solve-sum-minmax 0.1.1

A package to solve the sum of min/max equations

About:
solve-sum-minmax is a Python module that allows you to solve a sum of min/max equations by taking advantage of the powerful sympy library. For instance, say you want to solve this equation: min(400, 500x) + min(200, 500x) + min(0, 500x) = 700 with the assumption that x is within range (0, 1).
In Math, the rigorous way would require you to set up all possible conditions, which might result in huge computation. Currently, there aren't any available packages in Python that allows you to solve this kind of equation fastly and efficiently. Thus, this package is developed to fill the void and hopefully be of use to the broad population.

---

Quick Start:
Let's say you want to solve the equation min(500, 600a) + max(400, 500a) = 500. However, solving it in Math means you would have to set up the conditions, then solve the check for each one of them, which sounds like a lot of work, especially for smart people like you who know how to take advantage of existing tools. So you ask yourself, "What if there is a library that lets me solve it like a piece of cake?" Well, there is a library for you now! First off, you need to install it via pip in your terminal like below:

pip install solve-sum-minmax

Then to solve your problem, simply type in these codes in your Python console:

>>> from solve-sum-minmax import solver
>>> eq = "min(500, 600*a) + max(400, 500*a) = 500"
>>> solver.auto_solve(eq, "a")
FiniteSet(1/6)

Whola! In fact, this is a pretty complex problem, but you just solved it with 3 lines of code. But hold on, what does it mean? Let's break it down: the core function auto_solve takes in two required parameters equation and var_name. equation takes in a string of the equation you want to solve and var_name lets you define your variable with flexibility, such as "a" or "x", although currently, it only supports "a". You can also pass in "low", "high", which lets you specify the range of your variable. Further details are included in the docstring if you are interested.

---

Perks:

• Fast: the module solves a set of complex min and max equations usually under 100 ms, depending on your hardware. For example, for an equation as complex as below, it takes 7 ms on average to give you a solution:

>>> from solve-sum-minmax import solver 
>>> eq = "max(600*a, 400) + min(200*a, 500) + min(100, 300*a) + 50*a = 600"
>>> %timeit solver.auto_solve(eq, "a")
FiniteSet(4/11)
7.1 ms ± 225 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)

• Accurate: it handles exact Rational numbers and intervals.
• Flexible：you have a lot of flexibility in defining your equation, see below.

---

Format guide:
Because the module depends heavily on regular expressions, please follow the guide on how to define your equations carefully, or the module might break.
In a nutshell, wrap the equation you want to solve in a string with the format similar to the example:

>>> eq = "20 + max(600*a, 400) + min(200*a, 500) + min(100, 300*a) + 50*a = 600"

Before we delve into explanations in details, let's define a few terms:

• value_term: the value you want to solve your equation for, here it's 600.
• minmax_term: it is what it means in English, for example, max(600*a, 400).
• cons_var_term: terms with constants times variables, such as 50*a.

In brief, what you can do include:

• put the variable either in the 1st or 2nd place inside the parenthesis, for example, either min(200, 300*a) or min(300*a, 200) is fine.
• use min and max together in one equation.
• use + and/or -.
• have constants in front of min or max, such as 2*min(400, 400a).
• have any space between each component.
• have leading 0s before variable, such as min(0*a, 200).
• have constants inside min or max, such as min(20, 30).

What you can't do include:

• use == instead of =.
• for the cons_var_term, have variables before constants, such as a*50 instead of 50*a.
• missing any parenthesis.
• use other operators instead of + or -.
• missing any necessary * operator for each variable.
• put any constants on the left-hand side of the equation. Do me a favor, if you have any constants, subtract it from the right-hand side and rearrange your terms before using the module.

---

Limitations:

• Currently, the module only supports "a" as the variable.
• Because the module heavily depends on regular expressions, the user needs to follow the format of the equation carefully, or the module might break.
• The equation must be uni-variate, i.e., there can only be one independent variable.

---

Version history:

Version	Core Ideas	Return Rationals	Return Intervals	Error Handling
v0.0.1	numerical methods	No	No	No
v0.0.2	numerical methods	No	No	No
v0.0.3	combinations	Yes	No	No
v0.0.4	intervals	Yes	Yes	No
v0.1.0	intervals	Yes	Yes	Yes

---

Contact:

• Email: [e-mail]
• Collaboration: collaborations are welcomed, please email me if you are interested.