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ExampleFreeModule

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Editor: hemmecke Time: 2026/02/27 08:25:13 GMT+0
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changed:
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How to use FreeFreeModule

Commit https://github.com/fricas/fricas/commit/e5785c16bf7552522aac47ab5bb698244bffe090
removed the domain FreeAbelianGroup from FriCAS.

See also
https://groups.google.com/g/fricas-devel/c/yYgfAC-KWhg/m/p23BP5ZSBQAJ .

It can be replaced by FreeModule as follows.

\begin{axiom}
)version
Z ==> Integer
FreeAbelianGroup X ==> FreeModule(Integer,X)
A ==> FreeAbelianGroup(M)
M ==> Matrix Z
m1 := matrix [[1,2],[3,4]]
m2 := matrix [[8,3]]
m3 := matrix [[6],[7]]
a1 := m1::A; a2:=m2::A;a3:=m3::A;
x1 := 2*a1+a2
x2 := 3*a1-5*a3
x1+x2
\end{axiom}

How to use FreeFreeModule?

Commit https://github.com/fricas/fricas/commit/e5785c16bf7552522aac47ab5bb698244bffe090 removed the domain FreeAbelianGroup? from FriCAS.

It can be replaced by FreeModule as follows.

fricas

(1) -> )version

"FriCAS 1.3.12 compiled at Sat  7 Jun 23:54:49 CEST 2025"
Z ==> Integer

Type: Void

fricas

FreeAbelianGroup X ==> FreeModule(Integer,X)

Type: Void

fricas

A ==> FreeAbelianGroup(M)

Type: Void

fricas

M ==> Matrix Z

Type: Void

fricas

m1 := matrix [[1,2],[3,4]]

$\label{eq1}\left[ \begin{array}{cc} 1 & 2 \ 3 & 4$

(1)

Type: Matrix(Integer)

fricas

m2 := matrix [[8,3]]

$\label{eq2}\left[ \begin{array}{cc} 8 & 3$

(2)

Type: Matrix(Integer)

fricas

m3 := matrix [[6],[7]]

$\label{eq3}\left[ \begin{array}{c} 6 \ 7$

(3)

Type: Matrix(Integer)

fricas

a1 := m1::A; a2:=m2::A;a3:=m3::A;

Type: FreeModule(Integer,Matrix(Integer))

fricas

x1 := 2*a1+a2

$\label{eq4}{2 \ {\left[ \begin{array}{cc} 1 & 2 \ 3 & 4$

(4)

Type: FreeModule(Integer,Matrix(Integer))

fricas

x2 := 3*a1-5*a3

$\label{eq5}\begin{array}{@{}l} \displaystyle {3 \ {\left[ \begin{array}{cc} 1 & 2 \ 3 & 4$

(5)

Type: FreeModule(Integer,Matrix(Integer))

fricas

x1+x2

$\label{eq6}\begin{array}{@{}l} \displaystyle {5 \ {\left[ \begin{array}{cc} 1 & 2 \ 3 & 4$

(6)

Type: FreeModule(Integer,Matrix(Integer))