Look: rs:=rule cos(x)*sin(y)-sin(x)*cos(y) == sin(y-x) rc:=rule cos(x)*cos(y)-sin(x)*sin(y) == cos(x+y)
t1 := paren(cos(x)*sin(y)-sin(x)*cos(y)) t2 := paren(cos(x)*cos(y)-sin(x)*sin(y)) expr := t1*cos(x3) + 5 + tan(q)*tan(w) + t2*w*cos(a)+ t1*t2*r3 rc rs expr -- voilà ;-) more below ... On Monday, 30 January 2017 15:45:50 UTC+1, Bill Page wrote: > > Why do you find it interesting? 'box' and 'paren' are just kernels > with no automatic simplifications. That's the interesting part (at least to me) when dealing with rules. If I had known 'paren' before I wouldn't have suggested the construction using equations (see former post). > On output 'box' is invisible but > Indeed, but tex or html output uses parens ... so I'm wondering why not in algebraic mode? > 'paren' displays as parenthesis. As with all kernels in Expression the > arguments of the kernel are themselves members of Expression > (recursively). This seems to be of limited usefulness to me - a kind > of a hack to avoid some forms of autosimplification. 'distribute' just > evaluates 'box' and 'paren' as identities (selectively in the two > argument for). It would certainly be of limited use without 'distribute', however, as long as we have an 'inverse' it seems to me well defined as any other 'hack' ;-) > I rather think that it attempts to solve the problem at > the wrong level. > > Is it a problem at all? If you're alluding on symbolic expressions then I'll fully agree. > On 29 January 2017 at 22:37, Kurt Pagani <[email protected] <javascript:>> > wrote: > > I wasn't aware of "box" or "paren" in EXPR INT. That's really > interesting. > > Apparently "distribute" reliably works as advertised: > > > > distribute(f) expands all the kernels in f that are formally enclosed > by a > > box or paren expression. > > > > I've tried to figure out what "box" is actually doing. By (17) and (18) > > below I would bet it's like "invisible parentheses"? > > > > (1) -> paren(a+b)*(a+b) > > > > (1) (b + a)(b + a) > > Type: > > Expression(Integer) > > (2) -> distribute % > > > > 2 2 > > (2) b + 2a b + a > > Type: > > Expression(Integer) > > (3) -> kernels % > > > > (3) [b,a] > > Type: > > List(Kernel(Expression(Integer))) > > > > (4) -> kernels (paren(a+b)*(a+b)) > > > > (4) [(b + a),b,a] > > Type: > > List(Kernel(Expression(Integer))) > > > > (5) -> kernels (paren(a+b)*(a+b)).1 > > > > (5) (b + a) > > Type: > > Kernel(Expression(Integer)) > > (6) -> name % > > > > (6) %paren > > Type: > > Symbol > > > > > > ... > > > > (13) -> paren(a*(b+c)) > > > > (13) (a c + a b) > > Type: > > Expression(Integer) > > (14) -> paren(a*paren(b+c)) > > > > (14) (a(c + b)) > > Type: > > Expression(Integer) > > (15) -> distribute % > > > > (15) a c + a b > > Type: > > Expression(Integer) > > (16) -> box(a*(b+c)) > > > > (16) a c + a b > > Type: > > Expression(Integer) > > (17) -> box(a*box(b+c)) > > > > (17) ac + b > > Type: > > Expression(Integer) > > (18) -> distribute % > > > > (18) a c + a b > > Type: > > Expression(Integer) > > > > > > > > On Friday, 27 January 2017 17:04:45 UTC+1, Waldek Hebisch wrote: > >> > >> Constantine Frangos wrote: > >> > > ... > > > >> > >> Some people want to stop transformation of expressions to get > >> desired output for printing expressions. In FriCAS you can > >> use box and paren: > >> > >> (9) -> x*(y + x) > >> > >> 2 > >> (9) x y + x > >> Type: > >> Polynomial(Integer) > >> (10) -> x*box(x+z) > >> > >> (10) xz + x > >> Type: > >> Expression(Integer) > >> (11) -> x*paren(x+z) > >> > >> (11) x(z + x) > >> Type: > >> Expression(Integer) > >> > >> FriCAS will keep content of box (or paren) together. Box prints > without > >> parenthesis which is appropriate for sums, but as (10) above shows > >> is confusing for products. Note: if you want to do computations > >> with then note that in most cases you need to remove them by > >> hand if you want to combine content with what is outside. > >> > >> -- > >> Waldek Hebisch > > > > -- > > You received this message because you are subscribed to the Google > Groups > > "FriCAS - computer algebra system" group. > > To unsubscribe from this group and stop receiving emails from it, send > an > > email to [email protected] <javascript:>. > > To post to this group, send email to [email protected] > <javascript:>. > > Visit this group at https://groups.google.com/group/fricas-devel. > > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
