How to resolve the algorithm Continued fraction/Arithmetic/G(matrix ng, continued fraction n1, continued fraction n2) step by step in the Tcl programming language
How to resolve the algorithm Continued fraction/Arithmetic/G(matrix ng, continued fraction n1, continued fraction n2) step by step in the Tcl programming language
Table of Contents
Problem Statement
This task performs the basic mathematical functions on 2 continued fractions. This requires the full version of matrix NG: I may perform perform the following operations: I output a term if the integer parts of
a b
{\displaystyle {\frac {a}{b}}}
and
a
1
b
1
{\displaystyle {\frac {a_{1}}{b_{1}}}}
and
a
2
b
2
{\displaystyle {\frac {a_{2}}{b_{2}}}}
and
a
12
b
12
{\displaystyle {\frac {a_{12}}{b_{12}}}}
are equal. Otherwise I input a term from continued fraction N1 or continued fraction N2. If I need a term from N but N has no more terms I inject
∞
{\displaystyle \infty }
. When I input a term t from continued fraction N1 I change my internal state: When I need a term from exhausted continued fraction N1 I change my internal state: When I input a term t from continued fraction N2 I change my internal state: When I need a term from exhausted continued fraction N2 I change my internal state: When I output a term t I change my internal state: When I need to choose to input from N1 or N2 I act: When performing arithmetic operation on two potentially infinite continued fractions it is possible to generate a rational number. eg
2
{\displaystyle {\sqrt {2}}}
2
{\displaystyle {\sqrt {2}}}
should produce 2. This will require either that I determine that my internal state is approaching infinity, or limiting the number of terms I am willing to input without producing any output.
Let's start with the solution:
Step by Step solution about How to resolve the algorithm Continued fraction/Arithmetic/G(matrix ng, continued fraction n1, continued fraction n2) step by step in the Tcl programming language
Source code in the tcl programming language
oo::class create NG2 {
variable a b a1 b1 a2 b2 a12 b12 cf1 cf2
superclass Generator
constructor {args} {
lassign $args a12 a1 a2 a b12 b1 b2 b
next
}
method operands {N1 N2} {
set cf1 $N1
set cf2 $N2
return [self]
}
method Ingress1 t {
lassign [list [expr {$a2+$a12*$t}] [expr {$a+$a1*$t}] $a12 $a1 \
[expr {$b2+$b12*$t}] [expr {$b+$b1*$t}] $b12 $b1] \
a12 a1 a2 a b12 b1 b2 b
}
method Exhaust1 {} {
lassign [list $a12 $a1 $a12 $a1 $b12 $b1 $b12 $b1] \
a12 a1 a2 a b12 b1 b2 b
}
method Ingress2 t {
lassign [list [expr {$a1+$a12*$t}] $a12 [expr {$a+$a2*$t}] $a2 \
[expr {$b1+$b12*$t}] $b12 [expr {$b+$b2*$t}] $b2] \
a12 a1 a2 a b12 b1 b2 b
}
method Exhaust2 {} {
lassign [list $a12 $a12 $a2 $a2 $b12 $b12 $b2 $b2] \
a12 a1 a2 a b12 b1 b2 b
}
method Egress {} {
set t [expr {$a/$b}]
lassign [list $b12 $b1 $b2 $b \
[expr {$a12 - $b12*$t}] [expr {$a1 - $b1*$t}] \
[expr {$a2 - $b2*$t}] [expr {$a - $b*$t}]] \
a12 a1 a2 a b12 b1 b2 b
return $t
}
method DoIngress1 {} {
try {tailcall my Ingress1 [$cf1]} on break {} {}
oo::objdefine [self] forward DoIngress1 my Exhaust1
set cf1 ""
tailcall my Exhaust1
}
method DoIngress2 {} {
try {tailcall my Ingress2 [$cf2]} on break {} {}
oo::objdefine [self] forward DoIngress2 my Exhaust2
set cf2 ""
tailcall my Exhaust2
}
method Ingress {} {
if {$b==0} {
if {$b2 == 0} {
tailcall my DoIngress1
} else {
tailcall my DoIngress2
}
}
if {!$b2} {
tailcall my DoIngress2
}
if {!$b1} {
tailcall my DoIngress1
}
if {[my FirstSource?]} {
tailcall my DoIngress1
} else {
tailcall my DoIngress2
}
}
method FirstSource? {} {
expr {abs($a1*$b*$b2 - $a*$b1*$b2) > abs($a2*$b*$b1 - $a*$b1*$b2)}
}
method NeedTerm? {} {
expr {
($b*$b1*$b2*$b12==0) ||
!($a/$b == $a1/$b1 && $a/$b == $a2/$b2 && $a/$b == $a12/$b12)
}
}
method Done? {} {
expr {$b==0 && $b1==0 && $b2==0 && $b12==0}
}
method Produce {} {
# Until we've drained both continued fractions...
while {$cf1 ne "" || $cf2 ne ""} {
if {[my NeedTerm?]} {
my Ingress
} else {
yield [my Egress]
}
}
# Drain our internal state
while {![my Done?]} {
yield [my Egress]
}
}
}
set op [[NG2 new 0 1 1 0 0 0 0 1] operands [R2CF new 1/2] [R2CF new 22/7]]
printcf "\[3;7\] + \[0;2\]" $op
set op [[NG2 new 1 0 0 0 0 0 0 1] operands [R2CF new 13/11] [R2CF new 22/7]]
printcf "\[1:5,2\] * \[3;7\]" $op
set op [[NG2 new 0 1 -1 0 0 0 0 1] operands [R2CF new 13/11] [R2CF new 22/7]]
printcf "\[1:5,2\] - \[3;7\]" $op
set op [[NG2 new 0 1 0 0 0 0 1 0] operands [R2CF new 484/49] [R2CF new 22/7]]
printcf "div test" $op
set op1 [[NG2 new 0 1 1 0 0 0 0 1] operands [R2CF new 2/7] [R2CF new 13/11]]
set op2 [[NG2 new 0 1 -1 0 0 0 0 1] operands [R2CF new 2/7] [R2CF new 13/11]]
set op3 [[NG2 new 1 0 0 0 0 0 0 1] operands $op1 $op2]
printcf "layered test" $op3
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