RingElement ExtElement -- multiplication of a field element and a Ext-algebra element

Synopsis

Operator: SPACE
Usage:

y = a x
Inputs:
- a, a ring element, $a$ is an element in the field of $E$, where $E$ is of type ExtAlgebra
- x, an instance of the type ExtElement, $x$ is of type $E$
Outputs:
- y, an instance of the type ExtElement, $y$ is of type $E$, the product $a*x$

Description

The symbol SPACE is used as notation for multiplication by scalars. The scalars belong to the field of $E$. If the field is not QQ, then the scalars are of type RingElement. If the field is QQ, then the scalars are of type Number. 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]/{x^2+1})

o1 = F

o1 : PolynomialRing

i2 : L = lieAlgebra({a,b,c},Field=>F)/{a b,b c}

o2 = L

o2 : LieAlgebra

i3 : E = extAlgebra(3,L)

o3 = E

o3 : ExtAlgebra

i4 : (3*x+1) (ext_1 ext_2)+(2*x+3) (ext_2 ext_1)

o4 = (-x+2)ext_3

o4 : E

Ways to use this method: