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https://github.com/zeta611/polycalc

Polynomial Calculator
https://github.com/zeta611/polycalc

math mathematics polynomial polynomial-arithmetic polynomial-equations polynomial-multiplication polynomial-systems polynomials symbolic symbolic-computation symbolic-math

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Polynomial Calculator

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README 

        
# 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

```sh

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:

```sh

./build/poly

```



You can use [`rlwrap`](https://github.com/hanslub42/rlwrap), e.g., to use arrow

keys:

```sh

rlwrap ./build/poly

```