Exemplo n.º 1
0
void
yyhermite2(int n)
{
	int i;

	push_integer(1);
	push_integer(0);

	Y1 = pop();

	for (i = 0; i < n; i++) {

		Y0 = Y1;

		Y1 = pop();

		push(X);
		push(Y1);
		multiply();

		push_integer(i);
		push(Y0);
		multiply();

		subtract();

		push_integer(2);
		multiply();
	}
}
int
simplify_polar(void)
{
	int n;

	n = isquarterturn(p2);

	switch(n) {
	case 0:
		break;
	case 1:
		push_integer(1);
		return 1;
	case 2:
		push_integer(-1);
		return 1;
	case 3:
		push(imaginaryunit);
		return 1;
	case 4:
		push(imaginaryunit);
		negate();
		return 1;
	}

	if (car(p2) == symbol(ADD)) {
		p3 = cdr(p2);
		while (iscons(p3)) {
			n = isquarterturn(car(p3));
			if (n)
				break;
			p3 = cdr(p3);
		}
		switch (n) {
		case 0:
			return 0;
		case 1:
			push_integer(1);
			break;
		case 2:
			push_integer(-1);
			break;
		case 3:
			push(imaginaryunit);
			break;
		case 4:
			push(imaginaryunit);
			negate();
			break;
		}
		push(p2);
		push(car(p3));
		subtract();
		exponential();
		multiply();
		return 1;
	}

	return 0;
}
Exemplo n.º 3
0
void
expand_get_AF(void)
{	int d, i, j, n = 1;
	if (!find(F, X))
		return;
	if (car(F) == symbol(POWER)) {
		push(caddr(F));
		n = pop_integer();
		F = cadr(F);
	}
	push(F);
	push(X);
	degree();
	d = pop_integer();
	for (i = n; i > 0; i--) {
		for (j = 0; j < d; j++) {
			push(F);
			push_integer(i);
			power();
			reciprocate();
			push(X);
			push_integer(j);
			power();
			multiply();
		}
	}
}
Exemplo n.º 4
0
void
expand_get_CF(void)
{	int d, i, j, n;
	if (!find(F, X))
		return;
	trivial_divide();
	if (car(F) == symbol(POWER)) {
		push(caddr(F));
		n = pop_integer();
		P = cadr(F);
	} else {
		n = 1;
		P = F;
	}
	push(P);
	push(X);
	degree();
	d = pop_integer();
	for (i = 0; i < n; i++) {
		for (j = 0; j < d; j++) {
			push(T);
			push(P);
			push_integer(i);
			power();
			multiply();
			push(X);
			push_integer(j);
			power();
			multiply();
		}
	}
}
Exemplo n.º 5
0
static int pos_of(lua_State * L) {
    int nargs = lua_gettop(L);
    pos_info pos;
    if (nargs == 1)
        pos = gparser.pos_of(to_expr(L, 1));
    else
        pos = gparser.pos_of(to_expr(L, 1), pos_info(lua_tointeger(L, 2), lua_tointeger(L, 3)));
    push_integer(L, pos.first);
    push_integer(L, pos.second);
    return 2;
}
Exemplo n.º 6
0
void
darctanh(void)
{
    push(cadr(p1));
    push(p2);
    derivative();
    push_integer(1);
    push(cadr(p1));
    push_integer(2);
    power();
    subtract();
    inverse();
    multiply();
}
Exemplo n.º 7
0
void
remove_negative_exponents(void)
{
	int h, i, j, k, n;

	h = tos;
	factors(A);
	factors(B);
	n = tos - h;

	// find the smallest exponent

	j = 0;
	for (i = 0; i < n; i++) {
		p1 = stack[h + i];
		if (car(p1) != symbol(POWER))
			continue;
		if (cadr(p1) != X)
			continue;
		push(caddr(p1));
		k = pop_integer();
		if (k == (int) 0x80000000)
			continue;
		if (k < j)
			j = k;
	}

	tos = h;

	if (j == 0)
		return;

	// A = A / X^j

	push(A);
	push(X);
	push_integer(-j);
	power();
	multiply();
	A = pop();

