localRingValuation -- The valuation defined by a local ring.

Synopsis

• Usage:

  v = localRingValuation(R)

• Inputs:
  • R, a local ring, the ring whose maximal ideal determines the order
• Outputs:
  • v, an instance of the type Valuation, local ring valuation using a local ring R

Description

i1 : R = QQ[x,y];

i2 : I = ideal(x,y);

o2 : Ideal of R

i3 : S = R_I

o3 = S

o3 : LocalRing, maximal ideal (x, y)

i4 : localVal = localRingValuation(S)

o4 = valuation from S to ZZ

o4 : Valuation

i5 : localVal(1 + x + y)

o5 = 0

i6 : localVal(x^4 + x^2*y^2 + x^7 + y^3)

o6 = 3

i7 : localVal(x^2 + x*y + y^2)

o7 = 2

i8 : localVal(1/(x^2+x*y+y^3))

o8 = -2

See also

• valuation -- User-defined valuation object
• Valuation -- The type of all valuations
• leadTermValuation -- The valuation defined by leading terms
• lowestTermValuation -- The valuation defined by lowest terms
• padicValuation -- The p-adic valuation
• trivialValuation -- The trivial valuation