Eduardo Cavazos wrote:
Chapter 6 of the Elementary Algorithms volume by Cohen[1] covers basic
algorithms for manipulation of polynomial expressions. I've added
libraries which implement some of these techiques.
I added 'rationalize-expression' and 'rational-expand' also from
Chapter 6.
Examples from the unit tests are included.
Some of the code as currently written isn't in idiomatic Scheme style.
This is because I ususally do a more or less direct translation of the
pseudo code from the book. I'd like to get things working and stable
first before I fancy things up. The code is easier to debug when it
still resembles what's in the book. The good news is that, with a bunch
of unit tests, converting to idiomatic code down the line can be done
with more confidence.
Ed
;; rationalize-expression
(test-equal "EA: page 266 - 1"
(rationalize-expression (alge " (1 + 1/x)^2 "))
(alge " (x+1)^2 / x^2 "))
(test-equal "EA: page 266 - 1"
(rationalize-expression (alge " (1 + 1/x)^(1/2) "))
(alge " ( (x+1)/x ) ^ (1/2) "))
(test-equal "EA: Example 6.59"
(rationalize-expression
(alge " 1 / (1+1/x)^(1/2) + (1+1/x)^(3/2) "))
(alge " ( x^2 + (x+1)^2 ) / ( x^2 * ( (x+1) / x ) ^
(1/2) ) ")
)
(test-equal "EA: Example 6.60"
(rationalize-expression (alge " a + b/2 "))
(alge " (2 a + b)/2 ")
)
;; rational-expand
(test-equal "EA: Example 6.62"
(rational-expand
(alge
" ( ( ( 1 / ( (x+y)^2 + 1 ) ) ^ (1/2) + 1 )
*
( ( 1 / ( (x+y)^2 + 1 ) ) ^ (1/2) - 1 ) )
/
(x+1) "))
(alge
" ( - x^2 - 2 x y - y^2 )
/
( x^3 + x^2 + 2 x^2 y + 2 x y + x y^2 + y^2 + x + 1 ) ")
)
(test-equal
"EA: page 269"
(rational-expand
(alge
" 1 / ( 1/a + c / (a b) ) + ( a b c + a c^2 ) / (b+c)^2 - a "))
0)
