Relation Algebra

must have the same schema

symbolic manipulation to yield a result, which does not change the data set directly

Examples

π_name (Parts) =

{(Bolt),

(Elec Wiring), (Insulation),

(Solar Shield)}

π_name (Projects) =

{ (Appollo 8), (B, Apollo 10),

(Appollo 11), (Solar Shield)}

we can have multiple projections

π_part, proj (commitment) =

{(1, A) (2, B), (2, C) (3, A)

(3, B), (3, C)}

/we exclude duplicate values

π_proj (commitment) = {(A), (B), (C)}

we can combine relations

π_name(Parts) U pi_name(Projects) = …

we manipulate to yield elements of a set that satisify a condition

σ_QtyOnHand <= 100 (Parts) =

{(3, insulation, 100, sq.m), …}

σ_projid = A || ProjId = D (Projects) =

{(A, Apollo 8), (D, Solar Shield)}

σ_qty > 500 (Commitment) = 0

σ_qty > 0 (Commitment) = Commitment

Parts x Projects =

{((1, Bolt, 1000, null), (A, Apollo, 8)),

((1, Bolt, 1000, null), (B, Apollo, 10))

((1, Bolt, 1000, null), …)

((1, Bolt, 1000, null), …)

…}

by our definition tuples have to be flattened and not have nested tuples so the correct format is

Parts x Projects =

{(1, Bolt, 1000, null, A, Apollo 8),

(1, Bolt, 1000, null, B, Apollo 10)

(1, Bolt, 1000, null, …)

(1, Bolt, 1000, null, …)

…}

Schema? (PartNo, Name, QtyHand, Unit, ProjID, Name)

notice how we have two attributes with the same name

this is no good, we fix this with a simple fix

(PartNo, Parts.Name, QtyHand, Unit, ProjID, Projects.Name)