[____] [____] [_____] [____] [__] [Index] [Root]
Index other
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CrvCon_ (Example H86E10)
CrvCon_ (Example H86E9)
Magmas (or Structures) (OVERVIEW)
A ! a : AC, RngElt -> FldACElt
R ! a : AlgChtr, RngIntElt -> AlgChtrElt
A ! e : AlgFP, MonFPElt -> AlgFPElt
A ! Q : AlgGen, SeqEnum[RngElt] -> AlgGenElt
A ! g : AlgGrp, GrpElt -> AlgGrpElt
A ! r : AlgGrp, RngElt -> AlgGrpElt
A ! [c_1, ..., c_n] : AlgGrp, SeqEnum -> AlgGrpElt
S ! 1 : AlgGrpSub -> Grp
R ! g : AlgMat, GrpMatElt -> RngMatElt
R ! 0 : AlgMat, RngIntElt -> AlgMatElt
R ! 1 : AlgMat, RngIntElt -> AlgMatElt
R ! t : AlgMat, RngIntElt -> AlgMatElt
R ! Q : AlgMat, [ RngElt ] -> AlgMatElt
A ! 0 : AlgQuat, RngIntElt -> AlgQuatElt
A ! 1 : AlgQuat, RngIntElt -> AlgQuatElt
C ! u : Code, ModTupRngElt -> ModTupRngElt
C ! u : Code, ModTupRngElt -> ModTupRngElt
C ! 0 : Code, RngIntElt -> ModTupRngElt
C ! 0 : Code, RngIntElt -> ModTupRngElt
C ! [a_1, ..., a_n] : Code, [ RngElt ] -> ModTupRngElt
C ! [a_1, ..., a_n] : Code, [ RngElt ] -> ModTupRngElt
C ! e : Cop, Elt -> CopElt
C ! [a,...] : Crv,[RngElt] -> Pt
C ! P : CrvHyp, PtHyp -> PtHyp
C ! [x, y] : CrvHyp, [RngElt] -> PtHyp
Div ! D : DivCrv, DivFunElt -> DivCrvElt
Div ! p : DivCrv, PlcCrvElt -> DivCrvElt
Div ! 0 : DivCrv, RngIntElt -> DivCrvElt
D ! 0 : DivCrv,RngIntElt -> DivCrvElt
Div ! a : DivFun, RngElt -> DivFunElt
Div ! I : DivFun, RngFunOrdIdl -> DivFunElt
F ! a : FldAlg, RngElt -> FldAlgElt
F ! [a_0, a_1, ..., a_(m - 1)] : FldAlg, [RngElt] -> FldAlgElt
C ! a : FldCom, RngElt -> FldComElt
F ! a : FldFun, . -> FldFunElt
F ! [ a_0, a_1, ..., a_(n - 1) ] : FldFun, SeqEnum -> FldFunElt
F ! a : FldFunRat, FldElt -> FldFunRatElt
F ! [a, b] : FldFunRat, RngPolElt, RngPolElt -> FldFunRatElt
Q ! [a] : FldRat, RngElt -> FldRatElt
Q ! a : FldRat, RngIntElt -> FldRatElt
Q ! [a, b] : FldRat, RngIntElt, RngIntElt -> FldRatElt
R ! a : FldRe, RngElt -> FldReElt
G ! g : Grp, GrpElt -> GrpElt
G ! Q : Grp, [ Elt ] -> GrpElt
G ! g : GrpAb, GrpAbElt -> GrpAbElt
H ! g : GrpAb, GrpAbElt -> GrpAbElt
K ! g : GrpAb, GrpAbElt -> GrpAbElt
A ! n : GrpAb, RngIntElt -> GrpAbElt
A ! [a_1, ... ,a_n] : GrpAb, [RngIntElt] -> GrpAbElt
A ! e : GrpAbGen, Elt -> GrpAbGenElt
A ! g : GrpAbGen, GrpAbGenElt -> GrpAbGenElt
A ! [a_1, ... ,a_n] : GrpAbGen, [RngIntElt] -> GrpAbGenElt
G ! [ i_1, ..., i_s ] : GrpAtc, [ RngIntElt ] -> GrpAtcElt
A ! f : GrpAuto, Map -> GrpAutoElt
B ! [ i_1, ..., i_s ] : GrpBrd, [ RngIntElt ] -> GrpBrdElt
G ! [ i_1, ..., i_s ] : GrpFP, [ RngIntElt ] -> GrpFPElt
G ! g : GrpGPC, GrpGPCElt -> GrpGPCElt
H ! g : GrpGPC, GrpGPCElt -> GrpGPCElt
K ! g : GrpGPC, GrpGPCElt -> GrpGPCElt
G ! Q : GrpGPC, [RngIntElt] -> GrpGPCElt
E ! { u, v } : GrphEdgeSet, . -> GrphEdge
E ! [u, v] : GrphEdgeSet, [ . ] -> GrphEdge
V ! v : GrphVertSet, . -> GrphVert
G ! m : GrpMat, ModMatElt -> GrpMatElt
G ! r : GrpMat, RngMatElt -> GrpMatElt
G ! Q : GrpMat, [ RngElt ] -> GrpMatElt
G ! g : GrpPC, GrpPCElt -> GrpPCElt
H ! g : GrpPC, GrpPCElt -> GrpPCElt
K ! g : GrpPC, GrpPCElt -> GrpPCElt
G ! Q : GrpPC, [RngIntElt] -> GrpPCElt
G ! (...)(...)...(...) : GrpPerm, Cycles -> GrpPermElt
G ! g : GrpPerm, GrpPermElt -> GrpPermElt
G ! \(...)(...)...(...) : GrpPerm, LiteralCycles -> GrpPermElt
G ! Q : GrpPerm, SeqEnum[SetIndx] -> GrpPermElt
G ! Q : GrpPerm, [ Elt ] -> GrpPermElt
G ! x : GrpPSL2, . -> GrpPSL2
G ! [ i_1, ..., i_s ] : GrpRWS, [ RngIntElt ] -> GrpRWSElt
G ! g : GrpSLP, GrpSLPElt -> GrpSLPElt
B ! S : IncBlkSet, SetEnum -> IncBlk
P ! x : IncPtSet, Elt -> Incpt
J ! P : JacHyp, JacHypPt -> JacHypPt
J ! 0 : JacHyp, RngIntElt -> JacHypPt
J ! [a, b] : JacHyp, [ RngUPolElt ] -> JacHypPt
L ! 0 : Lat, RngIntElt -> LatElt
L ! Q : Lat, [ RngElt ] -> LatElt
M ! x : ModBrdt, . -> ModBrdtElt
M ! v : ModDed, SeqEnum -> ModDedElt
M ! f : ModFrm, . -> ModFrmElt
M ! g : ModMat, GrpMatElt -> ModMatElt
H ! f : ModMatRng, Map -> ModMatRngElt
M ! Q : ModMatRng, [RngElt] -> ModMatRngElt
M ! v : ModMPol, ModTupRngElt -> ModMPolElt
M ! 0 : ModMPol, RngIntElt -> ModMPolElt
M ! Q : ModMPol, [ RngElt ] -> ModMPolElt
M ! x : ModSS, . -> ModSSElt
M ! x : ModSym, . -> ModSymElt
V ! 0 : ModTupFld, RngIntElt -> ModTupFldElt
V ! Q : ModTupFld, [RngElt] -> ModTupFldElt
M ! Q : ModTupRng, [RngElt] -> ModTupRngElt
M ! Q : ModTupRng, [RngElt] -> ModTupRngElt
O ! [w_1, ..., w_n] : MonOrd, [MonOrdElt] -> MonOrdElt
O ! [i_1, ..., i_n] : MonOrd, [RngIntElt] -> MonOrdElt
P ! w : MonPlc, MonOrdElt -> MonPlcElt
M ! Q : MonPlc, SeqEnum -> MonPlcElt
M ! Q : MonPlc, SeqEnum -> MonPlcElt
P ! t : MonPlc, Tbl -> MonPlcElt
P ! [w_1, ..., w_n] : MonPlc, [MonOrdElt] -> MonPlcElt
M ! [i_1, ..., i_n] : MonPlc, [MonPlcElt] -> MonPlcElt
P ! [u_1, ..., u_n] : MonPlc, [MonPlcElt] -> MonPlcElt
