algebrite
Version:
Computer Algebra System in Coffeescript
112 lines (82 loc) • 2.47 kB
text/coffeescript
### coeff =====================================================================
Tags
----
scripting, JS, internal, treenode, general concept
Parameters
----------
p,x,n
General description
-------------------
Returns the coefficient of x^n in polynomial p. The x argument can be omitted for polynomials in x.
###
#define P p1
#define X p2
#define N p3
Eval_coeff = ->
push(cadr(p1)); # 1st arg, p
Eval()
push(caddr(p1)); # 2nd arg, x
Eval()
push(cadddr(p1)); # 3rd arg, n
Eval()
p3 = pop(); # p3 is N
p2 = pop(); # p2 is X
p1 = pop(); # p1 is P
if (p3 == symbol(NIL)) # p3 is N # only 2 args?
p3 = p2; # p2 is X # p3 is N
p2 = symbol(SYMBOL_X); # p2 is X
push(p1); # p1 is P # divide p by x^n
push(p2); # p2 is X
push(p3); # p3 is N
power()
divide()
push(p2); # p2 is X # keep the constant part
filter()
#-----------------------------------------------------------------------------
#
# Put polynomial coefficients on the stack
#
# Input: as per params
#
# Output: Returns number of coefficients on stack
#
# tos-n Coefficient of x^0
#
# tos-1 Coefficient of x^(n-1)
#
#-----------------------------------------------------------------------------
coeff = (variable, polynomial)->
if DEBUG then console.log "coeff: " + variable + " " + polynomial
# works like this:
# 1) find the constant (by just evaluating the pol setting the variable to zero)
# 2) set aside the found constant: it's one of the coefficients to return
# 3) take the polynomial and remove the constant
# 4) divide that by variable, lowering the degree by one
# 5) go back to 1) until degree is zero
coeffsCount = 0
while true
push(polynomial)
push(variable)
push(zero)
subst()
Eval()
constant = pop()
# this will be a coefficient that will be returned
push(constant)
coeffsCount++
push(polynomial)
push(constant)
subtract()
polynomialWithoutConstant = pop()
if (equal(polynomialWithoutConstant, zero))
if DEBUG then console.log "coeff: result: " + coeffsCount
return coeffsCount
push(polynomialWithoutConstant)
push(variable)
prev_expanding = expanding
expanding = 1
divide()
expanding = prev_expanding
#console.log("just divided: " + stack[tos-1].toString())
# this is now the new polynomial with degree decreased by 1
polynomial = pop()