# holonomy(...,Field=>...) -- optional argument for holonomy

## Synopsis

• Usage:
L = holonomy(A,Field => F)
L = holonomy(A,B,Field => F)
• Inputs:
• F, a ring, the field of coefficients
• A, a list,
• B, a list,
• Outputs:

## Description

This is an option for holonomy to define the coefficient field, which is QQ by default. You may use any "exact" field (not the real numbers or the complex numbers), such as a prime field or an algebraic extension, e.g., toField(ZZ/7[x]/ideal\{x^2+1\}) or a fraction field, e.g., frac(QQ[x]). Observe that it is necessary to use the function toField when $F$ is defined as an algebraic extension of a prime field.

 i1 : F = toField(ZZ/7[x]/ideal{x^2+1}) o1 = F o1 : PolynomialRing i2 : L = holonomy({{a,d}},{{a,b,c}},Field=>F) o2 = L o2 : LieAlgebra i3 : (3*x+2) a b + (2*x+3) b a o3 = (-x+1)(c b) o3 : L

## Further information

• Default value: QQ
• Function: holonomy -- compute the holonomy Lie algebra associated to an arrangement or matroid
• Option key: Field -- name for an optional argument for lieAlgebra and holonomy