P ! [i_1, ..., i_n] : MonPlc, [RngIntElt] -> MonPlcElt
M ! [ i_1, ..., i_s ] : MonRWS, [ RngIntElt ] -> MonRWSElt
M ! w : MonTbl, MonOrdElt -> Tbl
M ! u : MonTbl, MonPlcElt -> Tbl
L ! l : PlaneLnSet, PlaneLn -> PlaneLn
L ! [a, b, c] : PlaneLnSet, SeqEnum -> PlaneLn
L ! [m, b] : PlaneLnSet, SeqEnum -> PlaneLn
L ! S : PlaneLnSet, SetEnum -> PlaneLn
V ! x : PlanePtSet, Elt -> PlanePt
V ! [a, b, c] : PlanePtSet, SeqEnum -> PlanePt
V ! [a, b] : PlanePtSet, SeqEnum -> PlanePt
S ! P : PlcCrv, PlcFunElt -> PlcCrvElt
S ! I : PlcFun, RngFunOrdIdl -> PlcFunElt
P ! S : PowSeqEnum, SeqEnum -> SeqEnum
P ! S : PowSetEnum, SetEnum -> SetEnum
P ! S : PowSetIndx, SetIndx -> SetIndx
P ! S : PowSetMulti, SetMulti -> SetMulti
Q ! f : QuadBin, QuadBinElt -> QuadBinElt
Q ! [a, b, c] : QuadBin, RngIntElt, RngIntElt, RngIntElt -> QuadBinElt
R ! a : Rng, RngElt -> RngElt
O ! a : RngFunOrd, . -> RngFunOrdElt
O ! [ a_1, a_2, ..., a_(n) ] : RngFunOrd, SeqEnum -> RngFunOrdElt
R ! a : RngGal, RngElt -> RngGalElt
Z ! a : RngInt, RngElt -> RngIntElt
R ! k : RngIntRes, RngIntElt -> RngIntResElt
O ! a : RngOrd, RngElt -> RngOrdElt
O ! [a_0, a_1, ..., a_(m - 1)] : RngOrd, [ RngElt ] -> RngOrdElt
OQ ! a : RngOrdRes, Elt -> RngOrdResElt
R ! c : RngPowLaz, RngElt -> RngPowLazElt
R ! s : RngPowLaz, RngPowLazElt -> RngPowLazElt
R ! S : RngPowLaz, [RngElt] -> RngPowLazElt
R ! s : RngSerSer, SeqEnum -> RngSerSerElt
P ! s : RngUPol, RngElt -> RngPolElt
V ! r : RngVal, FldFunElt -> RngValElt
X ! Q : Sch,SeqEnum -> Pt
A ! [a,...] : Sch,[RngElt] -> Pt
A ! [a,b,...] : Sch,[RngElt] -> Pt
C(L) ! [a,...] : SetPt,[RngElt] -> Pt
G ! Q : SgpFP, [ SgpFPElt ] -> SgpFPElt
S ! [i_1, ... i_s] : SgpFP, [RngIntElt] -> SgpFPElt
H ! x : SpcHyp, . -> SpcHypElt
K ! 0 : SrfKum, RngIntElt -> SrfKumPt
K ! P : SrfKum, SrfKumPt -> SrfKumPt
K ! [x1, x2, x3, x4] : SrfKum, [ RngElt ] -> SrfKumPt
S ! x : Str, Elt -> Elt
L ! n : SubFldLat, RngIntElt -> SubFldLatElt
L ! H: SubGrpLat, GrpFin -> SubGrpLatElt
L ! i: SubGrpLat, RngIntElt -> SubGrpLatElt
IntegerRing() ! e : SubGrpLatElt -> RngIntElt
L ! S: SubModLat, ModRng -> SubModLatElt
L ! i: SubModLat, RngIntElt -> SubModLatElt
IntegerRing() ! e : SubModLatElt -> RngIntElt
J ! [P,Q] : [PtHyp] -> JacHypPt
J ! [S,T] : [[PtHyp]] -> JacHypPt
Divisor(P) : PlcFunElt -> DivFunElt
Id(M) : MonFP -> MonFPElt
Id(O) : MonOrd -> MonOrdElt
Id(P) : MonPlc -> MonPlcElt
Identity(G) : Grp -> GrpPermElt
Identity(A) : GrpAb -> GrpAbElt
Identity(A) : GrpAbGen -> GrpAbGenElt
Identity(G) : GrpAtc -> GrpAtcElt
Identity(A) : GrpAuto -> GrpAutoElt
Identity(B) : GrpBrd -> GrpBrdElt
Identity(G) : GrpFP -> GrpFPElt
Identity(G) : GrpGPC -> GrpGPCElt
Identity(G) : GrpMat -> GrpMatElt
Identity(G) : GrpPC -> GrpPCElt
Identity(G) : GrpRWS -> GrpRWSElt
Identity(G) : GrpSLP -> GrpSLPElt
Identity(M) : MonRWS -> MonRWSElt
Identity(Q) : QuadBin -> QuadBinElt
One(A) : AlgGen -> AlgGenElt
ResolutionGraphVertex(g,i) : GrphRes,RngIntElt -> GrphResVert
Zero(A) : AlgGen -> AlgGenElt
Zero(M) : ModRng, RngIntElt -> ModRngElt
Zero(M) : ModRng, RngIntElt -> ModRngElt
elt<C | x, y> : FldCom, FldReElt, FldReElt -> FldComElt
elt<F | a> : FldFin, RngElt -> FldFinElt
elt< R | a_1, ..., a_k :parameters> : AlgChtr, FldCycElt, ..., FldCycElt -> AlgChtrElt
elt<L | u> : RngLoc, RngElt -> RngLocElt
elt<P | u> : RngLoc, RngElt -> RngLocElt
elt<L | s> : RngLoc, [ RngElt ] -> RngLocElt
elt< R | a > : RngMPol, RngElt -> RngMPolElt
elt< C | a_1, a_2, ..., a_k > : SetCart, Elt, ..., Elt -> Tup
F !! I : FldOrd, RngOrdFracIdl -> RngOrdFracIdl
G !! H : GrpPerm, GrpPerm -> GrpPerm
M1 !! M2 : ModSym, ModSym -> ModSym
Comparison (OVERVIEW)
Strings (OVERVIEW)
r``s : Rec, String -> Elt
"abc" : -> MonStgElt
Groups (OVERVIEW)
Rings, Fields, and Algebras (OVERVIEW)
# x : AlgChtrElt -> RngIntElt
# u : AlgFPElt -> RngIntElt
# A : AlgGen -> RngIntElt
# B : Bool -> RngIntElt
# C : Code -> RngIntElt
# C : Code -> RngIntElt
# C : Cop -> RngIntElt
# C : CrvHyp -> RngIntElt
# D : DB -> RngIntElt
# D : DB -> RngIntElt
# D : DB -> RngIntElt
# D : DB -> RngIntElt
# D : DB -> RngIntElt
# D: DB -> RngIntElt
# C : Elt -> RngIntElt
# u : GrpAtcElt -> RngIntElt
# u : GrpBrdElt -> RngIntElt
# V : GrpFPCos -> RngIntElt
# w : GrpFPElt -> RngIntElt
# u : GrpRWSElt -> RngIntElt
# u : GrpSLPElt -> RngIntElt
# J : JacHyp -> RngIntElt
# S : List -> RngIntElt
# u : MonRWSElt -> RngIntElt
# s : MonStgElt -> RngIntElt
# R : Rng -> RngIntElt
# R : RngGal -> RngIntElt
# L : RngLoc -> RngIntElt
# P : RngLoc -> RngIntElt
# P : RngUPolRes -> RngIntElt
# G: SchGrpEll -> RngIntElt
# S : SeqEnum -> RngIntElt
# T : SeqEnum -> RngIntElt
# C : SetCart -> RngIntElt
# R : SetIndx -> RngIntElt
# H: SetPtEll -> RngIntElt
# u : SgpFPElt -> RngIntElt
# L : SubFldLat -> RngIntElt
# L : SubGrpLat -> RngIntElt
# L : SubModLat -> RngIntElt
# G : SymGen -> RngIntElt
# T : Tup -> RngIntElt
BlockDegree(D, B) : Inc, IncBlk -> RngIntElt
