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Ronan

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12 years, 313 days
East Grinstead, United Kingdom
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These are questions asked by Ronan

How can an row Vector be extended...

Ronan 1311 Maple 2022
vector row
August 24 2022
1 4

I need to conver 2D points to projective points. Originally I used lists but now need to handle vectors too. To add to that that the projective coordinate for points is now being stated as [1,x,y] instead of [x,y,1]. That is was easy enough to handle for lists.

I have a lot of old worksheets that use the list form [x,y,1] that I want to maintain compatibility with. I only have one procedure I need to convert.
 

Mobposn := 1;
testP := [2, 7];
if Mobposn = 1 then
    [1, op(testP)];
else
    [op(testP), 1];
end if;

I need to do the same for vector definition of the points. The points are defined as row Vectors

A:=<2,7>^%T

to get

Ap:=<1,2,7>^%T

or

Ap:=<2,7,1>^%T

I know coud just do (as these are short vectors)
 

Ap:=<1,A_1,A_2>^%T

or
Ap:=<A_1,A_2,1>^%T

Is there a more general way?

How can an equation be sorted by numeric...

Ronan 1311 Maple 2022
polynomial sort
July 30 2022
2 8

I want to collect up the equation terms by the numerical value of the terms coefficient? Have tried sort collect combine...
So far the best I have come up with is nops(indets(on each term). And put them in seperate lists. This still doesn't quiet do the trick.
I am looking to achieve. Would to happy to have then as seperate lists or equations.

(a_1^5+a_2^5...)+5(a_1^4a_2+a_1^4a_3....)+10(a_1^3a_2^2 ....)+20(  ....   )+......+60(a_1^2a_2a_3a_4+ a_1a_2^2a_3a_4....)


 

restart

pn := (a[1]+a[2]+a[3]+a[4])^5

(a[1]+a[2]+a[3]+a[4])^5

pn1 := expand(pn)

a[1]^5+5*a[1]^4*a[2]+5*a[1]^4*a[3]+5*a[1]^4*a[4]+10*a[1]^3*a[2]^2+20*a[1]^3*a[2]*a[3]+20*a[1]^3*a[2]*a[4]+10*a[1]^3*a[3]^2+20*a[1]^3*a[3]*a[4]+10*a[1]^3*a[4]^2+10*a[1]^2*a[2]^3+30*a[1]^2*a[2]^2*a[3]+30*a[1]^2*a[2]^2*a[4]+30*a[1]^2*a[2]*a[3]^2+60*a[1]^2*a[2]*a[3]*a[4]+30*a[1]^2*a[2]*a[4]^2+10*a[1]^2*a[3]^3+30*a[1]^2*a[3]^2*a[4]+30*a[1]^2*a[3]*a[4]^2+10*a[1]^2*a[4]^3+5*a[1]*a[2]^4+20*a[1]*a[2]^3*a[3]+20*a[1]*a[2]^3*a[4]+30*a[1]*a[2]^2*a[3]^2+60*a[1]*a[2]^2*a[3]*a[4]+30*a[1]*a[2]^2*a[4]^2+20*a[1]*a[2]*a[3]^3+60*a[1]*a[2]*a[3]^2*a[4]+60*a[1]*a[2]*a[3]*a[4]^2+20*a[1]*a[2]*a[4]^3+5*a[1]*a[3]^4+20*a[1]*a[3]^3*a[4]+30*a[1]*a[3]^2*a[4]^2+20*a[1]*a[3]*a[4]^3+5*a[1]*a[4]^4+a[2]^5+5*a[2]^4*a[3]+5*a[2]^4*a[4]+10*a[2]^3*a[3]^2+20*a[2]^3*a[3]*a[4]+10*a[2]^3*a[4]^2+10*a[2]^2*a[3]^3+30*a[2]^2*a[3]^2*a[4]+30*a[2]^2*a[3]*a[4]^2+10*a[2]^2*a[4]^3+5*a[2]*a[3]^4+20*a[2]*a[3]^3*a[4]+30*a[2]*a[3]^2*a[4]^2+20*a[2]*a[3]*a[4]^3+5*a[2]*a[4]^4+a[3]^5+5*a[3]^4*a[4]+10*a[3]^3*a[4]^2+10*a[3]^2*a[4]^3+5*a[3]*a[4]^4+a[4]^5

els := convert({op(pn1)}, list)

