示例#1
0
def _(expr, assumptions):
    """
    * Unbounded ** NonZero -> Unbounded

    * Bounded ** Bounded -> Bounded

    * Abs()<=1 ** Positive -> Bounded

    * Abs()>=1 ** Negative -> Bounded

    * Otherwise unknown
    """
    if expr.base == E:
        return ask(Q.finite(expr.exp), assumptions)

    base_bounded = ask(Q.finite(expr.base), assumptions)
    exp_bounded = ask(Q.finite(expr.exp), assumptions)
    if base_bounded is None and exp_bounded is None:  # Common Case
        return None
    if base_bounded is False and ask(Q.extended_nonzero(expr.exp), assumptions):
        return False
    if base_bounded and exp_bounded:
        return True
    if (abs(expr.base) <= 1) == True and ask(Q.extended_positive(expr.exp), assumptions):
        return True
    if (abs(expr.base) >= 1) == True and ask(Q.extended_negative(expr.exp), assumptions):
        return True
    if (abs(expr.base) >= 1) == True and exp_bounded is False:
        return False
    return None
示例#2
0
def _(expr, assumptions):
    """
    Return True if expr is bounded, False if not and None if unknown.

    Truth Table:

    +-------+-----+-----------+-----------+
    |       |     |           |           |
    |       |  B  |     U     |     ?     |
    |       |     |           |           |
    +-------+-----+---+---+---+---+---+---+
    |       |     |   |   |   |   |   |   |
    |       |     |'+'|'-'|'x'|'+'|'-'|'x'|
    |       |     |   |   |   |   |   |   |
    +-------+-----+---+---+---+---+---+---+
    |       |     |           |           |
    |   B   |  B  |     U     |     ?     |
    |       |     |           |           |
    +---+---+-----+---+---+---+---+---+---+
    |   |   |     |   |   |   |   |   |   |
    |   |'+'|     | U | ? | ? | U | ? | ? |
    |   |   |     |   |   |   |   |   |   |
    |   +---+-----+---+---+---+---+---+---+
    |   |   |     |   |   |   |   |   |   |
    | U |'-'|     | ? | U | ? | ? | U | ? |
    |   |   |     |   |   |   |   |   |   |
    |   +---+-----+---+---+---+---+---+---+
    |   |   |     |           |           |
    |   |'x'|     |     ?     |     ?     |
    |   |   |     |           |           |
    +---+---+-----+---+---+---+---+---+---+
    |       |     |           |           |
    |   ?   |     |           |     ?     |
    |       |     |           |           |
    +-------+-----+-----------+---+---+---+

        * 'B' = Bounded

        * 'U' = Unbounded

        * '?' = unknown boundedness

        * '+' = positive sign

        * '-' = negative sign

        * 'x' = sign unknown

        * All Bounded -> True

        * 1 Unbounded and the rest Bounded -> False

        * >1 Unbounded, all with same known sign -> False

        * Any Unknown and unknown sign -> None

        * Else -> None

    When the signs are not the same you can have an undefined
    result as in oo - oo, hence 'bounded' is also undefined.
    """
    sign = -1  # sign of unknown or infinite
    result = True
    for arg in expr.args:
        _bounded = ask(Q.finite(arg), assumptions)
        if _bounded:
            continue
        s = ask(Q.extended_positive(arg), assumptions)
        # if there has been more than one sign or if the sign of this arg
        # is None and Bounded is None or there was already
        # an unknown sign, return None
        if sign != -1 and s != sign or \
                s is None and (s == _bounded or s == sign):
            return None
        else:
            sign = s
        # once False, do not change
        if result is not False:
            result = _bounded
    return result