DJJerome1976

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These are questions asked by DJJerome1976

I would like to define a graph in terms of its incidence matrix. It's very easy to go from the graph to the incidence matrix, but is it possible to go the other way? Here is the incidence matrix of interest:

M:=Matrix([[1,1,0,1,0,0,0],[0,1,1,0,1,0,0],[1,0,1,0,0,1,1],[0,0,0,1,1,1,0],[0,0,0,0,0,0,1]]):

I am using the ColumnSpace command (from the LinearAlgebra package) to generate a basis for the column space of a matrix. Is there any way to "force" the command to express the basis in terms of columns of A and not in the canonical form with leading 1's?

For example, for

A:=Matrix([[-3,6,-1,1-7],[1,-2,2,3,-1],[2,-4,5,8,-4]]):

I would like to obtain the following basis for the column space:

{[-3,1,2],[-1,2,5]}

 

I've been playing around with the Basis command in the LinearAlgebra package. It's very easy to get a Basis for any subspace of R^n. However, if you're dealing with finite-dimensional polynomial or matrix spaces, the Basis command doesn't work. Due to some basic isomorphism theorems, we can always associate these vectors with those in R^n. I was wondering if there is a way to get Maple, via the Basis command, to handle "other types" of vectors. For example, how might one get Maple to return a basis of {x^2+x+4,x+3,2x^2-x-5,5x^2+x-7} in P_2, the space of polynomials of degree less than or equal to 2, or, a basis for {[[2,3],[5,6]],[[3,2],[0,1]],[[1,1],[0,5]]} in M_{2,2}, the space of 2 x 2 matrices, without converting to R^n?

I'm trying to use the CriticalPoints command from the Student[Calculus1] package to determine the critical points of f(x) = x^2 * ln(x).

 

with(Student[Calculus1]):

f := proc (x) options operator, arrow; x^2*ln(x) end proc:

`assuming`([CriticalPoints(f(x))], [x > 0])

[0, exp(-1/2)]

(1)

``

My issue is this. A critical point is defined as a value of x in the domain of f(x) where either f'(x)=0 or f'(x) does not exist. Clearly x=0 is not in the domain of f(x) = x^2*ln(x). How may I "trick" Maple into returning only the value exp(-1/2)?  As seen above, my attempt to use the assuming command proved futile.

More troubling, however, is whether or not the CriticalPoints command is using the correct definition to compute critical points. Can anyone shed some light on this?

 

Download critpts.mw

I am trying to illustrate the effects of using finite-precision arithmetic on solving certain linear systems using elementary row operations. I am able to set Digits to the desired level and use the RowOperation command for each individual row operation. I would like to be use say, ReducedRowEchelonForm or LinearSolve with the desired level of precision. Is there anyway to force Maple to use whatever number of digits when using commands like ReducedRowEchelonForm or LinearSolve?...

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