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# Semiring 

#### trait Semiring[T] extends AnyRef

Operations in factored algorithms are defined by a semiring algebraic structure. Each semiring defines a product and sum operation, and a value for zero and one which satisfy a set of properties. Different semirings are appropriate for certain algorithms and data types.

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### Abstract Value Members

1. abstract val one: T

A value such that a*1 = a

2. abstract def product(x: T, y: T): T

Product of two entries, as defined by the particular inference problem.

3. abstract def sum(x: T, y: T): T

Sum of two entries, as defined by the particular inference problem.

Sum of two entries, as defined by the particular inference problem. E.g., for computing conditional probabilities, sum is ordinary addition; for most probable explanation, it is max.

4. abstract val zero: T

A value such that a + 0 = a

### Concrete Value Members

1. final def !=(arg0: Any): Boolean
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2. final def ##(): Int
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3. final def ==(arg0: Any): Boolean
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4. final def asInstanceOf[T0]: T0
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5. def clone(): AnyRef
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6. final def eq(arg0: AnyRef): Boolean
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7. def equals(arg0: Any): Boolean
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8. def finalize(): Unit
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9. final def getClass(): Class[_]
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10. def hashCode(): Int
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11. final def isInstanceOf[T0]: Boolean
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12. final def ne(arg0: AnyRef): Boolean
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13. final def notify(): Unit
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14. final def notifyAll(): Unit
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15. def sumMany(xs: Traversable[T]): T

Sum of many entries.

Sum of many entries. Typically, this would be implemented by the ordinary sum, but there may be more efficient implementations.

16. final def synchronized[T0](arg0: ⇒ T0): T0
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17. def toString(): String
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18. final def wait(): Unit
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19. final def wait(arg0: Long, arg1: Int): Unit
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20. final def wait(arg0: Long): Unit
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