Module lange.ap
Expand source code
# Copyright (c) 2021. Davi Pereira dos Santos
# This file is part of the lange project.
# Please respect the license - more about this in the section (*) below.
#
# lange is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# lange is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with lange. If not, see <http://www.gnu.org/licenses/>.
#
# (*) Removing authorship by any means, e.g. by distribution of derived
# works or verbatim, obfuscated, compiled or rewritten versions of any
# part of this work is a crime and is unethical regarding the effort and
# time spent here.
# Relevant employers or funding agencies will be notified accordingly.
from lange.abs.progression import Progression
class AP(Progression):
"""Arithmetic Progression. A flexible inductive sequence of numbers based on Haskell interval notation.
maxdigits: maximum amount of digits verified during precision detection
(includes numbers to the left and to the right of the decimal separator, if any)
Usage:
>>> AP(5)
[5]
>>> AP(5, 1)
[5 1]
>>> list(AP(1, 3, ..., 10))
[1, 3, 5, 7, 9]
>>> ap = AP(0.6, 0.8, ..., 1.2)
>>> ap
[0.6 0.8 .+. 1.2]
>>> list(ap)
[0.6, 0.8, 1.0, 1.2]
>>> ap[1]
0.8
>>> print(AP(0.2, 4.1, 0.9))
[0.2 4.1 0.9]
>>> ap = AP(0.6, 0.8, ...)
>>> ap
[0.6 0.8 .+. inf]
>>> list(ap[:5])
[0.6, 0.8, 1.0, 1.2, 1.4]
>>> AP()
[]
>>> print(AP())
[]
Usage (square brackets syntax):
>>> from lange import ap
>>> (ap[0.6, 0.8, ..., 2])
[0.6 0.8 .+. 2.0]
>>> ap[1, 2]
[1 2]
>>> list(ap[1, 2])
[1, 2]
>>> ap[1]
[1]
>>> list(ap[1])
[1]
>>> ap[3, 1, 6, 7, 0]
[3 1 6 7 0]
>>> list(ap[3, 1, 6, 7, 0])
[3, 1, 6, 7, 0]
>>> ap[4, 5, 2, 9, 4, 7, 3, 3][2:6]
[2 9 4 7]
>>> ap[4, 5, 2, 9, 4, 7, 3, 3][5]
[7]
>>> list(ap[3, 2, 6666, 7, 8, 6, 5555, 7, 3, 9][2:9:4])
[6666, 5555]
>>> list(ap[0.1, 0.2, ...][2:8])
[0.3, 0.4, 0.5, 0.6, 0.7, 0.8]
>>> ap[0.1, 0.2, ...][2:9:2]
[0.3 0.5 .+. 0.9]
>>> ap[1,2,...]
[1 2 .+. ∞]
>>> ap[1,2,...][1_000_000_000_000]
1000000000001
"""
def __init__(self, *args, maxdigits=28):
def f(a, b, c):
if b * c < 0: # pragma: no cover
raise Exception(
f"Cannot build arithmetic progression when direction ({c}) and target ({b}) have opposite signal."
)
return (b - a) / c
super().__init__(
"+",
0,
lambda a, b: a + b,
lambda a, b: a - b,
lambda a, b: a * b,
f,
args,
maxdigits,
)
def __reduce__(self): # pragma: no cover
return AP, self.args + (self.maxdigits,)Classes
class AP (*args, maxdigits=28)-
Arithmetic Progression. A flexible inductive sequence of numbers based on Haskell interval notation.
