unicode uppercase lowercase symmetry case-conversion

Unicode characters having asymmetric upper/lower case. Why?

Why do the following three characters have not symmetric toLower, toUpper results

/**
  * Written in the Scala programming language, typed into the Scala REPL.
  * Results commented accordingly.
  */
/* Unicode Character 'LATIN CAPITAL LETTER SHARP S' (U+1E9E) */
'\u1e9e'.toHexString == "1e9e" // true
'\u1e9e'.toLower.toHexString == "df" // "df" == "df"
'\u1e9e'.toHexString == '\u1e9e'.toLower.toUpper.toHexString // "1e9e" != "df"
/* Unicode Character 'KELVIN SIGN' (U+212A) */
'\u212a'.toHexString == "212a" // "212a" == "212a"
'\u212a'.toLower.toHexString == "6b" // "6b" == "6b"
'\u212a'.toHexString == '\u212a'.toLower.toUpper.toHexString // "212a" != "4b"
/* Unicode Character 'LATIN CAPITAL LETTER I WITH DOT ABOVE' (U+0130) */
'\u0130'.toHexString == "130" // "130" == "130"
'\u0130'.toLower.toHexString == "69" // "69" == "69"
'\u0130'.toHexString == '\u0130'.toLower.toUpper.toHexString // "130" != "49"

Solution

For the first one, there is this explanation:

In the German language, the Sharp S ("ß" or U+00df) is a lowercase letter, and it capitalizes to the letters "SS".

In other words, U+1E9E lower-cases to U+00DF, but the upper-case of U+00DF is not U+1E9E.

For the second one, U+212A (KELVIN SIGN) lower-cases to U+0068 (LATIN SMALL LETTER K). The upper-case of U+0068 is U+004B (LATIN CAPITAL LETTER K). This one seems to make sense to me.

For the third case, U+0130 (LATIN CAPITAL LETTER I WITH DOT ABOVE) is a Turkish/Azerbaijani character that lower-cases to U+0069 (LATIN SMALL LETTER I). I would imagine that if you were somehow in a Turkish/Azerbaijani locale you'd get the proper upper-case version of U+0069, but that might not necessarily be universal.

Characters need not necessarily have symmetric upper- and lower-case transformations.

Edit: To respond to PhiLho's comment below, the Unicode 6.0 spec has this to say about U+212A (KELVIN SIGN):

Three letterlike symbols have been given canonical equivalence to regular letters: U+2126 OHM SIGN, U+212A KELVIN SIGN, and U+212B ANGSTROM SIGN. In all three instances, the regular letter should be used. If text is normalized according to Unicode Standard Annex #15, “Unicode Normalization Forms,” these three characters will be replaced by their regular equivalents.

In other words, you shouldn't really be using U+212A, you should be using U+004B (LATIN CAPITAL LETTER K) instead, and if you normalize your Unicode text, U+212A should be replaced with U+004B.