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Alec Mihailovs

Dr. Aleksandrs Mihailovs

4495 Reputation

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20 years, 337 days
Mihailovs, Inc.
Owner, President, and CEO
Tyngsboro, Massachusetts, United States

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Contact Dr. Aleksandrs Mihailovs

I received my Ph.D. from the University of Pennsylvania in 1998 and I have been teaching since then at SUNY Oneonta for 1 year, at Shepherd University for 5 years, at Tennessee Tech for 2 years, at Lane College for 1 year, and this year I taught at the University of Massachusetts Lowell. My research interests include Representation Theory and Combinatorics.

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These are replies submitted by Alec Mihailovs

op or subs...

Alec Mihailovs 4495
October 20 2006
For example, you can execute one of the commands shown below, 
X:=op([1,1,1,2],temp);

                          X := 0.04917230508

X:=subs(ans1,a);

                          X := 0.04917230508

X:=eval(a,ans1);

                          X := 0.04917230508

I was asked to do that...

Alec Mihailovs 4495
October 20 2006
0 0
I was asked to do that. Well, my new picture is taken from my blog, Mandelbrot Set and Newton's Method Basins of Attraction ______________ Alec Mihailovs http://mihailovs.com/Alec/

I was asked to do that...

Alec Mihailovs 4495
October 20 2006
I was asked to do that. Well, my new picture is taken from my blog, Mandelbrot Set and Newton's Method Basins of Attraction ______________ Alec Mihailovs http://mihailovs.com/Alec/

indets and getassumptions...

Alec Mihailovs 4495
October 20 2006
0 0
No, you can't assume that it will be always the 5th entry in indets. One way of dealing with that is to sort the list of variables in indets. Also, getassumptions can be used instead of indets, especially if it is only one assumed variable, 
n:=op([1,1],getassumptions(test));

                               n := n~

coeff(test,n,5);

                                  -5
                                  --
                                  81
Besides, you can before unassigning n, assign it to some other variable; for example, 
m,n:=n,'n';

                            m, n := n~, n

coeff(test,m,5);

                                  -5
                                  --
                                  81

indets and getassumptions...

Alec Mihailovs 4495
October 20 2006
No, you can't assume that it will be always the 5th entry in indets. One way of dealing with that is to sort the list of variables in indets. Also, getassumptions can be used instead of indets, especially if it is only one assumed variable, 
n:=op([1,1],getassumptions(test));

                               n := n~

coeff(test,n,5);

                                  -5
                                  --
                                  81
Besides, you can before unassigning n, assign it to some other variable; for example, 
m,n:=n,'n';

                            m, n := n~, n

coeff(test,m,5);

                                  -5
                                  --
                                  81

Thanks...

Alec Mihailovs 4495
October 19 2006
Will, Thank you for taking care of that. The input textbox is located in the right place now in the IE. ______________ Alec Mihailovs http://mihailovs.com/Alec/

?plot,axis...

Alec Mihailovs 4495
October 18 2006
0 0
It's in the ?plot,axis __________ Alec Mihailovs http://mihailovs.com/Alec/

?plot,axis...

Alec Mihailovs 4495
October 18 2006
It's in the ?plot,axis __________ Alec Mihailovs http://mihailovs.com/Alec/

Getting rid of the gaps...

Alec Mihailovs 4495
October 18 2006
0 0
Combining color changing with location changing works, 
plot(x^2-1,x=-2..2,axis[2]=[color=white,location=low]);
Also, I have an example of manual drawing of axes, tickmarks, and numbers in How to control the thickness of axes and tickmarks? thread.

Getting rid of the gaps...

Alec Mihailovs 4495
October 18 2006
Combining color changing with location changing works, 
plot(x^2-1,x=-2..2,axis[2]=[color=white,location=low]);
Also, I have an example of manual drawing of axes, tickmarks, and numbers in How to control the thickness of axes and tickmarks? thread.

I don't see problems with 0...

