# SuanShu, a Java numerical and statistical library

com.numericalmethod.suanshu.algebra.structure

## Interface AbelianGroup<G>

• ### Method Summary

All Methods
Modifier and Type Method and Description
G add(G that)
+ : G × G → G
G minus(G that)
- : G × G → G

The operation "-" is not in the definition of of an additive group but can be deduced.

G opposite()
For each a in G, there exists an element b in G such that a + b = b + a = 0.
G ZERO()
The additive element 0 in the group, such that for all elements a in the group, the equation 0 + a = a + 0 = a holds.
• ### Method Detail

G add(G that)
+ : G × G → G
Parameters:
that - the object to be added
Returns:
this + that
• #### minus

G minus(G that)
- : G × G → G

The operation "-" is not in the definition of of an additive group but can be deduced. This function is provided for convenience purpose. It is equivalent to

this.add(that.opposite())
.
Parameters:
that - the object to be subtracted (subtrahend)
Returns:
this - that
• #### opposite

G opposite()
For each a in G, there exists an element b in G such that a + b = b + a = 0. That is, it is the object such as
this.add(this.opposite()) == this.ZERO
Returns:
-this, the additive opposite
G ZERO()