Data Model:

MarvelHeroes(hid, hero, realname)

DCHeroes(hid, hero, realname)

Movies(mid, moviename, year)

HeroInMovie(hid, mid)


Relational Algebra
----------------------

Basic Definitions:

input: set of tuples, a relation, or two relations
Output: set of tuples


Set Compatibility:

Two relations are set compatible, if they have the same schema: the same
set of attributes


Set Operations:

R Union S
R Intersection S
R Set Difference S

are defined for two relations R and S, only if R and S are set compatible.

R Union S = { tuples t such t is either in relation R or in relation S}

R Intersection S = { tuples t such that t is in both relation R and S }

R Set Difference S = { tuples t such that t is in R but not in S }

----

Rename

T1 = MarvelHeroes

T1 has the same schema as MarvelHeroes

T2(hid1, hero1, realname1) = T1

T3(hid1, hero, realname) = T1

number of attributes and number of tuples does not change.

Ugrad(RIN, Name)

Grad(GradRIN, FullName)

Ugrad and Grad are not set compatible.

T1(RIN, Name) = Grad

T2 = T1 union Ugrad

----------------

SELECTION

[[slice operation]]

SELECT_C R = {t in R such that t satisfies the boolean condition C}

The result of selection has the same schema as R, but has only those tuples
that satisfy the boolean condition

Movies

MID	MOVIENAME	                YEAR
--------------------------------------------
1	Superman: Man of Tomorrow	2020
2	Spiderman: Homecoming	        2017
3	Wonder Woman	                2017
4	Deadpool	                2016
5	Green Lantern	                2011
6	Black Panther	                2018
7	Thor	                        2011
8	Thor: The Dark World	        2013
9	Avengers	                2012


- Find all movies that are made after year 2011.

T1 = SELECT_{Year > 2011} (Movies)

T1

MID	MOVIENAME	                YEAR
--------------------------------------------
1	Superman: Man of Tomorrow	2020
2	Spiderman: Homecoming	        2017
3	Wonder Woman	                2017
4	Deadpool	                2016
8	Thor: The Dark World	        2013
9	Avengers	                2012


All movies with Thor in its title

T2 = SELECT_{Moviename like 'Thor%'} (Movies)

T2

MID	MOVIENAME	                YEAR
--------------------------------------------
7	Thor	                        2011
8	Thor: The Dark World	        2013


Find movies made after 2011 with title tat starts with Thor
T3 = SELECT_{Moviename like 'Thor%' AND year > 2011} (Movies)

MID	MOVIENAME	                YEAR
--------------------------------------------
8	Thor: The Dark World	        2013


Projection
-------------

PROJECT_{A1,...AN} (R) = {t in R but only the values for the attributes A1,...,AN}

where A1,...,AN are attributes in R


T4 = PROJECT_{MID, MOVIENAME} (Movies)


T4 
MID	MOVIENAME	        
---------------------------------
1	Superman: Man of Tomorrow
2	Spiderman: Homecoming	 
3	Wonder Woman	         
4	Deadpool	         
5	Green Lantern	         
6	Black Panther	         
7	Thor	                 
8	Thor: The Dark World	 
9	Avengers	         


All years a movie was made in !

T5 = PROJECT_{YEAR} (Movies)

[[A relation is a set of tuples]]

YEAR
----
2020
2017
2016
2018
2011
2013
2012


-- Find all heroes who have not been featured in a movie

-- T1: all heroes who have been features in a movie

T1 = PROJECT_{hid} (HeroInMovie)


-- T2: all heroes in my database

T2 = Marvel_Heroes UNION DC_Heroes


--- T2 is not set compatible with T1

T3 = PROJECT_{hid} (T2)


--- All heroes who have not been in a movie


Result = T3 - T1