Robert Israel

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18 years, 217 days
University of British Columbia
Associate Professor Emeritus
North York, Ontario, Canada

MaplePrimes Activity


These are replies submitted by Robert Israel

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> MakeUnique(Reverse(FindRepetitions(Reverse(L))));
  
     [a, c, d]


Exercise: why is this the right order?

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> MakeUnique(Reverse(FindRepetitions(Reverse(L))));
  
     [a, c, d]


Exercise: why is this the right order?

One way is to break up the region into (approximately) convex pieces.  For example:

> with(plots):
 with(plottools):
 plot1 := display([seq(plot(1, t = Pi*j/40 .. Pi*(j+1)/40, 
   filled = true, color = coral), j=30 .. 49)]):
 H := transform((t, r) -> [4*(1-r)*cos(t)+3*(r)*cos(t), 
    4*(1-r)*sin(t)+3*(r)*sin(t)]):
 display(H(plot1),view = [-5 .. 5, -4 .. 4], scaling=constrained);

 

 

What about it doesn't work?

It may be inefficient, but it does seem to work as far as I can tell.

 

What about it doesn't work?

It may be inefficient, but it does seem to work as far as I can tell.

 

The polygon-filling method used in all versions before Maple 11, and now in Classic, works for regions that are convex (or more generally, star-shaped with respect to the first point of the polygon).  It shades in every point that is a convex combination of the first vertex and a point on the outline.  Standard now uses a method that works on non-convex polygons. 

I don't know what Maple commands you're allowed to use in this, but you might find member and remove useful.  Good Maple style tries to avoid do loops as much as possible for constructing sets and lists, but I don't know if your instructor wants you to use good Maple style.

I don't know what Maple commands you're allowed to use in this, but you might find member and remove useful.  Good Maple style tries to avoid do loops as much as possible for constructing sets and lists, but I don't know if your instructor wants you to use good Maple style.

Go to Tools, Options, Display, and remove the check mark from "Automatically display legends in 2-D plots".  Then click on "Apply Globally".  Now your plots won't have legends unless you explicitly include a legend option.

An html version of that worksheet is at www.math.ubc.ca/~israel/challenge/challenge.html

More simply:

> setDiff := `minus`;

But if this is homework I suspect the instructor might not be happy with this as a solution: after all, polt.lauren did say "I need to write a procedure ...", not "I need to find a procedure that already exists".  On the other hand, it also wasn't "I need to get the people at MaplePrimes to write a procedure...".

More simply:

> setDiff := `minus`;

But if this is homework I suspect the instructor might not be happy with this as a solution: after all, polt.lauren did say "I need to write a procedure ...", not "I need to find a procedure that already exists".  On the other hand, it also wasn't "I need to get the people at MaplePrimes to write a procedure...".

Like most probability distributions, the negative binomial can be used (and often is used) in situations other than the one in which it was originally introduced.  So though a non-integer number of trials makes no sense, there is a perfectly good probability distribution on the nonnegative integers with probability function

p(n) = GAMMA(x+n)/GAMMA(x)/n!*p^x*(1-p)^n

for 0 <= p <= 1, x > 0.

I found columns, not rows, that are multiples.

In the case of columns, you want to look at the null space of the Matrix, i.e. the space of solutions X of A.X = 0.  This can be done with NullSpace in the LinearAlgebra package.
Columns i and j are multiples of each other if the null space contains a vector with nonzero entries only in positions i and j.

In the case of rows, you can do the same for the transpose of the Matrix.

 

I found columns, not rows, that are multiples.

In the case of columns, you want to look at the null space of the Matrix, i.e. the space of solutions X of A.X = 0.  This can be done with NullSpace in the LinearAlgebra package.
Columns i and j are multiples of each other if the null space contains a vector with nonzero entries only in positions i and j.

In the case of rows, you can do the same for the transpose of the Matrix.

 

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