-- MATH 531 -- Aug 30 -- Basics

-- every comment starts with "--"
QQ -- rational numbers
3/4
111.345
12124 + 121*ii
ZZ -- integers
ZZ/102 
isPrime 101
ZZ/101 -- finite fields (use a prime only)
a = 4/5
ring a -- the ring of a

--- Polynomial rings ---
R = QQ[x,y,z] -- a basic definition of a polynomial ring
R
describe R -- gives a better idea of what R is than just "R"
coefficientRing R
0_R -- this is a zero in the ring
0   -- this is an integer
1_R
8_R 
R_0 -- 0th var
R_2 -- 2nd var
index y
numgens R
gens R -- variables in a list
vars R -- variables in a matrix 

-- Polynomials --

f = random(3,R) -- a random polynomial of degree 3
degree f
y^2 > x*z      
y^2 ? x*z
restart -- restarts M2
R = QQ[x,y,z,MonomialOrder=>Lex] -- a ring with lex order
f = y^2-x*z
listForm f -- a list of exponent vectors 
           -- and corresponding coefficients
leadMonomial f
size f -- the number of monomials