	// B = B / X^j

	push(B);
	push(X);
	push_integer(-j);
	power();
	multiply();
	B = pop();
}
Exemplo n.º 8
0
void
eval_product(void)
{
	int i, j, k;

	// 1st arg (quoted)

	X = cadr(p1);
	if (!issymbol(X))
		stop("product: 1st arg?");

	// 2nd arg

	push(caddr(p1));
	eval();
	j = pop_integer();
	if (j == (int) 0x80000000)
		stop("product: 2nd arg?");

	// 3rd arg

	push(cadddr(p1));
	eval();
	k = pop_integer();
	if (k == (int) 0x80000000)
		stop("product: 3rd arg?");

	// 4th arg
	// fix

	p1 = cddddr(p1);
	p1 = car(p1);

	B = get_binding(X);
	A = get_arglist(X);

	push_integer(1);

	for (i = j; i <= k; i++) {
		push_integer(i);
		I = pop();
		set_binding(X, I);
		push(p1);
		eval();
		multiply();
	}

	set_binding_and_arglist(X, B, A);
}
Exemplo n.º 9
0
void
darcsin(void)
{
    push(cadr(p1));
    push(p2);
    derivative();
    push_integer(1);
    push(cadr(p1));
    push_integer(2);
    power();
    subtract();
    push_rational(-1, 2);
    power();
    multiply();
}
Exemplo n.º 10
0
void
darctan(void)
{
    push(cadr(p1));
    push(p2);
    derivative();
    push_integer(1);
    push(cadr(p1));
    push_integer(2);
    power();
    add();
    inverse();
    multiply();
    simplify();
}
Exemplo n.º 11
0
void
darccosh(void)
{
    push(cadr(p1));
    push(p2);
    derivative();
    push(cadr(p1));
    push_integer(2);
    power();
    push_integer(-1);
    add();
    push_rational(-1, 2);
    power();
    multiply();
}
Exemplo n.º 12
0
void
yymag(void)
{
	save();
	p1 = pop();
	if (isnegativenumber(p1)) {
		push(p1);
		negate();
	} else if (car(p1) == symbol(POWER) && equaln(cadr(p1), -1))
		// -1 to a power
		push_integer(1);
	else if (car(p1) == symbol(POWER) && cadr(p1) == symbol(E)) {
		// exponential
		push(caddr(p1));
		real();
		exponential();
	} else if (car(p1) == symbol(MULTIPLY)) {
		// product
		push_integer(1);
		p1 = cdr(p1);
		while (iscons(p1)) {
			push(car(p1));
			mag();
			multiply();
			p1 = cdr(p1);
		}
	} else if (car(p1) == symbol(ADD)) {
		// sum
		push(p1);
		rect(); // convert polar terms, if any
		p1 = pop();
		push(p1);
		real();
		push_integer(2);
		power();
		push(p1);
		imag();
		push_integer(2);
		power();
		add();
		push_rational(1, 2);
		power();
		simplify_trig();
	} else
		// default (all real)
		push(p1);
	restore();
}
void
multinomial_sum(int k, int n, int *a, int i, int m)
{
	int j;

	if (i < k - 1) {
		for (j = 0; j <= m; j++) {
			a[i] = j;
			multinomial_sum(k, n, a, i + 1, m - j);
		}
		return;
	}

	a[i] = m;

	// coefficient

	push(p1);

	for (j = 0; j < k; j++) {
		push_integer(a[j]);
		factorial();
		divide();
	}

	// factors

	for (j = 0; j < k; j++) {
		push(A(j, a[j]));
		multiply();
	}

	add();
}
Exemplo n.º 14
0
void
eval_transpose(void)
{
	push(cadr(p1));
	eval();
	if (cddr(p1) == symbol(NIL)) {
		push_integer(1);
		push_integer(2);
	} else {
		push(caddr(p1));
		eval();
		push(cadddr(p1));
		eval();
	}
	transpose();
}
Exemplo n.º 15
0
void
partition(void)
{
	save();

	p2 = pop();
	p1 = pop();

	push_integer(1);

	p3 = pop();
	p4 = p3;

	p1 = cdr(p1);

