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SandBoxFractionGCD

Edit detail for SandBoxFractionGCD revision 1 of 5

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Editor: Bill Page Time: 2017/05/14 17:36:08 GMT+0
Note:

changed:
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\begin{axiom}
Q := Fraction Integer
gcd(8,4) = retract gcd(8::Q, 4::Q)
\end{axiom}

\begin{axiom}
a:=13/6
b:=3/4
\end{axiom}

\begin{axiom}
g:=gcd(a,b)
l:=lcm(a,b)
g*l = a*b
\end{axiom}

\begin{axiom}
gcd2(x,y) == gcd(numerator x, numerator y) / lcm(denominator x, denominator y)
lcm2(x,y) == lcm(numerator x, numerator y) / gcd(denominator x, denominator y)
\end{axiom}

\begin{axiom}
g:=gcd2(a,b)
l:=lcm2(a,b)
g*l = a*b
\end{axiom}

\begin{axiom}
gcd3(x,y) == gcd(numerator x * denominator y, numerator y * denominator x) / (denominator x * denominator y)
lcm3(x,y) == lcm(numerator x * denominator y, numerator y * denominator x) / (denominator x * denominator y)
\end{axiom}

\begin{axiom}
g:=gcd3(a,b)
l:=lcm3(a,b)
g*l = a*b
\end{axiom}

fricas

Q := Fraction Integer

$\label{eq1}\hbox{\axiomType{Fraction}\ } (\hbox{\axiomType{Integer}\ })$

(1)

Type: Type

fricas

gcd(8,4) = retract gcd(8::Q, 4::Q)

$\label{eq2}4 = 1$

(2)

Type: Equation(PositiveInteger?)

fricas

a:=13/6

$\label{eq3}{13}\over 6$

(3)

Type: Fraction(Integer)

fricas

b:=3/4

$\label{eq4}3 \over 4$

(4)

Type: Fraction(Integer)

fricas

g:=gcd(a,b)

$\label{eq5}1$

(5)

Type: Fraction(Integer)

fricas

l:=lcm(a,b)

$\label{eq6}{13}\over 8$

(6)

Type: Fraction(Integer)

fricas

g*l = a*b

$\label{eq7}{{13}\over 8}={{13}\over 8}$

(7)

Type: Equation(Fraction(Integer))

fricas

gcd2(x,y) == gcd(numerator x, numerator y) / lcm(denominator x, denominator y)

Type: Void

fricas

lcm2(x,y) == lcm(numerator x, numerator y) / gcd(denominator x, denominator y)

Type: Void

fricas

g:=gcd2(a,b)

fricas

Compiling function gcd2 with type (Fraction(Integer),Fraction(
      Integer)) -> Fraction(Integer)

$\label{eq8}1 \over{24}$

(8)

Type: Fraction(Integer)

fricas

l:=lcm2(a,b)

fricas

Compiling function lcm2 with type (Fraction(Integer),Fraction(
      Integer)) -> Fraction(Integer)

$\label{eq9}39$

(9)

Type: Fraction(Integer)

fricas

g*l = a*b

$\label{eq10}{{13}\over 8}={{13}\over 8}$

(10)

Type: Equation(Fraction(Integer))

fricas

gcd3(x,y) == gcd(numerator x * denominator y, numerator y * denominator x) / (denominator x * denominator y)

Type: Void

fricas

lcm3(x,y) == lcm(numerator x * denominator y, numerator y * denominator x) / (denominator x * denominator y)

Type: Void

fricas

g:=gcd3(a,b)

fricas

Compiling function gcd3 with type (Fraction(Integer),Fraction(
      Integer)) -> Fraction(Integer)

$\label{eq11}1 \over{24}$

(11)

Type: Fraction(Integer)

fricas

l:=lcm3(a,b)

fricas

Compiling function lcm3 with type (Fraction(Integer),Fraction(
      Integer)) -> Fraction(Integer)

$\label{eq12}39$

(12)

Type: Fraction(Integer)

fricas

g*l = a*b

$\label{eq13}{{13}\over 8}={{13}\over 8}$

(13)

Type: Equation(Fraction(Integer))