/usr/share/axiom-20170501/src/algebra/AFSPCAT.spad is in axiom-source 20170501-3.
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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 | )abbrev category AFSPCAT AffineSpaceCategory
++ Author: Gaetan Hache
++ Date Created: 17 nov 1992
++ Date Last Updated: May 2010 by Tim Daly
++ Description:
++ The following is all the categories and domains related to projective
++ space and part of the PAFF package
AffineSpaceCategory(K) : Category == SIG where
K : Field
LIST ==> List
INT ==> Integer
NNI ==> NonNegativeInteger
SIG ==> SetCategoryWithDegree with
origin : () -> %
affinePoint : LIST(K) -> %
++ affinePoint creates a affine point from a list
definingField : % -> K
coerce : % -> List(K)
coerce : LIST(K) -> %
++ coerce a list of K to a affine 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.
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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