# moduliIdeal -- ideal generated by the coefficients of a differential form or vector field

## Synopsis

• Usage:
moduliIdeal(e)
• Inputs:
• e, an instance of the type DiffAlgElement, a differential form or vector field
• Outputs:
• an ideal, the ideal generated by the scalar coefficients of e

## Description

Given a differential form or vector field, this routine returns the ideal generated by the scalar coefficients of such element.

In this example we compute the equations that the scalar coefficients of a closed differential 1-form must satisfy.

 i1 : w = newForm(2,1,2,"a") 2 2 2 2 o1 = (a x + a x x + a x + a x x + a x x + a x )dx + (a x + a x x + 0 0 3 0 1 9 1 6 0 2 12 1 2 15 2 0 1 0 4 0 1 ------------------------------------------------------------------------ 2 2 2 2 a x + a x x + a x x + a x )dx + (a x + a x x + a x + a x x + 10 1 7 0 2 13 1 2 16 2 1 2 0 5 0 1 11 1 8 0 2 ------------------------------------------------------------------------ 2 a x x + a x )dx 14 1 2 17 2 2 o1 : DiffAlgForm i2 : diff w o2 = ((2a - a )x + (a - 2a )x + (a - a )x )dx dx + ((2a - a )x + (a 1 3 0 4 9 1 7 12 2 0 1 2 6 0 5 ------------------------------------------------------------------------ - a )x + (a - 2a )x )dx dx + ((a - a )x + (2a - a )x + (a - 12 1 8 15 2 0 2 5 7 0 11 13 1 14 ------------------------------------------------------------------------ 2a )x )dx dx 16 2 1 2 o2 : DiffAlgForm i3 : moduliIdeal(diff w) o3 = ideal (2a - a , a - 2a , a - a , 2a - a , a - a , a - 2a , a - 1 3 4 9 7 12 2 6 5 12 8 15 5 ------------------------------------------------------------------------ a , 2a - a , a - 2a ) 7 11 13 14 16 QQ[i] o3 : Ideal of ------[][a ..a ] 2 0 17 i + 1