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/* noninteractive.mac -- catch asksign and askprop queries and construct conditional expressions
* copyright 2007 by Robert Dodier
* I release this file under the terms of the GNU General Public License.
*/
/* Examples:
*
* throw (x); ("THROW NOT WITHIN CATCH" SUPPRESSED; THAT'S PROBABLY A BUG)
* asksign (x);
* asksign (log (x));
* asksign (abs (x));
* abs (asin (x + %i));
* (declare (xx, complex), abs (asin (xx + %i))); (TRIGGERS STACK OVERFLOW)
* realpart (sqrt (25 - x^2 - y^2));
* integrate (exp(a*x), x, 0, inf); (INCORRECT RESULT FOR A=0, NOT OUR PROBLEM)
* integrate (x^k, x);
* integrate (x^k, x, 1, b);
* integrate (x**a/(x + 1), x, 0, inf);
* integrate (x**a/(x + 1)**(5/2), x, 0, inf);
* integrate (exp(-%i*x) + a * exp(%i*x), x, 0, 2*%pi);
* integrate (sqrt (1 - s^2)/(z - s), s, -1, 1);
* (xmax(a, b) := (a + b + abs(a - b)) / 2, integrate (xmax (a - x, 0), x, 0, b));
* integrate (1 / (a^2 * cos(t)^2 + 1), t, 0, %pi);
* integrate (exp(- la*t) * la, t, 0, inf);
* integrate (sin(5*x) * exp(- s*x), x, 0, inf);
* integrate (1/x, x, a, 4);
* integrate (x^k, x, 0, 1);
* integrate (1 / sqrt(n + i),i,1,n);
* integrate (1 / (1 + a^2 * sin(x)^2), x, 0, 3*%pi);
* integrate (integrate (p2^2, x1, -4*%pi / kp, 4*%pi / kp), x2, 5*%pi / kp / 2, 7*%pi / kp / 2);
* integrate (1/log(t), t, x, 2*x);
* integrate ((6*cos(9*x) + 6*sin(8*x)) * (j - x), x, -%pi, %pi) / %pi; (TRIGGERS "TOO MANY CONTEXTS"; BUG IN MONSTERTRIG)
* integrate (cos(n*x) * sin(n*x), x, 0, t);
* integrate (1 / (sin(x)^2 + 1), x, 0, z);
* integrate (cos(x) - cos(x - c), x, 0, c/2) = %pi - c - integrate (cos (x - c), x, c, %pi / 2 + c);
* integrate (cot(x), x, 0, %pi/2);
* integrate (r, z, - sqrt (20 - r^2), sqrt (20 - r^2));
* integrate ((x^2 + x + 2)/(x^2 + x + c), c);
* specint (sqrt(t) * %e^(- p*t - a/t), t);
*
* (f(x) := x - 2 * log ((exp(x) + 1) / 2) + x**2/4,
* exp (- x**2/4) * ratsimp (taylor (exp (f(x)) * (x*kb + mu)**gamma, x, 0, 4)),
* integrate (%%, x, minf, inf));
*
* (aa : 3*kbt^4*x^4/(128*mu^4) - kbt^3*x^3/(16*mu^3) + 3*kbt^2*x^2/(8*mu^2) + 3*kbt*x/(2*mu) + 1,
* integrate (exp(x)/(exp(x) + 1)^2*aa, x, minf, inf));
*
* (tmpp : (x2/2 + x1/2)*sin((%pi * (- x3/2 - (- x3 - x2 - x1 + 1)/2 + x2/2 + x1/2)) / 2),
* integrate (integrate (integrate (tmpp, x3, 0, 1 - x1 - x2), x2, 0, 1 - x1), x1, 0, 1));
*
* limit (a * x, x, inf);
* limit (x^a, x, inf);
* limit (x^a, x, minf);
* declare (a, integer);
* limit (x^a, x, minf);
* tlimit (s/(1 + s^2) / sinh (s*T), s, inf);
* solve (x = log(a + sqrt( a^2 - r^2)), r); (MAKES A MESS; RESULTS INCORRECTLY MERGED INTO CONDITIONAL)
* solve (sqrt(x) + sqrt(y) = sqrt(a), y);
* solve (y^2 + x^2 + 2*a*e*x + a^2*e^2 = (2*a - sqrt (y^2 + x^2 - 2*a*e*x + a^2*e^2))^2, y);
* solve (b^(a*t) = 1, b); (ATTEMPTS DECLARE(A*T, INTEGER) => ERROR, STACK OVERFLOW)
* ode2 ('diff(x, t, 2) + a*x = b*sin(c*t), x, t);
* ode2 ('diff(x, t, 2) + a*'diff(x, t) + b*x = 0, x, t);
* ode2 ('diff(x, t, 2) + a*'diff(x, t) + b*x = d*sin(e*t), x, t);
* ode2 ('diff(y, x, 2) + a*y = c* x, y, x);
* ode2 ('diff(y, x, 2) + a*'diff(y, x) + b*y = c*x, y, x);
*
* gcd : spmod;
* expr : sin(a) / (1 - cos(a)^2*sin(t)^2);
* assume (cos(a) > 0, sin(a) > 0);