Alec Mihailovs 4495
October 18 2006
0 0
I don't see problems with 0. If it should be 0, it will become 0 :) The bivariate polynomials can be used for characteristic polynomial, 
CharPoly:=(a,t)->map(c->modp1(Rem(c,G[extension]),2),
modp2(ConvertIn(LinearAlgebra:-CharacteristicPolynomial(T(a),t),t,x),2));
For example, 
CharPoly(M,t);
                   2              2        2   2        3
             (x + x ) + (1 + x + x ) t + (x ) t  + (1) t
Efficiency is another question. But since at this moment this seems to be the only choice, we can't do the time (and memory) comparision. Random matrices also can be generated quite simple, 
RandMat:=()->Matrix(args,G['random']):
For example, 
RandMat(4);

                [     2         2       2            ]
                [1 + x     x + x       x         x   ]
                [                                    ]
                [     2         2                   2]
                [1 + x     1 + x       1       x + x ]
                [                                    ]
                [                         2         2]
                [1 + x       0       x + x     x + x ]
                [                                    ]
                [                         2          ]
                [1 + x       x       x + x       0   ]

RandMat(2,3);

                          [  0      1    x ]
                          [                ]
                          [               2]
                          [1 + x    x    x ]
Addition, too, 
`&+`:=(a,b)->map(G[ConvertIn],T(a)+T(b)):
For example, 
M &+ Inv(M);

                    [     2                   2  ]
                    [    x           0       x   ]
                    [                            ]
                    [       2                    ]
                    [  1 + x       1 + x    1 + x]
                    [                            ]
                    [         2                  ]
                    [1 + x + x       1        1  ]

I don't see problems with 0...

Alec Mihailovs 4495
October 18 2006
I don't see problems with 0. If it should be 0, it will become 0 :) The bivariate polynomials can be used for characteristic polynomial, 
CharPoly:=(a,t)->map(c->modp1(Rem(c,G[extension]),2),
modp2(ConvertIn(LinearAlgebra:-CharacteristicPolynomial(T(a),t),t,x),2));
For example, 
CharPoly(M,t);
                   2              2        2   2        3
             (x + x ) + (1 + x + x ) t + (x ) t  + (1) t
Efficiency is another question. But since at this moment this seems to be the only choice, we can't do the time (and memory) comparision. Random matrices also can be generated quite simple, 
RandMat:=()->Matrix(args,G['random']):
For example, 
RandMat(4);

                [     2         2       2            ]
                [1 + x     x + x       x         x   ]
                [                                    ]
                [     2         2                   2]
                [1 + x     1 + x       1       x + x ]
                [                                    ]
                [                         2         2]
                [1 + x       0       x + x     x + x ]
                [                                    ]
                [                         2          ]
                [1 + x       x       x + x       0   ]

RandMat(2,3);

                          [  0      1    x ]
                          [                ]
                          [               2]
                          [1 + x    x    x ]
Addition, too, 
`&+`:=(a,b)->map(G[ConvertIn],T(a)+T(b)):
For example, 
M &+ Inv(M);

                    [     2                   2  ]
                    [    x           0       x   ]
                    [                            ]
                    [       2                    ]
                    [  1 + x       1 + x    1 + x]
                    [                            ]
                    [         2                  ]
                    [1 + x + x       1        1  ]

Well...

Alec Mihailovs 4495
October 18 2006
0 0
Well, that is what most people do AFAICT, have Maple, Matlab, and Mathematica installed. Student versions are cheap (for example, Maple goes together with Stewart's Calculus just for $10 additional to the textbook cost.) I am going to change my user picture eventually. Glad you liked it.

Well...

Alec Mihailovs 4495
October 18 2006
Well, that is what most people do AFAICT, have Maple, Matlab, and Mathematica installed. Student versions are cheap (for example, Maple goes together with Stewart's Calculus just for $10 additional to the textbook cost.) I am going to change my user picture eventually. Glad you liked it.

You are welcome!...

Alec Mihailovs 4495
October 18 2006
0 0
You are welcome! I like to read replies like that - and I should say that they are very rare. In most cases I don't get any reply at all (and sometimes replies are quite insulting.)
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