void
eval_nroots(void)
{
volatile int h, i, k, n;
push(cadr(p1));
eval();
push(caddr(p1));
eval();
p2 = pop();
if (p2 == symbol(NIL))
guess();
else
push(p2);
p2 = pop();
p1 = pop();
if (!ispoly(p1, p2))
stop("nroots: polynomial?");
// mark the stack
h = tos;
// get the coefficients
push(p1);
push(p2);
n = coeff();
if (n > YMAX)
stop("nroots: degree?");
// convert the coefficients to real and imaginary doubles
for (i = 0; i < n; i++) {
push(stack[h + i]);
real();
yyfloat();
eval();
p1 = pop();
push(stack[h + i]);
imag();
yyfloat();
eval();
p2 = pop();
if (!isdouble(p1) || !isdouble(p2))
stop("nroots: coefficients?");
c[i].r = p1->u.d;
c[i].i = p2->u.d;
}
// pop the coefficients
tos = h;
// n is the number of coefficients, n = deg(p) + 1
monic(n);
for (k = n; k > 1; k--) {
findroot(k);
if (fabs(a.r) < DELTA)
a.r = 0.0;
if (fabs(a.i) < DELTA)
a.i = 0.0;
push_double(a.r);
push_double(a.i);
push(imaginaryunit);
multiply();
add();
divpoly(k);
}
// now make n equal to the number of roots
n = tos - h;
if (n > 1) {
sort_stack(n);
p1 = alloc_tensor(n);
p1->u.tensor->ndim = 1;
p1->u.tensor->dim[0] = n;
for (i = 0; i < n; i++)
p1->u.tensor->elem[i] = stack[h + i];
tos = h;
push(p1);
}
}
void
expand(void)
{
save();
X = pop();
F = pop();
if (istensor(F)) {
expand_tensor();
restore();
return;
}
// if sum of terms then sum over the expansion of each term
if (car(F) == symbol(ADD)) {
push_integer(0);
p1 = cdr(F);
while (iscons(p1)) {
push(car(p1));
push(X);
expand();
add();
p1 = cdr(p1);
}
restore();
return;
}
// B = numerator
push(F);
numerator();
B = pop();
// A = denominator
push(F);
denominator();
A = pop();
remove_negative_exponents();
// Q = quotient
push(B);
push(A);
push(X);
divpoly();
Q = pop();
// remainder B = B - A * Q
push(B);
push(A);
push(Q);
multiply();
subtract();
B = pop();
// if the remainder is zero then we're done
if (iszero(B)) {
push(Q);
restore();
return;
}
// A = factor(A)
push(A);
push(X);
factorpoly();
A = pop();
expand_get_C();
expand_get_B();
expand_get_A();
if (istensor(C)) {
push(C);
inv();
push(B);
inner();
push(A);
inner();
} else {
push(B);
push(C);
divide();
push(A);
multiply();
}
push(Q);
add();
restore();
}
