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Loyc.Math.IAdditionGroup< T > Interface Template Reference

This defines a Group with the operation +, the neutral element Zero, and an operation - that is defined in terms of the inverse. A Negate operation is not provided so that this interface makes more sense for use with unsigned types. More...


Source file:
Inheritance diagram for Loyc.Math.IAdditionGroup< T >:
Loyc.Math.IZeroProvider< T > Loyc.Math.IRing< T > Loyc.Math.IField< T > Loyc.Math.IComplexMath< T > Loyc.Math.IMath< T > Loyc.Math.ISignedMath< T > Loyc.Math.IUIntMath< T > Loyc.Math.IIntMath< T > Loyc.Math.IRationalMath< T > Loyc.Math.IFloatMath< T > Loyc.Math.MathF16 Loyc.Math.MathF23 Loyc.Math.MathF8 Loyc.Math.MathFL16 Loyc.Math.MathFL32

Remarks

This defines a Group with the operation +, the neutral element Zero, and an operation - that is defined in terms of the inverse. A Negate operation is not provided so that this interface makes more sense for use with unsigned types.

Axioms that have to be satisified by the operations: Commutativity of addition: Add(a,b)=Add(b,a) for all a,b in T Associativity of addition: Add(Add(a,b),c)=Add(a,Add(b,c)) Inverse of addition: Add(a,Negate(a))==Zero Subtraction: Subtract(a,b)==Add(a,Negate(b)) Neutral element: Add(Zero,a)==a for all a in T

Public Member Functions

Add (T a, T b)
 
Add (T a, T b, T c)
 
Sub (T a, T b)
 

Additional Inherited Members

- Properties inherited from Loyc.Math.IZeroProvider< T >
Zero [get]
 Returns the "zero" or additive identity of this type. More...