Universe

For automatic polynomial division.

Currently, only integer and fractional coefficients are supported. More number systems planned for future releases.

Quick start

For example, to evaluate $x^4 + 3x^3 + \frac{5}{2} x + 6$ divided by $x + 2$, specify the coefficients (1, 3, 0, "5/2", 6) and (1, 2) respectively.

#import "@preview/auto-div:0.1.0": poly-div, poly-div-working

Just the working itself (works both inside and outside math mode):

$ #poly-div-working((1, 3, 0, "5/2", 6), (1, 2)) $

Obtaining parts of the polynomial division as math:

#let result = poly-div((1, 3, 0, "5/2", 6), (1, 2))
$
  result.dividend = (result.quotient) (result.divisor) + (result.remainder)
$

Obtaining quotient and remainder as an array of polynomial coefficients:

Quotient: #result.quot-coeff

Remainder: #result.rem-coeff

Example image

💡 To do calculations with the returned coefficients’ fraction strings, use fractus.

Methods

poly-div

Polynomial long division.

If only displaying the working of a polynomial long division without needing results in an array of numbers, use poly-div-working instead.

Parameters

  • dividend (array, positional): Coefficients of the dividend. Last element is x^0. For fractional coefficients, specify as strings e.g. “15/4”, otherwise use integers.
  • divisor (array, positional): Coefficients of divisor. Last element is for x^0. For fractional coefficients, specify as strings e.g. “15/4”, otherwise use integers.
  • var (content, named): The variable of the polynomial. Default is $x$.

Returns

Returns a dict: (working:, quotient:, remainder:, quot-coeff:, rem-coeff:):

  • working (content): displayable content showing the working (as a table)
  • dividend (math.equation): the dividend as a math equation object
  • divisor (math.equation): the divisor as a math equation object
  • quotient (math.equation): the quotient as a math equation object
  • remainder (math.equation): the remainder as a math equation object
  • quot-coeff (array): the coefficients of the quotient polynomial as an array of fraction strings
  • rem-coeff (array): the coefficients of the remainder polynomial as an array of fraction strings

poly-div-working

Same as poly-div, but returns only the working.