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index -- numeric index of a ring variable

Synopsis

Description

Variables are indexed in the following way: the first variable has index 0, the second index 1, and so on, until n-1, where n is the number of generators of R, the ring of v. Then, if the coefficient ring is a polynomial ring, those variables are numbered starting at n, and so on.
i1 : R = ZZ/101[a..d,t]

o1 = R

o1 : PolynomialRing
i2 : index a

o2 = 0
i3 : index t

o3 = 4
i4 : A = ZZ[a..d]; B = A[r,s,t]; C = B[x,y,z]

o6 = C

o6 : PolynomialRing
i7 : index x

o7 = 0
i8 : index z

o8 = 2
i9 : index r

o9 = 0
Notice that r is an element of B, and so indices are taken from that ring. If we consider r as an element of C, we get a different answer. Variables of coefficient rings of coefficient rings have an index too.
i10 : index(r*1_C)

o10 = 3
i11 : index(b*1_C)

o11 = 7

The symbol index is also as a key used in GeneralOrderedMonoids to store a table that is used to map generator names to the position of the generator in the list of generators.

See also

Ways to use index :