Dave's Place: January 2013

Real Estate Intelligence Agency, Inc. (REIA) is a Huntsville based Real Estate Brokerage that serves residential and commercial real estate buyers and sellers in the North Alabama area. We specialize in customizing our services for each client based on their specific needs and requirements.

Our mission is to create a modern real estate agency and move beyond legacy programs, processes and outdated business models of the traditional real estate companies. We will accomplish our mission by approaching each opportunity with a strategic planning model that looks at industry, market, and competitive environment in order to better brand the property and focus marketing efforts.

Thursday, January 10, 2013

Making Change

Making Change with Coins
(%i1) load(basic)$

(%i2) powerdisp:true$
Number of terms to count down to in increments of five.
(%i3) Number_of_Terms:50;

Define coins as list of lists with coin name, denomination, and additonal format character for plurals.
(%i4) Coins:[[Quarter,25,""],[Dime,10,""],[Nickel,5,""],[Penn,1,"@"]];

Form formats for string output:
(%i5) fmts:makelist(sconcat("~d ",Coins[j][1],"~:",Coins[j][3],"P~% "),j,1,length(Coins));

Form the generating function.
(%i6) FD:1$
(%i7) for c in Coins do FD:FD/(1-c[1]*x^c[2])$
(%i8) display(FD);

(%i9) FT:taylor(FD,x,0,Number_of_Terms)$
Taylor series expansion of the generating function, e.g.,
(%i10) taylor(FD,x,0,11);

(%i11) C(n):=expand(coeff(taylor(FD,x,0,n),x,n))$
Grab the n-th coefficient, e.g.,
(%i12) display(C(10));

Create list of terms in reverse order
(%i13) terms(lst):=reverse(maplist(lambda([item],item),lst))$
(%i14) trms:terms((C(10)));

Grab the power of each Coins
(%i15) pwrs(t):=makelist(hipow(t,Coins[l][1]),l,1,length(Coins))$
(%i16) makelist(pwrs(trms[i]),i,1,length(trms));

(%i17) asum(lst):=block(sout:"",for k:1 thru length(Coins) do if lst[k]>0 then sout:sconcat(sout,printf(false,fmts[k],lst[k])),return(sout))$
(%i18) asum([1,0,2,10]);

(%i19) for j:Number_of_Terms step -5 thru Number_of_Terms do
(scoins:[],
tmp:terms(C(j)),
print("There are ",length(tmp)," ways to make change for ",j," cents, namely: "),
for i:1 thru length(tmp) do (
tmp2:pwrs(tmp[i]),
push([apply("+",tmp2),asum(tmp2)],scoins)
),
scoins:sort(scoins),
for s in scoins do print(s[2],"")
);

Created with wxMaxima.

hcard - Dave England

David E. England

Marketing Intelligence Agency, Inc.

dengland@mia6.com

107B Clinton Ave

Huntsville, AL 38450

This hCard created with the hCard creator.

Friday, January 4, 2013

Shooting Dice

(%i1) powerdisp:true$

Shooting Dice and Generating Functions

A die has six sides with pips. Thus, the generating function is:

(%i2) f:sum(x^j,j,1,6);

Although not explicitly written, each term has a coefficient of 1. Hence, there is only one way to shoot the numbers 1,2,3,4,5 and 6.

Craps (two dice)

(%i3) expand(f^2);

The above says there is 1 way to shoot a two (snake eyes), namely 2=1+1.
There are two ways to shoot a 3 (3=1+2=2+1).
There are 3 ways to shoot a four, namely 4=1+3=2+2=3+1.
...

(%i4) fg:sum(a(i)*x^i,i,1,6);