Dict, Callable
# A Function takes in an ndarray as an argument and produces an ndarray
Array_Function = Callable[[ndarray], ndarray]
Chain = List[Array_Function]

identity_function(x) = SR('x')

def compose(chain: Chain)-> Callable:
if not chain:
return identity_function
else:
return chain(compose(chain[1:]))

input_range = np.arange(-3, 3, 0.02)

c0: Chain = [x ** 2, max(0.2 * x,x), 1 / (1 + exp(-x))]
sigmoid,lru,square = c0
show([sigmoid,lru,square])

show(compose(c0))


"If I use the range(-3.0,3.0,0.02) I get swamped by the output."

In that case, I usually do L=range(-3.0,3.0,0.02) to avoid to be swamped by the output.

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This is not an abstract symbolic expression for a range - which I would still like, but this answer uses numpy to provide its default output summary with ellipses for large arrays. Solves my practical problem of too much output.
ref: https://doc.sagemath.org/html/en/thematic_tutorials/numerical_sage/numpy.html

  import numpy as np

l = np.array(srange(-3.0, 3.0, 0.002))
show(l)

[⎯𝟹.⎯𝟸.𝟿𝟿𝟾⎯𝟸.𝟿𝟿𝟼...𝟸.𝟿𝟿𝟺𝟸.𝟿𝟿𝟼𝟸.𝟿𝟿𝟾]

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The answer from @Sebastien displayed ellipses in its output summary, maybe this feature is broken in sage's jupyter notebook implementation?

1

I don't know for the symbolic range, but note that sage provides srange which takes floats as input:

sage: srange(-3.0,3.0,0.02)
[-3.00000000000000,
-2.98000000000000,
-2.96000000000000,
-2.94000000000000,
...
2.96000000000000,
2.98000000000000]


EDIT:

Above, the ellipse "..." replacing the long output was done by hand. To have the ellipse to appear automatically, the best is to create your own class. For example:

sage: class MyRange(SageObject):
....:     def __init__(self, start, stop, step):
....:         self._start = start
....:         self._stop = stop
....:         self._step = step
....:     def to_srange(self):
....:         return srange(self._start, self._stop, self._step)
....:     def __iter__(self):
....:         return iter(self.to_srange())
....:     def __repr__(self):
....:         L = self.to_srange()
....:         if len(L) < 10:
....:             return repr(L)
....:         else:
....:             Lellipse = L[:3] + ["..."] + L[-3:]
....:             return '['+', '.join(str(a) for a in Lellipse)+']'
....:
....:
sage: MyRange(-3,3,1)      # short list no ellipse
[-3, -2, -1, 0, 1, 2]
sage: MyRange(-3,3,0.02)    # long list with ellipse
[-3.00000000000000, -2.98000000000000, -2.96000000000000, ..., 2.94000000000000, 2.96000000000000, 2.98000000000000]
sage: sum(a^2 for a in MyRange(-3,3,0.02))
900.020000000001
sage: sum(a^2 for a in srange(-3,3,0.02))   # confirms that MyRange considers the whole list
900.020000000001


To learn how to use classes in Python/Sage, you may also look at this fruit.py example available in my optional package.

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Thanks, Have already tried that. Same swamped output. Want to be able to have symbolic parameters to the range expression. Or equivalent - with a compact show() output.

srange( a, b, delta)

I think you want to create a Python class and write your own __repr__ method. Let me update my answer...

Thanks @Sebastien - I think you are right. Though I found numpy arrays seem to do the ellipses nicely. Maybe I really need to write a class for a symbolically parameterised range, which can be realised. Seems weird not to have one. I keep feeling I’ve missed something obvious.

Very hard to work out which way to do things when starting out - unsurprisingly :-)

When I work with long ranges, I usually don't need to look at them. I just store them in a variable and that's it. But, it is true that such feature is useful. For example, the string representation of a pandas dataframe containing millions of lines will print only the few first and few last lines.