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SandBoxFractionGCD

Edit detail for SandBoxFractionGCD revision 2 of 5

	1 2 3 4 5
Editor: Bill Page Time: 2017/05/14 19:34:05 GMT+0
Note: retract before operators

changed:
-Q := Fraction Integer
R := Integer
Q := Fraction R

changed:
-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)
gcd2(x:Q,y:Q):Q == gcd(retract numerator x, retract numerator y)$R / lcm(retract denominator x, retract denominator y)$R
lcm2(x:Q,y:Q):Q == lcm(retract numerator x, retract numerator y)$R / gcd(retract denominator x, retract denominator y)$R

changed:
-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)
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
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

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))