"Mathematica" Cheat Sheet (Page 2 of 2) in pdf

Linear Algebra...

Page 2

Create a 2x2 matrix (we’re using symbols, but

Work with (x,y) data points from an external file.

In[1]:= w={{a,b},{c,d}}

In[3]:=!!mydata.dat

you could equally easily use numeric values)

!!mydata.dat shows us the contents of the file.

Out[1]= {{a, b}, {c, d}}

4.1 10.7

Read in pairs of numbers from that file, storing

[etc]

Use a dot product to apply that matrix of

In[2]:= w.{x,y}=={k1,k2}

the list of values by the name newvals. Plot the

In[4]:= newvals=ReadList[ \

coefficients to two variables to form a system

Out[2]= {a x + b y, c x + d y} ==

dataset. Fit a line to the points & plot that.

"mydata.dat",{Number,Number}]

of two equations with constants {k1, k2}

{k1, k2}

Finally, overlay both and save as a gif

Out[4]= {{4.1,10.7},[etc]}

In[5]:= plot1=ListPlot[newvals]

Mathematica can easily do most standard

In[3]:= Transpose[w]//MatrixForm

Out[5]= -Graphics- [not shown]

linear algebra operations, for example, we

Out[3]//MatrixForm= a

In[6]:= Fit[newvals,{1,x},{x}]

can easily transpose matrix w...

Out[6]= 5.14286 + 9.96429 x

Or compute the inverse of a 2x2 numeric

In[7]:= plot2=Plot[%,{x,1,8}]

In[4]:=Inverse[{{1,-1},{2,2}}]

Out[7]= -Graphics- [not shown]

matrix...

In[8]:= Show[plot1,plot2]

Out[4]={{-, -},{-(-), -}}

Out[8]= -Graphics-

In[9]:= Display["b.gif",%,"GIF"]

Or compute the determinant of a 3x3

In[5]:= Det[{{a,b,c},{d,e,f},\

Out[9]= -Graphics-

symbolic matrix...

{g,h,i}}]

Out[5]= -(c e g) + b f g + c d h

Mathematica As A Programming Language...

- a f h - b d i + a e i

If Mathematica doesn’t have precisely what you

(* Approach No. 1 *)

In addition to entering matrices on an element

In[6]:= Table[If[EvenQ[i]||EvenQ[j]\

need (or what it has is overkill), you can always

w=Join[Table[0,{7}],Table[5,{7}],\

by element basis, Mathematica will also let us

,1,0],{i,3},{j,3}]//MatrixForm

use Mathematica as a programming language

Table[10,{4}],{25}];

construct matrices using rules, such as this

Out[6]= 0

and write your own code. For example, assume

<<DiscreteMath`Combinatorica`

example that sets elements of a 3x3 matrix to

you have a pile of 5, 10 and 25 pound weights.

x=Union[KSubsets[w,7]];

be 1 if the column or row is an even number.

Select[x,(Plus@@##)<=45&]\

Using no more than 7 of them in any instance,

//TableForm

how many combinations can you form that will

Plotting in Mathematica...

Print["\n ",Length[%]," soln’s"]

total no more than 45 pounds?

Plot a function over an interval. If connecting

In[1]:= Plot[x^2,{x,-5,5}]

(* Approach No. 2 *)

from a Unix workstation or an X terminal, your

We can solve that problem using Mathematica’s

Out[1]= -Graphics-

solns=0;

graph will be shown in a new window; we also

Combinatorica package, or we can just write a

In[2]:= Display["a.gif",%,"GIF"]

Do[If[((25i+10j+5k<=45)&&\

show saving graphic output in gif format.

little program to solve that problem directly by

Out[2]= -Graphics-

(i+j+k<=7)),\

looping through a three way nested do loop,

solns++, Null],\

Note: besides GIF format, you can also use

using an if statement to tally only solutions

{i,0,1},{j,0,5},{k,0,7}];

the Display function to save Mathematica

that meet the specified restriction.

Print["\n",solns," soln’s"]

graphics in PDF, EPS, PCL, PBM and

other formats.

Mathematica on other platforms...

UO has a site license for Mathematica covering

For more information, please see

its installation on University owned PC’s, Macs,

and Unix systems.

More Information About Mathematica...

The Mathematica Book, 4th Ed., by Stephen

"Mathematica" Cheat Sheet Page 2

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