Index 0

!

R ! a : AlgChtr, RngIntElt -> AlgChtrElt

A ! e : AlgFP, MonFPElt -> AlgFPElt

R ! g : AlgMat, GrpMatElt -> RngMatElt

R ! 1 : AlgMat, RngIntElt -> AlgMatElt

R ! Q : AlgMat, [ RngElt ] -> AlgMatElt

C ! [a_1, ..., a_n] : Code, [ FldFinElt ] -> ModTupFldElt

K ! a : FldCyc, RngIntElt -> FldCycElt

K ! [a_0, ..., a_(m - 1)] : FldCyc, [FldCycElt] -> FldCycElt

F ! [a, b] : FldFun, RngPolElt, RngPolElt -> FldFunElt

R ! s : FldLoc, SeqEnum -> RngPowElt

K ! a : FldNum, RngIntElt -> FldNumElt

F ! [a_0, a_(1)] : FldQuad, [FldRatElt] -> FldQuadElt

Q ! [a, b] : FldRat, RngIntElt, RngIntElt -> FldRatElt

R ! a : FldRe, RngElt -> FldReElt

E ! [x, y, z] : GeomEC, [RngElt] -> GeomECElt

G ! g : Grp, GrpElt -> GrpElt

G ! Q : Grp, [ Elt ] -> GrpElt

G ! g : GrpAb, GrpAbElt -> GrpAbElt

A ! [a_1, ... ,a_n] : GrpAb, [RngIntElt] -> GrpAbElt

G ! [ i_1, ..., i_s ] : GrpFP, [ RngIntElt ] -> GrpFPElt

G ! Q : GrpMat, [ RngElt ] -> GrpMatElt

G ! g : GrpPC, GrpPCElt -> GrpPCElt

G ! Q : GrpPC, [RngIntElt] -> GrpPCElt

G ! g : GrpPerm, GrpPermElt -> GrpPermElt

G ! Q : GrpPerm, [ Elt ] -> GrpPermElt

L ! i: ModLat, RngIntElt -> ModLatElt

IntegerRing() ! e : ModLatElt -> RngIntElt

H ! f : ModMatRng, Map -> ModMatRngElt

M ! Q : ModMatRng, [RngElt] -> ModMatRngElt

V ! 0 : ModTupFld, RngIntElt -> ModTupFldElt

V ! Q : ModTupFld, [RngElt] -> ModTupFldElt

M ! Q : ModTupRng, [RngElt] -> ModTupRngElt

P ! S : PowSeqEnum, SeqEnum -> SeqEnum

P ! S : PowSetEnum, SetEnum -> SetEnum

R ! a : Rng, RngElt -> RngElt

Z ! a : RngInt, RngElt -> RngIntElt

R ! k : RngIntRes, RngIntElt -> RngIntResElt

R ! s : RngPowSer, SeqEnum -> RngPowSerElt

P ! s : RngUPol, RngElt -> RngPolElt

V ! r : RngVal, FldFunElt -> RngValElt

G ! Q : SgpFP, [ SgpFPElt ] -> SgpFPElt

S ! [i_1, ... i_s] : SgpFP, [RngIntElt] -> SgpFPElt

L ! i: SubGrpLat, RngIntElt -> SubGrpLatElt

IntegerRing() ! e : SubGrpLatElt -> RngIntElt

V ! i : VertSet, RngIntElt -> Vert

Id(M) : MonFP -> MonFPElt

Identity(E) : GeomEC -> GeomECElt

Identity(G) : Grp -> GrpElt

Identity(G) : Grp -> GrpPermElt

Identity(A) : GrpAb -> GrpAbElt

Identity(G) : GrpFP -> GrpFPElt

Identity(G) : GrpMat -> GrpMatElt

Identity(G) : GrpPC -> GrpPCElt

One(B) : MagForm -> MagFormElt

Zero(M) : ModRng, RngIntElt -> ModRngElt

elt< R | a_1, ..., a_k> : AlgChtr, FldCycElt, ..., FldCycElt -> AlgChtrElt

elt<F | a> : FldFin, RngElt -> FldFinElt

elt<R | a> : FldLoc, RngElt -> FldLocElt

elt<R | m, n> : FldRe, FldReElt, RngIntElt -> FldReElt

elt< B | a, b, c> : MagForm, RngIntElt, RngIntElt, RngIntElt -> MagFormElt

elt< R | a > : RngDPol, RngElt -> RngDPolElt

elt< C | a_1, a_2, ..., a_k > : SetCart, Elt, ..., Elt -> SetCartElt

!!

