Ronan

1042 Reputation

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12 years, 36 days
East Grinstead, United Kingdom

MaplePrimes Activity


These are questions asked by Ronan

I have 5 procedures saved in my library. Say Proc1, Proc2, Proc3, Proc4 and Proc5. They all work ok.

Proc5 calls Proc4 which calls Proc3 which calls Proc2 which calls Proc1. That is fine if I read them all in to the dodument.

Is it ok ok to put read commands in procedures 5..2 so I don't have to manually load them all myself into a new document or is there a better way to do this. These procedures are not part of a package.
I hace set 

currentdir();
      "C:\Users\Ronan\Documents\maple\Alibrary\Procedures"

which is where the procedures are stored. If I just load Proc5 it doesn't find the other procedures

I have a matrix and generate difference tables from it's diagonals. Works fine. Then I make a polynomial from the first row of the difference table. I have three polynomials. They are all acting inert, just will not evaluate.

I cannot see what the problem is.
 

restart

interface(rtablesize = 12)

[10, 10]

i) Recurrence relation

 

"Recurrence Relation for next column. . The matrix starts at 1,1 not 0,0 A(i,j)=A(i-1,j-1)*(j-2)+A(i,j-1)"
``

NULL``

Msize := 12

A := Matrix(Msize)

A[1, 1] := 1

1

for i from 2 to Msize do for j from i to Msize do A[i, j] := A[i, j-1]*(j-2)+A[i-1, j-1] end do end do

A

Matrix(%id = 36893489695842121836)

``

``

viia)  General formula for diagonals:-

Select diagonal  & Difference Table procedures

 

diag := proc (M::Matrix, dg::posint) local i, rd, c, dt; rd := LinearAlgebra:-RowDimension(M); dt := Matrix(rd, rd); for i from dg to rd do dt[1+i-dg, 1] := M[1+i-dg, i] end do; return dt end proc

proc (M::Matrix, dg::posint) local i, rd, c, dt; rd := LinearAlgebra:-RowDimension(M); dt := Matrix(rd, rd); for i from dg to rd do dt[1+i-dg, 1] := M[1+i-dg, i] end do; return dt end proc

diag(A, 5)

Matrix(%id = 36893489695866397388)

diftab := proc (M::Matrix) local i, j, cl, rd; rd := LinearAlgebra:-RowDimension(M); for i from rd by -1 to 1 do if M[i, 1] = 0 then rd := rd-1 else break end if end do; cl := rd; for i from 2 to cl do for j to rd-i do M[j, i] := M[j+1, i-1]-M[j, i-1] end do end do; print(M); return M end proc

proc (M::Matrix) local i, j, cl, rd; rd := LinearAlgebra:-RowDimension(M); for i from rd by -1 to 1 do if M[i, 1] = 0 then rd := rd-1 else break end if end do; cl := rd; for i from 2 to cl do for j to rd-i do M[j, i] := M[j+1, i-1]-M[j, i-1] end do end do; print(M); return M end proc

diftab(diag(A, 4))

Matrix(%id = 36893489695866348116)

gnrpoly := proc (M::Matrix) local i, p, rd, n; rd := LinearAlgebra:-RowDimension(M); for i from rd by -1 to 1 do if M[1, i] = 0 then rd := rd-1 else break end if end do; p := 0; for i from 0 to rd-1 do p := p+M[1, i+1]*binomial(n, i) end do; return p end proc

proc (M::Matrix) local i, p, rd, n; rd := LinearAlgebra:-RowDimension(M); for i from rd by -1 to 1 do if M[1, i] = 0 then rd := rd-1 else break end if end do; p := 0; for i from 0 to rd-1 do p := p+M[1, i+1]*binomial(n, i) end do; return p end proc

"for i from 0 to 3 do print("Diagonal  ",i);   eqn:=gnrpoly(diftab(diag(A,i+1)));    cat(poly,i):=unapply(factor(expand(eqn)),n);    print("--------------------------------------------------------------");  end do"

"--------------------------------------------------------------"

NULL

``

``

The equations do not evaluate. They are acting inert

poly1(n)

(1/2)*n*(1+n)

poly1(2)

(1/2)*n*(1+n)

poly2(n)

(1/24)*n*(3*n+5)*(n+2)*(n+1)

poly2(3)

(1/24)*n*(3*n+5)*(n+2)*(n+1)

poly3(n)

(1/48)*n*(n+1)*(n+3)^2*(n+2)^2

poly3(-1)

(1/48)*n*(n+1)*(n+3)^2*(n+2)^2

eqn

6*n+38*binomial(n, 2)+93*binomial(n, 3)+111*binomial(n, 4)+65*binomial(n, 5)+15*binomial(n, 6)

value(eval(eqn, n = 4))

6*n+38*binomial(n, 2)+93*binomial(n, 3)+111*binomial(n, 4)+65*binomial(n, 5)+15*binomial(n, 6)

eqn1 := expand(eqn)

(3/4)*n+2*n^2+(97/48)*n^3+(47/48)*n^4+(11/48)*n^5+(1/48)*n^6

eval(eqn1, [n = 4])

(3/4)*n+2*n^2+(97/48)*n^3+(47/48)*n^4+(11/48)*n^5+(1/48)*n^6

NULL


 

Download Q_10-10-22_gentrate_eqn.mw

I have a whole lot of conditions to test on the signum of answers. This gets difficult to read so I am wondering could something like the following be done?

a, b, c, d := 1, -1, 1, -1;
if a, b, c, d = 1, 0, -1, -1 then
    print("foo");
end if;

The above obviously doesn't work. The reason I would like to do this is it would be simple to read the patterns of 1's and 0's.

