Pooh program example 01-complex.p
Test 01-complex.p
Source of programm
# test complex number library - complex.inc
include 'complex.inc'
n = make_rect_complex( ~re 0 ~im 1 )
m = make_rect_complex( ~re 0 ~im 1 )
res = n . mult( ~num m )
println( ~msg 'square of i is' )
res . print()
res = res . add( ~num res )
println( ~msg '
twice i is' )
res . print()
println( ~msg '
absolute is [ res . absolute () ]' )
Included file: complex.inc
# make a complex number in polar coordinates
sub make_polar_complex( rad, theta )
return {
# complex number mode - polar coordinates
'mode' : 'polar',
# radius
'rad' : rad,
# angular value
'thet' : theta,
'add' : sub( num )
r = this.torect()
res = r.add( ~num num )
return res.topolar()
end,
'sub' : sub( num )
r = this.torect()
res = r.add( ~num num )
return res.topolar()
end,
'mult' : sub( num )
r = this.torect()
res = r.mult( ~num num )
return res.topolar()
end,
'div' : sub( num )
r = this.torect()
res = r.div( ~num num )
return res.topolar()
end,
# returns the absolute number of this value (length of vector)
'absolute' : sub()
r = this.torect()
return r.absolute()
end,
# convert to rectangular coordinate
'torect' : sub()
make_rect_complex( ~re this.rad * cos( ~num this.theta ) ~im this.rad * sin( ~num this.theta ) )
end,
'topolar' : sub()
return this
end,
# print the number
'print' : sub()
print( ~msg 'rectangular-polar: radius [ this.rad ] theta [ this.theta ]' )
end
}
end
# make a complex number in rectangular coordinates
sub make_rect_complex( re, im )
return {
# complex numer mode - rectangular/Cartesian coordinates
'mode' : 'rectangular',
# real value
're' : re,
#imaginairy value; return new object that is the result
'im' : im,
# add this to argument num and return the result; return new object that is the result
'add' : sub( num )
if num.mode ne 'rectangular'
num = num.torect()
end
return make_rect_complex( ~re this.re + num.re ~im this.im + num.im )
end,
# multiply this by argument num and return the result; return new object that is the result
'mult' : sub( num )
if num.mode ne 'rectangular'
num = num.torect()
end
return make_rect_complex( ~re this.re * num.re - this.im * num.im ~im this.im * num.re + this.re * num.im )
end,
# print the number
'print' : sub()
print( ~msg 'rectangular-complex: real [ this.re ] imaginary [this.im]' )
end,
# divide this by the argument num; return new object that is the result
'div' : sub( num )
if num.mode ne 'rectangular'
num = num.torect()
end
sq = this.re * num.re + this.im * num.im
re = ( this.re * num.re + this.im * num.im) / sq
im = ( num.im * this.re - this.re * num.im) / sq
return make_rect_complex( ~re re ~im im )
end,
# returns the absolute number of this value (length of vector)
'absolute' : sub()
return sqr( ~num 3 ) #this.re * this re + this.im * this im )
end,
# convert to rectangular coordinates - return this object.
'torect' : sub()
return this
end,
# convert to polar coordinates
'topolar' : sub()
rad = sqr( ~num this.re * this.re + this.im * this.im )
thet = atan2( ~x this.im ~y this.re )
return make_polar_complex( ~rad rad ~theta thet )
end
}
end
Standard output for 01-complex.p
square of i is
rectangular-complex: real -1 imaginary 0
twice i is
rectangular-complex: real -2 imaginary 0
absolute is 1.732051e+00
Trace output for 01-complex.p
004|... = make_rect_complex( ~re 0 ~im 1 )...
069| return { 'mode' : 'rectangular' , 're' : re:0 , 'im' : im:1 , 'add' : sub (~num) , 'mult' : sub (~num) , 'print' : sub () , 'div' : sub (~num) , 'absolute' : sub () , 'torect' : sub () , 'topolar' : sub () }
004|n = make_rect_complex( ~re 0 ~im 1 ):{ 'absolute' : sub , 'torect' : sub , 'topolar' : sub , 'mode' : -> 'rectangular', 'print' : sub , 'mult' : sub , 'div' : sub , 'im' : -> 1, 'add' : sub , 're' : -> 0 }
005|... = make_rect_complex( ~re 0 ~im 1 )...
069| return { 'mode' : 'rectangular' , 're' : re:0 , 'im' : im:1 , 'add' : sub (~num) , 'mult' : sub (~num) , 'print' : sub () , 'div' : sub (~num) , 'absolute' : sub () , 'torect' : sub () , 'topolar' : sub () }
005|m = make_rect_complex( ~re 0 ~im 1 ):{ 'absolute' : sub , 'torect' : sub , 'topolar' : sub , 'mode' : -> 'rectangular', 'print' : sub , 'mult' : sub , 'div' : sub , 'im' : -> 1, 'add' : sub , 're' : -> 0 }
007|... = n{'mult'}:sub ( ~num m:{ 'absolute' : sub (), 'torect' : sub (), 'topolar' : sub (), 'mode' : -> 'rectangular', 'print' : sub (), 'mult' : sub (~num), 'div' : sub (~num), 'im' : -> 1, 'add' : sub (~num), 're' : -> 0 } )...