[a[1]^5, a[2]^5, a[3]^5, a[4]^5, 5*a[1]*a[2]^4, 5*a[1]*a[3]^4, 5*a[1]*a[4]^4, 10*a[1]^2*a[2]^3, 10*a[1]^2*a[3]^3, 10*a[1]^2*a[4]^3, 10*a[1]^3*a[2]^2, 10*a[1]^3*a[3]^2, 10*a[1]^3*a[4]^2, 5*a[1]^4*a[2], 5*a[1]^4*a[3], 5*a[1]^4*a[4], 5*a[2]*a[3]^4, 5*a[2]*a[4]^4, 10*a[2]^2*a[3]^3, 10*a[2]^2*a[4]^3, 10*a[2]^3*a[3]^2, 10*a[2]^3*a[4]^2, 5*a[2]^4*a[3], 5*a[2]^4*a[4], 5*a[3]*a[4]^4, 10*a[3]^2*a[4]^3, 10*a[3]^3*a[4]^2, 5*a[3]^4*a[4], 20*a[1]*a[2]*a[3]^3, 20*a[1]*a[2]*a[4]^3, 30*a[1]*a[2]^2*a[3]^2, 30*a[1]*a[2]^2*a[4]^2, 20*a[1]*a[2]^3*a[3], 20*a[1]*a[2]^3*a[4], 20*a[1]*a[3]*a[4]^3, 30*a[1]*a[3]^2*a[4]^2, 20*a[1]*a[3]^3*a[4], 30*a[1]^2*a[2]*a[3]^2, 30*a[1]^2*a[2]*a[4]^2, 30*a[1]^2*a[2]^2*a[3], 30*a[1]^2*a[2]^2*a[4], 30*a[1]^2*a[3]*a[4]^2, 30*a[1]^2*a[3]^2*a[4], 20*a[1]^3*a[2]*a[3], 20*a[1]^3*a[2]*a[4], 20*a[1]^3*a[3]*a[4], 20*a[2]*a[3]*a[4]^3, 30*a[2]*a[3]^2*a[4]^2, 20*a[2]*a[3]^3*a[4], 30*a[2]^2*a[3]*a[4]^2, 30*a[2]^2*a[3]^2*a[4], 20*a[2]^3*a[3]*a[4], 60*a[1]*a[2]*a[3]*a[4]^2, 60*a[1]*a[2]*a[3]^2*a[4], 60*a[1]*a[2]^2*a[3]*a[4], 60*a[1]^2*a[2]*a[3]*a[4]]

NULL

add(els[i], i = 1 .. nops(els))

