Ronan

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12 years, 104 days
East Grinstead, United Kingdom

MaplePrimes Activity


These are questions asked by Ronan

  I would like to print my help pages to pdf. Is there a way to install A3 paper size. That would help in maintaining the layout as seen on the screen. 

Maybe there is an alternative approach.

Have a list of four projective points. I need to check that they are colinear projectively. If one point is at infinity i.e. 0 in z position I can chech if combination of cross product and dot product is 0.
a)  What is a good way to find if one ot the four has zero in z position?

b) Having found that is there a neat way of piching the next two/three points by making the count wrap automatically. e.g 3  then 4,5,6 i.e. 3,4,1,2

restart

with(LinearAlgebra)

pt := [`<,>`(1, 1, 1), `<,>`(2, 1, 1), `<,>`(3, 1, 0), `<,>`(4, 1, 1)]

pt := [Vector(3, {(1) = 1, (2) = 1, (3) = 1}), Vector(3, {(1) = 2, (2) = 1, (3) = 1}), Vector(3, {(1) = 3, (2) = 1, (3) = 0}), Vector(3, {(1) = 4, (2) = 1, (3) = 1})]

(1)

ListTools(Occurences([anything, anything, 0], pt))

ListTools(Occurences([anything, anything, 0], [Vector(3, {(1) = 1, (2) = 1, (3) = 1}), Vector(3, {(1) = 2, (2) = 1, (3) = 1}), Vector(3, {(1) = 3, (2) = 1, (3) = 0}), Vector(3, {(1) = 4, (2) = 1, (3) = 1})]))

(2)

``

`&x`(pt[1]-pt[3], pt[1]-pt[3]).(pt[4]-pt[3])

0

(3)

NULL

Download 2024-06-18_Q_4_points_projective_colinear.mw

I am using intersectplot  to make projective coordinate plots. Everything intersects the plane z=1. I find the plot quality poor, i.e. dotty dashy lines and circle. This seem to be the best linestyle=solid can do here. gridrefine can't be applied here. 
Any suggestions to improve quality here?
Maybe intersectplot is not the best aprroach here but so far it is all if have figured out.


restart

 

 

with(plottools)

[annulus, arc, arrow, circle, colorbar, cone, cuboid, curve, cutin, cutout, cylinder, disk, dodecahedron, ellipse, ellipticArc, exportplot, extrude, getdata, hemisphere, hexahedron, homothety, hyperbola, icosahedron, importplot, line, octahedron, parallelepiped, pieslice, point, polygon, polygonbyname, prism, project, pyramid, rectangle, reflect, rotate, scale, sector, semitorus, sphere, stellate, tetrahedron, torus, transform, translate, triangulate]

(1)

with(plots)

[animate, animate3d, animatecurve, arrow, changecoords, complexplot, complexplot3d, conformal, conformal3d, contourplot, contourplot3d, coordplot, coordplot3d, densityplot, display, dualaxisplot, fieldplot, fieldplot3d, gradplot, gradplot3d, implicitplot, implicitplot3d, inequal, interactive, interactiveparams, intersectplot, listcontplot, listcontplot3d, listdensityplot, listplot, listplot3d, loglogplot, logplot, matrixplot, multiple, odeplot, pareto, plotcompare, pointplot, pointplot3d, polarplot, polygonplot, polygonplot3d, polyhedra_supported, polyhedraplot, rootlocus, semilogplot, setcolors, setoptions, setoptions3d, shadebetween, spacecurve, sparsematrixplot, surfdata, textplot, textplot3d, tubeplot]

(2)

 

 

DistCircle:=x^2+y^2=1

x^2+y^2 = 1

(3)

pt1:=[1/4,3/4]

[1/4, 3/4]

(4)

pt2:=[7/8,-1/3]

[7/8, -1/3]

(5)

pt3:=[-3/2,3/7]

[-3/2, 3/7]

(6)

pt4:=[3/5,-4/5]

[3/5, -4/5]

(7)

pt5:=[-1/10,-3/2]

[-1/10, -3/2]

(8)

 

L12:=-(13*x)/12 - (5*y)/8 + 71/96; #LnPeqns(pt1,pt2);

-(13/12)*x-(5/8)*y+71/96

(9)

L13:=-(9*x)/28 + (7*y)/4 - 69/56; #LnPeqns(pt1,pt3);

-(9/28)*x+(7/4)*y-69/56

(10)

L23:=(16*x)/21 + (19*y)/8 + 1/8; #LnPeqns(pt2,pt3);

(16/21)*x+(19/8)*y+1/8

(11)

L35:=(27*x)/14 + (7*y)/5 + 321/140; #LnPeqns(pt5,pt3)

