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SandBoxFractionGCD

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Editor: Bill Page Time: 2017/05/23 20:22:27 GMT+0
Note: gcd in fraction fields thread

added:

From BillPage Tue May 23 20:22:26 +0000 2017
From: Bill Page
Date: Tue, 23 May 2017 20:22:26 +0000
Subject: gcd in fraction fields thread
Message-ID: <20170523202226+0000@axiom-wiki.newsynthesis.org>

Ralf suggested this version:

\begin{axiom}
fractionGcd(x,y) == gcd(numer x, numer y) / lcm(denom x, denom y)
a:=13/6
b:=3/4
fractionGcd(a,b)
\end{axiom}

fricas

R := Integer

$\label{eq1}\hbox{\axiomType{Integer}\ }$

(1)

Type: Type

fricas

Q := Fraction R

$\label{eq2}\hbox{\axiomType{Fraction}\ } (\hbox{\axiomType{Integer}\ })$

(2)

Type: Type

fricas

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

$\label{eq3}4 = 1$

(3)

Type: Equation(PositiveInteger?)

fricas

a:=13/6

$\label{eq4}{13}\over 6$

(4)

Type: Fraction(Integer)

fricas

b:=3/4

$\label{eq5}3 \over 4$

(5)

Type: Fraction(Integer)

fricas

g:=gcd(a,b)

$\label{eq6}1$

(6)

Type: Fraction(Integer)

fricas

l:=lcm(a,b)

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

(7)

Type: Fraction(Integer)

fricas

g*l = a*b

$\label{eq8}{{13}\over 8}={{13}\over 8}$

(8)

Type: Equation(Fraction(Integer))

fricas

gcd2(x:Q,y:Q):Q == gcd(retract numerator x, retract numerator y)$R / lcm(retract denominator x, retract denominator y)$R

   Function declaration gcd2 : (Fraction(Integer), Fraction(Integer))
       -> Fraction(Integer) has been added to workspace.

Type: Void

fricas

lcm2(x:Q,y:Q):Q == lcm(retract numerator x, retract numerator y)$R / gcd(retract denominator x, retract denominator y)$R

   Function declaration lcm2 : (Fraction(Integer), Fraction(Integer))
       -> Fraction(Integer) has been added to workspace.

Type: Void

fricas

g:=gcd2(a,b)

fricas

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

$\label{eq9}1 \over{12}$

(9)

Type: Fraction(Integer)

fricas

l:=lcm2(a,b)

fricas

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

$\label{eq10}{39}\over 2$

(10)

Type: Fraction(Integer)

fricas

g*l = a*b

$\label{eq11}{{13}\over 8}={{13}\over 8}$

(11)

Type: Equation(Fraction(Integer))

fricas

gcd3(x:Q,y:Q):Q == gcd(retract numerator x * retract denominator y, retract numerator y * retract denominator x)$R / (retract denominator x * retract denominator y)$R

   Function declaration gcd3 : (Fraction(Integer), Fraction(Integer))
       -> Fraction(Integer) has been added to workspace.

Type: Void

fricas

lcm3(x:Q,y:Q):Q == lcm(retract numerator x * retract denominator y, retract numerator y * retract denominator x)$R / (retract denominator x * retract denominator y)$R

   Function declaration lcm3 : (Fraction(Integer), Fraction(Integer))
       -> Fraction(Integer) has been added to workspace.

Type: Void

fricas

g:=gcd3(a,b)

fricas

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

$\label{eq12}1 \over{12}$

(12)

Type: Fraction(Integer)

fricas

l:=lcm3(a,b)

fricas

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

$\label{eq13}{39}\over 2$

(13)

Type: Fraction(Integer)

fricas

g*l = a*b

$\label{eq14}{{13}\over 8}={{13}\over 8}$

(14)

Type: Equation(Fraction(Integer))

fricas

gcd2(0,0)

$\label{eq15}0$

(15)

Type: Fraction(Integer)

fricas

lcm2(0,0)

$\label{eq16}0$

(16)

Type: Fraction(Integer)

gcd in fraction fields thread --Bill Page, Tue, 23 May 2017 20:22:26 +0000 reply

Ralf suggested this version:

fricas

fractionGcd(x,y) == gcd(numer x, numer y) / lcm(denom x, denom y)

Type: Void

fricas

a:=13/6

$\label{eq17}{13}\over 6$

(17)

Type: Fraction(Integer)

fricas

b:=3/4

$\label{eq18}3 \over 4$

(18)

Type: Fraction(Integer)

fricas

fractionGcd(a,b)

fricas

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

$\label{eq19}1 \over{12}$

(19)

Type: Fraction(Integer)