Unicode polynomial equation

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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.