MaxCalc

This calculator started as an idea for a project for [REDACTED: name of a particular online course] which I felt would be difficult enough to test my own limits as well as be an actual functional tool that I would use for my day job (math tutor).

• Intended to perform quick algebraic calculations.
• Main feature: Flexible and 'loose' parsing of algebraic expressions, much like how one would write them out.

Installation

1. Clone the repository.
2. Install windows dependancies

   pip install -r requirements.txt
   

3. Run calculator.py

   python calculator.py
   

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Commands

Command	Description
help	shows this page
vars	displays user-defined variables
del [v1] [v2] ...	deletes one or more user-defined variables
prec N	set working precision to 10^(-N), i.e. N decimal places
disp N	set final display precision to N decimal places
frac N	set length limit for fractions to be displayed
keyboard | kb [on/off]	enables / disables keyboard module for detection of Ctrl / Shift
debug [on/off]	debug mode shows calculation steps
sto[re] | = | -> <varName>	store previous calculation into 'varName'

Editing

Common text-editor functionality is available, i.e.

• Holding Ctrl enables word-jump,
• Holding Shift enables selection.
• Backtick ` switches the active window. While the display window is active, use up and down to select, then Enter to paste into the input window.

Hotkeys	Description
Shift + <Arrow>	Text selection
Ctrl + <Arrow>	Jumps forward/backward by one word
Ctrl + X / C / V	Cut / Copy / Paste
Ctrl + A	Select all
Ctrl + Bkspc	Delete word at cursor

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Things to try

Input	Notes
2{3-4[5+65(3!	Multiple bracket types are supported, and brackets are auto-closed
x = 2; 2x + 1/x	Semicolons separate expressions and evaluate to the rightmost expression

• Whitespace has an effect on precedence. Some examples:

Input	Notes
a = 2/3x; b = 2/3 x	a evaluates as 2/(3x), b evaluates as (2x)/3
a = sin pi/2; b = sinpi/2	a evaluates as sin (pi/2), b evaluates as (sin pi)/2
4x^3/5	evaluates as (4x^3)/5
a = 1/2/3/4; b = 1/2 / 3/4; c = 1 / 2/3 / 4	Give these a try!

• The previous calculation is automatically stored as ans:

Input	Notes
ans	shows previous calculation
2ans (repeatedly)	number keeps doubling
ans % 2 && 3ans + 1 || ans / 2 (repeatedly)	Collatz sequence starting with ans

• You can store and use your own variables:

Input	Notes
a = b = c = 9	assignments can be chained
(a = 3)a(b = 5)bb	not sure why you would ever do this, but it's 1125
a^bc^d	evaluates as a^(b*(c^d)), unless bc exists, in which case it would be a^(bc^d)
pi = 3.14; r = 3	pi and e are (re)defineable. Use del to reset
pir^2	evaluated as pi∙r^2, unless a variable pir also exists, in which case it would be (pir)^2
a = b = c = ab = bc = ac = abc = 1; abc	multiple possible parses will trigger a warning

• You can define your own functions. Use vars to see some preset functions.

Input	Notes
square(x) = x^2	simple square function!
quad(a, b, c) = ((-b - sqrt(b^2 - 4ac))/2a, (-b + sqrt(b^2 - 4ac))/2a)	quadratic solver
hero(a, b, c) = sqrt((a + b + c)(a + b - c)(b + c - a)(c + a - b)/16)	Hero's formula for area of triangles
g(x) = x > 3 && x^2 || x <= 3 && 2x	domains can be declared using booleans and logical and/or
h = gff	composite functions are supported
h = f^2g^3	declares h(x) = ffggg(x)
dot((x1, y1, z1), (x2, y2, z2)) = x1x2 + y1y2 + z1z2	multiple parameters are supported
cross((a, b, c), (d, e, f)) = (bf-ce, cd-af, ae-bd)	tuples are supported, even as parameters
sigma(f, l, u) = l <= u && f(l) + sigma(f, l+1, u) || f(l)	recursive functions are supported
luhn(n, q = 1) = d = n % 10; n ? (q ? d : 2d > 9 ? 2d - 9 : 2d) + luhn(n // 10, 1 - q) : 0	Luhn algorithm to calculate checksum
collatz(n) = n > 1 && 1 + (n % 2 && collatz(3n + 1) || collatz(n/2))	Collatz number-of-steps-to-reach-1
collatz(n) = n > 1 ? 1 + (n % 2 ? collatz(3n + 1) : collatz(n/2)) : 0	Alternative of above, using ternaries
(1 + i)(2 - 3i)	Complex numbers are fully implemented
a = 2e^(ipi/4); b = i^i^i; c = sin(i)	Try some fun complex calculations