089| if (num{'mode'}:'rectangular' ne 'rectangular'):false
090| end # if
092| return make_rect_complex( ~re ((this{'re'}:0 * num{'re'}:0):0 - (this{'im'}:1 * num{'im'}:1):1):-1 ~im ((this{'im'}:1 * num{'re'}:0):0 + (this{'re'}:0 * num{'im'}:1):0):0 )...
069| return { 'mode' : 'rectangular' , 're' : re:-1 , 'im' : im:0 , 'add' : sub (~num) , 'mult' : sub (~num) , 'print' : sub () , 'div' : sub (~num) , 'absolute' : sub () , 'torect' : sub () , 'topolar' : sub () }
092| return make_rect_complex( ~re ((this{'re'}:0 * num{'re'}:0):0 - (this{'im'}:1 * num{'im'}:1):1):-1 ~im ((this{'im'}:1 * num{'re'}:0):0 + (this{'re'}:0 * num{'im'}:1):0):0 ):{ 'absolute' : sub , 'torect' : sub , 'topolar' : sub , 'mode' : -> 'rectangular', 'print' : sub , 'mult' : sub , 'div' : sub , 'im' : -> 0, 'add' : sub , 're' : -> -1 }
007|res = n{'mult'}:sub ( ~num m:{ 'absolute' : sub (), 'torect' : sub (), 'topolar' : sub (), 'mode' : -> 'rectangular', 'print' : sub (), 'mult' : sub (~num), 'div' : sub (~num), 'im' : -> 1, 'add' : sub (~num), 're' : -> 0 } ):{ 'absolute' : sub , 'torect' : sub , 'topolar' : sub , 'mode' : -> 'rectangular', 'print' : sub , 'mult' : sub , 'div' : sub , 'im' : -> 0, 'add' : sub , 're' : -> -1 }
009|println( ~msg 'square of i is' )...
010|res{'print'}:sub ( )...
097| print( ~msg 'rectangular-complex: real ' .. this{'re'}:-1 .. ' imaginary ' .. this{'im'}:0 .. '' )...
013|... = res{'add'}:sub ( ~num res:{ 'absolute' : sub (), 'torect' : sub (), 'topolar' : sub (), 'mode' : -> 'rectangular', 'print' : sub (), 'mult' : sub (~num), 'div' : sub (~num), 'im' : -> 0, 'add' : sub (~num), 're' : -> -1 } )...
081| if (num{'mode'}:'rectangular' ne 'rectangular'):false
082| end # if
084| return make_rect_complex( ~re (this{'re'}:-1 + num{'re'}:-1):-2 ~im (this{'im'}:0 + num{'im'}:0):0 )...
069| return { 'mode' : 'rectangular' , 're' : re:-2 , 'im' : im:0 , 'add' : sub (~num) , 'mult' : sub (~num) , 'print' : sub () , 'div' : sub (~num) , 'absolute' : sub () , 'torect' : sub () , 'topolar' : sub () }
084| return make_rect_complex( ~re (this{'re'}:-1 + num{'re'}:-1):-2 ~im (this{'im'}:0 + num{'im'}:0):0 ):{ 'absolute' : sub , 'torect' : sub , 'topolar' : sub , 'mode' : -> 'rectangular', 'print' : sub , 'mult' : sub , 'div' : sub , 'im' : -> 0, 'add' : sub , 're' : -> -2 }
013|res = res{'add'}:sub ( ~num res:{ 'absolute' : sub (), 'torect' : sub (), 'topolar' : sub (), 'mode' : -> 'rectangular', 'print' : sub (), 'mult' : sub (~num), 'div' : sub (~num), 'im' : -> 0, 'add' : sub (~num), 're' : -> -1 } ):{ 'absolute' : sub , 'torect' : sub , 'topolar' : sub , 'mode' : -> 'rectangular', 'print' : sub , 'mult' : sub , 'div' : sub , 'im' : -> 0, 'add' : sub , 're' : -> -2 }
015|println( ~msg '
twice i is' )...
018|res{'print'}:sub ( )...
097| print( ~msg 'rectangular-complex: real ' .. this{'re'}:-2 .. ' imaginary ' .. this{'im'}:0 .. '' )...
021|println( ~msg '
absolute is ' .. res{'absolute'}:sub ( )...
115| return sqr( ~num 3 )...
115| return sqr( ~num 3 ):1.732051e+00
021|println( ~msg '
absolute is ' .. res{'absolute'}:sub ( ):1.732051e+00 .. '' )...