plangeo4
http://www.openmath.org/cd
http://www.openmath.org/cd/plangeo4.ocd
2006-06-01
experimental
2004-06-01
0
5
This CD defines symbols for planar Euclidean geometry.
In particular, it is concerned with projective and affine coordinates
of points and lines.
set_coordinates
This symbol defines the coordinates of a point or a line.
The coordinates are the projective coordinates and consist of a vector
of length 3. Points whose third coordinates are zero are the points at
infinity.
The line whose first two coordinates are zero is the line at
infinity.
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2
3
coordinates
This function yields the coordinates vector if applied to a point or line with
coordinates.
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1
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3
3
To extract the coordinates of a point A with coordinates (1,2,3):
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3
is_affine
Boolean function testing whether a point or line is affine.
3
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2
affine_coordinates
This function yields the affine coordinates vector if applied to a point or line with
coordinates in the affine plane.
The affine coordinates (1/3,2/3) are expressed as follows
for the point A with projective coordinates (1,2,3).
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3
set_affine_coordinates
Defines the affine coordinates of an affine point or line.
Assign the affine coordinates (1/3,2/3) to A.
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