Perhaps I should clarify a couple more things:

I have figured out how to do simple Macaulay 2 commands inside a sage
script as follows:

macaulay2("S = ZZ/101[t_1 .. t_9, u_1 .. u_9]")

However, many of my commands are not working.  The code in Macaulay2
which I would like to execute from sage looks like this:

mult = I -> (
minPrimes := minimalPrimes I;
monomialFreeMinPrimes := select(minPrimes, P -> saturate(P, product
gens S) =!= ideal (1_(ring(I))));
sum apply(monomialFreeMinPrimes, P -> degree(I : saturate(I,P)))
)

S = QQ[x,y,z]
I = ideal(y-x^2, y^2-x*z)
mult(I)


When I try to define the mult function using the macaulay2() command,
I get a syntax error because of the arrow (->).

macaulay2( mult = I -> ( minPrimes := minimalPrimes I;
monomialFreeMinPrimes := select(minPrimes, P -> saturate(P, product
gens S) =!= ideal (1_(ring(I)))); sum apply(monomialFreeMinPrimes, P -
> degree(I : saturate(I,P))) )

Also, when I type

I=macaulay2(ideal(x^2+y))

I get "error: syntax error at 'of' "


Anyway, I know this is a lot of things to ask about, but any help
would be appreciated.  Thanks!

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