a[1]^5+5*a[1]^4*a[2]+5*a[1]^4*a[3]+5*a[1]^4*a[4]+10*a[1]^3*a[2]^2+20*a[1]^3*a[2]*a[3]+20*a[1]^3*a[2]*a[4]+10*a[1]^3*a[3]^2+20*a[1]^3*a[3]*a[4]+10*a[1]^3*a[4]^2+10*a[1]^2*a[2]^3+30*a[1]^2*a[2]^2*a[3]+30*a[1]^2*a[2]^2*a[4]+30*a[1]^2*a[2]*a[3]^2+60*a[1]^2*a[2]*a[3]*a[4]+30*a[1]^2*a[2]*a[4]^2+10*a[1]^2*a[3]^3+30*a[1]^2*a[3]^2*a[4]+30*a[1]^2*a[3]*a[4]^2+10*a[1]^2*a[4]^3+5*a[1]*a[2]^4+20*a[1]*a[2]^3*a[3]+20*a[1]*a[2]^3*a[4]+30*a[1]*a[2]^2*a[3]^2+60*a[1]*a[2]^2*a[3]*a[4]+30*a[1]*a[2]^2*a[4]^2+20*a[1]*a[2]*a[3]^3+60*a[1]*a[2]*a[3]^2*a[4]+60*a[1]*a[2]*a[3]*a[4]^2+20*a[1]*a[2]*a[4]^3+5*a[1]*a[3]^4+20*a[1]*a[3]^3*a[4]+30*a[1]*a[3]^2*a[4]^2+20*a[1]*a[3]*a[4]^3+5*a[1]*a[4]^4+a[2]^5+5*a[2]^4*a[3]+5*a[2]^4*a[4]+10*a[2]^3*a[3]^2+20*a[2]^3*a[3]*a[4]+10*a[2]^3*a[4]^2+10*a[2]^2*a[3]^3+30*a[2]^2*a[3]^2*a[4]+30*a[2]^2*a[3]*a[4]^2+10*a[2]^2*a[4]^3+5*a[2]*a[3]^4+20*a[2]*a[3]^3*a[4]+30*a[2]*a[3]^2*a[4]^2+20*a[2]*a[3]*a[4]^3+5*a[2]*a[4]^4+a[3]^5+5*a[3]^4*a[4]+10*a[3]^3*a[4]^2+10*a[3]^2*a[4]^3+5*a[3]*a[4]^4+a[4]^5

L1 := []; L2 := []; L3 := []; L4 := []; for i to nops(els) do if nops(indets(els[i])) = 1 then L1 := [op(L1), els[i]] elif nops(indets(els[i])) = 2 then L2 := [op(L2), els[i]] elif nops(indets(els[i])) = 3 then L3 := [op(L3), els[i]] else L4 := [op(L4), els[i]] end if end do; L1; L2; L3; L4

[60*a[1]*a[2]*a[3]*a[4]^2, 60*a[1]*a[2]*a[3]^2*a[4], 60*a[1]*a[2]^2*a[3]*a[4], 60*a[1]^2*a[2]*a[3]*a[4]]

indets(els[7])

{a[1], a[4]}

NULL

indets(els(5))

{}

`~`[op](1 .. -1, L2)

[5, a[1], a[2]^4, 5, a[1], a[3]^4, 5, a[1], a[4]^4, 10, a[1]^2, a[2]^3, 10, a[1]^2, a[3]^3, 10, a[1]^2, a[4]^3, 10, a[1]^3, a[2]^2, 10, a[1]^3, a[3]^2, 10, a[1]^3, a[4]^2, 5, a[1]^4, a[2], 5, a[1]^4, a[3], 5, a[1]^4, a[4], 5, a[2], a[3]^4, 5, a[2], a[4]^4, 10, a[2]^2, a[3]^3, 10, a[2]^2, a[4]^3, 10, a[2]^3, a[3]^2, 10, a[2]^3, a[4]^2, 5, a[2]^4, a[3], 5, a[2]^4, a[4], 5, a[3], a[4]^4, 10, a[3]^2, a[4]^3, 10, a[3]^3, a[4]^2, 5, a[3]^4, a[4]]

NULL

op(2, L2[1])

a[1]

op(3, L2[1])

a[2]^4``

Download 30-7-22_Q_sort_equation_by_numerical_coeffs.mw

How to make Exported equations readable ...

Ronan 1311 Maple 2022
matrix exceltools export
June 10 2022
0 0

I have a set of formulas I saved in a matrix and the exported the matrix to Excel. However when I open the file in Excel the equations are in prefix notation (I think).  That's not exactly human readable friendly.  If I copy and paste straight into excel they are readable.

It there a way to make the Maple export similar?