Length(w) : MonOrdElt -> RngIntElt
Length(u) : MonPlcElt -> RngIntElt
NumberOfBlocks(D) : Inc -> RngIntElt
NumberOfLines(P) : Plane -> RngIntElt
NumberOfPoints(D) : Inc -> RngInt
NumberOfPoints(P) : Plane -> RngIntElt
Order(G) : GrpAb -> RngIntElt
Order(A) : GrpAbGen -> RngIntElt
Order(G) : GrpAtc -> RngIntElt
Order(A) : GrpAuto -> RngIntElt
Order(G) : GrpFin -> RngIntElt
Order(G) : GrpGPC -> RngIntElt
Order(G) : GrpMat -> RngIntElt
Order(G) : GrpPC -> RngIntElt
Order(G) : GrpPerm -> RngIntElt
Order(G) : GrpRWS -> RngIntElt
Order(M) : MonRWS -> RngIntElt
Generator Assignment (OVERVIEW)
Recursion (OVERVIEW)
Recursive functions (OVERVIEW)
History (OVERVIEW)
%
%n
%n_1 n_2
Performing shell commands from Magma (OVERVIEW)
%! shell-command
%! shell-command
%
%e
%en
%en_1 n_2
%P
%Pn
%Pn_1 n_2
%p
%pn
%pn_1 n_2
%S
%Sn
%Sn_1 n_2
%s
%sn
%sn_1 n_2
& o S : Op, SeqEnum -> Elt
& o S : Op, SetIndx -> Elt
&* s : [ MonStgElt ] -> MonStgElt
&cat s : [ MonStgElt ] -> MonStgElt
&* s : [ MonStgElt ] -> MonStgElt
&cat s : [ MonStgElt ] -> MonStgElt
&meet S : [ ModTupFld ] -> ModTupFld
&meet S : [ RngMPol ] -> RngMPol
&meet S : [ SubFldLatElt ] -> SubFldLatElt
Comparison (OVERVIEW)
Prompt (OVERVIEW)
Comparison (OVERVIEW)
Comparison (OVERVIEW)
Aggregate (OVERVIEW)
Comparison (OVERVIEW)
Generator Assignment (OVERVIEW)
E<x_1, x_2, ...x_n> := expression;
< a_1, a_2, ..., a_k > : Elt, ..., Elt -> Tup
Comparison (OVERVIEW)
E<[x]> := expression;
Expression (OVERVIEW)
x(g) : AlgChtrElt, GrpElt -> FldCycElt
E(m) : CrvEll, Map -> SetPtEll
E(L) : CrvEll, Rng -> SetPtEll
f(r) : Hom(GrpFP), GrpFPRel -> GrpFPRel
m(e) : Map, Elt -> CopElt
v * a : ModTupFldElt, ModMatFldElt -> ModTupFldElt
u * a : ModTupRngElt, ModMatRngElt -> ModTupRngElt
a @ f : Elt, Map -> Elt
B @ f : GrpBrd, Map -> Grp
e @ f : GrpBrdElt, Map -> GrpElt
H @ f : GrpFP, Map -> Grp
<i, w> @ T : GrpFPCosElt, GrpFPElt, Map -> GrpFPElt
w @ f : GrpFPElt, Map -> GrpElt
S @ f : SetEnum, Map -> SetEnum
C @ f : Struct, Map -> Struct
InnerProduct(v, w) : LatElt, LatElt -> RngElt
(u, v) : GrpAtcElt, GrpAtcElt -> GrpAtcElt
(g, h) : GrpElt, GrpElt -> GrpElt
(u, v) : GrpFPElt, GrpFPElt -> GrpFPElt
( g, h ) : GrpLieElt, GrpLieELt -> GrpLieElt
(g, h) : GrpMatElt, GrpMatElt -> GrpMatElt
(g, h) : GrpPermElt, GrpPermElt -> GrpPermElt
(u, v) : GrpRWSElt, GrpRWSElt -> GrpRWSElt
(u, v) : ModTupFldElt, ModTupFldElt -> FldElt
(u, v) : ModTupRngElt, ModTupRngElt -> RngElt
(u, v) : ModTupRngElt, ModTupRngElt : -> RngElt
(u, v) : ModTupRngElt, ModTupRngElt : -> RngElt
LieBracket(a, b) : AlgAssElt, AlgAssElt -> AlgAssElt
(u_1, ..., u_r) : GrpAtcElt, ..., GrpAtcElt -> GrpAtcElt
(g_1, ..., g_r) : GrpAutoElt, ..., GrpAutoElt -> GrpAutoElt
(g_1, ..., g_r) : GrpElt, ..., GrpElt -> GrpElt
(g_1, ..., g_r) : GrpMatElt, ..., GrpMatElt -> GrpMatElt
(g_1, ..., g_r) : GrpPermElt, ..., GrpPermElt -> GrpPermElt
(u_1, ..., u_r) : GrpRWSElt, ..., GrpRWSElt -> GrpRWSElt
(u_1, ..., u_n) : List(GrpFPElt) -> GrpFPElt
(g_1, ..., g_n) : List(GrpGPCElt) -> GrpGPCElt
(g_1, ..., g_n) : List(GrpPCElt) -> GrpPCElt
Groups (OVERVIEW)
Operators (OVERVIEW)
Rings, Fields, and Algebras (OVERVIEW)
a * b : AlgBasElt, AlgBasElt -> AlgBasElt
u * v : AlgFPElt, AlgFPElt -> AlgFPElt
A * B : AlgGen, AlgGen -> AlgGen
a * b : AlgGenElt, AlgGenElt -> AlgGenElt
a * r : AlgGenElt, RngElt -> AlgGenElt
a * I : AlgGrpElt, AlgGrpSub -> AlgGrpSub
a * r : AlgGrpElt, RngElt -> AlgGrpElt
I * a : AlgGrpSub, AlgGrpElt -> AlgGrpSub
a * b : AlgMatElt, AlgMatElt -> AlgMatElt
T * L : AlgMatElt, Lat -> Lat
a * b : AlgMatElt, ModHomElt -> ModHomElt
x * y : AlgQuatElt, AlgQuatElt -> AlgQuatElt
I * J : AlgQuatOrd, AlgQuatOrd -> AlgQuatOrd
x * u : FldElt, ModTupFldElt -> ModTupFldElt
u * v : GrpAtcElt, GrpAtcElt -> GrpAtcElt
f * g : GrpAutoElt, GrpAutoElt -> GrpAutoElt
u * v : GrpBrdElt, GrpBrdElt -> GrpBrdElt
g * a : GrpElt, AlgGrpElt -> AlgGrpElt
g * h : GrpElt, GrpElt -> GrpElt
H * g : GrpFP, GrpFPElt -> GrpFPCosElt
C * D : GrpFPCosElt, GrpFPCosElt -> GrpFPCosElt
C * g : GrpFPCosElt, GrpFPElt -> GrpFPCosElt
u * v : GrpFPElt, GrpFPElt -> GrpFPElt
g * h : GrpGPCElt, GrpGPCElt -> GrpGPCElt
x * y : GrphDrchElt, GrphDrchElt -> GrpDrchElt
g * h : GrpLieElt, GrpLieElt -> GrpLieElt
g * h : GrpMatElt, GrpMatElt -> GrpMatElt
g * h : GrpPCElt, GrpPCElt -> GrpPCElt
G * H : GrpPerm, GrpPerm -> { GrpPermElt }
H * g : GrpPerm, GrpPermElt -> Elt
g * h : GrpPermElt, GrpPermElt -> GrpPermElt
g * h : GrpPSL2Elt, GrpPSL2Elt -> GrpPSL2Elt
u * v : GrpRWSElt, GrpRWSElt -> GrpRWSElt
u * v : GrpSLPElt, GrpSLPElt -> GrpSLPElt
g * z : GrpSPL2Elt, SpcHypElt -> SpcHypElt
v * T : LatElt, AlgMatElt -> LatElt
v * s : LatElt, RngIntElt -> .