!=

"

""

#

Rings, Fields, and Algebras (OVERVIEW)

# x : AlgChtrElt -> RngIntElt

# u : AlgFPElt -> RngIntElt

# C : Code -> RngIntElt

# C : Elt -> RngIntElt

# C : Elt -> RngIntElt

[Future release] # C : Elt -> RngIntElt

# V : GrpFPCos -> RngIntElt

# u : GrpFPElt -> RngIntElt

# L : ModLat -> RngIntElt

# s : MonStgElt -> RngIntElt

# R : Rng -> RngIntElt

# R : Rng -> RngIntElt

# P : RngUPolRes -> RngIntElt

# S : SeqEnum -> RngIntElt

# T : SetCartElt -> RngIntElt

# R : SetIndx -> RngIntElt

# u : SgpFPElt -> RngIntElt

# L : SubGrpLat -> RngIntElt

# S : VertSet -> RngIntElt

Order(G) : GrpAb -> RngIntElt

Order(G) : GrpFin -> RngIntElt

Order(G) : GrpPC -> RngIntElt

Order(G) : GrpPerm -> RngIntElt

$

$$

Recursive functions (OVERVIEW)

$-key

%

%

%!

%! shell-command

%! shell-command

%-key

%e

%p

&

& o S : Op, SetIndx -> Elt

&cat

()

x(g) : AlgChtrElt, GrpElt -> FldCycElt

f(r) : Hom(GrpFP), GrpFPRel -> GrpFPRel

v * a : ModTupFldElt, ModMatFldElt -> ModTupFldElt

u * a : ModTupRngElt, ModMatRngElt -> ModTupRngElt

a @ f : Elt, Map -> Elt

<i, w> @ T : GrpFPCosElt, GrpFPElt, Map -> GrpFPElt

(,)

(u, v) : GrpFPElt, GrpFPElt -> GrpFPElt

(g, h) : GrpMatElt, GrpMatElt -> GrpMatElt

(g, h) : GrpPermElt, GrpPermElt -> GrpPermElt

(,,)

(g_1, ..., g_r) : GrpMatElt, ..., GrpMatElt -> GrpMatElt

(g_1, ..., g_r) : GrpPermElt, ..., GrpPermElt -> GrpPermElt

(u_1, ..., u_n) : List(GrpFPElt) -> GrpFPElt

(g_1, ..., g_n) : List(GrpPCElt) -> GrpPCElt

*

Operators (OVERVIEW)

Rings, Fields, and Algebras (OVERVIEW)

u * v : AlgFPElt, AlgFPElt -> AlgFPElt

a * b : AlgMatElt, AlgMatElt -> AlgMatElt

x * u : FldElt, ModTupFldElt -> ModTupFldElt

x * I : FldNumElt, RngOrdIdl -> RngOrdIdl

H * g : Grp, GrpElt -> GrpRcosElt

g * h : GrpElt, GrpElt -> GrpElt

G * H : GrpFin, GrpFin -> { GrpFinElt }

H * g : GrpFP, GrpFPElt -> GrpFPCosElt

u * v : GrpFPElt, GrpFPElt -> GrpFPElt

[Future release] H * g : GrpMat, GrpMatElt -> Elt

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

f * M : MagFormElt, GrpMatElt -> MagFormElt

f * g : MagFormElt, MagFormElt -> MagFormElt

f * g : Map, Map -> Map

u * g : ModGrpElt, GrpElt -> ModGrpElt

u * g : ModTupElt, GrpMatElt -> ModTupElt

v * a : ModTupFldElt, ModMatFldElt -> ModTupFldElt

u * a : ModTupRngElt, ModMatRngElt -> ModTupRngElt

I * J : RngDPol, RngDPol -> RngDPol

x * u : RngElt, ModTupElt -> ModTupElt

a * u : RngElt, ModTupFldElt -> ModTupFldElt

a * b : RngElt, RngElt -> RngElt

I * J : RngIdl, RngIdl -> RngIdl

m * P : RngIntElt, GeomECElt -> GeomECElt

m * u : RngIntElt, GrpAbElt-> GrpAbElt

I * J : RngOrdIdl, RngOrdIdl -> RngOrdIdl

I * J : RngUPol, RngUPol -> RngUPol

u * v : SgpFPElt, SgpFPElt -> SgpFPElt

s cat t : MonStgElt, MonStgElt -> MonStgElt

*/

*:=

g *:= h : GrpPCElt, GrpPCElt -> GrpPCElt

s cat:= t : MonStgElt, MonStgElt -> MonStgElt

+

Rings, Fields, and Algebras (OVERVIEW)

