lcz

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2 years, 15 days

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These are questions asked by lcz

 12 yeas later, the probelm  is not still improved in following links 

https://www.mapleprimes.com/posts/38473-Simplify-Ceil-And-Floor

simplify(ceil(x)+floor(-x));

                         floor(-x) + ceil(x)



I think extending simplify by Joe Riel 8221  is a little complicated. 

restart;
`simplify/ceil` := proc(ex)
    evalindets(ex, 'specfunc(anything,ceil)', x -> -floor(-op(x)));
end proc:

simplify(floor(-x) + ceil(x));

 It seems that maple know  ceil(x)=-floor(-x) 

 

why does not maple2020 still handle that?  

 

 

A torus can be defined parametrically by:

{\displaystyle {\begin{aligned}x(\theta ,\varphi )&=(R+r\cos \theta )\cos {\varphi }\\y(\theta ,\varphi )&=(R+r\cos \theta )\sin {\varphi }\\z(\theta ,\varphi )&=r\sin \theta \end{aligned}}}

where θ, φ are angles which make a full circle, so that their values start and end at the same point, R is the distance from the center of the tube to the center of the torus, r  is the radius of the tube.

R:=10:
r:=5:
plot3d( [ ( R+r(u,v)*cos(v))*sin(u),
          ( R+r(u,v)*cos(v))*cos(u),
            r*sin(v)
        ],
            u=0..2*Pi,
            v=0..2*Pi,style=patchnogrid,
            scaling=constrained,
          scaling=constrained,
coordinateview=[-15..15, -15..15,-5..5],
lightmodel=light3, viewpoint = circleleft);

I set range [-5..5] of the Z axis,but  the range of  Z axis tickmarks  in the above image maybe in [-4.5..4.5] .

How to have tickmarks included at -5 and 5 on the Z axis?

The code 

S:=sum(1/x__i,i=1..5)

will give us the following ouput

Why not 

S:=add(1/x__i,i=1..5)

 also give same result. why?How to do?

I also note that:

S:=add(1/x||i,i=1..5)

S:=sum(1/x||i,i=1..5)

 

By the code

P := plot( [ sin(x)-x+(x^3)/3! ] ) :
L := plots[textplot]( [ 3 , 15 , sin(x)-x+(x^3)/3! ],  axes = none) :
plots[display]( P ,L, axes = normal )

I'd like to put the text sin(x)-x+(x^3)/3!  not  sin(x)-x+(x^3)/6   in the image.

I thought  that parse can do that

parse("sin(x)-x+(x^3)/3!")

But One use it in plots[textplot] , it is not useful!

P := plot( [ sin(x)-x+(x^3)/3! ] ) :
L := plots[textplot]( [ 3 , 15 , parse("sin(x)-x+(x^3)/3!") ],  axes = none) :
plots[display]( P ,L, axes = normal )

How to do? Thanks!

 The code

s:=solve(sin(x)=3*x/Pi,x)

gives us following output:

s := RootOf(-sin(_Z)*Pi + 3*_Z)

The allvalues command attempts to find symbolic representations of the roots using solve.
But  the code:

allvalues(s);
solve(sin(x)=3*x/Pi,x,AllSolutions)

gives us 

RootOf(-sin(_Z)*Pi + 3*_Z, 0.5235987756), RootOf(-sin(_Z)*Pi + 3*_Z, -0.5235987756), 0

RootOf(-sin(_Z)*Pi + 3*_Z)

To see the roots of sin(x)-3*x/Pi   we use plot

plot(sin(x)-3*x/Pi,x=-100..100)

 

plot(sin(x)-3*x/Pi,x=-Pi/4..Pi/4)

And we can also figure out  three roots of this function are 0  Pi/6 and -Pi/6

High probability it has no other root.

seq(eval(sin(x)-3*x/Pi,x=i),i in [-Pi/6,0,Pi/6])

0, 0, 0

Why doesn't Maple do anything about it

 

 

 

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