f * g : Map, Map -> Map
f * g : Map, Map -> Map
f * g : MapIsoSch, MapIsoSch -> MapIsoSch
g * f : MapSch,MapSch -> MapSch
m * b : ModAlgElt, AlgBasElt -> ModAlgElt
x * T : ModBrdtElt, AlgMatElt -> ModBrdtElt
u * c : ModDedElt, RngElt -> ModDedElt
u * I : ModDedElt, RngOrdIdl -> ModDed
f * g : ModFrmElt, ModFrmElt -> ModFrmElt
u * g : ModGrpElt, GrpElt -> ModGrpElt
a * b : ModHomElt, AlgMatElt -> ModHomElt
f * g : ModMatCpxElt , ModMatCpxElt -> ModMatCpxElt
a * b : ModMatElt, ModMatElt -> ModMatElt
a * b : ModMatRngElt, ModMatRngElt -> ModMatRngElt
f * s : ModMPolElt, RngMPolElt -> ModMPolElt
u * a : ModTupElt, AlgElt -> ModTupElt
u * a : ModTupElt, AlgMatElt -> ModTupElt
u * g : ModTupElt, GrpMatElt -> ModTupElt
u * k : ModTupElt, RngElt -> ModTupElt
u * x : ModTupElt, RngElt -> ModTupElt
v * a : ModTupFldElt, ModMatFldElt -> ModTupFldElt
v * A : ModTupRng, MtrxSprs -> ModTupRng
u * a : ModTupRngElt, ModMatRngElt -> ModTupRngElt
w1 * w2 : MonOrdElt, MonOrdElt -> MonOrdElt
u1 * u2 : MonPlcElt, MonPlcElt -> MonPlcElt
u * v : MonRWSElt, MonRWSElt -> MonRWSElt
A * B : Mtrx, Mtrx -> Mtrx
f * M : QuadBinElt, GrpMatElt -> QuadBinElt
f * g : QuadBinElt, QuadBinElt -> QuadBinElt
a * g : RngElt , ModMatCpxElt -> ModMatCpxElt
t * a : RngElt, AlgMatElt -> AlgMatElt
r * x : RngElt, DiffFunElt -> DiffFunElt
s * L : RngElt, Lat -> Lat
a * x : RngElt, ModBrdtElt -> ModBrdtEltx * a : ModBrdtElt, RngElt -> ModBrdtElt
a * f : RngElt, ModFrmElt -> ModFrmElt
k * u : RngElt, ModTupElt -> ModTupElt
x * u : RngElt, ModTupElt -> ModTupElt
a * u : RngElt, ModTupRngElt -> ModTupRngElt
a * u : RngElt, ModTupRngElt -> ModTupRngElt
x * A : RngElt, Mtrx -> Mtrx
a * b : RngElt, RngElt -> RngElt
x * O : RngElt, RngFunOrd -> RngFunOrdIdl
x * O : RngElt, RngOrd -> RngOrdFracIdl
x * I : RngElt, RngOrdFracIdl -> RngOrdFracIdl
c * s : RngElt, RngPowLazElt -> RngPowLazElt
f * x : RngElt,DiffFunElt -> DiffFunElt
I * J : RngIdl, RngIdl -> RngIdl
m * u : RngIntElt, GrpAbElt-> GrpAbElt
n * g : RngIntElt, GrpAbGenElt-> GrpAbGenElt
n * P : RngIntElt, JacHypPt -> JacHypPt
n * P : RngIntElt, PtEll -> PtEll
n * P : RngIntElt, SrfKumPt -> SrfKumPt
x * y : RngLocElt, RngLocElt -> RngLocElt
I * J : RngMPol, RngMPol -> RngMPol
s * f : RngMPolElt, ModMPolElt -> ModMPolElt
I * J : RngMPolRes, RngMPolRes -> RngMPolRes
I * J : RngOrdFracIdl, RngOrdFracIdl -> RngOrdFracIdl
I * M : RngOrdIdl, ModDed -> ModDed
I * u : RngOrdIdl, ModDedElt -> ModDed
s * n : RngPowLazElt, RngIntElt -> RngPowLazElt
s * t : RngPowLazElt, RngPowLazElt -> RngPowLazElt
I * J : RngUPol, RngUPol -> RngUPol
u * v : SgpFPElt, SgpFPElt -> SgpFPElt
e * f : SubFldLatElt, SubFldLatElt -> SubFldLatElt
t1 * t2 : Tbl, Tbl -> Tbl
D + E : DivCrvElt,DivCrvElt -> DivCrvElt
Divisor(P) : PlcFunElt -> DivFunElt
s cat t : MonStgElt, MonStgElt -> MonStgElt
Comments (OVERVIEW)
a *:= b : RngElt, RngElt -> RngElt
g *:= h : GrpGPCElt, GrpGPCElt ->
g *:= h : GrpPCElt, GrpPCElt -> GrpPCElt
P *:= n : JacHypPt, RngIntElt ->
v *:= n : LatElt, RngIntElt ->
P *:= n : PtEll, RngIntElt ->
u *:= v : GrpBrdElt, GrpBrdElt ->
s cat:= t : MonStgElt, MonStgElt -> MonStgElt
Operators (OVERVIEW)
Rings, Fields, and Algebras (OVERVIEW)
r * x : RngElt, DiffFunElt -> DiffFunElt
f * x : RngElt,DiffFunElt -> DiffFunElt
a + b : AlgBasElt, AlgBasElt -> AlgBasElt
u + v : AlgFPElt, AlgFPElt -> AlgFPElt
a + b : AlgGenElt, AlgGenElt -> AlgGenElt
a + g : AlgGrpElt, GrpElt -> AlgGrpElt
a + r : AlgGrpElt, RngElt -> AlgGrpElt
a + b : AlgMatElt, AlgMatElt -> AlgMatElt
a + t : AlgMatElt, RngElt -> AlgMatElt
x + y : AlgQuatElt, AlgQuatElt -> AlgQuatElt
C + D : Code, Code -> Code
C + D : Code, Code -> Code
D + E : DivCrvElt,DivCrvElt -> DivCrvElt
u + v : GrpAbElt, GrpAbElt -> GrpAbElt
g + d : GrpAbGenElt, GrpAbGenElt -> GrpAbGenElt
G + [u, v] : GrphDir, [GrphVert] -> GrphDir
G + S : GrphDir, { [GrphVert] } -> GrphDir
G + { u, v } : GrphUnd, { GrphVert } -> GrphUnd
G + S : GrphUnd, { { GrphVert } } -> GrphUnd
P + Q : JacHypPt, JacHypPt -> JacHypPt
L + M : Lat, Lat -> Lat
v + w : LatElt, LatElt -> LatElt
x + y : ModBrdtElt, ModBrdtElt -> ModBrdtElt
M1 + M2 : ModDed, ModDed -> ModDed
x + y : ModDedElt, ModDedElt -> ModDedElt
f + g : ModFrmElt, ModFrmElt -> ModFrmElt
f + g : ModFrmElt, RngSerPowElt -> RngSerPowElt
f + g : ModMatCpxElt , ModMatCpxElt -> ModMatCpxElt
M + N : ModMPol, ModMPol -> ModMPol
f + g : ModMPolElt, ModMPolElt -> ModMPolElt
M1 + M2 : ModSS, ModSS -> ModSS
u + v : ModTupElt, ModTupElt -> ModTupElt
u + v : ModTupElt, ModTupElt -> ModTupElt
U + V : ModTupFld, ModTupFld -> ModTupFld
u + v : ModTupFldElt, ModTupFldElt -> ModTupFldElt
M + N : ModTupRng, ModTupRng -> ModTupRng
M + N : ModTupRng, ModTupRng -> ModTupRng