	while (iscons(p1)) {
		if (find(car(p1), p2)) {
			push(p4);
			push(car(p1));
			multiply();
			p4 = pop();
		} else {
			push(p3);
			push(car(p1));
			multiply();
			p3 = pop();
		}
		p1 = cdr(p1);
	}

	push(p3);
	push(p4);

	restore();
}
Exemplo n.º 16
0
void
dhermite(void)
{
    push(cadr(p1));
    push(p2);
    derivative();
    push_integer(2);
    push(caddr(p1));
    multiply();
    multiply();
    push(cadr(p1));
    push(caddr(p1));
    push_integer(-1);
    add();
    hermite();
    multiply();
}
void
power_sum(int n)
{
	int *a, i, j, k;

	// number of terms in the sum

	k = length(p1) - 1;

	// local frame

	push_frame(k * (n + 1));

	// array of powers

	p1 = cdr(p1);
	for (i = 0; i < k; i++) {
		for (j = 0; j <= n; j++) {
			push(car(p1));
			push_integer(j);
			power();
			A(i, j) = pop();
		}
		p1 = cdr(p1);
	}

	push_integer(n);
	factorial();
	p1 = pop();

	a = (int *) malloc(k * sizeof (int));

	if (a == NULL)
		stop("malloc failure");

	push(zero);

	multinomial_sum(k, n, a, 0, n);

	free(a);

	pop_frame(k * (n + 1));
}
Exemplo n.º 18
0
void
factor_small_number(void)
{
	int d, expo, i, n;

	save();

	n = pop_integer();

	if (n == (int) 0x80000000)
		stop("number too big to factor");

	if (n < 0)
		n = -n;

	for (i = 0; i < MAXPRIMETAB; i++) {

		d = primetab[i];

		if (d > n / d)
			break;

		expo = 0;

		while (n % d == 0) {
			n /= d;
			expo++;
		}

		if (expo) {
			push_integer(d);
			push_integer(expo);
		}
	}

	if (n > 1) {
		push_integer(n);
		push_integer(1);
	}

	restore();
}
Exemplo n.º 19
0
void
sgn(void)
{
	save();

	p1 = pop();

	if (!isnum(p1)) {
		push_symbol(SGN);
		push(p1);
		list(2);
	} else if (iszero(p1))
		push_integer(0);
	else if (isnegativenumber(p1))
		push_integer(-1);
	else
		push_integer(1);

	restore();
}
Exemplo n.º 20
0
static int value_of(lua_State * L) {
    auto it = value_of(to_token_table(L, 1));
    if (it) {
        push_boolean(L, it->is_command());
        push_name(L, it->value());
        push_integer(L, it->expr_precedence());
        return 3;
    } else {
        push_nil(L);
        return 1;
    }
}
Exemplo n.º 21
0
void
derfc(void)
{
    push(cadr(p1));
    push_integer(2);
    power();
    push_integer(-1);
    multiply();
    exponential();
    push_symbol(PI);
    push_rational(-1,2);
    power();
    multiply();
    push_integer(-2);
    multiply();
    push(cadr(p1));
    push(p2);
    derivative();
    multiply();

