Description
When a ring (or a monoid) is assigned to a global variable, this function is automatically called for it.
It is possible to have several polynomial rings defined, perhaps with a variable belonging to several rings.
i1 : R = QQ[a..d]
o1 = R
o1 : PolynomialRing
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i2 : S = QQ[b,c,d,e]
o2 = S
o2 : PolynomialRing
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i3 : b
o3 = b
o3 : S
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At this point, b is thought to be a variable of S. If one typed
a+b, an error would occur, since Macaulay2 doesn't know how to add elements of R and S together. This is fixed via:
i4 : use R
o4 = R
o4 : PolynomialRing
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i5 : b
o5 = b
o5 : R
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i6 : a+b
o6 = a + b
o6 : R
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There are several functions that create rings for you. Generally, their variables are not globally visible. However, once you 'use' the ring, the variables are available.For example, the numerator of the Hilbert function is a polynomial in a ring with a variable T.
i7 : T
o7 = T
o7 : Symbol
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i8 : hf = poincare ideal vars S
2 3 4
o8 = 1 - 4T + 6T - 4T + T
o8 : ZZ[T]
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i9 : T
o9 = T
o9 : Symbol
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i10 : use ring hf
o10 = ZZ[T]
o10 : PolynomialRing
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i11 : T
o11 = T
o11 : Symbol
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