# Polynomial calculator specs

## Input sources
* Array of polynomials (size $n$)
* Array of variables

## Outputs
* Array of polynomials

## Program
A list of expressions using the following operations:

* Add
* Mul
* Sub
* Neg

References:
* Poly(n) - refers to the current value of the $n$th input polyomial.
* Poly_next(n) - refers to the next value of the $n$th input polynomial.
* Var(n) - refers to the $n$th input variable
* Const(n) - refers to the $n$th constant.
* Ref(n) - refers to a perviously defined expression at the $n$th index.

A node reference:

{
  type: POL, POL_NEXT, VAR, CONST, REF
  id: integer
}

An expression node:

{
  op: ADD | SUB | MUL,
  lhs: node_reference,
  rhs: node_reference, 
}

Program:

{
  num_of_polys: integer,
  num_of_variables: integer,
  consts: [ arry of field elements],
  exprs: [ array of expression nodes],
  outputs: [array of node_reference]
}

Inputs:
* Array of polynomials
* Length of polynomials
* Array of variables
* Next row offset

Outputs:
* Array of polynomials