Items tagged with assuming

When I input

cos(k*Pi) assuming k::odd

The result is -1

but

(-1)^k assuming k::odd

The result is (-1)^k

Why doesn't the second expression work?

 

This is one of these silly ones that crop up every-so-often (and yes, beta, gamma are just the relativistic v/c and energy):

gamma=1/sqrt(1-beta^2);
solve(%,beta);

comes up with ±I*sqrt(-gamma^2+1)/gamma.

While this is not wrong it is nothing I want to throw at any student trying hard enough as it is to keep his/her head above water. What I want is beta=sqrt(1-1/gamma^2) and I am having a devil of a time getting Maple to do this. even doing it "by hand" the I comes in the moment I take the sqrt. "assuming" does not help (and when I try ...assuming beta::positive, gamma > 1 I get an error claiming these to be inconsistent).

What gives?

Mac Dude

The following limit does not return a value. Then the evalf gives a wrong answer.

The answer should be "undefined" or -infinity .. infinity.

limit(exp(n)/(-1)^n, n = infinity) assuming n::posint; evalf(%);


                       /exp(n)              \
                  limit|------, n = infinity|
                       |    n               |
                       \(-1)                /

                               0.

The same happens if you delete the assumption.

 

A similar problem occurs with

limit(sin(Pi/2+2*Pi*n), n = infinity) assuming n::posint;
                            -1 .. 1
without the assumption this would be appropriate.

Why does the following statement not evaluate, or better yet, how can I make it do so?

 

A:=value(floor(p)) assuming p>0,p<1,p::real;

or

A:=simplify(floor(p)) assuming p>0,p<1,p::real;

or any one of a lot of different attempts along the above lines, all of which seem (to me) that they should yield

A:=0

rather than

A:=floor(p)

which is what I get.

Thanks in advance

``

-(-2*N__1*`&omega;__2`*`&omega;__1`^2*lambda-8*N__2*lambda^3*`&omega;__2`-sqrt(4*N__1^2*lambda^2*`&omega;__1`^2*`&omega;__2`^2+16*N__1*N__2*lambda^4*`&omega;__2`^2+N__1*N__2*`&omega;__1`^2*`&omega;__2`^4+4*N__2^2*lambda^2*`&omega;__2`^4)*`&omega;__1`)/(4*N__1*lambda*`&omega;__1`^2*`&omega;__2`+16*N__2*lambda^3*`&omega;__2`)

-(-2*N__1*`&omega;__2`*`&omega;__1`^2*lambda-8*N__2*lambda^3*`&omega;__2`-(4*N__1^2*lambda^2*`&omega;__1`^2*`&omega;__2`^2+16*N__1*N__2*lambda^4*`&omega;__2`^2+N__1*N__2*`&omega;__1`^2*`&omega;__2`^4+4*N__2^2*lambda^2*`&omega;__2`^4)^(1/2)*`&omega;__1`)/(4*N__1*lambda*`&omega;__1`^2*`&omega;__2`+16*N__2*lambda^3*`&omega;__2`)

(1)

`assuming`([simplify(-(-2*N__1*`&omega;__2`*`&omega;__1`^2*lambda-8*N__2*lambda^3*`&omega;__2`-(4*N__1^2*lambda^2*`&omega;__1`^2*`&omega;__2`^2+16*N__1*N__2*lambda^4*`&omega;__2`^2+N__1*N__2*`&omega;__1`^2*`&omega;__2`^4+4*N__2^2*lambda^2*`&omega;__2`^4)^(1/2)*`&omega;__1`)/(4*N__1*lambda*`&omega;__1`^2*`&omega;__2`+16*N__2*lambda^3*`&omega;__2`), 'size')], [all, positive])

(1/4)*(4^(1/2)*((N__1*lambda^2+(1/4)*N__2*`&omega;__2`^2)*`&omega;__2`^2*(N__1*`&omega;__1`^2+4*N__2*lambda^2))^(1/2)*`&omega;__1`+2*lambda*`&omega;__2`*(N__1*`&omega;__1`^2+4*N__2*lambda^2))/(lambda*`&omega;__2`*(N__1*`&omega;__1`^2+4*N__2*lambda^2))

(2)

`assuming`([combine((1/4)*(4^(1/2)*((N__1*lambda^2+(1/4)*N__2*`&omega;__2`^2)*`&omega;__2`^2*(N__1*`&omega;__1`^2+4*N__2*lambda^2))^(1/2)*`&omega;__1`+2*lambda*`&omega;__2`*(N__1*`&omega;__1`^2+4*N__2*lambda^2))/(lambda*`&omega;__2`*(N__1*`&omega;__1`^2+4*N__2*lambda^2)), 'size')], [N__1 > 0, N__2 > 0, `&omega;__1` > 0, `&omega;__2` > 0, lambda > 0])

(1/4)*(`&omega;__1`*`&omega;__2`*((4*N__1*lambda^2+N__2*`&omega;__2`^2)*(N__1*`&omega;__1`^2+4*N__2*lambda^2))^(1/2)+2*lambda*`&omega;__2`*(N__1*`&omega;__1`^2+4*N__2*lambda^2))/(lambda*`&omega;__2`*(N__1*`&omega;__1`^2+4*N__2*lambda^2))

(3)

 

``

``


Download question_13.12.06.mw

Hello,

I got problem with assuming and solve.

