$SPAD/src/input hyperell.input

Timothy Daly December 3, 2016

Abstract

Contents

2

— * —

)set break resume
)sys rm -f hyperell.output
)spool hyperell.output
)set message auto off
)clear all
--S 1 of 26
p:= nextPrime(2^20)
--R
--R
--R   (1)  1048583
--R                                                        Type: PositiveInteger
--E 1
--S 2 of 26
K:=PF p
--R
--R
--R   (2)  PrimeField(1048583)
--R                                                                 Type: Domain
--E 2
--S 3 of 26
R:=DMP([x,y,z],K)
--R
--R
--R   (3)  DistributedMultivariatePolynomial([x,y,z],PrimeField(1048583))
--R                                                                 Type: Domain
--E 3
--S 4 of 26
P:=PAFFFF( K, [x,y,z], BLQT)
--R
--R
--R   (4)
--R  PackageForAlgebraicFunctionFieldOverFiniteField(PrimeField(1048583),[x,y,z],B
--R  lowUpWithQuadTrans)
--R                                                                 Type: Domain
--E 4
--S 5 of 26
ProjPl := PROJPLPS PrimeField p
--R
--R
--R   (5)
--R   ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField(PrimeField(1048583))
--R                                                                 Type: Domain

--E 5
--S 6 of 26
f:R:= y^2 - (x-1)*(x-2)*(x-3)*(x-4)*(x-5)
--R
--R
--R                5      4           3       2               2
--R   (6)  1048582x  + 15x  + 1048498x  + 225x  + 1048309x + y  + 120
--R         Type: DistributedMultivariatePolynomial([x,y,z],PrimeField(1048583))
--E 6
--S 7 of 26
fh:R:= homogenize( f , 3 )$P
--R
--R
--R                5      4            3 2       2 3             4    2 3       5
--R   (7)  1048582x  + 15x z + 1048498x z  + 225x z  + 1048309x z  + y z  + 120z
--R         Type: DistributedMultivariatePolynomial([x,y,z],PrimeField(1048583))
--E 7
--S 8 of 26
setCurve(fh)$P
--R
--R
--R                5      4            3 2       2 3             4    2 3       5
--R   (8)  1048582x  + 15x z + 1048498x z  + 225x z  + 1048309x z  + y z  + 120z
--R         Type: DistributedMultivariatePolynomial([x,y,z],PrimeField(1048583))
--E 8
--S 9 of 26
g:=genus()$P
--R
--R
--R   (9)  2
--R                                                     Type: NonNegativeInteger
--E 9
--S 10 of 26
divZ := intersectionDivisor(z)$P
--R
--R
--R              1
--I   (10)  5 %I7
--RType: Divisor(PlacesOverPseudoAlgebraicClosureOfFiniteField(PrimeField(1048583)))
--E 10
--S 11 of 26
pInf:= first supp divZ
--R
--R

--R            1
--I   (11)  %I7
--R     Type: PlacesOverPseudoAlgebraicClosureOfFiniteField(PrimeField(1048583))
--E 11
--S 12 of 26
p1:= projectivePoint( [1,0,1] :: List K )$ProjPl
--R
--R
--R                1
--R   (12)  (1:0:1)
--RType: ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField(PrimeField(1048583))
--E 12
--S 13 of 26
pl1:= first placesAbove( p1 )$P
--R
--R
--R                1
--R   (13)  [1:0:1]
--R     Type: PlacesOverPseudoAlgebraicClosureOfFiniteField(PrimeField(1048583))
--E 13
--S 14 of 26
p2:= projectivePoint( [2,0,1] :: List K )$ProjPl
--R
--R
--R                1
--R   (14)  (2:0:1)
--RType: ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField(PrimeField(1048583))
--E 14
--S 15 of 26
pl2:= first placesAbove( p2 )$P
--R
--R
--R                1
--R   (15)  [2:0:1]
--R     Type: PlacesOverPseudoAlgebraicClosureOfFiniteField(PrimeField(1048583))
--E 15
--S 16 of 26
p3:= projectivePoint( [3,0,1] :: List K )$ProjPl
--R
--R
--R                1
--R   (16)  (3:0:1)
--RType: ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField(PrimeField(1048583))
--E 16

--S 17 of 26
pl3:= first placesAbove( p3 )$P
--R
--R
--R                1
--R   (17)  [3:0:1]
--R     Type: PlacesOverPseudoAlgebraicClosureOfFiniteField(PrimeField(1048583))
--E 17
--S 18 of 26
p4:= projectivePoint( [4,0,1] :: List K )$ProjPl
--R
--R
--R                1
--R   (18)  (4:0:1)
--RType: ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField(PrimeField(1048583))
--E 18
--S 19 of 26
pl4:= first placesAbove( p4 )$P
--R
--R
--R                1
--R   (19)  [4:0:1]
--R     Type: PlacesOverPseudoAlgebraicClosureOfFiniteField(PrimeField(1048583))
--E 19
--S 20 of 26
p5:= projectivePoint( [5,0,1] :: List K )$ProjPl
--R
--R
--R                1
--R   (20)  (5:0:1)
--RType: ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField(PrimeField(1048583))
--E 20
--S 21 of 26
pl5:= first placesAbove( p5 )$P
--R
--R
--R                1
--R   (21)  [5:0:1]
--R     Type: PlacesOverPseudoAlgebraicClosureOfFiniteField(PrimeField(1048583))
--E 21
--S 22 of 26
D:= pl1+pl2+ 3*pl3   -  5* pInf
--R
--R
--R                1          1            1        1

--I   (22)  [1:0:1]  + [2:0:1]  + 3 [3:0:1]  - 5 %I7
--RType: Divisor(PlacesOverPseudoAlgebraicClosureOfFiniteField(PrimeField(1048583)))
--E 22
--S 23 of 26
lb:= lBasis( D + g*pInf )$P
--R
--R   Trying to interpolate with forms of degree:
--R   2
--R   Trying to interpolate with forms of degree:
--R   3
--R   Denominator found
--R   Intersection Divisor of Denominator found
--R
--R   (23)
--R                           2              3    2             2         2     3
--R   [num= [873819x y z + y z ],den= 873819x  + x z + 174762x z  + 87382y z + z ]
--IType: Record(num: List(DistributedMultivariatePolynomial(...
--E 23
--S 24 of 26
g1:= first lb.num
--R
--R
--R                          2
--R   (24)  873819x y z + y z
--R         Type: DistributedMultivariatePolynomial([x,y,z],PrimeField(1048583))
--E 24
--S 25 of 26
g0:= lb.den
--R
--R
--R                3    2             2         2     3
--R   (25)  873819x  + x z + 174762x z  + 87382y z + z
--R         Type: DistributedMultivariatePolynomial([x,y,z],PrimeField(1048583))
--E 25
-- Voici le diviseur equivalent a D ayant un diviseur des zeros (partie effective)
-- de degree au plus 2  ( g=2)
--S 26 of 26
intersectionDivisor(g1)$P - intersectionDivisor(g0)$P + D
--R
--R
--R                1          1        1
--I   (26)  [5:0:1]  + [4:0:1]  - 2 %I7
--RType: Divisor(PlacesOverPseudoAlgebraicClosureOfFiniteField(PrimeField(1048583)))
--E 26

)spool )lisp (bye) ———-

8

References^{[1] nothing}

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