Mathematica Help for Negative Numbers and Functional Programming

[mzu]

Hi,

Quick question about Mathematica. As far as I know, squaring a negative number should give a positive result, right ? Let's say -2² should be 4 or is that wrong ? When doing this in Mathematica I get -4 as a result. Shouldn't it be 4 ?

Any help is greatly appreciated.

Also, does anybody know a good tutorial on functional programming in Mathematica ?

Thanks,
Michael

 

[mzu]

OK I found it myself. Instead of just writing -2^2, I have to write (-2)^2 and this gives the correct result.
However, the question about a functional programming tutorial still stands.

Michael

 

[ewant]

Hi,

Personally I found the help/guides in Mathematica to be fairly sufficient to get me started. There is also lots of tutorials and seminars available online at wolfram.com:

http://www.wolfram.com/services/education/seminars/
http://demonstrations.wolfram.com/
http://www.wolfram.com/support/learn/
http://www.wolfram.com/mathematica/resources/

University websites tend also to be a good resource for Mathematica guides, often the computing support provide some help for beginners. A quick google search brings up one at:

http://www.cs.umd.edu/~atif/Teaching/Spring2007/Lectures/FunctionalProgramming.pdf

Or, if willing to spend some money then there are quite a few books available for Mathematica:

http://www.wolfram.com/books/

I have to say that I started many years ago with just the installed documentation and picked it up as I went along. It hasn't done me too much harm!

Good luck :-),

Ewan

 

[mzu]

Hi,

Thanks for the info. I've been looking around on Wolframs website and looked at a few examples. I just got the book "An Introduction to Programming with Mathematica". This one seems quite good in explaining things.
I've done quite some calculations in Mathematica during the learning process and love it. This software is so powerful and I want to learn a lot more about it.
I've read that it should be possible to program Lego Mindstorms with Mathematica. Is this true ? Does anybody have more info on this ?

Thanks,
Michael

 

[76Ahmad]

Hi all
Im tring to write a program statement using mathematica...
and please i need help.

How can i define P where P is Primenumbers between 2 and m^2.
where m = {1,2,...,200}
and i need to define m also.
please help.

 

[gb7nash]

where m = {1,2,...,200}
and i need to define m also.

Not really sure what you want here. If m is a specific number, use:

Table[Prime[n], {n,m^2}]

If you want m to loop from 1 to 200, then just write a for loop and call Table[Prime[n], {n,m^2}] each time you cycle through.

 

[76Ahmad]

Thank you for your help
what I'm trying to do is
I have this polynomial (1+x)^m where m is the set {2,3,...200}
and I want to Expand this polynomial for every m.
during that for every m expand reslt need to be Mod p
where p is Primenumbers between 2 and m^2

So its like a loop for example
if m =10
P will be the set {2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97}

and the expand of (1+x)^10 is

1+10x+45x^2+120x^3+210x^4+252x^5+210x^6+120x^7+45x^8+10x^9+x^10

and for that answer the coffeicent should be Mod p from 2 to 97 and give all ressult
......
so for that i need first to define two parameters m and p
please help
and thanks again

 

[gb7nash]

Thank you for your help
what I'm trying to do is
I have this polynomial (1+x)^m where m is the set {2,3,...200}
and I want to Expand this polynomial for every m.
during that for every m expand reslt need to be Mod p
where p is Primenumbers between 2 and m^2

So its like a loop for example
if m =10
P will be the set {2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97}

and the expand of (1+x)^10 is

1+10x+45x^2+120x^3+210x^4+252x^5+210x^6+120x^7+45x^8+10x^9+x^10

and for that answer the coffeicent should be Mod p from 2 to 97 and give all ressult
......
so for that i need first to define two parameters m and p
please help
and thanks again

Do a nested for loop. Psudocode follows:

for (m = 2; m <= 200; m++)
for (p = 2; p <= m^2; p = next prime)

expand (1+x)^m (mod p)
print result

end
end

I haven't figured out how to tab on here.

 

[76Ahmad]

i try to do it like you said::

For[m = 2, m ≤ 200, m++]
For[p = 2, p ≤ m^2, p = NextPrime]

i think the mathematica could not accept the word... p= NextPrime

then i write
Expand[(1+x)^m]Mod[p]

but i think some thing missing ?

 

[gb7nash]

i try to do it like you said::

For[m = 2, m ≤ 200, m++]
For[p = 2, p ≤ m^2, p = NextPrime]

i think the mathematica could not accept the word... p= NextPrime

then i write
Expand[(1+x)^m]Mod[p]

but i think some thing missing ?

I just gave you psudocode (not actual code, just an idea of what you want to do since I'm no mathematica guru). You want to figure out what the correct syntax is for mathematica.

 

[76Ahmad]

Thanks you are really help me so much...

i try to do loop by writing

Do[Print[Mod[Expand[(1 + x)^m], p]]]

i got good result but still not sure of it

 

[Bill Simpson]

If you have an older version of Mathematica you must include this line, newer versions don't need it:

<<NumberTheory`NumberTheoryFunctions`

Either way then this will calculate your desired result

For[m=2,m≤200,m++,
For[p=2,p≤m^2,p=NextPrime[p],
Print[Mod[Expand[(1+x)^m],p]]
]
]

That will calculate your polynomial mod p.
But I'm not certain whether what you actually want is the coefficients of the polynomial mod p.
If that is what you want then perhaps this will do it.