u + v : ModTupRngElt, ModTupRngElt -> ModTupRngElt
u + v : ModTupRngElt, ModTupRngElt -> ModTupRngElt
A + B : Mtrx, Mtrx -> Mtrx
P + Q : PtEll, PtEll -> PtEll
+ a : RngElt -> RngElt
a + b : RngElt, RngElt -> RngElt
I + J : RngIdl, RngIdl -> RngIdl
x + y : RngLocElt, RngLocElt -> RngLocElt
I + J : RngMPol, RngMPol -> RngMPol
I + J : RngMPolRes, RngMPolRes -> RngMPolRes
O + P : RngOrd, RngOrd -> RngOrd
I + J : RngOrdFracIdl, RngOrdFracIdl -> RngOrdFracIdl
s + r : RngPowLazElt, RngElt -> RngPowLazElt
s + t : RngPowLazElt, RngPowLazElt -> RngPowLazElt
I + J : RngUPol, RngUPol -> RngUPol
z + a : SpcHypElt, RngIntElt -> SpcHypElt
e + f : SubModLatElt, SubModLatElt -> SubModLatElt
a +:= b : RngElt, RngElt -> RngElt
P +:= Q : JacHypPt, JacHypPt ->
P +:= Q : PtEll, PtEll ->
v +:= w : LatElt, LatElt ->
AddEdge(~G, i, j) : Grph, RngIntElt, RngIntElt ->
AddVertices(~G, n) : Grph, RngIntElt ->
x_1, x_2, ..., x_n := expression;
,
Operators (OVERVIEW)
Rings, Fields, and Algebras (OVERVIEW)
r * x : RngElt, DiffFunElt -> DiffFunElt
f * x : RngElt,DiffFunElt -> DiffFunElt
D + E : DivCrvElt,DivCrvElt -> DivCrvElt
u - v : AlgFPElt, AlgFPElt -> AlgFPElt
- a : AlgGenElt -> AlgGenElt
a - b : AlgGenElt, AlgGenElt -> AlgGenElt
a - g : AlgGrpElt, GrpElt -> AlgGrpElt
a - r : AlgGrpElt, RngElt -> AlgGrpElt
- a : AlgMatElt -> AlgMatElt
a - b : AlgMatElt, AlgMatElt -> AlgMatElt
a - t : AlgMatElt, RngElt -> AlgMatElt
x - y : AlgQuatElt, AlgQuatElt -> AlgQuatElt
- u : GrpAbElt -> GrpAbElt
u - v : GrpAbElt, GrpAbElt -> GrpAbElt
- g : GrpAbGenElt -> GrpAbGenElt
g - d : GrpAbGenElt, GrpAbGenElt -> GrpAbGenElt
G - e : Grph, GrphEdge -> Grph
G - v : Grph, GrphVert -> Grph
G - F : Grph, { GrphEdge } -> Grph
G - U : Grph, { GrphVert } -> Grph
- P : JacHypPt -> JacHypPt
P - Q : JacHypPt, JacHypPt -> JacHypPt
- v : LatElt -> LatElt
v - w : LatElt, LatElt -> LatElt
x - y : ModBrdtElt, ModBrdtElt -> ModBrdtElt
x - y : ModDedElt, ModDedElt -> ModDedElt
f - g : ModFrmElt, ModFrmElt -> ModFrmElt
- f : ModMPolElt -> ModMPolElt
f - g : ModMPolElt, ModMPolElt -> ModMPolElt
- u : ModTupElt -> ModTupElt
- u : ModTupElt -> ModTupElt
u - v : ModTupElt, ModTupElt -> ModTupElt
u - v : ModTupElt, ModTupElt -> ModTupElt
- u : ModTupFldElt -> ModTupFldElt
u - v : ModTupFldElt, ModTupFldElt -> ModTupFldElt
- u : ModTupRngElt -> ModTupRngElt
- u : ModTupRngElt -> ModTupRngElt
u - v : ModTupRngElt, ModTupRngElt -> ModTupRngElt
u - v : ModTupRngElt, ModTupRngElt -> ModTupRngElt
- A : Mtrx -> Mtrx
A - B : Mtrx, Mtrx -> Mtrx
- P : PtEll -> PtEll
P - Q : PtEll, PtEll -> PtEll
- P : PtHyp -> PtHyp
- a : RngElt -> RngElt
a - b : RngElt, RngElt -> RngElt
- x : RngLocElt -> RngLocElt
x - y : RngLocElt, RngLocElt -> RngLocElt
- s : RngPowLazElt -> RngPowLazElt
s - t : RngPowLazElt, RngPowLazElt -> RngPowLazElt
- P : SrfKumPt -> SrfKumPt
a -:= b : RngElt, RngElt -> RngElt
P -:= Q : JacHypPt, JacHypPt ->
P -:= Q : PtEll, PtEll ->
v -:= w : LatElt, LatElt ->
RemoveEdge(~G, i, j) : Grph, RngIntElt, RngIntElt ->
RemoveVertex(~G, i) : Grph, RngIntElt ->
magma -b
<Meta>-B
<Meta>-b
magma -c filename
magma -d
<Meta>-F
<Meta>-f
$
magma -n
magma -r workspace
magma -S integer
magma -s filename
Generator Assignment (OVERVIEW)
B . i : AlgBas, RngIntElt -> AlgBasElt
A . i : AlgFP, RngIntElt -> AlgFPElt
R . i : AlgMat, RngIntElt -> AlgMatElt
A . i : AlgQuat, RngIntElt -> AlgQuatElt
C . i : Code, RngIntElt -> ModTupFldElt
C . i : Code, RngIntElt -> ModTupRngElt
A . i : FldAC, RngIntElt -> FldACElt
F . 1 : FldFin -> FldFinElt
F . 1 : FldFin, RngIntElt -> FldFinElt
F . 1 : FldFun -> FldFunElt
K . i : FldFunRat, RngIntElt -> FldFunRatElt
K . 1 : FldNum -> FldNumElt
F . i : FldOrd, RngIntElt -> FldOrdElt
G . i : Grp, RngIntElt -> GrpElt
A . i : GrpAb, RngIntElt -> GrpAbElt
A . i : GrpAbGen, RngIntElt -> GrpAbGenElt
G . i : GrpAtc, RngIntElt -> GrpAtcElt
A . i : GrpAuto, RngIntElt -> GrpAutoElt
B . i : GrpBrd, RngIntElt -> GrpBrdElt
G . i : GrpFP, RngIntElt -> GrpFPElt
G . i : GrpGPC, RngIntElt -> GrpGPCElt
E . i : GrphEdgeSet, RngIntElt -> GrphEdge
V . i : GrphVertSet, RngIntElt -> GrphVert
G . i : GrpMat, RngIntElt -> GrpMatElt
G . i : GrpPC, RngIntElt -> GrpPCElt
G . i : GrpPerm, RngIntElt -> GrpPermElt
G . i : GrpRWS, RngIntElt -> GrpRWSElt
G . i : GrpSLP, RngIntElt -> GrpSLPElt
B . i : IncBlkSet, RngIntElt -> IncBlk
P . i : IncPtSet, RngIntElt -> IncPt
L . i : Lat, RngIntElt -> LatElt
M . i : ModBrdt, RngIntElt -> ModBrdtElt
M . i : ModDed, RngIntElt -> ModTupRngElt
M . i : ModFrm, RngIntElt -> ModFrmElt
M . i : ModMPol, RngIntElt -> ModMPolElt
M . i : ModSS, RngIntElt -> ModSSElt
V . i : ModTupFld, RngIntElt -> ModTupFldElt
M . i : ModTupRng, RngIntElt -> ModElt
