Introduction
This post defines the Wave Number math operations: Addition, rotation, rotication, multiplication and flipping.
Addition
a + b denotes the result of adding two Opposite Values a and b. This result is referred to as the sum of a and b.
Rotation (↺?)
The second operation is rotation. a ↺? b denotes the result of rotating an Opposite Value b by the angle a. This result is referred to as the rotation of b by a. The angle a can be expressed in degrees or radians. When a has a ^ Opposite Sign, a ↺? b represents a counterclockwise rotation, and when a has a v Opposite Sign, the operation performs a clockwise rotation.
The symbol ? represents the point or axis of rotation indicated by Opposite Values. If the symbol is blank, assume the rotation is around an imaginary z-axis, a point at the origin (0, 0) in R1 and R2.
If blank in R3, assume the rotation is around the z-axis (0, 0, j^). When included, it represents a rotation around the point indicated in R1 and R2 and the axis indicated in R3.
Rotication (R↺? )
The third operation is rotication. a R↺? b denotes the rotication of an Opposite Value b by the angle a. This result is referred to as the rotication of b by a . Rotication consists of two steps. The first step is a rotation of b by a. The second step multiplies the result of this rotation by the magnitude of the axis of rotation.
Multiplication
The fourth operation is multiplication. a*b or ab denotes the result of multiplying two Opposite Values a and b. This result is referred to as the product of a and b. Multiplication is assumed when an Opposite Value precedes or follows a round bracket, or when two round brackets are adjacent.
Flipping
The final operation is flipping, which specifically rotates an Opposite Value a to its equivalent with the Opposite Sign changed. This corresponds to flipping from one side of the axis to the other. The superscript symbol (–) denotes the flipping operation. Consequently, flipping a results in the additive inverse of a, such that a + –a= 0.
The number 0 is special and does not have an Opposite Type or Sign. Flipping 0 makes no sense. However, calculations may yield –0, in which case –0 = 0.
Flipping necessitates the use of an alternative orthogonal axis to the one on which the point is located. This can be a real axis, such as the x-axis in R2 for a point on the y-axis, or the imaginary z-axis in R1 or R2.
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