EDIT:-  I exported as a.csv file because if export as .xlsx    all the equation change into "#NUM!" in the spreadsheed.

restart

NULL

Digits := 5

5

 (1)

interface(displayprecision = 5); interface(rtablesize = 30)

5

 (2)

cosrule := proc (a, b, c, A) options operator, arrow; a^2 = b^2+c^2-2*b*c*cos(A) end proc

proc (a, b, c, A) options operator, arrow; a^2 = b^2+c^2-2*b*c*cos(A) end proc

 (3)

Ang := solve(cosrule(a, b, c, A), A)

Pi-arccos((1/2)*(a^2-b^2-c^2)/(b*c))

 (4)

Formulas := Matrix(20, 4)

 

 

 

 

data := [L[1] = 619.35, L[2] = 891.12, pos = 180, tos = 90, x1 = 600, y1 = -800, z1 = 500, x2 = 900, y2 = -200, z2 = 850, `&Theta;t` = 29.34*Pi*(1/180), `&Theta;p` = 53.98*Pi*(1/180)]
 

 

 

 

i := 3

res0 := `&Delta;Z` = z2-z1; Formulas[i, 1] := lhs(res0); Formulas[i, 2] := rhs(res0)

`&Delta;Z` = z2-z1

 (5)

res0 := eval(res0, data); Formulas[i, 3] := rhs(res0); Formulas; i := i+1

`&Delta;Z` = 350

 (6)

res1 := dt[1] = sqrt(tos^2+L[1]^2); Formulas[i, 1] := lhs(res1); Formulas[i, 2] := rhs(res1); res1 := eval(res1, data); Formulas[i, 3] := rhs(res1); Formulas; i := i+1

dt[1] = 625.85

 (7)

NULL

res2 := d[1] = sqrt(pos^2+tos^2+L[1]^2); Formulas[i, 1] := lhs(res2); Formulas[i, 2] := rhs(res2); res2 := eval(res2, data); Formulas[i, 3] := rhs(res2); Formulas; i := i+1

d[1] = 651.22

 (8)

res3 := dt[2] = sqrt(tos^2+L[2]^2); Formulas[i, 1] := lhs(res3); Formulas[i, 2] := rhs(res3); res3 := eval(res3, data); Formulas[i, 3] := rhs(res3); Formulas; i := i+1

dt[2] = 895.65

 (9)

NULL

res4 := d[2] = sqrt(pos^2+tos^2+L[2]^2); Formulas[i, 1] := lhs(res4); Formulas[i, 2] := rhs(res4); res4 := eval(res4, data); Formulas[i, 3] := rhs(res4); Formulas; i := i+1

d[2] = 913.56

 (10)

NULL

res7 := tau = arctan(tos/L[1]); Formulas[i, 1] := lhs(res7); Formulas[i, 2] := rhs(res7); res7 := eval(res7, data); Formulas[i, 3] := rhs(res7); 180*(eval(rhs(`%%`), data))/Pi; Formulas[i, 4] := %; Formulas; i := i+1

8.2678

 (11)

NULL

res8 := rho = arctan(tos/L[2]); Formulas[i, 1] := lhs(res8); Formulas[i, 2] := rhs(res8); res8 := eval(res8, data); Formulas[i, 3] := rhs(res8); 180*(eval(rhs(`%%`), data))/Pi; Formulas[i, 4] := %; Formulas; i := i+1; data := [op(data), res0, res1, res2, res3, res4, res7, res8]

5.7674

 (12)

NULL

res9 := alpha = `&Theta;t`+tau-rho; Formulas[i, 1] := lhs(res9); Formulas[i, 2] := rhs(res9); res9 := eval(res9, data); Formulas[i, 3] := rhs(res9); 180*(eval(rhs(`%%`), data))/Pi; Formulas[i, 4] := %; Formulas; i := i+1; data := [op(data), res9]

31.840

 (13)