For[m = 2, m ≤ 200, m++,
For[p = 2, p ≤ m^2, p = NextPrime[p],
Print[Expand[(1 + x)^m] /. Times[n_, v_] -> Times[Mod[n, p], v]
]
]
]

 

[76Ahmad]

Thanks Bill for your help, the last 4 days i was very ill , so sorry for my lait answer.

yes really what I'm looking for is the coefficients of the polynomial (1-x)^m when I must do these steps:

1- define m such that m goes from 2 to 200
2- define p such that p is a prime number goes from 2 to m^2
3- expand (1-x)^m and every expand i need to do PolynomialMod t p from 2 to m^2

for example: (when the program reach to m = 10)

In[1]:= Expand[(1-x)^10]

Out[1]= 1-10x+45x^2-120x^3+210x^4-252x^5+210x^6-120x^7+45x^8-10x^9+x^10

In[2]:= PolynomialMod[%, 2]

Out[2]= 1 + x^2 + x^8 + x^10 ...this is only mod (p = 2) for m = 10
and i also need (p=3,5,7) for the same m = 10

 

[76Ahmad]

after that i need to get all the coefficients that comes with every Mod operation to m=10

the last Coefficient when p=2 are: 1 0 1 0 0 0 0 0 1 0 1
what about p=3,5,7

 

[gb7nash]

Thanks Bill for your help, the last 4 days i was very ill , so sorry for my lait answer.

yes really what I'm looking for is the coefficients of the polynomial (1-x)^m when I must do these steps:

1- define m such that m goes from 2 to 200
2- define p such that p is a prime number goes from 2 to m^2
3- expand (1-x)^m and every expand i need to do PolynomialMod t p from 2 to m^2

for example: (when the program reach to m = 10)

In[1]:= Expand[(1-x)^10]

Out[1]= 1-10x+45x^2-120x^3+210x^4-252x^5+210x^6-120x^7+45x^8-10x^9+x^10

In[2]:= PolynomialMod[%, 2]

Out[2]= 1 + x^2 + x^8 + x^10 ...this is only mod (p = 2) for m = 10
and i also need (p=3,5,7) for the same m = 10

The code Bill Simpson listed above should do all of this.

after that i need to get all the coefficients that comes with every Mod operation to m=10

the last Coefficient when p=2 are: 1 0 1 0 0 0 0 0 1 0 1
what about p=3,5,7

Try CoefficientList: http://reference.wolfram.com/mathematica/ref/CoefficientList.html

 

[Bill Simpson]

If you need the results in some sort of expression you can later use for some other purpose, instead of just printing them, then perhaps this will help you

In[19]:=
maxm=5;
Reap[
For[m=2,m≤maxm,m++,
Map[
Sow[CoefficientList[PolynomialMod[Expand[(1+x)^m],#],x]]&,
Select[Range[2,m^2],PrimeQ]
]
]
][[2,1]]

Out[20]=
{{1,0,1},{1,2,1},{1,1,1,1},{1,0,0,1},{1,3,3,1},{1,3,3,1},{1,0,0,0,1},{1,1,0,1,1},{1,4,1,4,1},{1,4,6,4,1},{1,4,6,4,1},{1,4,6,4,1},{1,1,0,0,1,1},{1,2,1,1,2,1},{1,0,0,0,0,1},{1,5,3,3,5,1},{1,5,10,10,5,1},{1,5,10,10,5,1},{1,5,10,10,5,1},{
1,5,10,10,5,1},{1,5,10,10,5,1}}

Just change the maxm=5 to maxm=200 and wait

If that won't fit in memory or just printing them is enough then perhaps this will be more understandable

maxm = 5;
For[m = 2, m ≤ maxm, m++,
For[p = 2, p ≤ m^2, p++,
If[PrimeQ[p], Print[CoefficientList[PolynomialMod[Expand[(1 + x)^m], p], x]]]
]
]

but I think you should be prepared for a large result of about 305023 items
if I haven't made another mistake.

 

[76Ahmad]

Thanks[Bill_Simpson], Tnaks[gb7nash]
For[ your great help ]

i did run the program and it work 100%
and I'm so happppy

 

[76Ahmad]

One more thing please
during the run process if my laptop hang or shut down

how can i make the mathematica save my work and resume the
process from the point that it stopped from?

 

[Bill Simpson]

See if this will give you information to let you do what you want.

http://www.google.com/search?q=mathematica+dumpsave+restart

Test this carefully before you risk loosing something important.

 

[76Ahmad]

Hi all again, new quistion about how to add the cofficients list?
here is an example:

For[m = 2, m ≤ 4 , m++,
For[p = 2, p ≤ m^2, p++,
If[PrimeQ[p], Print[CoefficientList[PolynomialMod[Expand[(1 - x)^m], p], x]]]]]

{1,0,1}
{1,1,1}

{1,1,1,1}
{1,0,0,2}
{1,2,3,4}
{1,4,3,6}

{1,0,0,0,1}
{1,2,0,2,1}
{1,1,1,1,1}
{1,3,6,3,1}
{1,7,6,7,1}
{1,9,6,9,1}


How to add every grup of cofficients together?
the reuslt should be like that:

{2,1,2}

{4,7,7,13}

{6,22,19,22,6}

please help