/usr/share/axiom-20170501/src/algebra/PRSPCAT.spad is in axiom-source 20170501-3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 | )abbrev category PRSPCAT ProjectiveSpaceCategory
++ Author: Gaetan Hache
++ Date Created: 17 nov 1992
++ Date Last Updated: May 2010 by Tim Daly
++ References:
++ Hold11 Algebraic Geometry Codes
++ Description:
++ This is part of the PAFF package, related to projective space.
ProjectiveSpaceCategory(K) : Category == SIG where
K : Field
LIST ==> List
INT ==> Integer
NNI ==> NonNegativeInteger
SIG ==> SetCategoryWithDegree with
lastNonNul : % -> INT
homogenize : (%,INT) -> %
++ homogenize the point according to the coordinate specified
++ by the integer
projectivePoint : LIST(K) -> %
++ projectivePoint creates a projective point from a list
definingField : % -> K
coerce : % -> List(K)
++ coerce a a projective point list of K
coerce : LIST(K) -> %
++ coerce a list of K to a projective point.
orbit : % -> LIST %
++ orbit(p) returns the orbit of the point p according to the
++ characteristic of K, that is, for q= char K,
++ orbit(p) = \{ p, p**q, p**(q**2), p**(q**3), ..... \}
orbit : (%,NNI) -> LIST %
++ orbit(p,n) returns the orbit of the point p according to n, that is
++ orbit(p,n) = \{ p, p**n, p**(n**2), p**(n**3), ..... \}
conjugate : (%,NNI) -> %
++ conjugate(p,n) returns p**n, that is all the coordinates of p
++ to the power of n
conjugate : % -> %
++ conjugate(p) returns conjugate(p,n) where n is the
++ characteristic of the ground field.
removeConjugate : (LIST(%),NNI) -> LIST(%)
++ removeConjugate(lp,n) returns a list of points such that no points
++ in the list is the conjugate (according to n) of another point.
removeConjugate : LIST(%) -> LIST(%)
++ removeConjugate(lp) returns removeConjugate(lp,n)
++ where n is the characteristic of the ground field.
rational? : (%,NNI) -> Boolean
++ rational?(p,n) test if the point is rational according to n.
rational? : % -> Boolean
++ rational?(p) test if the point is rational according to the
++ characteristic of the ground field.
homogenize : % -> %
++ homogenize(pt) the point according to the coordinate
++ which is the last non null.
lastNonNull : % -> INT
++ lastNonNull returns the integer corresponding to the last
++ non null coordinates.
list : % -> LIST(K)
++ list returns the list of the coordinates
elt : (%,INT) -> K
++ elt returns the value of a specified coordinates
setelt : (%,INT,K) -> K
++ setelt sets the value of a specified coordinates
pointValue : % -> LIST(K)
++ pointValue returns the coordinates of the point or of the point
++ of origin that represent an infinitly close point
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