u + v : AlgFPElt, AlgFPElt -> AlgFPElt

a + b : AlgMatElt, AlgMatElt -> AlgMatElt

C + D : Code, Code -> Code

P + Q : GeomECElt, GeomECElt -> GeomECElt

u + v : GrpAbElt, GrpAbElt -> GrpAbElt

G + { u, v } : GrphUnd, { Vert } -> GrphUnd

e + f : ModLatElt, ModLatElt -> ModLatElt

u + v : ModTupElt, ModTupElt -> ModTupElt

U + V : ModTupFld, ModTupFld -> ModTupFld

[Future release] v + U : ModTupFldElt, ModTupFld -> ModTupFld

u + v : ModTupFldElt, ModTupFldElt -> ModTupFldElt

u + v : ModTupFldElt, ModTupFldElt -> ModTupFldElt

M + N : ModTupRng, ModTupRng -> ModTupRng

I + J : RngDPol, RngDPol -> RngDPol

+ a : RngElt -> RngElt

a + b : RngElt, RngElt -> RngElt

I + J : RngIdl, RngIdl -> RngIdl

I + J : RngUPol, RngUPol -> RngUPol

+:=

,

,-key

-

Rings, Fields, and Algebras (OVERVIEW)

u - v : AlgFPElt, AlgFPElt -> AlgFPElt

- a : AlgMatElt -> AlgMatElt

- Q : GeomECElt -> GeomECElt

- v : GrpAbElt -> GrpAbElt

G - v : Grph, Vert -> Grph

- u : ModTupElt -> ModTupElt

- u : ModTupFldElt -> ModTupFldElt

- u : ModTupFldElt -> ModTupFldElt

- a : RngElt -> RngElt

a - b : RngElt, RngElt -> RngElt

-:=

-d

-S

-s

.

A . i : AlgFP, RngIntElt -> AlgFPElt

R . i : AlgMat, RngIntElt -> AlgMatElt

C . i : Code, RngIntElt -> ModTupFldElt

F . 1 : FldFin -> FldFinElt

F . 1 : FldFin, RngIntElt -> FldFinElt

K . i : FldFun, RngIntElt -> FldFunElt

R . 1 : FldLoc -> FldLocElt

R . 1 : FldLoc, RngInt -> RngElt

K . 1 : FldNum -> FldNumElt

G . i : Grp, RngIntElt -> GrpElt

A . i : GrpAb, RngIntElt -> GrpAbElt

G . i : GrpFP, RngIntElt -> GrpFPElt

G . i : Grph, RngIntElt -> Vert

G . i : GrpMat, RngIntElt -> GrpMatElt

G . i : GrpPC, RngIntElt -> GrpPCElt

G . i : GrpPerm, RngIntElt -> GrpPermElt

V . i : ModTupFld, RngIntElt -> ModTupFldElt

M . i : ModTupRng, RngIntElt -> ModElt

P . i : RngDPol, RngInt -> RngDPolElt

d . eefpg : RngIntElt, RngIntElt, RngIntElt -> FldReElt

R . 1 : RngPowSer, RngInt -> RngSerElt

Q . i : RngQPol, RngIntElt -> RngQPolElt

I . 1 : RngUPol -> RngUPolElt

P . 1 : RngUPol, RngInt -> RngPolElt

S . i : SgpFP, RngIntElt -> SgpFPElt

Name(R, 1) : FldPow, RngIntElt -> FldPowElt

..

Sets (OVERVIEW)

/

Rings, Fields, and Algebras (OVERVIEW)

A / I : AlgFP, AlgFPIdl -> AlgFP

G / N : Grp, Grp -> Grp

A / B : GrpAb, GrpAb -> GrpAb

g / h : GrpElt, GrpElt -> GrpElt

G / H : GrpFP, GrpFP -> GrpFP

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 / x : ModTupElt, RngElt -> ModTupElt

V / U : ModTupFld, ModTupFld -> ModTupFld

u / x : ModTupFldElt, FldElt -> ModTupFldElt

M / N : ModTupRng, ModTupRng -> ModTupRng

R / I : Rng, RngIdl -> Rng

I / J : RngDPol, RngDPol -> RngQPol

a / b : RngElt, RngElt -> RngElt

a / b : RngIntElt, RngIntElt -> FldRatElt

I / J : RngOrdIdl, RngOrdIdl -> RngOrdIdl

S / I : SgpFP, SgpFPIdl -> SgpFP

/*

/**/

//

//

/:=

g /:= h : GrpPCElt, GrpPCElt -> GrpPCElt

/=

0

1

Release Notes V1.10-1 (OVERVIEW)

Release Notes V1.11-1 (OVERVIEW)

3

4

5

Release Notes V1.01-5 (OVERVIEW)

:=

x := expression;

;

;-key

<

<=

<>

Generator Assignment (OVERVIEW)

E<x_1, x_2, ...x_n> := expression;

< a_1, a_2, ..., a_k > : Elt, ..., Elt -> SetCartElt

=

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

>

Prompt (OVERVIEW)

>=

?

