MathAction SandboxDemoFreeMonoid/-Module

e:=[e[i]::X for i in 1..5]

-- Some terms
t1:= e.1*e.2

t2:= t1^3

-- Equality
eq1:=t1=e.2*e.1

test(eq1)

eq2:=t2=t1*t1*t1

test(eq2)

-- Any symbol admissible ;)
s::X

s*t1

a*%

first %

-- Methods
varList t1

varList t2

retractIfCan t1

retract e.1

length t1

length t2

size t2

factors t2

-- etc.

-- Restrict to b_1, b_2, b_3.
B:=OrderedVariableList [b[i] for i in 1..3]

Y:=FreeMonoid(B)

b:=[x::Y for x in enumerate()$B]

t3:=b.1*b.2*b.3*b.1

factors t3

t3*b.1 -- note exps

test(b.1*b.2=b.2*b.1)

-- FreeModule(R: Join(SemiRng,AbelianMonoid),S: SetCategory) 
-- combine

R:=Expression Integer

Z:=FreeModule(R,Y)

bb:=[x::Z for x in b]

t4:=bb.1 + t3::Z

t5:=sin(x*y)*t4+z^k*bb.2