diff options
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 |