??

@

a @ f : Elt, Map -> Elt

<i, w> @ T : GrpFPCosElt, GrpFPElt, Map -> GrpFPElt

@@

[!!]

[]

x[expr_1][expr_2]...[expr_n] := expression;

x[i] : AlgChtrElt, RngIntElt -> FldCycElt

a[i] : AlgMatElt, RngIntElt -> ModTupElt

r[1] : GrpAbRel, RngIntElt -> GrpAbElt

r[1] : GrpFPRel, RngIntElt -> GrpFPElt

g[i] : GrpMatElt, RngIntElt -> ModTupElt

a[i] : MatHomElt, RngIntElt -> ModTupRngElt

u[i] : ModTupFldElt, RngIntElt -> RngElt

u[i] : ModTupFldElt, RngIntElt -> RngElt

u[i] : ModTupRngElt, RngIntElt -> RngElt

s[i] : MonStgElt, RngIntElt -> MonStgElt

[ ] : Null -> ESeqEnum

[ i..j ] : RngIntElt, RngIntElt -> SeqEnum

S[i] : SeqEnum, RngIntElt -> Elt

S[I] : SeqEnum, [RngIntElt] -> SeqEnum

T[i] : SetCartElt -> Elt

S[i] : SetIndx, RngIntElt -> Elt

T[i] : TabChtr, RngIntElt -> AlgChtrElt

\

\[]

^

Operators (OVERVIEW)

Rings, Fields, and Algebras (OVERVIEW)

Class(H, g) : GrpAb, GrpAbElt -> { GrpAbElt }

Class(H, g) : GrpPC, GrpPCElt -> { GrpPCElt }

x ^ g : AlgChtrElt, GrpElt -> AlgChtrElt

u ^ n : AlgFPElt, RngIntElt -> AlgFPElt

a ^ n : AlgMatElt, RngIntElt -> AlgMatElt

y ^ g : Elt, GrpMatElt -> Elt

x ^ G : Elt, GrpPerm -> GSet

x ^ g : Elt, GrpPermElt -> Elt

H ^ g : GrpAb, GrpAbElt -> GrpAb

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 ^ u : GrpFP, GrpFPElt -> GrpFP

u ^ n : GrpFPElt, RngIntElt -> GrpFPElt

G ^ n : GrphUnd, RngIntElt -> GrphUnd

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, GrpPCElt -> GrpPC

g ^ h : GrpPCElt, GrpPCElt -> GrpPCElt

g ^ n: GrpPCElt, RngIntElt -> GrpPCElt

H ^ G : GrpPerm -> GrpPerm

H ^ G : GrpPerm, GrpPerm -> GrpPerm

H ^ g : GrpPerm, GrpPermElt -> GrpPerm

g ^ h : GrpPermElt, GrpPermElt -> GrpPermElt

g ^ n : GrpPermElt, RngIntElt -> GrpPermElt

f ^ n : MagFormElt, RngIntElt -> MagFormElt

M ^ T : ModGrp, AlgMatElt -> ModGrp

a ^ -1 : ModMatRngElt, RngIntElt -> ModMatRngElt

v ^ x : ModTupFldElt, GrpPermElt -> ModTupFldElt

s ^ n : MonStgElt, RngIntElt -> MonStgElt

I ^ k : RngDPol, RngIntElt -> RngDPol

f ^ a : RngDPolElt, GrpMatElt -> RngDPolElt

f ^ g : RngDPolElt, GrpPermElt -> RngDPolElt

a ^ k : RngElt, RngIntElt -> RngElt

I ^ k : RngOrdIdl, RngIntElt -> RngOrdIdl

u ^ n : SgpFPElt, RngIntElt -> SgpFPElt

u ^ a : Vert, GrpPermElt -> Vert

^:=

a ^:= k : RngElt, RngIntElt -> RngElt

g ^:= n: GrpPCElt, RngIntElt -> GrpPCElt

_

_ := expression;

`

``

{!!}

{! x in F | P(x) !}

{@@}

{@ @} : Null -> SetIndx

{}

{ } : Null -> Set

{ i..j } : RngIntElt, RngIntElt -> Set

{ U | e_1, e_2, ..., e_n } : Struct, Elt, ..., Elt -> Set

|

~