Any ideas?

I was experimenting on and found coeff and degrees  do not work with algebraic type powers. So I set aboud dismanteling  a example polynomial. I certainly went around the houses doing this. I wanted to put the powers and coefficinets of x in an array.

I sure there must be a simpler way.

restart

NULLNULL

r := proc (x) options operator, arrow; a[0]+a[1]*x-a[2]*x^2+a[8]*x^(8/5)-a[h]*x^h+k*x^(-b/a) end proc

proc (x) options operator, arrow; a[0]+a[1]*x-a[2]*x^2+a[8]*x^(8/5)-a[h]*x^h+k*x^(-b/a) end proc

mnmls := [op(r(x))]

[a[0], a[1]*x, -a[2]*x^2, a[8]*x^(8/5), -a[h]*x^h, k*x^(-b/a)]

A := Array(1 .. 2, 1 .. nops(mnmls))

Array(%id = 36893489621187187044)

mnmls, x0 := selectremove(has, mnmls, x)

[a[1]*x, -a[2]*x^2, a[8]*x^(8/5), -a[h]*x^h, k*x^(-b/a)], [a[0]]

NULL

A[2, 1] := op(x0)

a[0]

coeff(r(x), x, 2)

Error, unable to compute coeff

coeffs(r(x), x)

Error, invalid arguments to coeffs

degree(mnmls[1], x)

1

degree(mnmls[4], x)

FAIL

degree(mnmls[5], x)

FAIL

indets(r(x))

{a, b, h, k, x, a[0], a[1], a[2], a[8], a[h], x^h, x^(-b/a), x^(8/5)}

bits := [seq([op(mnmls[i])], i = 1 .. nops(mnmls))]

[[a[1], x], [-1, a[2], x^2], [a[8], x^(8/5)], [-1, a[h], x^h], [k, x^(-b/a)]]

deeperbits := [seq(op(op(bits)[i]), i = 1 .. nops(bits))]

[a[1], x, -1, a[2], x^2, a[8], x^(8/5), -1, a[h], x^h, k, x^(-b/a)]

varpwrs, cofsl := selectremove(has, deeperbits, x)

[x, x^2, x^(8/5), x^h, x^(-b/a)], [a[1], -1, a[2], a[8], -1, a[h], k]

is(nops(vars) = nops(cofsl))

false

cofs := convert(cofsl, Array)

Array(%id = 36893489621220545228)

for i to numelems(cofs)-1 do if cofs[i] = -1 then cofs[i] := 0; cofs[i+1] := -cofs[i+1]; i = i+2 end if end do; cofs; cofs := remove[flatten](has, cofs, 0)

Array(%id = 36893489621220530764)

cofs

Array(%id = 36893489621220530764)

is(nops(vars) = numelems(cofs))

false

NULL

pwrs := `assuming`([simplify(`~`[log[x]](varpwrs))], [x > 0, a::'real', b::'real', h::'real'])

[1, 2, 8/5, h, -b/a]

A

Array(%id = 36893489621187187044)

for i to nops(mnmls) do A[1, i+1] := pwrs[i]; A[2, i+1] := cofs[i] end do; A

Array(%id = 36893489621187187044)

 

NULL


Download Q_11-9-22_monomial_powers_and_coeffs.mw

How should I handle the limit in the integration answe?. I don't see why it is necessary.

restart

_local(gamma)

p := `assuming`([proc (alpha) options operator, arrow; alpha^m end proc], [m]); LinearAlgebra:-Transpose(integer)

integer

q := `assuming`([proc (alpha) options operator, arrow; alpha^n end proc], [n]); LinearAlgebra:-Transpose(integer)

integer

Sa := eval((1/2)*(int(simplify(p(alpha)*(D(q))(alpha)), alpha = 0 .. 1)))

-(1/2)*(limit(alpha^(m+n), alpha = 0, right)-1)*n/(m+n)

s1 := eval((1/2)*(int(simplify(p(alpha)*(D(q))(alpha)), alpha)))

(1/2)*alpha^(m+n)*n/(m+n)

eval(s1, alpha = 1)-(eval(s1, alpha = 0))

(1/2)*n/(m+n)

NULL

Download Q_9-9-22_limit_in_integral.mw

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