`assuming`([solve(abs(-2*r*(-1/2)*(1+sqrt(1+4*r))/r)<1)],[r>-1/4]);

There is nothing happens... Neither solution or some errors

What am I doing wrong?

I have a situation

restart:
with(IntegrationTools):
with(PDEtools):
declare(w(r));
assume(delta::constant, R::constant, K:: constant, U::constant):
ODE_1:=diff(w(r),r)+R*(diff(w(r), r))^3-K/r;
 
declare(u(r));
ODE_T_1:=collect(algsubs(w(r)=u(r)+(r-1)*(U-0)/(delta-1), ODE_1),diff(u(r), r)) ;
eq1:=int(phi[i](r)*ODE_T_1,r=1..delta) assuming delta > 1;
eq2:=Expand(eq1);
eq3 := applyop(u->Parts(u,phi[i...

Hi all,

I have the following functions.

restart:
with(IntegrationTools):
N:=4:

i:='i':
for i from 1 to N do
assume(x[i-1]::constant):
assume(x[i+1]::constant):
assume(x[i-1]::constant):
assume(h::constant):
 phi[i](t):=piecewise(t>=x[i-1] and x[i]>t, (t-x[i])/(h), x[i]
(x[i+1]-t)/(h), 0);
end do;
## my goal is solve the integrals involving phi[i]'s as integrand and x[i]'s as its limits.

This example was reported to me after a Calculus II student encountered this ridiculous result:

f := (k+5)/sqrt(k^7+k^2):
Int( f, k=1..infinity ):
% = value( % );
/infinity
| k + 5
| -------------- dk = -infinity
| (1/2)
/1 / 7 2\
\k + k /

Hello,

I have a system of two ODEs.  The solutions of the system (U(t) and V(t)) should never take on negative values, but may approach zero.  When using dsolve (numeric) to solve the system and odeplot to plot the system, I can see that dsolve gives slightly negative values to the solutions when close to zero.  This may result in the solutions becomes increasingly negative over time.

How can I prevent dsolve from assigning negative values to...

Dear Maple Users,

I'm solving quite a complicated task, so I tried to simplified an example.

There is an equation:

SOL := fsolve(Nz+int(int(StrssCctXY(x, y), x = -(1/2)*b .. (1/2)*b), y = -(1/2)*h .. (1/2)*h) = 0, {C1 = -(1/2)*h .. (1/2)*h})

 StrssCctXY(x,y) is piecewise function containing C1 variable, to solve an equation I had to use assumptions on C1 via assume(C1<num1, C1>-num2) command, after that C1 becomes C1~;

 

can you explain me when i solve equation beta-t*beta=0 with condition beta<>0. I write command:
r :=solve(beta-t*beta, t, UseAssumptions), assuming beta <> 0
It works well. But it will be a problem when command is:
r :=solve(beta-t*beta, t, UseAssumptions), assuming beta <> 0, gamma<>0;
Error: Error, (in assuming) when calling 'assume'. Received: 'cannot assume on a constant object'.
thank you very much.

How can I most succinctly and straightforwardly get Maple to simplify f below to g below?

> f:=(6*x^2-6*x+6)^(1/2)*(2*x^2-2*x+2)^(1/2);

                          (1/2)                 (1/2)
          /   2          \      /   2          \     
          \6 x  - 6 x + 6/      \2 x  - 2 x + 2/     

> g:=simplify(f) assuming x::real;

                        (1/2) / 2        \
                     2 3      \x  - x + 1/

> simplify(g-f...

I need maple to perform the following:

"int((1+m^2*(alpha-theta)^2*sin(theta)^2/sin(alpha)^2/alpha^2)^(1/2),theta = 0 .. alpha)"

but maple does not integrate. I have tried assuming that the term inside the square root is positive, with no result. What else can I do?

I really need a result to the integration below but Maple 13 just won't return one. Could you please help me or advise me as to what might be wrong or what I might try ? I'm integrating on the real line in x but even when I alter the limits of integration maple just returns the integrand.

 

s1:= int((1/8)*sqrt(2)*exp((1/2)*k^2*cos(x)^2/sigma^2)*exp(-(1/2)*k^2/sigma^2...

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