# rich1126/mrmath

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Classes
asymptote.py
mrmath.py

# mrmath

This holds some homemade classes and functions for various mathematical purposes. Nothing here is groundbreaking, or even particularly useful when compared to any modules available in Python. This is a hobbyist "Learn more Python" type project.

Navigate to the mrmath folder after downloading and run Python from there. Then just from mrmath import * to access all this has to offer.

## Fractions

A class called frac that acts as a common fraction.

frac(a, b) gives a common fraction of the form a/b, reduced to lowest terms. If a single argument is given, frac(a), it converts the float (or integer) into a fraction based on the decimal. So, frac(1.25) will return 5/4.

Accepts addition, subtraction, multiplication, and division by another frac, as well as int and float types, returning a frac in each instance. Similarly, one can divide an int or float by a frac and get another frac in return.

Supports float(myFrac) to get its floating point representation. Naturally supports comparison, exponentiation (by an int, which returns a frac; or by a float or frac which returns a float.)

Has a simple method myFrac.roundInt() which just rounds it to the nearest integer. This is so round() method built-in to Python is not overloaded.

## 2D Vectors

A class vtwo that works as a two-dimensional vector over the real numbers. Tentative plans to add another class later for three-dimensional, then arbitrary-dimensional vectors as well.

A vtwo is represented as (x,y). You can add vectors component-wise, scale using vec.scale(constant), get the magnitude using abs(vec), find the dot (or inner) product using vec1.dot(vec2), as well as the 2D scalar cross product, vec1.cross(vec2) which returns v_1 x v_2.

Other methods include finding the angle in standard position: vec.angle('r') for radians or vec.angle('d') for degrees. You can also find the angle between two vectors: vec1.angle('r', vec2) (with similar support for d). You can project vectors using vec1.proj(vec2) which is the projection of vec1 onto vec2.

Vectors also support the frac type. That is, in addition to the components x and y being int or float, they can also be frac. You can turn them directly by using vec.asFrac(), which returns another vtwo object where the components are frac.

Finally, you can take a vector and represent it in the complex plane using vec.asComplex() which returns a Complex object.

## Complex Numbers

A standard complex number class. You can do normal arithmetic operations (add, subtract, multiply, divide). Perhaps future diving into exponentation, but that gets a bit complicated.

Initiated by Complex(Real, Imaginary = 0) so you can just put in a real number so that it acts as a complex number. Arithmetic operations can interface with int, float, or frac types. (So, the hierarchy here is that if int or float interface with a frac, they become frac. If any of the below interface with Complex, they become Complex.

Supports magnitude and conjugation. Can convert to vector using com.asVector(). Similarly, can convert Real and Imaginary to frac types using com.asFrac().

## Polynomials

A standard real-number polynomial class. You can do addition, subtraction, and multiplication. The multiplication operation supports scaling by an integer or float (full frac support coming later), or by another polynomial.

Displays in the "Mathematica style" that looks like 1 + x^1 + -2x^2 + x^4 for clarity.

You can evaluate the polynomial at a certain value by doing myPoly.eval(n).

## Graphics (in development)

I like to use the Asymptote Vector Graphics language to create diagrams. I use it at work, and it's an absolutely fantastic language with a pretty intuitive way of drawing things. It does a lot of the work for you.

So, naturally, I would like to be able to implement it to draw figures based on at least the vtwo objects, and probably Complex objects. However, you would need to have an installation of Asymptote and a postScript viewer. (Asymptote comes with TeXLive if you have that. The standard PostScript viewer at least on Debian-based Linux distros is gv. It seems this is also available on Mac via brew, and I'm unsure about Windows.)

Here is a minimum working example for using Asymptote with vtwo. The general format is vec1.draw(ctx, vec2) which draws vec1 on the asymptote context ctx, with origin vec2.

You can also use vec.label(ctx, string, origin, direction) where string is a valid LaTeX-type string defining the label text, origin is the origin of where you're drawing the vector (so you can label vectors arbitrarily), and direction is a cardinal direction. Currently the direction is relative to the mid-point of the vector.

from mrmath import *

## Create vector objects
origin = vtwo(0,0)
vec1 = vtwo(3,4)
vec2 = vtwo(1,2)
vec3 = vec1 - vec2

## Create asymptote object
g = asy()
g.size(200)

## Draw vectors
vec1.draw(g, origin)
vec2.draw(g, origin)
vec3.draw(g, vec2)

## Label vec1 as \vec{a}
## Use a raw string r' ' to make sure slashes work
vec1.label(g, r'"$\vec{a}$"', origin, 'SE')
vec2.label(g, r'"$\vec{b}$"', origin, 'NW')
vec3.label(g, r'"$\vec{a}-\vec{b}$"', vec2, 'NW')

del g

The result is a pretty basic image:

If you want to interface more directly with Asymptote within a Python script, because you want to do anything beyond drawing and labeling vectors, check out some of the basics here. Theoretically everything you could want can be done via the send method in asymptote.py, but some of the main functions like draw, label, fill, and path are written as methods to make things about 15% easier.

Of course, at that point it's probably easier to directly write Asymptote code. But hey, sometimes it's good to have things in the same place.

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