Maple 2020 Questions and Posts

These are Posts and Questions associated with the product, Maple 2020

I have just come across this curious but really boring problem.
In the code snippet below, expr1 and expr2 are identical.

data := [a=1, b=2]:
  piecewise(And(x(t) > a, x(t) < b), 1, 0),
expr1 := eval(eval(%, data),  x(t)=z):
plot(expr1, z=0..3);

  piecewise(And(z > a, z< b), 1, 0),
expr2 := eval(%, data),:
plot(expr2, z=0..3);

But if I change the parameterization of the problem, expr2 is still correct but expr1 is not

data := [d=1.5, a=0.5]:
  piecewise(And(x(t) > d-a, x(t) < d+a), 1, 0),
expr1 := eval(eval(%, data),  x(t)=z):
plot(expr1, z=0..3);

  piecewise(And(z > d-a, z< d+a), 1, 0),
expr2 := eval(%, data),:
plot(expr2, z=0..3);

Where does this come from?

PS: I'm sorry not to be able loading the mw file

Hello there, 

Would you allow me to ask these two questions?

1) is there any way to collect the expression 'eq14_2' w.r.t. DeltaP? The question is labeled as 'Q1' in the worksheet. 

2) Why does the 'DeltaP' term survive at the RHS of the expression 'eq14_2_3'? In other words, is it possible to cancel out the same term, 'DeltaP', in numerator and denominator?


eq14_1_3 := w[NET] = Delta*T[Sfg];

w[NET] = Delta*T[Sfg]


eq14_2 := w[NET] = -((v[2] + v[3])/2)((-DeltaP + P) - P) - ((v[1] + v[4])/2)((P - P) + DeltaP);

w[NET] = -(1/2)*v[2](-DeltaP)-(1/2)*v[3](-DeltaP)-(1/2)*v[1](DeltaP)-(1/2)*v[4](DeltaP)



w[NET] = -(1/2)*v[2](-DeltaP)-(1/2)*v[3](-DeltaP)-(1/2)*v[1](DeltaP)-(1/2)*v[4](DeltaP)


collect(expand(eq14_2), DeltaP, distributed); # Q1

w[NET] = -(1/2)*v[2](-DeltaP)-(1/2)*v[3](-DeltaP)-(1/2)*v[1](DeltaP)-(1/2)*v[4](DeltaP)


Desired1 := w[NET] = DeltaP * (-v[2]*(-1)/2 - v[3]*(-1)/2 - v[1]*(1)/2 - v[4]*(1)/2);

w[NET] = DeltaP*((1/2)*v[2]+(1/2)*v[3]-(1/2)*v[1]-(1/2)*v[4])


eq14_2_2 := rhs(eq14_1_3) = rhs(eq14_2);

Delta*T[Sfg] = -(1/2)*v[2](-DeltaP)-(1/2)*v[3](-DeltaP)-(1/2)*v[1](DeltaP)-(1/2)*v[4](DeltaP)


eq14_2_3 := eq14_2_2 / DeltaP; # Q2

Delta*T[Sfg]/DeltaP = (-(1/2)*v[2](-DeltaP)-(1/2)*v[3](-DeltaP)-(1/2)*v[1](DeltaP)-(1/2)*v[4](DeltaP))/DeltaP


Desired2 := w[NET]/DeltaP =  (-v[2]*(-1)/2 - v[3]*(-1)/2 - v[1]*(1)/2 - v[4]*(1)/2);

w[NET]/DeltaP = (1/2)*v[2]+(1/2)*v[3]-(1/2)*v[1]-(1/2)*v[4]




Thank you everyone!

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I hope this helps you answer my question

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Here is my attempt.

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Run these codes


y := t -> invlaplace(exp(-s)/s, s, t)

The following gives correct answer

y(t - 1)

The following gives junk answer

y(t - 1.1)

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