--This file contains some of the commands used during the Macaulay2
--demonstration

1+1
3!
binomial(4,2)
factor(60)

QQ
ZZ/3
ZZ/32749
GF(4)

RR -- don't use!
CC -- or this one!

--Ideals
R=QQ[x_0,x_1,x_2,x_3]

I=ideal(x_0*x_2-x_1^2, x_0*x_3-x_1*x_2, x_1*x_3-x_2^2)

gb I
gens gb I
leadTerm I

isPrime I

dim(I)

degree(I)

hilbertPolynomial(I,Projective=>false)

--Matrices

A = matrix {{1,1,1,1},{0,1,2,3}}

rank A

kernel A

gens kernel A

entries transpose gens kernel A

B = transpose(A)*A;

det(B)

rank(B)

R=QQ[x,y,z]

A=matrix {{1,x,x^2},{1,y,y^2},{1,z,z^2}}

det(A)

factor(det(A))

help det

viewHelp det

--First break 

--if/then
a = 7;
if a<8 then <<"a is less than 8"<<endl;   --  << is the print command

--loops (three versions)

scan(10,i->(<<i^2<<endl;))   -- loops start at 0

apply(10,i->i^2)

for i from 0 to 9 do
    <<i^2<<endl;

--Functions

--evaluate a polynomial

p = n ->(n^2+2*n+3);

p(3)
p(x)
--find the ith smallest entry of a matrix

f = (A,i) ->(B =sort flatten entries A;
    	     return(B_(i-1));
);



A=matrix{{100,10,1},{5,6,7}}

f(A,1)
f(A,2)
f(A,3)
f(A,10)


--Finish by showing webpage of packages
http://www2.macaulay2.com/Macaulay2/Packages/


--Other useful commands
A=matrix {{1},{2},{3}}
B = entries(A)
C= flatten B

R=QQ[x,y]
S=QQ[t]
f = map(R,S,{t,t^2})

diff(x,f)
minors(2,A)
jacobian ideal f

Grassmannian(1,3)