To create a quaternion calculator that can divide, we first need to define what quaternions are and how they can be divided.
In mathematics, a quaternion is a four-dimensional number that extends the concept of complex numbers. It can be written in the form:
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where w
, x
, y
, and z
are real numbers, and i
, j
, and k
are the imaginary units.
To divide two quaternions, we can use the formula:
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where q1
and q2
are the quaternions being divided, and q2^-1
is the inverse of q2
.
Now, we can create a Python class for the quaternion calculator that can perform division. Here's an example implementation:
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In this implementation, we define a Quaternion
class that contains the four components of the quaternion (w
, x
, y
, z
). We also define the multiplication and division operators (*
and /
), which are used to multiply and divide two quaternions.
The __mul__
method performs the quaternion multiplication operation, which is defined as:
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The __truediv__
method performs the quaternion division operation, which is defined as:
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where q1
and q2
are the quaternions being divided, and q2^-1
is the inverse of q2
.
The inverse
method computes the inverse of the quaternion, which is defined as:
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where norm_squared
is the norm squared of the quaternion, defined as w^2 + x^2 + y^2 + z^2
.
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