Packages

  • package root
    Definition Classes
    root
  • package org
    Definition Classes
    root
  • package opentorah
    Definition Classes
    org
  • package angles
  • package astronomy
  • package calendar
  • package numbers

    Number System.

    Number System.

    Each number system S (derived from org.opentorah.numbers.Numbers#Number) supports two flavors of org.opentorah.numbers.Numbers#Number: S#Point (derived from org.opentorah.numbers.Numbers#PointNumber and S#Vector (derived from org.opentorah.numbers.Numbers#VectorNumber.

    This distinction allows definitions of operations to be constrained to the types where a give operation makes sense: -: (Vector, Vector) => Vector with right unit Vector.zero; +: (Vector, Vector) => Vector with unit Vector.zero; -: (Point, Point) => Vector; +: (Point, Vector) => Point with left unit Point.zero and its "commutation" +: (Vector, Point) => Point with right unit Point.zero.

    This distinction may seem to be artificial: after all, given operations -: (Point, Point) => Vector and +: (Point, Vector) => Point, we have an isomorphism between Points and Vectors: ptov(p) = p - Point.zero, vtop(v) = Point.zero + v.

    Indeed, there is not much difference between the two when we are talking about angles. However, for dates (Points) it makes sense to ask what year/month the date is in - but not for time intervals (Vectors)!

p

org

opentorah

package opentorah

Package Members

  1. package angles
  2. package astronomy
  3. package calendar
  4. package numbers

    Number System.

    Number System.

    Each number system S (derived from org.opentorah.numbers.Numbers#Number) supports two flavors of org.opentorah.numbers.Numbers#Number: S#Point (derived from org.opentorah.numbers.Numbers#PointNumber and S#Vector (derived from org.opentorah.numbers.Numbers#VectorNumber.

    This distinction allows definitions of operations to be constrained to the types where a give operation makes sense: -: (Vector, Vector) => Vector with right unit Vector.zero; +: (Vector, Vector) => Vector with unit Vector.zero; -: (Point, Point) => Vector; +: (Point, Vector) => Point with left unit Point.zero and its "commutation" +: (Vector, Point) => Point with right unit Point.zero.

    This distinction may seem to be artificial: after all, given operations -: (Point, Point) => Vector and +: (Point, Vector) => Point, we have an isomorphism between Points and Vectors: ptov(p) = p - Point.zero, vtop(v) = Point.zero + v.

    Indeed, there is not much difference between the two when we are talking about angles. However, for dates (Points) it makes sense to ask what year/month the date is in - but not for time intervals (Vectors)!

Ungrouped