NULL

NULL

NULL

res10 := dt[3] = solve(cosrule(dt[3], dt[2], dt[1], alpha), dt[3])[1]; Formulas[i, 1] := lhs(res10); Formulas[i, 2] := rhs(res10); res10 := eval(res10, data); Formulas[i, 3] := rhs(res10); Formulas; i := i+1; data := [op(data), res10]

dt[3] = 491.45

 (14)

NULL

NULL

res11 := beta = solve(cosrule(dt[1], dt[2], dt[3], beta), beta); Formulas[i, 1] := lhs(res11); Formulas[i, 2] := rhs(res11); res11 := eval(res11, data); Formulas[i, 3] := rhs(res11); 180*(eval(rhs(`%%`), data))/Pi; Formulas[i, 4] := %; Formulas; i := i+1; data := [op(data), res11]

42.215

 (15)

NULL

NULL

NULL

NULL

res12 := Zeta = arccos(`&Delta;Z`/dt[3]); Formulas[i, 1] := lhs(res12); Formulas[i, 2] := rhs(res12); res12 := eval(res12, data); Formulas[i, 3] := rhs(res12); 180*(eval(rhs(`%%`), data))/Pi; Formulas[i, 4] := %; Formulas; i := i+1; data := [op(data), res12]

44.588

 (16)

NULL

NULL

res13 := dt[4] = dt[3]*sin(Zeta); Formulas[i, 1] := lhs(res13); Formulas[i, 2] := rhs(res13); res13 := eval(res13, data); Formulas[i, 3] := rhs(res13); Formulas; i := i+1; data := [op(data), res13]

Matrix(%id = 36893490716944981036)

 (17)

 

``

NULL

``

NULL

currentdir()

"C:\Users\Ronan\Documents\MAPLE\A & Q Maple primes"

 (18)

NULL

with(ExcelTools)

[Export, Import, WorkbookData]

 (19)

NULLExport(Formulas, "Frmls.csv")NULL

Download test_eqn_export.mw

How do I only plot certain points from a...

Ronan 1311 Maple 2021
seq plotting
March 13 2022
3 4

I have a set of points. I only want to plot ones with x and y less that 5 units from [0,0]. I can do it with for do loop. Can't get it to work with seq. Ideally I don't want to create another list.

restart

NULL

points := [[-.4821957161, -.3251957485], [-1.079859775, -1.473869954], [.7429089919, .1649759550], [1.329939269, 0.7259335832e-1], [-.1254930617, .1268183497], [-10.63408888, -2.637665397], [-0.1855663689e-1, .1572001339], [8.963609684, 7.419424024], [.7724026996, .1662719092], [1.278337644, 0.7583092624e-1]]

``

" points2:= [seq('if'(" abs"(points[i,1])<5 and abs(points[i,2])<5, points[i] ,0) ,i=1..10)] "

[[-.4821957161, -.3251957485], [-1.079859775, -1.473869954], [.7429089919, .1649759550], [1.329939269, 0.7259335832e-1], [-.1254930617, .1268183497], [-10.63408888, -2.637665397], [-0.1855663689e-1, .1572001339], `if`(false, [8.963609684, 7.419424024]), [.7724026996, .1662719092], [1.278337644, 0.7583092624e-1]]

 (1)

``

redp := plots:-pointplot(points, colour = red, symbolsize = 4, symbol = solidcircle)

  

plots:-pointplot(points2, colour = red, symbolsize = 4, symbol = solidcircle)

Error, invalid input: `if` expects 3 arguments, but received 2

  

NULL

NULL

Download 13-3-22_remove_points_plotting.mw

Simplify with Side Relations and then ev...

Ronan 1311 Maple 2021
eval simplify
March 06 2022
1 0

I simplified a vector column using side relations. Then I wanted to evaluate using

eval( equation,  [x1=3,  x2=5......})

But side relations uses the reverse order i.e. after evaluation

[3=x1, 5=x2......]

