PolyCalc

PolyCalc is a polynomial calculator. It calculates and expands polynomials, equations, and relations. It supports simple variable assignments for the ease of handling expressions.

Usage

PolyCalc can be used as a simple calculator:

2^10 - 1
AST: (- (^ 2 10) 1)
VAL: 1023

2 * 3.14159265 * 7
AST: (* (* 2 3.141593) 7)
VAL: 43.982297

Both AST and VAL are generated by PolyCalc--you can check AST to ensure that PolyCalc indeed parsed the given input as you have intended. VAL is the result of the expression.

If AST is not necessary, you can hide the parsed result and remove both AST: and VAL: labels altogether by invoking PolyCalc with the -q flag. The -v flag does nothing--PolyCalc is by default verbose--but it is there for completeness. The -q flag is useful if you want to redirect the output to a file via shell output redirection.

PolyCalc can also calculate and expand polynomials:

(x + y)^3
AST: (^ (+ x y) 3)
VAL: x^3 + 3 x^2 y + 3 x y^2 + y^3

(a^2 + 2ab + b^2)(a^2 - 2ab + b^2)
AST: (* (+ (+ (^ a 2) (* (* 2 a) b)) (^ b 2)) (+ (- (^ a 2) (* (* 2 a) b)) (^ b 2)))
VAL: a^4 + -2 a^2 b^2 + b^4

(x + y)(x - y) + y^2
AST: (+ (* (+ x y) (- x y)) (^ y 2))
VAL: x^2

Use assignments to improve readability and avoid repetitions:

'sum := a + b
AST: (:= sum (+ a b))
ASN: sum := a + b

'sub := a - b
AST: (:= sub (- a b))
ASN: sub := a + -1 b

'sum * 'sub
AST: (* sum sub)
VAL: a^2 + -1 b^2

Note that the assignment operator is :=, not = which represents a relation presented below.

It can simplify (a system of) equations/inequalities as well:

a + b + c = 2a - b
AST: (= (+ (+ a b) c) (- (* 2 a) b))
REL: a + -2 b + -1 c = 0

x >= y & x = y & x - y <= 0
AST: (>= x y) & (= x y) & (<= (- x y) 0)
REL: x + -1 y = 0

a > 2a
AST: (> a (* 2 a))
REL: a < 0 

y < y
AST: (< y y)
REL: INCONSISTENT SYSTEM

The result will start with VAL if you have typed an expression without a relation--REL will be shown otherwise. PolyCalc will prompt you INCONSISTENT SYSTEM if it can figure out that the given system has no solution.

If you need a variable with a name longer than a letter, put a quote(') before the name:

'long = 1
AST: (= long 1)
REL: long + -1 = 0

Since PolyCalc sorts the input variables composing a product, you can use it creatively:

sorttheseletters
AST: (* (* (* (* (* (* (* (* (* (* (* (* (* (* (* s o) r) t) t) h) e) s) e) l) e) t) t) e) r) s)
VAL: e^4 h l o r^2 s^3 t^4

PolyCalc also accepts a file as an input. For example, consider a file named input.poly with the below content:

x := 3
y := 2
x + y

Invoking PolyCalc via ./build/poly input.poly outputs:

AST: (:= x 3)
ASN: x := 3 

AST: (:= y 3)
ASN: y := 3 

AST: (+ x y)
VAL: 6 

You can combine shell redirection and the -q flag to save the output:

./build/poly -q input.poly >out.txt

Note that the flag must precede the filename.

Building Source

make

Requires GNU Bison and flex. Tested on Ubuntu 20.04.2 LTS using GNU Bison 3.5.1 and flex 2.6.4.

Running

After make, the executable is placed under build directory:

./build/poly

You can use rlwrap, e.g., to use arrow keys:

rlwrap ./build/poly