lcz

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These are questions asked by lcz

 I want to find all real roots of   equation x^2 + floor(x) - 10=0

restart: 
solve(x^2+floor(x)-10,x) assuming x::real 

maple tells me:

  RootOf(_Z^2 + floor(_Z) - 10)

allvalues(%) 

RootOf(_Z^2 + floor(_Z) - 10, 2.828427125 + 0.*I)

even though  usRealDomain.

use RealDomain in  solve(x^2+floor(x)-10,x) end use

We get nothing!

So I trun to use fsolve.

plot(x^2+floor(x)-10,x=-5..5)

                                  

s:=fsolve(x^2+floor(x)-10,{x});
fsolve(x^2+floor(x)-10,x,avoid={s})

                     s := {x = 2.828427125}

                          -3.741657387

 

I try to use mathematica, it is good:

Solve[x^2 + Floor[x] - 10 == 0, x, Reals]

Could Maple  do that?

 

 

 

 

 

 

I'd like to solve the equation b^4+12*b^2+22*b^2-20*b+1=0

M:=b^4+12*b^2+22*b^2-20*b+1;
s:=solve(M,{b}):
s1:=allvalues(s[1])[]:# first solution

I find   first solution has  common subexpressions 5435 + 3*sqrt(515793), so I want to repalce by t. but unfortunately failed.

eq:=5435 + 3*sqrt(515793)=t:
applyrule(eq,s1);
# failed

why? in  following simple instance, it is OK!

eq:=5435 + 3*sqrt(515793)=t:
applyrule(eq,sqrt(5435 + 3*sqrt(515793)));

 

 

 

 

 

 I try to solve the general solutions of  sin(x^2)=1/2. And then I would  like to check the solution,but failed. How to do?

s:=solve(sin(x^2)=1/2,allsolutions);
about(_Z1);  #Originally _Z1, renamed _Z1~: is assumed to be: integer
about(_B1);  #Originally _B1, renamed _B1~: is assumed to be: OrProp(0,1)
test:=simplify(subs(x=s[1],sin(x^2)))

it sholud be 1/2. Thanks!

Theoretically, if the multiplication sign  is missed Maple needs to give reminders or warnings.But the following is not the case, why?I am surprised its output. 

x:=1
                             x := 1
x(2+1)Actually, I want to enter x*(2+1)

                               1
x(sin(y))Actually, I want to enter x*(sin(y))
                               1

I read  help document of :

with(Physics[Vectors]):
(%Nabla)(f(x,y,z))
value(%)

 

But if I want to use Composition function , is it not useful? why? how to do?

(%Nabla@@4)(f(x,y,z));
value(%)

we know that:

(Nabla@@4)(f(x,y,z))

 

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