So then the internals of the list need to be swaped tto work with eval.That is easy. I am just wondering is there a neater way to achieve this?

restart

NULL

P1 := Vector(3, {(1) = -(y[1]-y[3])*(y[2]-y[3])*((x[2]^2-x[2]*x[3]+x[3]^2)*x[1]^2-x[2]*x[3]*(x[2]+x[3])*x[1]+x[2]^2*x[3]^2)*(y[1]-y[2]), (2) = -(x[1]-x[3])*(x[2]-x[3])*(x[1]-x[2])*((y[2]^2-y[2]*y[3]+y[3]^2)*y[1]^2-y[2]*y[3]*(y[2]+y[3])*y[1]+y[2]^2*y[3]^2), (3) = ((-y[1]^2*y[2]+(3*y[2]*y[3]-y[3]^2)*y[1]-y[2]^2*y[3])*x[2]+x[3]*(y[1]^2*y[3]+y[2]*(y[2]-3*y[3])*y[1]+y[2]*y[3]^2))*x[1]^2+((y[1]^2*y[3]+y[2]*(y[2]-3*y[3])*y[1]+y[2]*y[3]^2)*x[2]^2+3*x[3]*(y[2]-y[3])*(y[1]-y[3])*(y[1]-y[2])*x[2]-x[3]^2*(y[1]^2*y[2]+(-3*y[2]*y[3]+y[3]^2)*y[1]+y[2]^2*y[3]))*x[1]-x[3]*((y[1]^2*y[2]+(-3*y[2]*y[3]+y[3]^2)*y[1]+y[2]^2*y[3])*x[2]-x[3]*(y[1]^2*y[3]+y[2]*(y[2]-3*y[3])*y[1]+y[2]*y[3]^2))*x[2]})

eqns := {(x[1]-x[2])*(x[2]-x[3])*(x[3]-x[1]) = R, (y[1]-y[2])*(y[2]-y[3])*(y[3]-y[1]) = S, x[1]^2*x[2]^2-x[1]^2*x[2]*x[3]+x[1]^2*x[3]^2-x[1]*x[2]^2*x[3]-x[1]*x[2]*x[3]^2+x[2]^2*x[3]^2 = Y, y[1]^2*y[2]^2-y[1]^2*y[2]*y[3]+y[1]^2*y[3]^2-y[1]*y[2]^2*y[3]-y[1]*y[2]*y[3]^2+y[2]^2*y[3]^2 = X, x[1]^2*x[2]+x[1]^2*x[3]+x[1]*x[2]^2-6*x[1]*x[2]*x[3]+x[1]*x[3]^2+x[2]^2*x[3]+x[2]*x[3]^2 = Z, y[1]^2*y[2]+y[1]^2*y[3]+y[1]*y[2]^2-6*y[1]*y[2]*y[3]+y[1]*y[3]^2+y[2]^2*y[3]+y[2]*y[3]^2 = W}

P1new := simplify(P1, eqns)

Vector[column](%id = 36893490132854572084)

 (1)

values := {x[1] = 3, x[2] = 5, x[3] = 7, y[1] = 2, y[2] = -11, y[3] = 13}

{x[1] = 3, x[2] = 5, x[3] = 7, y[1] = 2, y[2] = -11, y[3] = 13}

 (2)

vals1 := eval(eqns, values)

{-3432 = S, 16 = R, 120 = Z, 316 = Y, 2018 = W, 22753 = X}

 (3)

eval(P1new, vals1)

Vector[column](%id = 36893490132854572084)

 (4)

vals1swap := [seq(rhs(vals1[i]) = lhs(vals1[i]), i = 1 .. nops(vals1))]

[S = -3432, R = 16, Z = 120, Y = 316, W = 2018, X = 22753]

 (5)

eval(P1new, vals1swap)

Vector[column](%id = 36893490132849052116)

 (6)

eval(P1, values)

Vector[column](%id = 36893490132871267020)

 (7)

``

NULL

``

Download Q_6-03-2022_side_rels_and_eval.mw

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