RA (Relational Algebra ) -- QL (Query Language). Reading: Chapter 2
Set of elements - set of relations
Set of operations - RA operations
Categories:
1. Set operations: union, difference, intersection
2. Remove parts : projection, selection
3. Combination : Cartesian product, joins
4. Renaming
Union R1(S), R2(S),
t  R1  R2
Deposit_1
Min
Weight Hard
zircon 190
7.5
topaz 182
8
R = R1  R2
if
t  R1  t  R2
Deposit_2
Min
Weight Hard
calcite 100
3
zircon 190
7.5
Deposit_1  Deposit_2
Min
Weight Hard
zircon 190
7.5
topaz
182
8
calcite 100
3
Difference R1(S), R2(S), R = R1 - R2
t  R1 - R2 if
t  R1  t  R2
Deposit_1 - Deposit_2
Min Weight Hard
topaz 182
8
Deposit_2 - Deposit_1
Min
Weight Hard
calcite 100
3
Projection R(S), S'  S, π S' R
t'  π S' R if
Minerals
Min
Weight
zircon 190
topaz 182
calcite 100
zircon 190
topaz 182
Hard
7.5
8
3
7.5
8
Streak
white
white
white
white
white
t' = restriction(t) S' , t  R
Color
green
blue
white
brown
yellow
π Min,Hard,Weight Minerals
Min
Hard Weight
zircon 7.5
190
topaz 8
182
calcite 3
100
Selection R(S), σ C R
C: attributes, const, comparisons, logical connectives
t  σ C R if t  R, C(t) = true
σ Weight>150 AND Hard<8 Minerals
Min
Weight Hard Streak Color
zircon 190
7.5
white green
zircon 190
7.5
white brown
Cartesian product R1(S1), R2(S2), R(S), S = S1,S2, R = R1  R2
t  R1  R2 if t = t1,t2, t1  R1, t2  R2
Branches
Branch Address
Br_1
Addr_1
Br_2
Addr_2
Br_3
Addr_3
Deposit_1  Branches
Min
Weight Hard
zircon 190
7.5
zircon 190
7.5
zircon 190
7.5
topaz 182
8
topaz 182
8
topaz 182
8
Branch
Br_1
Br_2
Br_3
Br_1
Br_2
Br_3
Address
Addr_1
Addr_2
Addr_3
Addr_1
Addr_2
Addr_3
Basis: independent set of generators
Intersection
R1(S), R2(S),
R = R1  R2
t  R1  R2 if
t  R1  t  R2
R = R1 - (R1 - R2)
Deposit_1  Deposit_2
Min
Weight Hard
zircon 190
7.5
Joins: natural, theta, semi
Natural join
H_group
Hard Group
3
soft
7
hard
8
hard
Theta join
R1(S1), R2(S2), R(S), S = S1  S2,
A = S1  S2
R = π S (σ R1.A=R2.A (R1  R2))
Minerals |  | H_group
Min
Weight Hard
topaz 182
8
calcite 100
3
topaz 182
8
Streak
white
white
white
R1(S1), R2(S2), R(S), S = S1,S2,
R = σ C (R1  R2)
Minerals |  | Color=white OR Color=blue H_group
Min
Weight Minerals.Hard Streak Color
topaz 182
8
white blue
topaz 182
8
white blue
topaz 182
8
white blue
calcite 100
3
white white
calcite 100
3
white white
calcite 100
3
white white
Semi-join
R1 |  R2 = π S1 (R1 |  | R2)
R = R1 |  | R2
Color
blue
white
yellow
Group
hard
soft
hard
R = R1 |  | C R2
H_group.Hard
3
7
8
3
7
8
Group
soft
hard
hard
soft
hard
hard