# subring -- Constructs a subring of a polynomial ring.

## Synopsis

• Usage:
A = subring M
A = subring L
A = subring S
• Inputs:
• M, , a one-row matrix whose entries are the generators for the constructed Subring.
• L, a list, a list of generators for the constructed Subring.
• S, an instance of the type SAGBIBasis,
• Optional inputs:
• VarBaseName => , default value p, determines the symbol used for the variables of the tensorRing for the constructed Subring.
• Outputs:
• A, an instance of the type Subring,

## Description

This function serves as the canonical constructor for the Subring type.

Generators that are constants are ignored because all subrings are assumed to contain the field of coefficients. An error is thrown if the given set of generators does not contain at least one non-constant generator. The generators of a subring need not be reduced.

 i1 : gndR = QQ[x]; i2 : A = subring {x^4+x^3, x^2+x} o2 = subring of gndR o2 : Subring i3 : subring sagbi A o3 = subring of gndR o3 : Subring i4 : (x^3+x^2)%A 3 o4 = p - p 0 0 o4 : QQ[p ..p ] 0 2