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(kill(all), 'done);
'done$
(load("format"), 'done);
'done$
/* A basic rearrangement: */
format((a+b*x)*(c-x)^2,%poly(x),%factor);
b*x^3+(a-2*b*c)*x^2+c*(b*c-2*a)*x+a*c^2$
/* A `mathematical' alternative to map or substpart...*/
format((1+2*a+a^2)*b + a*(1+2*b+b^2),%sum,%product,%factor);
a*(b+1)^2+(a+1)^2*b$
/* Focussing simplifications */
block([foo],
foo:x^2*sin(y)^4-2*x^2*sin(y)^2+x^4*cos(y)^4-2*x^4*cos(y)^2+x^4+x^2+1,
format(foo,%poly(x),trigsimp));
x^4*sin(y)^4+x^2*cos(y)^4+1$
format((1+2*eps*(q+r*cos(g))^2)^4,%series(eps,2),%trig(g),factor);
1+eps*(4*(r^2+2*q^2)+4*cos(2*g)*r^2+16*cos(g)*q*r)
+eps^2*(3*(3*r^4+24*q^2*r^2+8*q^4)+3*cos(4*g)*r^4+24*cos(3*g)*q*r^3
+24*cos(g)*q*r*(3*r^2+4*q^2)
+12*cos(2*g)*r^2*(r^2+6*q^2))$
format((1+2*a+a^2)*b + a*(1+2*b+b^2),%sum,%product,%factor);
a*(b+1)^2+(a+1)^2*b$
format(expand((1+a)^2/(1+b)^2),%ratsimp,%factor);
(a+1)^2/(b+1)^2$
block([t1:expand((1+x^4)*y^2+(1+x^8)*y^4)],
[format(t1,%p(y),%f), format(t1,%p(y),%f(a^2-2))]);
[(x^8+1)*y^4+(x^4+1)*y^2,
(x^4-a*x^2+1)*(x^4+a*x^2+1)*y^4+(x^2-a*x+1)*(x^2+a*x+1)*y^2]$
format(expand((a+x)^3-a^3),%f-a^3);
(x+a)^3-a^3$
/* Contrast power series & Taylor series: */
format((1+sin(x)-x)^3,%series(x,3),%f);
-x^3+3*x^2*(sin(x)+1)-3*x*(sin(x)+1)^2+(sin(x)+1)^3$
format((1+sin(x)-x)^3,%taylor(x,3),%f);
1-x^3/2$
block([], local(sqrtp),
sqrtp(f):=not(atom(f)) and part(f,0)='sqrt,
first(solve(a*x^2+b*x-(b-2*a)/4,x)),
format(%%,%rhs,%preformat(%p(match(sqrtp))),%match(sqrtp),%arg(1),%f));
x = -sqrt((b-a)*(b+2*a))/(2*a)-b/(2*a)$
/***********************************************************************
Subtemplates & template chains. Compare: */
block([t2:expand((1+a)^2*(1+x)^2/(1+b^2)/(1+y)^2)],
[format(t2,%r[%p(x)],%f), format(t2,%r[[%p(x),%f]])]);
[((a+1)^2*x^2+2*(a+1)^2*x+(a+1)^2)/((b^2+1)*(y+1)^2),
((a+1)^2*x^2+2*(a+1)^2*x+(a+1)^2)/((b^2+1)*y^2+(2*b^2+2)*y+b^2+1)]$
/* Contrast these subtemplates */
block([l1:[1+2*a+a^2,1+2*b+b^2,1+2*c+c^2]],
[format(l1,%list,%f), format(l1,%list[%noop,%f]), format(l1,%list[%noop,%ditto(%f)])]);
[[(a+1)^2,(b+1)^2,(c+1)^2],[a^2+2*a+1,(b+1)^2,c^2+2*c+1],
[a^2+2*a+1,(b+1)^2,(c+1)^2]]$
/* Contrast various templates & subtemplate usage */
format((1+a)^2/(1+2*b+b^2),%frac[expand,%f]);
(a^2+2*a+1)/(b+1)^2$
format((1+a)^2/(1+2*b+b^2),%expression[expand,%f]);
(a^2+2*a+1)/(b+1)^2$
format((1+a)^2/(1+2*b+b^2),%denom,%f);
(a+1)^2/(b+1)^2$
format((1+a)^2/(1+2*b+b^2),%num,expand);
(a^2+2*a+1)/(b^2+2*b+1)$
/***********************************************************************
Bags: Lists, Relations & Matrices */
format([a=b,c=d,e=f],%equation);
[a,c,e] = [b,d,f]$
format([a,c,e] = [b,d,f],%list);
[a = b,c = d,e = f]$
format(1+2*a+a^2 < 1+2*b+b^2,%rel("<")[%f]);
(a+1)^2 < b^2+2*b+1$
format(1+2*a+a^2 < 1+2*b+b^2,%rhs("<"),%f);
a^2+2*a+1 < (b+1)^2$
format(1+2*a+a^2 < 1+2*b+b^2,%lhs("<"),%f);
(a+1)^2 < b^2+2*b+1$
format(1+2*a+a^2 = 1+2*b+b^2,%lhs,%f);
(a+1)^2 = b^2+2*b+1$
block([m],
m1:matrix([a^2+2*a+1=q,b^2+2*b+1=r],[c^2+2*c+1=s,d^2+2*d+1=t]),
format(m1,%equation,%matrix[%list[%factor]]));
matrix([(a+1)^2,b^2+2*b+1],[c^2+2*c+1,d^2+2*d+1]) = matrix([q,r],[s,t])$
block([m],
m1:matrix([a^2+2*a+1=q,b^2+2*b+1=r],[c^2+2*c+1=s,d^2+2*d+1=t]),
format(m1,%eq,%element(1,1),%f));
matrix([(a+1)^2,b^2+2*b+1],[c^2+2*c+1,d^2+2*d+1]) = matrix([q,r],[s,t])$
block([m],
m1:matrix([a^2+2*a+1=q,b^2+2*b+1=r],[c^2+2*c+1=s,d^2+2*d+1=t]),
format(m1,%equation,%matrix[%noop,%list[%noop,%factor]]));
matrix([a^2+2*a+1,b^2+2*b+1],[c^2+2*c+1,(d+1)^2]) = matrix([q,r],[s,t])$
block([m],
m1:matrix([a^2+2*a+1=q,b^2+2*b+1=r],[c^2+2*c+1=s,d^2+2*d+1=t]),
format(m1,%eq,%element(2,2),%f));
matrix([a^2+2*a+1,b^2+2*b+1],[c^2+2*c+1,(d+1)^2]) = matrix([q,r],[s,t])$
/***********************************************************************
Conditionals */
format(a*(1+2*x+x^2)+b*(1+2*y+y^2),%sum,%if(lambda([xx],freeof(x,xx)))[%f,%subst(x=q)]);
b*(y+1)^2+a*(q^2+2*q+1)$
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