maxdigits: maximum amount of digits verified during precision detection (includes numbers to the left and to the right of the decimal separator, if any)
Usage
>>> AP(5) [5] >>> AP(5, 1) [5 1] >>> list(AP(1, 3, ..., 10)) [1, 3, 5, 7, 9] >>> ap = AP(0.6, 0.8, ..., 1.2) >>> ap [0.6 0.8 .+. 1.2] >>> list(ap) [0.6, 0.8, 1.0, 1.2] >>> ap[1] 0.8 >>> print(AP(0.2, 4.1, 0.9)) [0.2 4.1 0.9] >>> ap = AP(0.6, 0.8, ...) >>> ap [0.6 0.8 .+. inf] >>> list(ap[:5]) [0.6, 0.8, 1.0, 1.2, 1.4] >>> AP() [] >>> print(AP()) []Usage (square brackets syntax): >>> from lange import ap >>> (ap[0.6, 0.8, …, 2]) [0.6 0.8 .+. 2.0] >>> ap[1, 2] [1 2] >>> list(ap[1, 2]) [1, 2] >>> ap[1] [1] >>> list(ap[1]) [1] >>> ap[3, 1, 6, 7, 0] [3 1 6 7 0] >>> list(ap[3, 1, 6, 7, 0]) [3, 1, 6, 7, 0] >>> ap[4, 5, 2, 9, 4, 7, 3, 3][2:6] [2 9 4 7] >>> ap[4, 5, 2, 9, 4, 7, 3, 3][5] [7] >>> list(ap[3, 2, 6666, 7, 8, 6, 5555, 7, 3, 9][2:9:4]) [6666, 5555] >>> list(ap[0.1, 0.2, …][2:8]) [0.3, 0.4, 0.5, 0.6, 0.7, 0.8] >>> ap[0.1, 0.2, …][2:9:2] [0.3 0.5 .+. 0.9] >>> ap[1,2,…] [1 2 .+. ∞] >>> ap[1,2,…][1_000_000_000_000] 1000000000001
Expand source code
class AP(Progression): """Arithmetic Progression. A flexible inductive sequence of numbers based on Haskell interval notation. maxdigits: maximum amount of digits verified during precision detection (includes numbers to the left and to the right of the decimal separator, if any) Usage: >>> AP(5) [5] >>> AP(5, 1) [5 1] >>> list(AP(1, 3, ..., 10)) [1, 3, 5, 7, 9] >>> ap = AP(0.6, 0.8, ..., 1.2) >>> ap [0.6 0.8 .+. 1.2] >>> list(ap) [0.6, 0.8, 1.0, 1.2] >>> ap[1] 0.8 >>> print(AP(0.2, 4.1, 0.9)) [0.2 4.1 0.9] >>> ap = AP(0.6, 0.8, ...) >>> ap [0.6 0.8 .+. inf] >>> list(ap[:5]) [0.6, 0.8, 1.0, 1.2, 1.4] >>> AP() [] >>> print(AP()) [] Usage (square brackets syntax): >>> from lange import ap >>> (ap[0.6, 0.8, ..., 2]) [0.6 0.8 .+. 2.0] >>> ap[1, 2] [1 2] >>> list(ap[1, 2]) [1, 2] >>> ap[1] [1] >>> list(ap[1]) [1] >>> ap[3, 1, 6, 7, 0] [3 1 6 7 0] >>> list(ap[3, 1, 6, 7, 0]) [3, 1, 6, 7, 0] >>> ap[4, 5, 2, 9, 4, 7, 3, 3][2:6] [2 9 4 7] >>> ap[4, 5, 2, 9, 4, 7, 3, 3][5] [7] >>> list(ap[3, 2, 6666, 7, 8, 6, 5555, 7, 3, 9][2:9:4]) [6666, 5555] >>> list(ap[0.1, 0.2, ...][2:8]) [0.3, 0.4, 0.5, 0.6, 0.7, 0.8] >>> ap[0.1, 0.2, ...][2:9:2] [0.3 0.5 .+. 0.9] >>> ap[1,2,...] [1 2 .+. ∞] >>> ap[1,2,...][1_000_000_000_000] 1000000000001 """ def __init__(self, *args, maxdigits=28): def f(a, b, c): if b * c < 0: # pragma: no cover raise Exception( f"Cannot build arithmetic progression when direction ({c}) and target ({b}) have opposite signal." ) return (b - a) / c super().__init__( "+", 0, lambda a, b: a + b, lambda a, b: a - b, lambda a, b: a * b, f, args, maxdigits, ) def __reduce__(self): # pragma: no cover return AP, self.args + (self.maxdigits,)Ancestors
Inherited members