M . i : ModTupRng, RngIntElt -> ModElt
O . i : MonOrd, RngIntElt -> MonOrdElt
P . i : MonPlc, RngIntElt -> MonPlcElt
M . i : MonRWS, RngIntElt -> MonRWSElt
L . i : PlanePtSet, RngIntElt -> PlanePt
V . i : PlanePtSet, RngIntElt -> PlanePt
R . 1 : RngGal -> RngGalElt
d . eefpg : RngIntElt, RngIntElt, RngIntElt -> FldReElt
P . i : RngMPol, RngInt -> RngMPolElt
Q . i : RngMPolRes, RngIntElt -> RngMPolResElt
O . i : RngOrd, RngIntElt -> RngOrdElt
R . i : RngPowLaz, RngIntElt -> RngPowLazElt
R . 1 : RngSerSer, RngInt -> RngSerElt
I . 1 : RngUPol -> RngUPolElt
P . 1 : RngUPol, RngInt -> RngPolElt
A . i : Sch,RngIntElt -> RngMPolElt
X . i : Sch,RngIntElt -> RngMPolElt
H . i : SetPtEll, RngIntElt -> PtEll
H . i : SetPtEll, RngIntElt -> PtEll
S . i : SgpFP, RngIntElt -> SgpFPElt
BasisElement(A, i) : AlgGen, RngIntElt -> AlgGenElt
InertiaElement(L) : RngLoc -> RngLocElt
Name(K, i) : FldNum, RngIntElt -> FldNumElt
Name(S, 1) : RngSer, RngIntElt -> RngSerElt
Prime(P) : FldLoc -> RngIntElt
UniformizingElement(L) : RngLoc -> RngLocElt
Sequences (OVERVIEW)
Sets (OVERVIEW)
Operators (OVERVIEW)
Rings, Fields, and Algebras (OVERVIEW)
r * x : RngElt, DiffFunElt -> DiffFunElt
f * x : RngElt,DiffFunElt -> DiffFunElt
A / I : AlgFP, AlgFPIdl -> AlgFP
A / S : AlgGen, AlgGen -> AlgGen
a / r : AlgGenElt, RngElt -> AlgGenElt
A / S : AlgGrp, AlgGrpSub -> AlgAss
x / y : AlgQuatElt, AlgQuatElt -> AlgQuatElt
G / N : Grp, Grp -> Grp
A / B : GrpAb, GrpAb -> GrpAb
u / v : GrpAtcElt, GrpAtcElt -> GrpAtcElt
u / v : GrpBrdElt, GrpBrdElt -> GrpBrdElt
g / h : GrpElt, GrpElt -> GrpElt
G / H : GrpFP, GrpFP -> GrpFP
G / N : GrpGPC, GrpGPC -> GrpGPC
g / h : GrpGPCElt, GrpGPCElt -> GrpGPCElt
G / N : GrpMat, GrpMat -> GrpMat
g / h : GrpMatElt, GrpMatElt -> GrpMatElt
G / N : GrpPC, GrpPC -> GrpPC
g / h : GrpPCElt, GrpPCElt -> GrpPCElt
G / N : GrpPerm, GrpPerm -> GrpPerm
g / h : GrpPermElt, GrpPermElt -> GrpPermElt
u / v : GrpRWSElt, GrpRWSElt -> GrpRWSElt
L / S : Lat, Lat -> GrpAb, Map
L / s : Lat, RngElt -> Lat
v / s : LatElt, RngIntElt -> .
u / c : ModDedElt, RngElt -> ModDedElt
f / a : ModFrmElt, RngElt -> ModFrmElt
M / N : ModMPol, ModMPol -> ModMPol
u / k : ModTupElt, RngElt -> ModTupElt
u / x : ModTupElt, RngElt -> ModTupElt
V / U : ModTupFld, ModTupFld -> ModTupFld
u / x : ModTupFldElt, FldElt -> ModTupFldElt
R / I : Rng, RngIdl -> Rng
a / b : RngElt, RngElt -> RngElt
c / I : RngElt, RngFunOrdIdl -> RngFunOrdIdl
a / b : RngIntElt, RngIntElt -> FldRatElt
I / J : RngMPol, RngMPol -> RngMPolRes
P / J : RngMPol, RngMPol -> RngMPolRes
I / x : RngOrdFracIdl, RngElt -> RngOrdFracIdl
I / J : RngOrdFracIdl, RngOrdFracIdl -> RngOrdFracIdl
S / I : SgpFP, SgpFPIdl -> SgpFP
x div y : RngLocElt, RngLocElt -> RngLocElt
Comments (OVERVIEW)
/* */
Comments (OVERVIEW)
//
a /:= b : RngElt, RngElt -> RngElt
g /:= h : GrpGPCElt, GrpGPCElt ->
g /:= h : GrpPCElt, GrpPCElt -> GrpPCElt
u /:= v : GrpBrdElt, GrpBrdElt ->
Comparison (OVERVIEW)
0
Release Notes V1.02-1 (3 March 1995) (OVERVIEW)
Release Notes V1.10-1 (8 June 1995) (OVERVIEW)
Release Notes V1.20-1 (8 January 1996) (OVERVIEW)
Release Notes V1.20-1 (8 January 1996) since June 1995 (OVERVIEW)
Release Notes V1.30-1 (5 March 1996) (OVERVIEW)
Release Notes V2.01-1 (21 June 1996) (OVERVIEW)
Release Notes V2.10-1 (14 October 1996) (OVERVIEW)
The 2-Selmer Group (HYPERELLIPTIC CURVES)
The 2-Selmer Group (HYPERELLIPTIC CURVES)
Release Notes V1.01-3 (28 September 1994) (OVERVIEW)
Release Notes V1.00-4 (19 May 1994) (OVERVIEW)
Release Notes V1.00-5 (10 June 1994) (OVERVIEW)
Release Notes V1.01-5 (25 November 1994) (OVERVIEW)
RngInt_70digitnfs (Example H38E10)
RngInt_80digitnfs (Example H38E11)
RngInt_87digitnfs (Example H38E12)
Release Notes V1.20-1 (8 January 1996) since June 1995 (OVERVIEW)
Assignment (OVERVIEW)
x := expression;
Statements (OVERVIEW)
;
Comparison (OVERVIEW)
w_1 = w_2 : AlgFPElt, AlgFPElt -> Rel
w_1 = w_2 : GrpAbElt, GrpAbElt -> Rel
w_1 = w_2 : GrpFPElt, GrpFPElt -> GrpFPRel
w_1 = w_2 : SgpFPElt, SgpFPElt -> Rel
Overview (OVERVIEW)
Overview (OVERVIEW)
g @ x : GrpElt, AlgChtrElt -> FldCycElt
x(g) : AlgChtrElt, GrpElt -> FldCycElt
a @ f : Elt, Map -> Elt
B @ f : GrpBrd, Map -> Grp
e @ f : GrpBrdElt, Map -> GrpElt
H @ f : GrpFP, Map -> Grp
<i, w> @ T : GrpFPCosElt, GrpFPElt, Map -> GrpFPElt
w @ f : GrpFPElt, Map -> GrpElt
P @ f : PtHyp, MapIsoSch -> PtHyp
S @ f : SetEnum, Map -> SetEnum
C @ f : Struct, Map -> Struct
y @@ f : Elt, Map -> Elt
H @@ f : Grp, Map -> GrpFP
g @@ f : GrpElt, Map -> GrpBrdElt
g @@ f : GrpElt, Map -> GrpFPElt
p @@ f : Pt,MapSch -> Pt
P @@ f : PtHyp, MapIsoSch -> PtHyp
X @@ f : Sch, MapSch -> Sch
R @@ f : SetEnum, Map -> SetEnum
D @@ f : Struct, Map -> Struct
[! x in F | P(x) !]
