subring -- Constructs a subring of a polynomial ring.

Synopsis

• Usage:

  A = subring M

  A = subring L

  A = subring S

• Inputs:
  • M, a matrix, whose entries are the generators for the constructed Subring.
  • L, a list, containing generators for the constructed Subring.
  • S, a SAGBIBasis,
• Optional inputs:
  • GeneratorSymbol => a symbol, default value null, a symbol to be used for the variables of the presentationRing.
• Outputs:
  • A, a subring, generated by the input generators.

Description

i1 : R = QQ[x];

i2 : S = subring {x^4+x^3, x^2+x}

o2 = QQ[p_0..p_1], subring of R

o2 : Subring

i3 : SB = sagbi S;

i4 : gens SB

o4 = | x2+x x3-x |

             1      2
o4 : Matrix R  <-- R

i5 : (x^3+x^2)%S

o5 = 0

o5 : R

See also

• Subring -- The type of all subrings
• generators(Subring) -- A generating set of a subring
• ambient(Subring) -- The ambient ring of a subring
• numgens(Subring) -- The number of generators of a subring
• net(Subring) -- Short summary of a subring
• sagbi -- Compute a subalgebra basis (sagbi basis)
• SAGBIBasis -- The type of all subalgebra bases