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SubalgebraBases :: PresRing

PresRing -- Stores data on the lifted presentation ring of a subring.

Description

The PresRing type contains about a Subring instance is related to the lifted presentation ring of a subring. In the code, the lifted presentation of a subring is referred to as the tensorRing.

An instance of the PresRing type contains the following keys:

  • tensorRing: The lifted presentation ring of the given subring.
  • sagbiInclusion: A map from tensorRing to tensorRing
  • projectionAmbient: A map from tensorRing to the ambient ring.
  • inclusionAmbient: A map from the ambient ring to tensorRing
  • substitution: A map from tensorRing to tensorRing
  • fullSubstitution: Composition of substitution and projectionAmbient.
  • syzygyIdeal: This is used in the function sagbi to calculate toric syzygies.
  • liftedPres: This is used in normal form calculations.

To understand the maps stored inside of a PresRing instance, it is informative to look at the output of debugPrintAllMaps:

i1 : gndR = QQ[x, y];
i2 : subR = subring {y, y*x-x^2, y*x^2};
i3 : debugPrintAllMaps subR
- sagbiInclusion:
maps p_0 to 0
maps p_1 to 0
maps p_2 to p_2
maps p_3 to p_3
maps p_4 to p_4
- projectionAmbient:
maps p_0 to x
maps p_1 to y
maps p_2 to 0
maps p_3 to 0
maps p_4 to 0
- inclusionAmbient:
maps x to p_0
maps y to p_1
- substitution:
maps p_0 to p_0
maps p_1 to p_1
maps p_2 to p_1
maps p_3 to -p_0^2+p_0*p_1
maps p_4 to p_0^2*p_1
- fullSubstitution:
maps p_0 to x
maps p_1 to y
maps p_2 to y
maps p_3 to -x^2+x*y
maps p_4 to x^2*y

This type is typically not used externally to Subring type.

See also

Functions and methods returning an object of class PresRing :

Methods that use an object of class PresRing :

For the programmer

The object PresRing is a type, with ancestor classes HashTable < Thing.