Aggregate (OVERVIEW)
[* *] : -> List
[* e_1, e_2, ..., e_n *] : Elt,.., Elt -> List
Aggregate (OVERVIEW)
Sequences (OVERVIEW)
L ! n : SubFldLat, RngIntElt -> SubFldLatElt
Coefficient(a, g) : AlgGrpElt, GrpElt -> RngElt
Component(C, i) : SetCart, RngIntElt -> Str
Coordinates(p) : Pt -> SeqEnum
x[expr_1][expr_2]...[expr_n] := expression;
a[i] := r : AlgGenElt, RngIntElt, RngElt -> AlgGenElt
a[i, j] := t : AlgMatElt, RngIntElt, RngIntElt, RngElt -> AlgMatElt
a[i] := u : AlgMatElt, RngIntElt, RngElt -> AlgMatElt
A[i] := v : Mtrx, RngIntElt, Mtrx ->
S[i] := x : List, RngIntElt, Elt ->
u[i] : = x : ModTupFldElt, RngIntElt, RngElt -> ModTupFldElt
u[i] := x : ModTupRngElt, RngIntElt, RngElt -> ModTupRngElt
u[i] := x : ModTupRngElt, RngIntElt, RngElt -> ModTupRngElt
A[i, j] := x : Mtrx, RngIntElt, RngIntElt, RngElt ->
A[i, j] := x : MtrxSprs, RngIntElt, RngIntElt, RngElt ->
u[i] := x;
u[i] := x;
x[i] : AlgChtrElt, RngIntElt -> FldCycElt
a[i] : AlgGenElt, RngIntElt -> RngElt
a[i] : AlgMatElt, RngIntElt -> ModTupElt
a[i, j] : AlgMatElt, RngIntElt, RngIntElt -> RngElt
[ e_1, e_2, ..., e_n ] : Elt, ..., Elt -> SeqEnum
a[i] : FldAlgElt, RngIntElt -> FldRatElt
r[1] : GrpAbRel, RngIntElt -> GrpAbElt
r[2] : GrpAbRel, RngIntElt -> GrpAbElt
r[1] : GrpFPRel, RngIntElt -> GrpFPElt
r[2] : GrpFPRel, RngIntElt -> GrpFPElt
r[1] = w : GrpFPRel, RngIntElt, GrpFPElt -> GrpFPRel
r[2] = w : GrpFPRel, RngIntElt, GrpFPElt -> GrpFPRel
P[i] : JacHypPt, RngIntElt -> RngElt
S[i] : List, RngIntElt -> Elt
f[i] : ModMPolElt, RngIntElt -> RngMPolElt
u[i] : ModTupFldElt, RngIntElt -> RngElt
u[i] : ModTupRngElt, RngIntElt -> RngElt
u[i] : ModTupRngElt, RngIntElt -> RngElt
u[i] : ModTupRngElt, RngIntElt -> RngElt
u[i] : ModTupRngElt, RngIntElt -> RngElt
w[i] : MonOrdElt, RngIntElt -> RngElt
s[i] : MonStgElt, RngIntElt -> MonStgElt
A[i] : Mtrx, RngIntElt -> ModTupRngElt
A[i, j] : Mtrx, RngIntElt, RngIntElt -> RngElt
A[Q] : Mtrx, [ RngIntElt ] -> RngElt
A[i] : MtrxSprs, RngIntElt -> ModTupRngElt
A[i, j] : MtrxSprs, RngIntElt, RngIntElt -> RngElt
[ ] : Null -> ESeqEnum
l[i] : PlaneLn, RngIntElt -> FldFinElt
p[i] : PlanePt, RngIntElt -> FldFinElt
p[i] : Pt, RngIntElt -> RngElt
p[i] : Pt, RngIntElt -> RngElt
P[i] : PtEll, RngIntElt -> RngElt
P[i] : PtHyp, RngIntElt -> RngElt
f[i] : QuadBinElt, RngIntElt -> RngIntElt
[ i..j ] : RngIntElt, RngIntElt -> SeqEnum
[ i .. j by k ] : RngIntElt, RngIntElt, RngIntElt -> SeqEnum
S[i] : SeqEnum, RngIntElt -> Elt
S[I] : SeqEnum, [RngIntElt] -> SeqEnum
S[i] : SetIndx, RngIntElt -> Elt
P[i] : SrfKumPt, RngIntElt -> RngElt
[ U | ] : Struct -> SeqEnum
[ U | e_1, e_2, ..., e_m ] : Struct, Elt, ..., Elt -> SeqEnum
T[i] : TabChtr, RngIntElt -> AlgChtrElt
T[i][j] : TabChtr, RngIntElt, RngIntElt -> FldCycElt
T[i] : Tup -> Elt
[ e(x) : x in E | P(x) ]
[ U | e(x) : x in E | P(x) ]
[ e(x_1,...,x_k) : x_1 in E_1, ..., x_kin E_k | P(x_1, ..., x_k) ]
[ U | e(x_1,...,x_k) : x_1 in E_1, ...,x_k in E_k | P(x_1, ..., x_k) ]
\[ m_1, ..., m_n ] : RngIntElt, ..., RngIntElt -> [ RngIntElt ]
Groups (OVERVIEW)
Operators (OVERVIEW)
Rings, Fields, and Algebras (OVERVIEW)
Class(H, g) : GrpAb, GrpAbElt -> { GrpAbElt }
Class(H, g) : GrpPC, GrpPCElt -> { GrpPCElt }
a ^ n : AlgBasElt, RngIntElt -> AlgBasElt
x ^ H : AlgChtrElt, Grp -> { AlgChtrElt }
x ^ g : AlgChtrElt, GrpElt -> AlgChtrElt
u ^ n : AlgFPElt, RngIntElt -> AlgFPElt
A ^ n : AlgGen, RngIntElt -> AlgGen
a ^ n : AlgGenElt, RngIntElt -> AlgGenElt
a ^ n : AlgMatElt, RngIntElt -> AlgMatElt
C ^ G : Code, GrpPerm -> GSet{ Code }
C ^ x : Code, GrpPermElt -> Code
y ^ G : Elt, GrpMat -> SetEnum
y ^ g : Elt, GrpMatElt -> Elt
x ^ G : Elt, GrpPerm -> GSet
y ^ G : Elt, GrpPerm -> GSet
x ^ g : Elt, GrpPermElt -> Elt
y ^ g : Elt, GrpPermElt -> Elt
H ^ G : GrpAb, GrpAb -> GrpAb
H ^ g : GrpAb, GrpAbElt -> GrpAb
u ^ v : GrpAtcElt, GrpAtcElt -> GrpAtcElt
u ^ n : GrpAtcElt, RngIntElt -> GrpAtcElt
f ^ n : GrpAutoElt, RngIntElt -> GrpAutoElt
u ^ v : GrpBrdElt, GrpBrdElt -> GrpBrdElt
