Function Property Analysis (functions/functions.py)

functions/functions.py provides range, monotonic intervals, parity, period, and extrema analysis. All functions take the function f, variable s, and domain d as strings, with fs the function dictionary.

Note

In the functions below, is_increase and arg are reserved/placeholder parameters: passing them does not affect parsing of frange/monotonic_interval; odd_or_even/period are currently called with arg=None.

frange — range

Purpose: compute the range of a function over a given domain.

def frange(f, s, d, is_increase, fs):
    ...

Param	Type	Meaning
`f`	`str`	function expression, e.g. `"x**2"`
`s`	`str`	variable symbol, e.g. `"x"`
`d`	`str`	domain, a SymPy `Interval` string, e.g. `"Interval(0, 3)"`
`is_increase`	`bool`	placeholder (unused)
`fs`	`dict`	function dictionary

Returns: the range as a SymPy Set (from function_range).

monotonic_interval — monotonic intervals

Purpose: compute the increasing or decreasing intervals of a function.

def monotonic_interval(f, s, d, is_increase, fs):
    ...

Param	Type	Meaning
`f`	`str`	function expression
`s`	`str`	variable symbol
`d`	`str`	domain (`Interval` form)
`is_increase`	`bool`	`True` for increasing, `False` for decreasing
`fs`	`dict`	function dictionary

Returns: monotonic interval as a SymPy Set.

odd_or_even — parity

Purpose: determine the parity of a function.

def odd_or_even(f, s, d, arg, fs):
    ...

Param	Type	Meaning
`f`	`str`	function expression
`s`	`str`	variable symbol
`d`	`str`	domain
`arg`	placeholder	unused (pass `None`)
`fs`	`dict`	function dictionary

Returns: "既奇又偶函数" / "奇函数" / "偶函数" / "非奇非偶函数".

period — period

Purpose: compute the period of a function.

def period(f, s, d, arg, fs):
    ...

Param	Type	Meaning
`f`	`str`	function expression
`s`	`str`	variable symbol
`d`	`str`	domain
`arg`	placeholder	unused (pass `None`)
`fs`	`dict`	function dictionary

Returns: period expression; "该函数无周期" when aperiodic.

mvalues — extrema

Purpose: compute the maximum or minimum value of a function over its domain.

def mvalues(f, s, d, is_max, fs):
    ...

Param	Type	Meaning
`f`	`str`	function expression
`s`	`str`	variable symbol
`d`	`str`	domain (`Interval` form)
`is_max`	`bool`	`True` for maximum, `False` for minimum
`fs`	`dict`	function dictionary

Returns: extreme-value expression (SymPy maximum / minimum).

get_function_attr — unified entry

Purpose: dispatch the above analyses by the attr index; used by the UI palette.

def get_function_attr(f, s, d, attr, fs):
    ...

Param	Type	Meaning
`f`	`str`	function expression
`s`	`str`	variable symbol
`d`	`str`	domain
`attr`	`int`	attribute index 0–7 (see table below)
`fs`	`dict`	function dictionary

Returns: the result for the chosen attribute.

attr mapping

attr	meaning	calls
0	function expression & domain	`(sympify(f), sympify(d))`
1	range	`frange`
2	increasing interval	`monotonic_interval(is_increase=True)`
3	decreasing interval	`monotonic_interval(is_increase=False)`
4	parity	`odd_or_even`
5	period	`period`
6	maximum	`mvalues(is_max=True)`
7	minimum	`mvalues(is_max=False)`

Example

python frange("x**2", "x", "Interval(0, 3)", True, {}) # -> Interval(0, 9) odd_or_even("x**3", "x", "Interval(-oo, oo)", None, {}) # -> "奇函数" get_function_attr("x**2", "x", "Interval(0, 3)", 1, {}) # -> range Interval(0, 9)