digerdiga

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11 years, 81 days

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These are questions asked by digerdiga

If I have an expression which contains an unknown function f(t) e.g.

ex:=1+exp(f(t))*f(t+1)+f(t/2)

how do I replace it with some defined function F(t)?

Do I need to work with ::anything, i.e. something like

subs(f(t::anything)=F(t::anything),ex)

?

However this doesn't work.

I have big expressions containing RootOf() which are however pretty simple.

For example something like

RootOf(x^2+1,x)

Is it possible to convert this later into the actual solution? e.g. +-*I ??

Hey and Thanks for your input.


 

restart; f := ((1/2-I*t)^(-s)-(1/2+I*t)^(-s))/(2*I); fc := evalc(f); `assuming`([simplify(int(f, t = 0 .. infinity))], [s > 1]); `assuming`([simplify(int(fc, t = 0 .. infinity))], [s > 1])

-((1/2)*I)*((1/2-I*t)^(-s)-(1/2+I*t)^(-s))

 

exp(-(1/2)*s*ln(1/4+t^2))*sin(s*arctan(2*t))

 

2^(s-1)/(s-1)

 

(1/2)*4^s/(s-1)

(1)

``


 

Download function_evaluation_goes_wrong.mw

 

 

Am I doing something wrong?

Hello,

I'm currently wondering about the "real" difference.

is() or type() can be used both for true/false checks. However when should what be used preferably?

For example I do not see what is better over the other when doing simple checks such as

is(2,'integer')

type(2,'integer')

 

Thanks for clarifying.

I'm currently wondering about the cut I'm looking for in the following worksheet.

I evaluate it in 2 ways but get different answers. Any idea what the problem here is?

Thanks


 

restart; dIs := sqrt(Pi/(I*s))*exp(I*s*t-I*s*omega0^2); Is1 := `assuming`([simplify(int(dIs, s))], [s > 0]); dIs := `assuming`([int(exp(-I*(omega^2+omega0^2-t)*s), omega = -infinity .. infinity)], [s > 0]); Is2 := int(%, s); plot3d(Im(eval(Is1, [t = x+I*y, s = 1, omega0 = 1])), x = -3 .. 3, y = -3 .. 3)

(-I*Pi/s)^(1/2)*exp(I*s*t-I*s*omega0^2)

 

(1/2-(1/2)*I)*Pi*2^(1/2)*erf(s^(1/2)*(I*(omega0^2-t))^(1/2))/(I*(omega0^2-t))^(1/2)

 

exp(I*s*t-I*s*omega0^2)*Pi^(1/2)/(I*s)^(1/2)

 

-I*Pi*erf((omega0^2-t)^(1/2)*(I*s)^(1/2))/(omega0^2-t)^(1/2)

 

 

``


 

Download CutErrorFunction.mw

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