Base for intervals

ufpy/algebra/__init__.py

@@ -1 +1,2 @@
+from ufpy.algebra.interval import *
 from ufpy.algebra.sets import *

ufpy/algebra/interval.py

@@ -0,0 +1,94 @@
+from __future__ import annotations
+
+from ufpy.cmp import cmp_generator
+from ufpy.typ.type_alias import NumberLiteral
+
+__all__ = (
+    'UInterval',
+    'inf',
+)
+
+from typing import Generic, Literal, Optional, TypeVar
+
+
+@cmp_generator
+class Inf:
+    def __init__(self, sign: Literal[-1, 0, 1]) -> None:
+        self.sign = sign
+
+    def __neg__(self) -> Inf:
+        return Inf(-1)
+
+    def __pos__(self) -> Inf:
+        return Inf(+1)
+
+    def __invert__(self) -> Inf:
+        return Inf(+1 if self.sign == -1 else -1 if self.sign == 1 else 0)
+
+    def __cmp__(self, other) -> int:
+        if isinstance(other, Inf) and other.sign < self.sign:
+            return 0
+        return 1
+
+    def __repr__(self) -> str:
+        r = ''
+        if self.sign == 1:
+            r += '+'
+        elif self.sign == -1:
+            r += '-'
+
+        return f'{r}∞'
+
+inf = Inf(0)
+
+IntervalNumber = NumberLiteral | list[NumberLiteral] | Inf
+
+class UInterval:
+    def __init__(self, start: IntervalNumber, end: IntervalNumber = +inf) -> None:
+        self.__start = start[0] if isinstance(start, list) else start
+        self.__end = end[0] if isinstance(end, list) else end
+        self.inc = [int(isinstance(start, list)), int(isinstance(end, list))]
+
+    @property
+    def start(self) -> NumberLiteral | Inf:
+        return self.__start
+
+    @start.setter
+    def start(self, value: IntervalNumber):
+        self.__start = value[0] if isinstance(value, list) else value
+        if isinstance(value, list):
+            self.inc[0] = 1
+        else:
+            self.inc[0] = 0
+
+    @property
+    def end(self) -> NumberLiteral | Inf:
+        return self.__end
+
+    @end.setter
+    def end(self, value: IntervalNumber):
+        self.__end = value[0] if isinstance(value, list) else value
+        if isinstance(value, list):
+            self.inc[1] = 1
+        else:
+            self.inc[1] = 0
+
+    def __repr__(self) -> str:
+        fbracket = '[' if self.inc[0] else '('
+        sbracket = ']' if self.inc[1] else ')'
+        return f'u{fbracket}{self.__start}; {self.__end}{sbracket}'
+
+    def in_interval(self, x: NumberLiteral | Inf) -> bool:
+        b = True
+
+        if self.inc[0]:
+            b &= x >= self.__start
+        else:
+            b &= x > self.__start
+
+        if self.inc[1]:
+            b &= x <= self.__end
+        else:
+            b &= x < self.__end        
+
+        return b