diff options
| author | dos-reis <gdr@axiomatics.org> | 2009-05-29 19:09:54 +0000 |
|---|---|---|
| committer | dos-reis <gdr@axiomatics.org> | 2009-05-29 19:09:54 +0000 |
| commit | c39287d87b632b3582b0e179b08d44dc6c27510f (patch) | |
| tree | 88c661ea1bd325ad74b4f3f472c052687e8ca1d4 /src/algebra/ffcat.spad.pamphlet | |
| parent | a17c2d47d4df5af5ef5e624ac6c5636b2741dd4a (diff) | |
| download | open-axiom-c39287d87b632b3582b0e179b08d44dc6c27510f.tar.gz | |
* algebra/algext.spad.pamphlet: Qualify `characteristic'.
* algebra/clifford.spad.pamphlet: Likewise.
* algebra/complet.spad.pamphlet: Likewise.
* algebra/contfrac.spad.pamphlet: Likewise.
* algebra/curve.spad.pamphlet: Likewise.
* algebra/ddfact.spad.pamphlet: Likewise.
* algebra/derham.spad.pamphlet: Likewise.
* algebra/equation2.spad.pamphlet: Likewise.
* algebra/ffcat.spad.pamphlet: Likewise.
* algebra/ffcg.spad.pamphlet: Likewise.
* algebra/fff.spad.pamphlet: Likewise.
* algebra/ffnb.spad.pamphlet: Likewise.
* algebra/ffp.spad.pamphlet: Likewise.
* algebra/ffpoly.spad.pamphlet: Likewise.
* algebra/ffx.spad.pamphlet: Likewise.
* algebra/fmod.spad.pamphlet: Likewise.
* algebra/fortmac.spad.pamphlet: Likewise.
* algebra/fr.spad.pamphlet: Likewise.
* algebra/fraction.spad.pamphlet: Likewise.
* algebra/fspace.spad.pamphlet: Likewise.
* algebra/gaussian.spad.pamphlet: Likewise.
* algebra/gpol.spad.pamphlet: Likewise.
* algebra/intclos.spad.pamphlet: Likewise.
* algebra/interval.spad.pamphlet: Likewise.
* algebra/laurent.spad.pamphlet: Likewise.
* algebra/matrix.spad.pamphlet: Likewise.
* algebra/modring.spad.pamphlet: Likewise.
* algebra/oct.spad.pamphlet: Likewise.
* algebra/opalg.spad.pamphlet: Likewise.
* algebra/padic.spad.pamphlet: Likewise.
* algebra/perman.spad.pamphlet: Likewise.
* algebra/pf.spad.pamphlet: Likewise.
* algebra/pfr.spad.pamphlet: Likewise.
* algebra/poly.spad.pamphlet: Likewise.
* algebra/polycat.spad.pamphlet: Likewise.
* algebra/puiseux.spad.pamphlet: Likewise.
* algebra/quat.spad.pamphlet: Likewise.
* algebra/radix.spad.pamphlet: Likewise.
* algebra/reclos.spad.pamphlet: Likewise.
* algebra/resring.spad.pamphlet: Likewise.
* algebra/sf.spad.pamphlet: Likewise.
* algebra/si.spad.pamphlet: Likewise.
* algebra/solvefor.spad.pamphlet: Likewise.
* algebra/sups.spad.pamphlet: Likewise.
* algebra/taylor.spad.pamphlet: Likewise.
* algebra/vector.spad.pamphlet: Likewise.
* algebra/xpoly.spad.pamphlet: Likewise.
Diffstat (limited to 'src/algebra/ffcat.spad.pamphlet')
| -rw-r--r-- | src/algebra/ffcat.spad.pamphlet | 19 |
1 files changed, 9 insertions, 10 deletions
diff --git a/src/algebra/ffcat.spad.pamphlet b/src/algebra/ffcat.spad.pamphlet index 2f3c1ba4..e7ae41ae 100644 --- a/src/algebra/ffcat.spad.pamphlet +++ b/src/algebra/ffcat.spad.pamphlet @@ -57,8 +57,8 @@ FieldOfPrimeCharacteristic:Category == _ ++ primeFrobenius(a,s) returns \spad{a**(p**s)} where p ++ is the characteristic. add - primeFrobenius(a) == a ** characteristic() - primeFrobenius(a,s) == a ** (characteristic()**s) + primeFrobenius(a) == a ** characteristic$% + primeFrobenius(a,s) == a ** (characteristic$%**s) @ \section{category XF ExtensionField} @@ -379,7 +379,7 @@ FiniteAlgebraicExtensionField(F : Field) : Category == _ error "trace: second argument must divide degree of extension" size() == size()$F ** extensionDegree() createNormalElement() == - characteristic() = size() => 1 + characteristic$% = size() => 1 res : $ for i in 1.. repeat res := index(i :: PI) @@ -595,15 +595,15 @@ FiniteFieldCategory() : Category ==_ l:=nullSpace mat empty? l or every?(zero?, first l) => "failed" map(charthRoot,first l) - charthRoot(x:$):$ == x**(size() quo characteristic()) + charthRoot(x:$):$ == x**(size()$% quo characteristic$%) charthRoot(x:%):Union($,"failed") == (charthRoot(x)@$)::Union($,"failed") createPrimitiveElement() == - sm1 : PositiveInteger := (size()$$-1) pretend PositiveInteger + sm1 : PositiveInteger := (size()$%-1) pretend PositiveInteger start : Integer := -- in the polynomial case, index from 1 to characteristic-1 -- gives prime field elements - representationType = "polynomial" => characteristic()::Integer + representationType = "polynomial" => characteristic$% 1 found : Boolean := false e : $ @@ -615,15 +615,14 @@ FiniteFieldCategory() : Category ==_ -- add special implementation for prime field case zero?(a) => false explist := factorsOfCyclicGroupSize() - q:=(size()-1)@Integer + q:=(size()$%-1)@Integer equalone : Boolean := false for exp in explist while not equalone repeat equalone := one?(a**(q quo exp.factor)) not equalone order(e: %): PositiveInteger == e = 0 => error "order(0) is not defined " - ord:Integer:= size()-1 -- order e divides ord - a:Integer:= 0 + ord:Integer:= size()$%-1 -- order e divides ord lof:=factorsOfCyclicGroupSize() for rec in lof repeat -- run through prime divisors a := ord quo (primeDivisor := rec.factor) @@ -649,7 +648,7 @@ FiniteFieldCategory() : Category ==_ b = gen => 1 disclog:Integer:=0 mult:Integer:=1 - groupord := (size() - 1)@Integer + groupord := (size()$% - 1)@Integer exp:Integer:=groupord for f in faclist repeat fac:=f.factor |