Unicode polynomial equation

From Rosetta Code
This task has been flagged for clarification due to it being believed to be too difficult to implement in a reasonable amount of effort in more than one (usually very specialised) language. It may need to be divided into multiple tasks or modified substantially so that multiple implementations are practical, and that may cause code on this page in its current state to be flagged incorrect afterwards. See this page's Talk page for discussion.
Unicode polynomial equation is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

The objective of this task is to parse in a difficult polynomial, and generate a "pretty" representation of the polynomial in Unicode.

In the target language define a "polynomial" object (or structure or record). Using this object also define the routines for parsing a polynomial as input, and generating a normalised Unicode representation of the polynomial as output.

Task details:

Given a string containing an untidy Unicode polynomial, e.g.

-0.00x⁺¹⁰ + 1.0·x ** 5 + -2e0x^4 + +0,042.00 × x ⁺³ + +.0x² + 20.000 000 000x¹ - -1x⁺⁰ + .0x⁻¹ + 20.x¹

Coerce (or convert) the string into the "polynomial" object, at the same time normalise the polynomial to a canonical form. The ideal normalised output (in this example) would be:

x⁵ - 2x⁴ + 42x³ + 40x + 1
Specific examples of Unicode and polynomial texts to be parsed as test cases.
Description Input example test cases
"Zero" coefficients are removed x⁵ - 2x⁴ + 42x³ + 0x² + 40x + 1
The "0" polynomial case 0e+0x⁰⁰⁷ + 00e-00x + 0x + .0x⁰⁵ - 0.x⁴ + 0×x³ + 0x⁻⁰ + 0/x + 0/x³ + 0x⁻⁵
"One" coefficients are normalised 1x⁵ - 2x⁴ + 42x³ + 40x + 1x⁰
Signs are normalised +x⁺⁵ + -2x⁻⁻⁴ + 42x⁺⁺³ + +40x - -1
ASCII representations are parsed x^5 - 2x**4 + 42x^3 + 40x + 1
Non-ASCII representations are parsed x↑5 - 2.00·x⁴ + 42.00·x³ + 40.00·x + 1 (c.f. & ·)
Specifically permit non-polynomials where terms have negative exponents x⁻⁵ - 2⁄x⁴ + 42x⁻³ + 40/x + 1x⁻⁰ (n.b. Unicode Fraction)
Spaces in numbers and between operators are ignored x⁵ - 2x⁴ + 42.000 000x³ + 40x + 1
Single commas are ignored in numbers x⁵ - 2x⁴ + 0,042x³ + 40.000,000x + 1
A coefficient may be duplicated, zero, or missing 0x⁷ + 10x + 10x + x⁵ - 2x⁴ + 42x³ + 20x + 1
Support Scientific notation and optionally
support Unicode Decimal Exponent Symbol U+23E8/⏨
1E0x⁵ - 2,000,000.e-6x⁴ + 4.2⏨1x³ + .40e+2x + 1
Unicode characters that must be specifically supported are: ⁰ ¹ ² ³ ⁴ ⁵ ⁶ ⁷ ⁸ ⁹ ⁻ ⁺ · × ⁄ ↑ ⏨.
Where · & × are multiplication, and ⁄ is Unicode Fraction.
Support fractions for both input and output. x⁵ - x⁴⁄2 + 405x³⁄4 + 403x⁄4 + 5⁄2
On output round the decimal to appropriate fraction.
Optionally support Unicode Vulgar fractions for both input and output.
¼ ½ ¾ ⅐ ⅑ ⅒ ⅓ ⅔ ⅕ ⅖ ⅗ ⅘ ⅙ ⅚ ⅛ ⅜ ⅝ ⅞ ↉
x⁵ - ½x⁴ + 101¼x³ + 100¾x + 2½
On output round the decimal to appropriate fraction.

There are (at least) three possible ways of achieving this task.

  • Using an external parsing library.
  • Using a built-in parsing/formatting library.
  • Coding a custom polynomial parsing routing.

Either one, or all of these approaches are accepted and appear as a subtitle.