u ^ n : GrpBrdElt, RngIntElt -> GrpBrdElt
x ^ n : GrpDrchElt, RngIntElt -> GrpDrchElt
g ^ h : GrpElt, GrpElt -> GrpElt
g ^ n : GrpElt, RngIntElt -> GrpElt
H ^ G : GrpFin -> GrpFin
H ^ G : GrpFin, GrpFin -> GrpFin
H ^ g : GrpFin, GrpFinElt -> GrpFin
H ^ G : GrpFP, GrpFP -> GrpFP
H ^ u : GrpFP, GrpFPElt -> GrpFP
u ^ v : GrpFPElt, GrpFPElt -> GrpFPElt
u ^ n : GrpFPElt, RngIntElt -> GrpFPElt
H ^ G : GrpGPC, GrpGPC -> GrpGPC
H ^ g : GrpGPC, GrpGPCElt -> GrpGPC
g ^ h : GrpGPCElt, GrpGPCElt -> GrpGPCElt
g ^ n: GrpGPCElt, RngIntElt -> GrpGPCElt
G ^ n : GrphUnd, RngIntElt -> GrphUnd
g ^ h : GrpLieElt, GrpLieELt -> GrpLieElt
g ^ n : GrpLieElt, RngIntElt -> GrpLieElt
H ^ G : GrpMat -> GrpMat
H ^ G : GrpMat, GrpMat -> GrpMat
H ^ g : GrpMat, GrpMatElt -> GrpMat
g ^ h : GrpMatElt, GrpMatElt -> GrpMatElt
g ^ n : GrpMatElt, RngIntElt -> GrpMatElt
H ^ G : GrpPC, GrpPC -> GrpPC
H ^ g : GrpPC, GrpPCElt -> GrpPC
g ^ h : GrpPCElt, GrpPCElt -> GrpPCElt
g ^ n: GrpPCElt, RngIntElt -> GrpPCElt
H ^ G : GrpPerm, GrpPerm -> GrpPerm
H ^ g : GrpPerm, GrpPermElt -> GrpPerm
g ^ h : GrpPermElt, GrpPermElt -> GrpPermElt
g ^ n : GrpPermElt, RngIntElt -> GrpPermElt
g ^ n : GrpPSL2Elt, RngIntElt -> GrpPSL2Elt
u ^ v : GrpRWSElt, GrpRWSElt -> GrpRWSElt
u ^ n : GrpRWSElt, RngIntElt -> GrpRWSElt
u ^ v : GrpSLPElt, GrpSLPElt -> GrpSLPElt
u ^ m : GrpSLPElt, RngIntElt -> GrpSLPElt
f ^ n : ModFrmElt, RngIntElt -> ModFrmElt
M ^ T : ModGrp, AlgMatElt -> ModGrp
M ^ T : ModGrp, AlgMatElt -> ModGrp
a ^ -1 : ModMatRngElt, RngIntElt -> ModMatRngElt
v ^ G : ModTupFldElt, GrpPerm -> GSet{ ModTupFldElt }
v ^ x : ModTupFldElt, GrpPermElt -> ModTupFldElt
u ^ n : MonRWSElt, RngIntElt -> MonRWSElt
s ^ n : MonStgElt, RngIntElt -> MonStgElt
A ^ n : Mtrx, RngIntElt -> Mtrx
f ^ n : QuadBinElt, RngIntElt -> QuadBinElt
a ^ -k : RngElt, RngIntElt -> RngElt
a ^ k : RngElt, RngIntElt -> RngElt
x ^ k : RngLocElt, RngIntElt -> RngLocElt
I ^ k : RngMPol, RngIntElt -> RngMPol
f ^ G : RngMPolElt, GrpMat -> { RngMPolElt }
f ^ a : RngMPolElt, GrpMatElt -> RngMPolElt
f ^ G : RngMPolElt, GrpPerm -> { RngMPolElt }
f ^ g : RngMPolElt, GrpPermElt -> RngMPolElt
I ^ n : RngMPolRes, RngIntElt -> BoolElt
I ^ k : RngOrdFracIdl, RngIntElt -> RngOrdFracIdl
s ^ n : RngPowLazElt, RngIntElt -> RngPowLazElt
u ^ n : SgpFPElt, RngIntElt -> SgpFPElt
S ^ x : { Code }, GrpPermElt -> { Code }
S ^ x : { ModTupFldElt }, GrpPermElt -> { ModTupFldElt }
A ^-1 : Mtrx, RngIntElt -> Mtrx
g ^:= h : GrpGPCElt, GrpGPCElt ->
g ^:= h : GrpPCElt, GrpPCElt -> GrpPCElt
a ^:= k : RngElt, RngIntElt -> RngElt
u ^:= n : GrpBrdElt, RngIntElt ->
g ^:= n: GrpGPCElt, RngIntElt ->
g ^:= n: GrpPCElt, RngIntElt -> GrpPCElt
u ^:= v : GrpBrdElt, GrpBrdElt ->
Multiple Assignment (OVERVIEW)
_ := expression;
L`DefaultPrecision
L`Minimum
L`SeriesPrinting
P`DefaultPrecision
P`SeriesPrinting
r`fieldname := expression;
S`fieldname := expression;
r`fieldname : Rec, Fieldname -> Elt
S`fieldname : Str, Fieldname -> Elt
Aggregate (OVERVIEW)
Sets (OVERVIEW)
{! x in F | P(x) !}
Aggregate (OVERVIEW)
Aggregate (OVERVIEW)
Sets (OVERVIEW)
{@ e_1, e_2, ..., e_n @} : Elt, ..., Elt -> SetIndx
{@ @} : Null -> SetIndx
{@ U | @} : Struct -> SetIndx
{@ U | e_1, e_2, ..., e_m @} : Struct, Elt, ..., Elt -> SetIndx
{@ e(x) : x in E | P(x) @}
{@ U | e(x) : x in E | P(x) @}
{@ e(x_1,...,x_k) : x_1 in E_1, ..., x_kin E_k | P(x_1, ..., x_k) @}
{@ U | e(x_1,...,x_k) : x_1 in E_1, ...,x_k in E_k | P(x_1, ..., x_k)@}
Aggregate (OVERVIEW)
Sets (OVERVIEW)
{ e_1, e_2, ..., e_n } : Elt, ..., Elt -> Set
{ } : Null -> Set
{ i..j } : RngIntElt, RngIntElt -> Set
{ i .. j by k } : RngIntElt, RngIntElt, RngIntElt -> Set
{ U | } : Struct -> Set
{ U | e_1, e_2, ..., e_n } : Struct, Elt, ..., Elt -> Set
{ e(x) : x in E | P(x) }
{ U | e(x) : x in E | P(x) }
{ e(x_1,...,x_k) : x_1 in E_1, ..., x_kin E_k | P(x_1, ..., x_k) }
{ U | e(x_1,...,x_k) : x_1 in E_1, ...,x_k in E_k | P(x_1, ..., x_k) }
Sets (OVERVIEW)
Procedures (OVERVIEW)
[____] [____] [_____] [____] [__] [Index] [Root]