Advanced Search

Harry Garst

224 Reputation

5 Badges

17 years, 210 days
Contact Harry Garst

MaplePrimes Activity


These are questions asked by Harry Garst

Statistical procedures?...

Harry Garst 224 Maple
statistics correlation
March 19 2019
1 4

For a statistical course I will give next year, I would like to demonstrate the calculation of tetrachoric and polychoric correlations. Furthermore, it would be nice to show the students how the expectation-maximization algorithm works.

Has anyone already programmed this in Maple?

best regards,

Harry

 

combinations on subsets...

Harry Garst 224 Maple
combinatorics
February 19 2019
2 1

This works fine, but I was wondering whether it could be done in a simple way.
 

``

> 

restart; kernelopts(version); interface(version)

`Maple 2018.2, X86 64 WINDOWS, Nov 16 2018, Build ID 1362973`

  

`Standard Worksheet Interface, Maple 2018.2, Windows 10, November 16 2018 Build ID 1362973`

 (1)
> 

kollect := proc (p::`+`, y) local x; subs(x = y, collect(subs(y = x, p), x)) end proc
> 

kollect(kollect(kollect(kollect(expand(add(mul(k)*add(k), `in`(k, combinat:-choose([i1, i2, i3, i4], 3)))), i1^2), i2^2), i3^2), i4^2)

(i1*i2+i1*i3+i2*i3)*i4^2+(i1*i2+i1*i4+i2*i4)*i3^2+(i1*i3+i1*i4+i3*i4)*i2^2+(i2*i3+i2*i4+i3*i4)*i1^2

 (2)

``


thanks in advance,

Harry

Download nested_comb.mw

hidden characters in worksheet...

Harry Garst 224 Maple 2018
2dmath hidden
January 06 2019
2 2

Two lines that look the same, produce different results. The first lines gives an error message, but the next line that looks the same, does not.

copying and pasting both lines in Notepad reveals the difference:

Determinant*(R1 . B+R2 . B+R3 . B+R4 . A)

Determinant(R1 . B+R2 . B+R3 . B+R4 . A)

It seems that there is a hidden character (the asterisk) in the first line that produces the error.

In the worksheet itself you cannot see the asterisk, but using the arrow keys you can notice that there is another character.

It's hard to debug your code if there are hidden characters.

``

> 

restart; with(LinearAlgebra)
> 

kernelopts(version)*interface(version)

`Maple 2018.2, X86 64 WINDOWS, Nov 16 2018, Build ID 1362973`*`Standard Worksheet Interface, Maple 2018.2, Windows 10, November 16 2018 Build ID 1362973`

 (1)
> 

A := Matrix(4, 4, symbol = a, shape = symmetric)
> 

B := Matrix(4, 4, symbol = b, shape = symmetric)
> 

R1 := Matrix(4, 4); R1[1, 1] := 1; R2 := Matrix(4, 4); R2[2, 2] := 1; R3 := Matrix(4, 4); R3[3, 3] := 1; R4 := Matrix(4, 4); R4[4, 4] := 1
> 

Determinant*(R1.B+R2.B+R3.B+R4.A)

Error, (in LinearAlgebra:-Multiply) invalid arguments

  
> 

Determinant(R1.B+R2.B+R3.B+R4.A)

-a[1, 4]*b[1, 2]*b[2, 3]*b[3, 4]+a[1, 4]*b[1, 2]*b[2, 4]*b[3, 3]+a[1, 4]*b[1, 3]*b[2, 2]*b[3, 4]-a[1, 4]*b[1, 3]*b[2, 3]*b[2, 4]-a[1, 4]*b[1, 4]*b[2, 2]*b[3, 3]+a[1, 4]*b[1, 4]*b[2, 3]^2+a[2, 4]*b[1, 1]*b[2, 3]*b[3, 4]-a[2, 4]*b[1, 1]*b[2, 4]*b[3, 3]-a[2, 4]*b[1, 2]*b[1, 3]*b[3, 4]+a[2, 4]*b[1, 2]*b[1, 4]*b[3, 3]+a[2, 4]*b[1, 3]^2*b[2, 4]-a[2, 4]*b[1, 3]*b[1, 4]*b[2, 3]-a[3, 4]*b[1, 1]*b[2, 2]*b[3, 4]+a[3, 4]*b[1, 1]*b[2, 3]*b[2, 4]+a[3, 4]*b[1, 2]^2*b[3, 4]-a[3, 4]*b[1, 2]*b[1, 3]*b[2, 4]-a[3, 4]*b[1, 2]*b[1, 4]*b[2, 3]+a[3, 4]*b[1, 3]*b[1, 4]*b[2, 2]+a[4, 4]*b[1, 1]*b[2, 2]*b[3, 3]-a[4, 4]*b[1, 1]*b[2, 3]^2-a[4, 4]*b[1, 2]^2*b[3, 3]+2*a[4, 4]*b[1, 2]*b[1, 3]*b[2, 3]-a[4, 4]*b[1, 3]^2*b[2, 2]

 (2)

``


 

Download weird.mw

split a polynomial based on leading inte...