* integrate (expr, t, 0, 2*%pi);
*
* (load (simplify_sum),
* sum (r/k*binom(n, r) * binom(m, k - r)/binom(n + m, k), r, 0, k),
* simplify_sum (intosum (%%))); (TRIGGERS "CONTEXT ALREADY EXISTS"; THROW LEAVES CONTEXT HANGING AROUND)
*
* (load (topoly_solver), to_poly_solve ([sqrt(x) + sqrt(y) = a , x^2=y] , [x, y]));
*
* (load (Solver), Solver ([x=2, y=3], [x], [y])); (TRIGGERS "ZERO OR NONZERO" QUERY; SOLVER HAS ITS OWN ASKSIGN-LIKE FUNCTION)
* (load (Solver), Solver ([x=a, y=b], [x], [y, b])); (TRIGGERS "ZERO OR NONZERO" QUERY; SOLVER HAS ITS OWN ASKSIGN-LIKE FUNCTION)
*/
load (boolsimp);
load ("noninteractive.lisp");
within_MEVAL1 : false;
MEVAL1 () :=
if within_MEVAL1
then block
([r%: catch (ev (e%))], /* by the time we get here, e% is bound by TOPLEVEL-MACSYMA-EVAL */
if not atom(r%) and (op(r%) = 'asksign or op(r%) = 'askprop)
then e%
else r%)
else block
([r%: catch (ev (e%)), /* by the time we get here, e% is bound by TOPLEVEL-MACSYMA-EVAL */
within_MEVAL1 : true],
if not atom(r%) and op(r%) = 'asksign
then block ([a%, s%, c%, L%],
a%: args(r%)[1],
s%: args(r%)[2],
c%:
if s% = 'pnz then [a% < 0, equal (a%, 0), a% > 0]
elseif s% = 'nz then [a% < 0, equal (a%, 0)]
elseif s% = 'pz then [equal (a%, 0), a% > 0]
elseif s% = 'pn then [a% < 0, a% > 0]
elseif s% = 'znz then [equal (a%, 0), not equal (a%, 0)]
else throw (oops_unknown (s%)),
L%: apply (enumerate_cases, [c%]),
if s% = 'pnz or s% = 'znz then c% [length(c%)]: true, /* to make final "else" */
funmake ("if", interleave (c%, L%)))
else if not atom(r%) and op(r%) = 'askprop
/* FOLLOWING ASKPROP STUFF NEEDS WORK */
then block ([a%, s%, c%, L%],
a%: args(r%)[1],
s%: args(r%)[2],
c%: ['kind (a%, 'integer), true],
L%:
[block ([w%, z%: gensym()],
newcontext (z%),
apply (declare, [a%, 'integer]),
w%: MEVAL1(),
killcontext (z%),
w%),
block ([w%, z%: gensym()],
newcontext (z%),
apply (declare, [a%, 'noninteger]),
w%: MEVAL1(),
killcontext (z%),
w%)],
funmake ("if", interleave (c%, L%)))
else r%);
enumerate_cases (L%) :=
map (lambda ([p%], assuming ([p%], MEVAL1 ())), L%);
interleave (L1, L2) := flatten (map (lambda ([e1, e2], [e1, e2]), L1, L2));
/* Pattern-matching rules for collapsing conditionals.
* These rules have the desired effect.
* I'm commenting them out as an experiment because sometimes
* it might be slightly more informative to leave
* conditionals with redundant clauses as they stand
* (because the predicate expressions show something).
*
matchdeclare ([aa, bb, cc, dd], true);
simp: false;
tellsimpafter (if aa then bb else bb, bb);
tellsimpafter (if aa then bb elseif cc then bb else bb, bb);
tellsimpafter (if aa then bb elseif cc then dd else dd, if aa then bb else dd);
tellsimpafter (if aa then bb elseif cc then bb else dd, if aa or cc then bb else dd);
tellsimpafter ('if aa then bb else bb, bb);
tellsimpafter ('if aa then bb elseif cc then bb else bb, bb);
tellsimpafter ('if aa then bb elseif cc then dd else dd, 'if aa then bb else dd);
tellsimpafter ('if aa then bb elseif cc then bb else dd, 'if aa or cc then bb else dd);
simp: true;
*/
/* Load revised toplevel loop AFTER defining the Maxima function it calls */
load ("asksign1.lisp");
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