• Tuples have their own operators:

Operator	Explanation
<+>	Concatenation, e.g. arr1 <+> arr2
@	Indexing, e.g. arr1 @ 1
$	Length operator, e.g. arr$
</ and />	Left and Right knife operators (for slicing!)
2 </ (1, 2, 3, 4, 5)	Outward knife: Removes 2 elements from the left -> (3, 4, 5)
2 /> (1, 2, 3, 4, 5)	Inward knife: Keeps the 2 elements from the left -> (1, 2)
(1, 2, 3, 4, 5) /> 2	Outward knife: Removes 2 elements from the right -> (1, 2, 3)
(1, 2, 3, 4, 5) </ 2	Inward knife: Keeps 2 elements from the right -> (4, 5)
1 </ (1, 2, 3, 4, 5) /> 1	Outward knives on left and right: Removes first and last element -> (2, 3, 4)

• As you may have noticed, this calculator is heavily influenced by Haskell.
• Here are examples of functions written in a "functional" style:

Input	Notes
map(f, v) = v$ ? (f(v @ 0):) <+> map(f, 1 </ v) : ()	map function
map(x => x^2)	a function which squares all elements in a list
map(x => x^2)(range(5))	[0, 1, 4, 9, 16]
reduce(f, v, a) = v$ ? reduce(f, 1 </ v, f(a, v @ 0)) : a	reduce function
dotProduct(u, v) = u$ ? u @ 0 conj(v @ 0) + dotProduct(1 </ u, 1 </ v) : 0	improved vector dot-product (any dimension)
transpose(m, result = (), col = (), r = 0, c = 0) = result$ == (m @ 0)$ ? result : r == m$ ? transpose(m, result <+> (col:), (), 0, c + 1) : transpose(m, result, col <+> (m @ r @ c:), r + 1, c)	matrix transposition
matrixMult(A, B) = B = transpose(B); (helper(result = (), row = (), r = 0, c = 0) = r == A$ ? result : c == B$ ? helper(result <+> (row:), (), r + 1, 0) : helper(result, row <+> (dotProduct(A @ r, B @ c):), r, c + 1))()	matrix multiplication. Observe that helper is an IIFE.
euler(grad, (x, y), endX, stepSize, thisGrad = grad(x, y), thisRow = ((x, y, thisGrad):)) = x >= endX ? thisRow : thisRow <+> euler(grad, (x + stepSize, y + thisGrad * stepSize), endX, stepSize)	Euler's method

Update (v3.5.0) Lambda functions are now available

Input	Notes
square = x => x^2	another way to define a square function
(x => x^2)(5)	immediately invoked square function
map = f => v => v$ ? (f(v @ 0):) <+> map(f)(1 </ v) : ()	curried map function
reduce = f => (v, a = 0) = v$ ? reduce(f)(1 </ v, f(a, v @ 0)) : a	curried reduce function

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List of currently supported math operators/functions:

Type	Operator
Arithmetic	+, -, *, /, %, ^, sqrt
Combinatoric	P, C, !
Trigonometric	sin, cos, tan, sec, cosec|csc, cot
Inverse Trig	a[rc]sin, a[rc]cos, a[rc]tan
Hyperbolic	sinh, cosh, tanh
Logarithmic	ln, lg
Logical	&&, ||
Equality	==, !=
Relational	<, <=, >, >=
Ternary	<expression> ? <trueVal> : <falseVal>
Complex	abs, arg, conj, Re, Im
Tuple manipulaton	<+>, @, $, </, /> (see above)
Vector dot and cross product	., ><
Lambda functions	=>