Harry Garst 224 Maple
polynomial lcoeff
November 25 2018
2 5

I could not find a command that splits a polynomial in parts based on leading integer coefficients, so I wrote a procedure. It works well, but I still wonder if there is no simpler way of doing this?
My aim is to investigate whether there is some way of factoring this and other polynomials.
 

kind regards,
Harry Garst
 

``

> 

restart; with(ListTools); with(LinearAlgebra)
> 

p := 2*x^3*y+2*x^3*z+4*x^2*y^2+24*x^2*y*z+4*x^2*z^2+2*x*y^3+24*x*y^2*z+24*x*y*z^2+2*x*z^3+2*y^3*z+4*y^2*z^2+2*y*z^3-40*x^2*y-40*x^2*z-40*x*y^2-40*x*z^2-40*y^2*z-40*y*z^2+108*x*y+108*x*z+108*y*z-9*x-9*y-9*z+36

2*x^3*y+2*x^3*z+4*x^2*y^2+24*x^2*y*z+4*x^2*z^2+2*x*y^3+24*x*y^2*z+24*x*y*z^2+2*x*z^3+2*y^3*z+4*y^2*z^2+2*y*z^3-40*x^2*y-40*x^2*z-40*x*y^2-40*x*z^2-40*y^2*z-40*y*z^2+108*x*y+108*x*z+108*y*z-9*x-9*y-9*z+36

 (1)
> 

p1 := 2*x^3*y+2*x^3*z+2*x*y^3+2*x*z^3+2*y^3*z+2*y*z^3

2*x^3*y+2*x^3*z+2*x*y^3+2*x*z^3+2*y^3*z+2*y*z^3

 (2)
> 

p2 := 24*x^2*y*z+24*x*y^2*z+24*x*y*z^2

24*x^2*y*z+24*x*y^2*z+24*x*y*z^2

 (3)
> 

p3 := 4*x^2*y^2+4*x^2*z^2+4*y^2*z^2

4*x^2*y^2+4*x^2*z^2+4*y^2*z^2

 (4)
> 

p4 := -40*x^2*y-40*x^2*z-40*x*y^2-40*x*z^2-40*y^2*z-40*y*z^2

-40*x^2*y-40*x^2*z-40*x*y^2-40*x*z^2-40*y^2*z-40*y*z^2

 (5)
> 

p5 := 108*x*y+108*x*z+108*y*z

108*x*y+108*x*z+108*y*z

 (6)
> 

p6 := -9*x-9*y-9*z

-9*x-9*y-9*z

 (7)
> 

p7 := 36

36

 (8)
> 

simplify(p-p1-p2-p3-p4-p5-p6-p7)

0

 (9)
> 

Knip := proc (p) local g, h, i, j, N, X, Q; g := sort(ListTools:-MakeUnique([seq(lcoeff([op(p)][j]), j = 1 .. nops([op(p)]))])); h := 0; N := Matrix(nops([op(p)]), 1); X := Matrix(nops([op(g)]), 1); Q := convert([op(p)], Matrix); for j in g do h := h+1; N[h, 1] := convert([seq(ifelse(has(lcoeff([op(p)][i]), j), 1, 0), i = 1 .. nops([op(p)]))], Matrix); X[h, 1] := LinearAlgebra:-Trace(Q.N[h, 1]^%T) end do; return X end proc

proc (p) local g, h, i, j, N, X, Q; g := sort(ListTools:-MakeUnique([seq(lcoeff([op(p)][j]), j = 1 .. nops([op(p)]))])); h := 0; N := Matrix(nops([op(p)]), 1); X := Matrix(nops([op(g)]), 1); Q := convert([op(p)], Matrix); for j in g do h := h+1; N[h, 1] := convert([seq(ifelse(has(lcoeff([op(p)][i]), j), 1, 0), i = 1 .. nops([op(p)]))], Matrix); X[h, 1] := LinearAlgebra:-Trace(Typesetting:-delayDotProduct(Q, N[h, 1]^%T)) end do; return X end proc

 (10)
> 

Knip(p)

Matrix(%id = 18446747088530918086)

 (11)
> 

simplify(p-Trace(Matrix(1, 7, 1).Knip(p)))

0

 (12)

``


 

Download knip.mw

 

Kronecker product symbol ⊗...

Harry Garst 224 Maple 2018
product kronecker
November 10 2018
2 4

Is het possible to use the circletimes symbol  ⊗ from Maple's Operators palette as an alias for KroneckerProduct(A,B)?

Instead of KroneckerProduct(A,B) :  A ⊗ B

An abbriviation would be convenient for the following expression:

A ⊗ B ⊗ C ⊗ D ⊗ E ⊗ F ⊗ G

 

I tried alias, macro, applyrule but was not successfull.

Is is possible or should I add it to the Maple 2019 wishlist?

Harry

 

1 2 3 4 5 6 7 Page 3 of 10