ExtElement -- the class of all Ext-algebra elements

Description

This type represents elements in Ext-algebras. Each object of type ExtAlgebra is itself a type E, and homogeneous elements in E belong also to the type ExtElement, which is the parent of E. Internally an element of type ExtElement is of type BasicList consisting of two basic lists, the first is a list of coefficients and the second is a list of indices for the generators occurring in the element.

i1 : L = lieAlgebra{a,b}/{a a b,b b a}

o1 = L

o1 : LieAlgebra

i2 : E = extAlgebra(5,L)

o2 = E

o2 : ExtAlgebra

i3 : x = 4 ext_2 - ext_3

o3 = 4ext_2 - ext_3

o3 : E

i4 : x#0

o4 = BasicList{4, -1}

o4 : BasicList

i5 : x#1

o5 = BasicList{2, 3}

o5 : BasicList

Functions and methods returning an object of class ExtElement :

ZZ _ ExtAlgebra -- get the zero element

Methods that use an object of class ExtElement :

- ExtElement -- unary negation
ExtElement + ExtElement -- addition of Ext-algebra elements
ExtElement - ExtElement -- subtraction of Ext-algebra elements
ExtElement ExtElement -- multiplication of Ext-algebra elements
"firstDegree(ExtElement)" -- see firstDegree -- get the degree of an element
Number ExtElement -- multiplication of a number and an Ext-algebra element
RingElement ExtElement -- multiplication of a field element and a Ext-algebra element
"sign(ExtElement)" -- see sign -- get the sign of a homogeneous element
"weight(ExtElement)" -- see weight -- get the weight of a homogeneous element

For the programmer

The object ExtElement is a type, with ancestor classes BasicList < Thing.

ExtElement -- the class of all Ext-algebra elements

Description

See also

Functions and methods returning an object of class ExtElement :

Methods that use an object of class ExtElement :

For the programmer