/usr/share/axiom-20170501/src/algebra/INFCLCT.spad is in axiom-source 20170501-3.
This file is owned by root:root, with mode 0o644.
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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 74 75 76 77 78 79 | )abbrev category INFCLCT InfinitlyClosePointCategory
++ Authors: Gaetan Hache
++ Date Created: may 1997
++ Date Last Updated: April 2010, by Tim Daly
++ Description:
++ This category is part of the PAFF package
InfinitlyClosePointCategory(K,symb,PolyRing,E,ProjPt,PCS,Plc,Divisor,BLMET) :
Category == SIG where
K : Field
symb : List(Symbol)
PolyRing : PolynomialCategory(K,E,OrderedVariableList(symb))
E : DirectProductCategory(#symb,NonNegativeInteger)
ProjPt : ProjectiveSpaceCategory(K)
PCS : LocalPowerSeriesCategory(K)
Plc : PlacesCategory(K,PCS)
DIVISOR : DivisorCategory(Plc)
BLMET : BlowUpMethodCategory
bls ==> ['X,'Y]
BlUpRing ==> DistributedMultivariatePolynomial(bls , K)
AFP ==> AffinePlane(K)
SIG ==> SetCategoryWithDegree with
create : (ProjPt , BlUpRing, AFP , NonNegativeInteger,BLMET, _
NonNegativeInteger, DIVISOR,K,Symbol) -> %
++ create(p,b,a,n1,c,n2,d,k,s) an infinitly close point
create : (ProjPt,PolyRing) -> %
setpoint_! : (%,ProjPt) -> ProjPt
setcurve_! : (%,BlUpRing) -> BlUpRing
setlocalPoint_! : (%,AFP) -> AFP
setsubmult_! : (%, NonNegativeInteger) -> NonNegativeInteger
setmult_! : (%,NonNegativeInteger) -> NonNegativeInteger
setchart_! : (%,BLMET) -> BLMET -- CHH
setexcpDiv_! : (%,DIVISOR) -> DIVISOR
setlocalParam_! : (%,List PCS) -> List(PCS)
setsymbName_! : (%,Symbol) -> Symbol
subMultV : % -> NonNegativeInteger
localParamV : % -> List PCS
symbNameV : % -> Symbol
pointV : % -> ProjPt
++ pointV(p) returns the infinitly close point.
curveV : % -> BlUpRing
++ curveV(p) returns the defining polynomial of the strict transform
++ on which lies the corresponding infinitly close point.
localPointV : % -> AFP
++ localPointV(p) returns the coordinates of the local infinitly
++ close point
multV : % -> NonNegativeInteger
++ multV(p) returns the multiplicity of the infinitly close point.
chartV : % -> BLMET -- CHH
++ chartV(p) is the chart of the infinitly close point. The first integer
++ correspond to variable defining the exceptional line, the last one
++ the affine neighboorhood and the second one is the
++ remaining integer. For example [1,2,3] means that
++ Z=1, X=X and Y=XY. [2,3,1] means that X=1, Y=Y and Z=YZ.
excpDivV : % -> DIVISOR
++ excpDivV returns the exceptional divisor of the infinitly close point.
actualExtensionV : % -> K
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