Carl Love

19789 Reputation

8 years, 56 days
Mt Laurel, New Jersey, United States
My name was formerly Carl Devore.

It's a sledgehammer...

@Markiyan Hirnyk The Maple approach is a sledgehammer that I don't like because it involves checking 2^15 cases to do something that should be (at least in principle) doable with secondary-school combinatorics. But I had to find out where my analysis went wrong.

It's a sledgehammer...

@Markiyan Hirnyk The Maple approach is a sledgehammer that I don't like because it involves checking 2^15 cases to do something that should be (at least in principle) doable with secondary-school combinatorics. But I had to find out where my analysis went wrong.

I could show you how to do it with evalhf, but it is a little complicated. So, first I ask Did you mean evalf? I don't see any benefit to using evalhf in this case. So let me know if you really want evalhf, and why.

I get it...

@Joe Riel Finally, I get it! Thank you for your patient explanation. Put more succintly (I think), in all cases I was missing the choice of whether the element(s) of (A xor B) were or were not in C. In the |AB|=4 case, there is one such element, for a factor of 2; in the |AB|=3 case, there are two such elements, for a factor of 2^2.

I editted my solution at the top of this subthread to reflect these corrections.

I get it...

@Joe Riel Finally, I get it! Thank you for your patient explanation. Put more succintly (I think), in all cases I was missing the choice of whether the element(s) of (A xor B) were or were not in C. In the |AB|=4 case, there is one such element, for a factor of 2; in the |AB|=3 case, there are two such elements, for a factor of 2^2.

I editted my solution at the top of this subthread to reflect these corrections.

PolynomialIdeals...

My experience with this, admittedly very limited, is that the ?PolynomialIdeals package gives you access the Groebner package with a more ideal-oriented syntax.

You're right, I was using the wrong vers...

@Markiyan Hirnyk You're right, I was using the wrong version of Maple. I just sent you an email with more info.

You're right, I was using the wrong vers...

@Markiyan Hirnyk You're right, I was using the wrong version of Maple. I just sent you an email with more info.

A simulation in Maple...

@Markiyan Hirnyk By doing a simulation in Maple, I know that my answer is wrong and that Joe's edit of his original answer is correct. But I either don't understand or don't agree with Joe's analysis of what was wrong with my answer. My simulation showed that my count of the |AB|=4 case was short by a factor of 2, and my counts of both subcases of the |AB|=3 case were short by a factor of 4. Here's the simulation code:

S:= combinat[powerset](5):
n:= 0: ab3:= 0: ab4:= 0: ab5:= 0: b4:= 0:
for A in S do  for B in S do  for C in S do
if nops(A union B) = 5 and nops(A intersect B intersect C) = 3 then
n:= n+1;
abn:= nops(A intersect B);
if abn=3 then
ab3:= ab3+1;
if nops(B)=4 then b4:= b4+1 end if
elif abn=4 then ab4:= ab4+1
end if
end if
end do  end do  end do:
n, ab3, ab4, b4;

So, the final answer is 250*binomial(30,5)*2^25, which is the same as what Joe got, although he expressed it differently.

A simulation in Maple...

@Markiyan Hirnyk By doing a simulation in Maple, I know that my answer is wrong and that Joe's edit of his original answer is correct. But I either don't understand or don't agree with Joe's analysis of what was wrong with my answer. My simulation showed that my count of the |AB|=4 case was short by a factor of 2, and my counts of both subcases of the |AB|=3 case were short by a factor of 4. Here's the simulation code:

S:= combinat[powerset](5):
n:= 0: ab3:= 0: ab4:= 0: ab5:= 0: b4:= 0:
for A in S do  for B in S do  for C in S do
if nops(A union B) = 5 and nops(A intersect B intersect C) = 3 then
n:= n+1;
abn:= nops(A intersect B);
if abn=3 then
ab3:= ab3+1;
if nops(B)=4 then b4:= b4+1 end if
elif abn=4 then ab4:= ab4+1
end if
end if
end do  end do  end do:
n, ab3, ab4, b4;

So, the final answer is 250*binomial(30,5)*2^25, which is the same as what Joe got, although he expressed it differently.

Code Edit Region...

The best way to enter multi-line code into a Maple worksheet is to use a Code Edit Region. Place your cursor where you want the window, then select Code Edit Region from the Insert menu. It gives you a Notepad-like editor with tabs and hanging indents. Also, you can use ordinary Enter (or Return) instead of Shift-Enter (Shift-Return).