Synopsis
-
- Inputs:
- d, of integers denoting a multidegree
- F, an element in a polynomial ring
- Outputs:
If the polynomial ring is singly graded (the default case), then d may be an integer denoting this degree.
i1 : R = QQ[a..d]
o1 = R
o1 : PolynomialRing
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i2 : f = (a^2-b-1)*(c^3-b*d-2)
2 3 3 2 3 2 2
o2 = a c - b*c - a b*d - c + b d - 2a + b*d + 2b + 2
o2 : R
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i3 : part({3},f)
3 2
o3 = - c + b d
o3 : R
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Here is an alternate syntax.
i4 : part_{3} f
3 2
o4 = - c + b d
o4 : R
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In multigraded rings, degrees are lists of integers.
i5 : R = QQ[a..d,Degrees=>{{1,0},{0,1},{1,-1},{0,-1}}]
o5 = R
o5 : PolynomialRing
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i6 : F = a^3 + (b*d+1)^2
2 2 3
o6 = b d + a + 2b*d + 1
o6 : R
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i7 : part_{0,0} F
2 2
o7 = b d + 2b*d + 1
o7 : R
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Polynomial rings over other polynomial rings are multigraded, by default.
i8 : A = QQ[a,b,c]
o8 = A
o8 : PolynomialRing
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i9 : B = A[x,y]
o9 = B
o9 : PolynomialRing
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i10 : degree(a*x)
o10 = {1, 1}
o10 : List
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i11 : part_{2,2} (a*x+b*y-1)^3
2 2 2 2
o11 = - 3a x - 6a*b*x*y - 3b y
o11 : B
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