Expression 11: beta Subscript, "X" , Baseline left parenthesis, "c" Subscript, "L" , Baseline , "x" Subscript, "b" , Baseline , right parenthesis equals "x" Superscript, "b" , Baseline left bracket, 0...length left parenthesis, "c" Subscript, "L" , Baseline , right parenthesis , right bracket undefinedβXcL,xb=x0...lengthcLb
11
Expression 12: beta Subscript, "Y" "i" , Baseline left parenthesis, "c" Subscript, "L" , Baseline , "x" Subscript, "b" , Baseline , "x" Subscript, "i" , Baseline , right parenthesis equals Start sum from "i" equals 1 to min left parenthesis, "x" Subscript, "i" , Baseline , length left parenthesis, "c" Subscript, "L" , Baseline , right parenthesis , right parenthesis , end sum, "c" Subscript, "L" , Baseline left bracket, "i" , right bracket "x" Superscript, "b" , Baseline "i" minus 1 undefinedβYicL,xb,xi=minxi,lengthcL∑i=1cLixi−1b
12
Expression 13: beta Subscript, "Y" , Baseline left parenthesis, "c" Subscript, "L" , Baseline , "x" Subscript, "b" , Baseline , right parenthesis equals beta Subscript, "Y" "i" , Baseline left parenthesis, "c" Subscript, "L" , Baseline , "x" Subscript, "b" , Baseline , left bracket, 0...length left parenthesis, "c" Subscript, "L" , Baseline , right parenthesis , right bracket , right parenthesisβYcL,xb=βYicL,xb,0...lengthcL
13
Expression 14: beta Subscript, "C" "h" "o" "r" "d" , Baseline left parenthesis, "c" Subscript, "L" , Baseline , "x" Subscript, "b" , Baseline , right parenthesis equals left parenthesis, beta Subscript, "X" , Baseline left parenthesis, "c" Subscript, "L" , Baseline , "x" Subscript, "b" , Baseline , right parenthesis , beta Subscript, "Y" , Baseline left parenthesis, "c" Subscript, "L" , Baseline , "x" Subscript, "b" , Baseline , right parenthesis , right parenthesisβChordcL,xb=βXcL,xb,βYcL,xb
14
TODO: this repr isn't quite right...
15
Expression 16: beta Subscript, "Y" "A" "l" "t" , Baseline left parenthesis, "c" Subscript, "L" , Baseline , "x" Subscript, "b" , Baseline , right parenthesis equals mod left parenthesis, beta Subscript, "S" "u" "m" , Baseline left parenthesis, "c" Subscript, "L" , Baseline , beta , right parenthesis , beta Subscript, "X" , Baseline left parenthesis, "c" Subscript, "L" , Baseline , "x" Subscript, "b" , Baseline , right parenthesis , right parenthesis plus beta Subscript, "X" , Baseline left parenthesis, "c" Subscript, "L" , Baseline , "x" Subscript, "b" , Baseline , right parenthesis left brace, "c" Subscript, "L" , Baseline left bracket, 0...length left parenthesis, "c" Subscript, "L" , Baseline , right parenthesis , right bracket greater than "x" Subscript, "b" , Baseline minus 1 : 1 , 0 , right braceβYAltcL,xb=modβSumcL,β,βXcL,xb+βXcL,xbcL0...lengthcL>xb−1:1,0
16
alt hyperbinary chords
Hide this folder from students.
17
Hidden Label: beta Subscript, "C" "h" "o" "r" "d" , Baseline left parenthesis, left bracket, 1 , 1 , 0 , 1 , 1 , right bracket , beta , right parenthesisβChord1,1,0,1,1,β
Label
equals=
left parenthesis, 1 , 0 , right parenthesis1,0
left parenthesis, 2 , 1 , right parenthesis2,1
left parenthesis, 4 , 3 , right parenthesis4,3
left parenthesis, 8 , 3 , right parenthesis8,3
left parenthesis, 16 , 11 , right parenthesis16,11
left parenthesis, 32 , 27 , right parenthesis32,27
18
Hidden Label: beta Subscript, "C" "h" "o" "r" "d" , Baseline left parenthesis, left bracket, 1 , 1 , 2 , 0 , 1 , right bracket , beta , right parenthesisβChord1,1,2,0,1,β
Label
equals=
left parenthesis, 1 , 0 , right parenthesis1,0
left parenthesis, 2 , 1 , right parenthesis2,1
left parenthesis, 4 , 3 , right parenthesis4,3
left parenthesis, 8 , 11 , right parenthesis8,11
left parenthesis, 16 , 11 , right parenthesis16,11
left parenthesis, 32 , 27 , right parenthesis32,27
19
Hidden Label: beta Subscript, "C" "h" "o" "r" "d" , Baseline left parenthesis, left bracket, 1 , 1 , 2 , 2 , right bracket , beta , right parenthesisβChord1,1,2,2,β
Label
equals=
left parenthesis, 1 , 0 , right parenthesis1,0
left parenthesis, 2 , 1 , right parenthesis2,1
left parenthesis, 4 , 3 , right parenthesis4,3
left parenthesis, 8 , 11 , right parenthesis8,11
left parenthesis, 16 , 27 , right parenthesis16,27