}
Exemplo n.º 22
0
void
dsgn(void)
{
    push(cadr(p1));
    push(p2);
    derivative();
    push(cadr(p1));
    dirac();
    multiply();
    push_integer(2);
    multiply();
}
Exemplo n.º 23
0
void
dtanh(void)
{
    push(cadr(p1));
    push(p2);
    derivative();
    push(cadr(p1));
    ycosh();
    push_integer(-2);
    power();
    multiply();
}
Exemplo n.º 24
0
void
imag(void)
{
	save();
	rect();
	p1 = pop();
	push(p1);
	push(p1);
	conjugate();
	subtract();
	push_integer(2);
	divide();
	push(imaginaryunit);
	divide();
	restore();
}
Exemplo n.º 25
0
void
trivial_divide(void)
{
	int h;
	if (car(A) == symbol(MULTIPLY)) {
		h = tos;
		p0 = cdr(A);
		while (iscons(p0)) {
			if (!equal(car(p0), F)) {
				push(car(p0));
				eval(); // force expansion of (x+1)^2, f.e.
			}
			p0 = cdr(p0);
		}
		multiply_all(tos - h);
	} else
		push_integer(1);
	T = pop();
}
Exemplo n.º 26
0
void
expand_get_C(void)
{
	int h, i, j, n;
	U **a;
	h = tos;
	if (car(A) == symbol(MULTIPLY)) {
		p1 = cdr(A);
		while (iscons(p1)) {
			F = car(p1);
			expand_get_CF();
			p1 = cdr(p1);
		}
	} else {
		F = A;
		expand_get_CF();
	}
	n = tos - h;
	if (n == 1) {
		C = pop();
		return;
	}
	C = alloc_tensor(n * n);
	C->u.tensor->ndim = 2;
	C->u.tensor->dim[0] = n;
	C->u.tensor->dim[1] = n;
	a = stack + h;
	for (i = 0; i < n; i++) {
		for (j = 0; j < n; j++) {
			push(a[j]);
			push(X);
			push_integer(i);
			power();
			divide();
			push(X);
			filter();
			C->u.tensor->elem[n * i + j] = pop();
		}
	}
	tos -= n;
}
Exemplo n.º 27
0
void
expand_get_B(void)
{
	int i, n;
	if (!istensor(C))
		return;
	n = C->u.tensor->dim[0];
	T = alloc_tensor(n);
	T->u.tensor->ndim = 1;
	T->u.tensor->dim[0] = n;
	for (i = 0; i < n; i++) {
		push(B);
		push(X);
		push_integer(i);
		power();
		divide();
		push(X);
		filter();
		T->u.tensor->elem[i] = pop();
	}
	B = T;
}
Exemplo n.º 28
0
void
yybessely(void)
{
	double d;
	int n;

	N = pop();
	X = pop();

	push(N);
	n = pop_integer();

	if (isdouble(X) && n != (int) 0x80000000) {
		d = yn(n, X->u.d);
		push_double(d);
		return;
	}
	
	if (isnegativeterm(N)) {
		push_integer(-1);
		push(N);
		power();
		push_symbol(BESSELY);
		push(X);
		push(N);
		negate();
		list(3);
		multiply();
		return;
	}

	push_symbol(BESSELY);
	push(X);
	push(N);
	list(3);
	return;
}
Exemplo n.º 29
0
void
yyfloor(void)
{
	double d;

	p1 = pop();

	if (!isnum(p1)) {
		push_symbol(FLOOR);
		push(p1);
		list(2);
		return;
	}

	if (isdouble(p1)) {
		d = floor(p1->u.d);
		push_double(d);
		return;
	}

	if (isinteger(p1)) {
		push(p1);
		return;
	}

	p3 = alloc();
	p3->k = NUM;
	p3->u.q.a = mdiv(p1->u.q.a, p1->u.q.b);
	p3->u.q.b = mint(1);
	push(p3);

	if (isnegativenumber(p1)) {
		push_integer(-1);
		add();
	}
}
void
add_terms(int n)
{
    stackAddsCounts++;
    int i, h;
	U **s;

	h = tos - n;

	s = stack + h;

    printf("stack before adding terms #%d\n", stackAddsCounts);
    if (stackAddsCounts == 137)
        printf("stop here");

    for (i = 0; i < tos; i++) {
        print1(stack[i]);
        printstr("\n");
    }

	/* ensure no infinite loop, use "for" */

	for (i = 0; i < 10; i++) {

		if (n < 2)
			break;

		flag = 0;

		qsort(s, n, sizeof (U *), cmp_terms);

		if (flag == 0)
			break;

		n = combine_terms(s, n);
	}

	tos = h + n;

	switch (n) {
	case 0:
		push_integer(0);
		break;
	case 1:
		break;
	default:
		list(n);
		p1 = pop();
		push_symbol(ADD);
		push(p1);
		cons();
		break;
	}

    printf("stack after adding terms #%d\n", stackAddsCounts);
    if (stackAddsCounts == 5)
        printf("stop here");
    for (i = 0; i < tos; i++) {
        print1(stack[i]);
        printstr("\n");
    }

}