(27/14)*x+(7/5)*y+321/140

(12)

nullline:=3/5*x-4/5*y-1

(3/5)*x-(4/5)*y-1

(13)

ptplt:=point([pt1,pt2,pt3,pt4,pt5],color="Green",symbol=solidcircle,symbolsize=10):
txtplt:=textplot([pt4[],typeset("pt4")],align={below,right}):

plt1:=display(txtplt,implicitplot([DistCircle,L12,L13,L23,L35,nullline],x=-2..2,y=-1.5...1.5,color=[red,blue,blue,blue,blue,cyan]),ptplt,scaling=constrained)

 

 

# Projective Geometry Version

DistCirclez:=x^2+y^2-z^2;  #a Cone

 

x^2+y^2-z^2

(14)

pt1p:=[pt1[],1];
pt2p:=[pt2[],1];
pt3p:=[pt3[],1];
pt4p:=[pt4[],1];
pt5p:=[pt5[],1];

[1/4, 3/4, 1]

 

[7/8, -1/3, 1]

 

[-3/2, 3/7, 1]

 

[3/5, -4/5, 1]

 

[-1/10, -3/2, 1]

(15)

 

 

 

L12p:=(13*x)/12 + (5*y)/8 - (71*z)/96;#LnPeqns([pt1p,pt2p,[0,0,0]]);

(13/12)*x+(5/8)*y-(71/96)*z

(16)

L13p:=(13*x)/12 + (5*y)/8 - (71*z)/96;#LnPeqns([pt1p,pt3p,[0,0,0]]);

(13/12)*x+(5/8)*y-(71/96)*z

(17)

L23p:=(9*x)/28 - (7*y)/4 + (69*z)/56;#LnPeqns([pt2p,pt3p,[0,0,0]]);

(9/28)*x-(7/4)*y+(69/56)*z

(18)

L35p:=(27*x)/14 + (7*y)/5 + (321*z)/140;#LnPeqns([pt3p,pt5p,[0,0,0]]);

(27/14)*x+(7/5)*y+(321/140)*z

(19)

L04p:=3/5*x-4/5*y-1*z;

(3/5)*x-(4/5)*y-z

(20)

ptpltp:=point([pt1p,pt2p,pt3p,pt4p,pt5p],symbol=solidsphere, symbolsize=8,color="green"):
intp1:=intersectplot(DistCirclez,z=1,x=-2.5..2.5,y=-2.5..2.5,z=0..1,linestyle=solid):#unit circle at z=1
intp12p:=intersectplot(L12p,z=1,x=-2.5..2.5,y=-2.5..2.5,z=0..1,color=blue):
intp13p:=intersectplot(L13p,z=1,x=-2.5..2.5,y=-2.5..2.5,z=0..1,color=blue):
intp23p:=intersectplot(L23p,z=1,x=-2.5..2.5,y=-2.5..2.5,z=0..1,color=blue):
intp35p:=intersectplot(L35p,z=1,x=-2.5..2.5,y=-2.5..2.5,z=0..1,color=blue):
intp04p:=intersectplot(L04p,z=1,x=-2.5..2.5,y=-2.5..2.5,z=0..1,color=cyan):

 

display(ptpltp,intp1,intp12p,intp13p,intp23p,intp35p,intp04p,scaling=constrained,caption="Projective Co-ords on plane z=1",axes=normal,axis[3]=[tickmarks=[1]])

 

 


Download 2024-06-10_Q_Intersectplot_quality.mw

How do I get the susset that contains unknowns on the rhs of the elements?

restart

 

# I need this subset {a=1/sqrt(2+A), b=6*sqrt(4+N),  d=5*H}

 

C:={a=1/sqrt(2+A),b=6*sqrt(4+N) ,c=sqrt(7),d=5*H,,e=-12,f=-96}

{a = 1/(2+A)^(1/2), b = 6*(4+N)^(1/2), c = 7^(1/2), d = 5*H, e = -12, f = -96}

(1)

selectremove(has,indets(rhs~(C)),C)

{}, {A, H, K, N, 1/(2+A)^(1/2), (4+N)^(1/2)}

(2)

selectremove(has,lhs~(C)=indets(rhs~(C)),C)

() = (), {a, b, c, d, e} = {H, K, N, (4+N)^(1/2)}

(3)
 

 

Download 2024-06-05_Q_Select_Remove_indet_elements.mw

This question is as much an observation of somthing I accidently stumbled across. I was using eval[recurse] to evaluate expressions reduced with LargeExpressions. I found eval['recurse'](eval['recurse']([Expr1 , Expr2] , [Q=.. Q1=.....])[]) to be better than simplify(eval['recurse']([Expr1 , Expr2] , [Q=.. Q1=.....])[]).

I only realised what was happening  when I put the below together. Then I could see the wood from the trees. 

