Constantine Frangos cited Kurt:
> Am 25.01.2017 um 17:56 schrieb Constantine Frangos:
> >
> > (a) any symbolic arguments appearing in the trigonometric
> > functions, for example,
> > cos(x1)*sin(y)-sin(x1)*cos(y),
> > cos(x3)*sin(z)-sin(x3)*cos(z), etc
>
> That's the point. If you're using t1,t2 this way, look what happens:
>
> (1) -> t1 := cos(x)*sin(y) - cos(y)*sin(x)
>
> (1) cos(x)sin(y) - cos(y)sin(x)
> Type: Expression(Integer)
> (2) -> t2 := - sin(x)*sin(y) + cos(x)*cos(y)
>
> (2) - sin(x)sin(y) + cos(x)cos(y)
> Type: Expression(Integer)
> (3) -> expr := tan(q)*tan(w) + t1*cos(x3) + t2*w*cos(a) + r3*t1*t2 + 5
>
> (3)
> 2
> tan(q)tan(w) - r3 cos(x)sin(x)sin(y)
> +
> 2 2
> (r3 cos(y)sin(x) - w cos(a)sin(x) + r3 cos(x) cos(y) + cos(x)cos(x3))
> *
> sin(y)
> +
> 2
> (- r3 cos(x)cos(y) - cos(x3)cos(y))sin(x) + w cos(a)cos(x)cos(y) + 5
> Type: Expression(Integer)
> (4) ->
>
>
and wrote:
> %I was not aware of this behaviour. However, I believe that fricas should not
> %automatically expand expressions that the user inputs. If this can be
> %modified then it would be very helpful.
> %Note that another public domain CAS called Maxima does not expand the above
> %expression. In addition, the user can perform the above simplification
> %by using a built-in Maxima function called trigreduce().
> %Maybe fricas should consider having such a built-in function. This will
> %only add to the strong points that it has.
A little additon: FriCAS actually have a function which works
like Maxima trigreduce(), namely expandTrigProducts:
(11) -> expandTrigProducts(cos(x1)*sin(y)-sin(x1)*cos(y))
(11) sin(y - x1)
Type: Expression(Integer)
(12) -> t1 := cos(x)*sin(y) - cos(y)*sin(x)
(12) cos(x)sin(y) - cos(y)sin(x)
Type: Expression(Integer)
(13) -> t2 := - sin(x)*sin(y) + cos(x)*cos(y)
(13) - sin(x)sin(y) + cos(x)cos(y)
Type: Expression(Integer)
(14) -> expr := tan(q)*tan(w) + t1*cos(x3) + t2*w*cos(a) + r3*t1*t2 + 5
(14)
2
tan(q)tan(w) - r3 cos(x)sin(x)sin(y)
+
2 2
(r3 cos(y)sin(x) - w cos(a)sin(x) + r3 cos(x) cos(y) + cos(x)cos(x3))
*
sin(y)
+
2
(- r3 cos(x)cos(y) - cos(x3)cos(y))sin(x) + w cos(a)cos(x)cos(y) + 5
Type: Expression(Integer)
(15) -> expandTrigProducts(expr)
(15)
2 2
2tan(q)tan(w) + (r3 sin(x) + r3 cos(x) )sin(2y) + sin(y + x3 - x)
+
2 2
- r3 sin(2x)sin(y) + sin(y - x3 - x) - r3 cos(y) sin(2x)
+
w cos(y + x + a) + w cos(y + x - a) + 10
/
2
Type: Expression(Integer)
Let me add that both Maxima trigreduce() and expandTrigProducts
works by _expanding_ products, namely:
(16) -> expandTrigProducts(sin(x)*cos(y))
sin(y + x) - sin(y - x)
(16) -----------------------
2
Type: Expression(Integer)
(17) -> expandTrigProducts(sin(x)*cos(y)*sin(z))
- cos(z + y + x) + cos(z + y - x) - cos(z - y + x) + cos(z - y - x)
(17) -------------------------------------------------------------------
4
Type: Expression(Integer)
that is _each_ product is replaced, regardless if it leads
to simplification or not.
--
Waldek Hebisch
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