--Week 0 Macaulay 2 script : Basics on rings and ideals
--Lines following two dashes are comments
--read this into Macaulay by placing this file in a directory and typing 
-------input "week0.m2"
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--Macaulay knows the rings RR, QQ, ZZ, ZZ/101, ZZ/32749 etc
--Construct a quotient ring by R/I for a ring R and Ideal I
--Create polynomial rings by listing the variables 
---------------------------inside [] after the ring

R=QQ[x,y,z,w]	       	--polynomials in 4 variables with rational coefficients

--Create ideals by giving the generators
I=ideal(x^2-y,z*w)
J=ideal(x*y*z,w^3)


--Macaulay can do the usual ideal operations and return generators for the result

I*J
intersect(I,J)
I+J
I^2

--Macaulay can compute the radical of an ideal
radical J