It would be interesting to know why.

restart

 

Pt:=[[(sqrt(2*sqrt(Q[2]) + 2*Q[10])*sqrt(Q[6])*(t^2 + 1)/(sqrt(sqrt(Q[2])/(4*a*c - b^2)^2)*sqrt((2*sqrt(Q[2])*a*c^2*e^2 + 2*sqrt(Q[2])*b^2*c^2*f - 8*sqrt(Q[2])*a^3*c*f + 2*sqrt(Q[2])*a^2*b^2*f + 16*sqrt(Q[2])*a^2*c^2*f + 2*sqrt(Q[2])*a^2*c*d^2 - 4*sqrt(Q[2])*a^2*c*e^2 - 8*sqrt(Q[2])*a*c^3*f - 4*sqrt(Q[2])*a*c^2*d^2 + 2*sqrt(Q[2])*a^3*e^2 + 2*sqrt(Q[2])*c^3*d^2 - 2*sqrt(Q[2])*b*c^2*d*e + 4*sqrt(Q[2])*a*b*c*d*e - 2*sqrt(Q[2])*a^2*b*d*e - 4*sqrt(Q[2])*a*b^2*c*f + sqrt(Q[2])*sqrt(2*sqrt(Q[2]) + 2*Q[10])*sqrt(2*sqrt(Q[2]) - 2*Q[10])*Q[7] - 2*Q[11])*signum((sqrt(Q[2])*sqrt(2*sqrt(Q[2]) + 2*Q[10])*sqrt(2*sqrt(Q[2]) - 2*Q[10])*Q[7] - 8*((a - c)^2*sqrt(Q[2])/4 + Q[5]/4)*Q[8])*Q[4])*Q[4])*(t^2 - 1)) + 2*sqrt(2*sqrt(Q[2]) - 2*Q[10])*t*sqrt(Q[6])*Q[9]/(sqrt(sqrt(Q[2])/(4*a*c - b^2)^2)*sqrt((2*sqrt(Q[2])*a*c^2*e^2 + 2*sqrt(Q[2])*b^2*c^2*f - 8*sqrt(Q[2])*a^3*c*f + 2*sqrt(Q[2])*a^2*b^2*f + 16*sqrt(Q[2])*a^2*c^2*f + 2*sqrt(Q[2])*a^2*c*d^2 - 4*sqrt(Q[2])*a^2*c*e^2 - 8*sqrt(Q[2])*a*c^3*f - 4*sqrt(Q[2])*a*c^2*d^2 + 2*sqrt(Q[2])*a^3*e^2 + 2*sqrt(Q[2])*c^3*d^2 - 2*sqrt(Q[2])*b*c^2*d*e + 4*sqrt(Q[2])*a*b*c*d*e - 2*sqrt(Q[2])*a^2*b*d*e - 4*sqrt(Q[2])*a*b^2*c*f + sqrt(Q[2])*sqrt(2*sqrt(Q[2]) + 2*Q[10])*sqrt(2*sqrt(Q[2]) - 2*Q[10])*Q[7] + 2*Q[11])*signum((sqrt(Q[2])*sqrt(2*sqrt(Q[2]) + 2*Q[10])*sqrt(2*sqrt(Q[2]) - 2*Q[10])*Q[7] + 8*(-(a - c)^2*sqrt(Q[2])/4 + Q[5]/4)*Q[8])*Q[4])*Q[4])*(t^2 - 1)) + b*e - 2*c*d)/(4*a*c - b^2),

 (-sqrt(2*sqrt(Q[2]) - 2*Q[10])*sqrt(Q[6])*(t^2 + 1)*Q[9]/(sqrt(sqrt(Q[2])/(4*a*c - b^2)^2)*sqrt((2*sqrt(Q[2])*a*c^2*e^2 + 2*sqrt(Q[2])*b^2*c^2*f - 8*sqrt(Q[2])*a^3*c*f + 2*sqrt(Q[2])*a^2*b^2*f + 16*sqrt(Q[2])*a^2*c^2*f + 2*sqrt(Q[2])*a^2*c*d^2 - 4*sqrt(Q[2])*a^2*c*e^2 - 8*sqrt(Q[2])*a*c^3*f - 4*sqrt(Q[2])*a*c^2*d^2 + 2*sqrt(Q[2])*a^3*e^2 + 2*sqrt(Q[2])*c^3*d^2 - 2*sqrt(Q[2])*b*c^2*d*e + 4*sqrt(Q[2])*a*b*c*d*e - 2*sqrt(Q[2])*a^2*b*d*e - 4*sqrt(Q[2])*a*b^2*c*f + sqrt(Q[2])*sqrt(2*sqrt(Q[2]) + 2*Q[10])*sqrt(2*sqrt(Q[2]) - 2*Q[10])*Q[7] - 2*Q[11])*signum((sqrt(Q[2])*sqrt(2*sqrt(Q[2]) + 2*Q[10])*sqrt(2*sqrt(Q[2]) - 2*Q[10])*Q[7] - 8*((a - c)^2*sqrt(Q[2])/4 + