API Reference

magcall(Val(C), f, args...; opts...)

Call the Magma function f with the given arguments and keyword options according to calling convention C.

If f is a Symbol, then it is interpreted as the name of a Magma intrinsic.

C may be:

• :p: f is a procedure and nothing is returned. Note that if f is actually a function, its return value will be printed.
• :f: f is a function and its first return value is returned.
• :fN: f is a function and its first N return values are returned as a tuple.
• :b: f is a function returning a boolean, which is returned as a Bool.
• :i: f is a function returning an integer, which is returned as an Int.
• :g: f is a function returning a structure S. args[1] is a tuple of generator names, which are applied to S. Returns a tuple of S and generator names.
• :pN: Same as :p (procedure) but the Nth argument is passed by reference.

Equivalently, you can call magcallC(f, args...; opts...) or magC.f(args...; opts...).

magcallp(f, args...; opts...)

Call the Magma procedure f with the given arguments and keyword options.

Equivalent to magcall(Val(:p), f, args...; opts...).

magcallf(f, args...; opts...)

Call the Magma function f with the given arguments and keyword options. Return the first return value.

Equivalent to magcall(Val(:f), f, args...; opts...).

magcallf2(f, args...; opts...)

Call the Magma function f with the given arguments and keyword options. Return the first two return values.

Equivalent to magcall(Val(:f2), f, args...; opts...).

magcallf3(f, args...; opts...)

Call the Magma function f with the given arguments and keyword options. Return the first three return values.

Equivalent to magcall(Val(:f3), f, args...; opts...).

magcallf4(f, args...; opts...)

Call the Magma function f with the given arguments and keyword options. Return the first four return values.

Equivalent to magcall(Val(:f4), f, args...; opts...).

magcallf5(f, args...; opts...)

Call the Magma function f with the given arguments and keyword options. Return the first five return values.

Equivalent to magcall(Val(:f5), f, args...; opts...).

magcallf6(f, args...; opts...)

Call the Magma function f with the given arguments and keyword options. Return the first six return values.

Equivalent to magcall(Val(:f6), f, args...; opts...).

magcallf7(f, args...; opts...)

Call the Magma function f with the given arguments and keyword options. Return the first seven return values.

Equivalent to magcall(Val(:f7), f, args...; opts...).

magcallf8(f, args...; opts...)

Call the Magma function f with the given arguments and keyword options. Return the first eight return values.

Equivalent to magcall(Val(:f8), f, args...; opts...).

magcalli(f, args...; opts...)

Call the Magma function f with the given arguments and keyword options. It must return an integer, which is returned as an Int.

Equivalent to magcall(Val(:i), f, args...; opts...).

magcallb(f, args...; opts...)

Call the Magma function f with the given arguments and keyword options. It must return a boolean, which is returned as a Bool.

Equivalent to magcall(Val(:b), f, args...; opts...).

magcallp1(f, args...; opts...)

Call the Magma procedure f with the given arguments and keyword options, passing the first argument by reference.

Equivalent to magcallp1(Val(:p1), args...; opts...).

magcallp2(f, args...; opts...)

Call the Magma procedure f with the given arguments and keyword options, passing the second argument by reference.

Equivalent to magcallp2(Val(:p2), args...; opts...).

magcallp3(f, args...; opts...)

Call the Magma procedure f with the given arguments and keyword options, passing the third argument by reference.

Equivalent to magcallp3(Val(:p3), args...; opts...).

magcallp4(f, args...; opts...)

Call the Magma procedure f with the given arguments and keyword options, passing the fourth argument by reference.

Equivalent to magcallp4(Val(:p4), args...; opts...).

magcallg(f, names, args...; opts...)

Call the Magma function f with the given arguments and keyword options. Assign the given names to the result. Return a tuple of the result and the generators.

Equivalent to magcall(Val(:g), f, names, args...; opts...).

magcallm(f, args...; opts...)

Call the Magma function f with the given arguments and keyword options. If the first return value is true, return the second return value, else return nothing.

Equivalent to magcall(Val(:m), args...; opts...).

magadd(x, y)

Equivalent to x + y in Magma.

magsub(x, y)

Equivalent to x - y in Magma.

magmul(x, y)

Equivalent to x * y in Magma.

magtruediv(x, y)

Equivalent to x / y in Magma.

magpow(x, y)

Equivalent to x ^ y in Magma.

magdiff(x, y)

Equivalent to x diff y in Magma.

magdiv(x, y)

Equivalent to x div y in Magma.

magjoin(x, y)

Equivalent to x join y in Magma.

magmeet(x, y)

Equivalent to x meet y in Magma.

magmod(x, y)

Equivalent to x mod y in Magma.

magsdiff(x, y)

Equivalent to x sdiff y in Magma.

magcat(x, y)

Equivalent to x cat y in Magma.

mageq(x, y)

True if x eq y in Magma.

magne(x, y)

True if x ne y in Magma.

magcmpeq(x, y)

True if x cmpeq y in Magma.

magcmpne(x, y)

True if x cmpne y in Magma.

magle(x, y)

True if x le y in Magma.

maglt(x, y)

True if x lt y in Magma.

magge(x, y)

True if x ge y in Magma.

maggt(x, y)

True if x gt y in Magma.

magin(x, y)

True if x in y in Magma.

magnotin(x, y)

True if x notin y in Magma.

magadj(x, y)

True if x adj y in Magma.

magnotadj(x, y)

True if x notadj y in Magma.

magsubset(x, y)

True if x subset y in Magma.

magnotsubset(x, y)

True if x notsubset y in Magma.

magsum(x)

Equivalent to &+ x in Magma.

magprod(x)

Equivalent to &* x in Magma.

magreduceand(x)

Equivalent to &and x in Magma.

magreduceor(x)

Equivalent to &or x in Magma.

magreducejoin(x)

Equivalent to &join x in Magma.

magreducemeet(x)

Equivalent to &meet x in Magma.

magreducecat(x)

Equivalent to &cat x in Magma.

maglist([xs])

A new Magma list, equivalent to [* *].

Optionally, values can be specified with iterable xs.

magtuple([xs])

A new Magma tuple, equivalent to < >.

Optionally, values can be specified with iterable xs.

magseq([xs]; [universe])

A new Magma sequence, equivalent to [ universe | ].

Optionally, values can be specified with iterable xs.

magset([xs]; [universe])

A new Magma set, equivalent to { universe | }.

Optionally, values can be specified with iterable xs.

magmset([xs]; [universe])

A new Magma multiset, equivalent to {* universe | *}.

Optionally, values can be specified with iterable xs.

magiset([xs]; [universe])

A new Magma indexed set, equivalent to {@ universe | @}.

Optionally, values can be specified with iterable xs.

magrecformat(field, ...)

Create a record format with the given fields.

Each field may be a symbol, giving the name, or a name=>type pair.

magrec(fmt; vals...)

A record with the given format and values.

magprint(io::IO, x, level=:default)

Print x to io at the given level, which must be one of :default, :magma, :maximal or :minimal.

magsprint(x, level=:default)

String representation of x at the given level (see magprint).

maggetindex(o, i, ...)

Equivalent to o[i, ...] in Magma.

magsetindex!(o, x, i...)

Equivalent to o[i, ...] := x in Magma.

maglength(o)

The length of o, equivalent to # o.

magimage(x, f)

The image of x under f, equivalent to x @ f.

magpreimage(x, f)

The preimage of x under f, equivalent to x @@ f.

magcoerce(s, x)

Coerce x into structure s, equivalent to s ! x.

maggen(x, n)

The nth generator of x, equivalent to x.n.

maggetattr(x, k)

Get attribute k from x, equivalent to x`k.

magsetattr!(x, k, v)

Set attribute k of x to v, equivalent to x`k := v.

magattrnames(x)

The attribute names of x.

mageval(ex; vars...)

Evaluate the Magma expression ex and return its value.

Keyword arguments can be used to name variables refereced by ex, e.g. mageval("x+x", x=3) returns 6.

This is the worker function behind @mag_str.

maghelp(query)

Equivalent to ? query.

magassigned(o::MagmaObject)

True if o is assigned. This should only occur if o = MagmaObject() or if magdelete(o) has been called.

Most functions do not expect unassigned values, and undefined behaviour occurs.

magdelete(o::MagmaObject)

Delete the object referenced by o.

Most functions do not expect deleted values, and undefined behaviour occurs.

magtypeof(o)

The Magma type of o.

magetypeof(o)

The Magma extended type of o.

magissubtype(t1, t2)

True if Magma type t1 is a subtype of t2.

Symbol arguments are interpreted as types.

magisinstance(o, t)

True if o is an instance of Magma type t.

If t is a Symbol, it is interpreted as a type.

MagmaValue <: Any
MagmaValue(x)

Abtract type for any kind of Magma value. Most functions accept any MagmaValue and return a MagmaObject.

Subtypes include MagmaObject, MagmaRef, MagmaExpr.

Overload MagmaValue(x) to provide conversions from Julia values to Magma ones.

MagmaObject <: MagmaValue
MagmaObject(x)

A Magma object value. Most functions return a MagmaObject.

It is represented by a handle to a variable in the Magma interpreter.

MagmaRef <: MagmaValue
MagmaRef(o::MagmaObject)

A reference to a Magma object, suitable for passing to mutating procedures such as Append or Sort.

MagmaExpr <: MagmaValue
MagmaExpr(ex::String)

A literal Magma value, represented by an expression which evaluates to the value.

For simple values such as integers and strings, MagmaValue(x) will return a MagmaExpr.

MagmaIntrinsic <: MagmaValue
MagmaIntrinsic(name)

The Magma intrinsic with the given name.

MagmaType <: MagmaValue
MagmaType(name, ...)

The Magma type with the given name.

Extra arguments make an extended type, e.g. MagmaType(:RngUPol, :RngInt) is Magma's RngUPol[RngInt].

MagmaCallable{C} <: MagmaValue
MagmaCallable{C}(o)

Wrap the value o, declaring it to be callable with calling convention C (see magcall).

The resulting object can use the usual function call syntax, instead of magcall.

magconvert(T, o)

Convert the Magma object o to a T.

mag"..."[C]

Evaluates the given string as a Magma expression.

Julia values may be interpolated with $ as usual.

If C is given, the returned value is wrapped as a MagmaCallable{C}, for example:

f = mag"func<x, y | x^2 + 3*x*y + y^2>"f
f(2, 3)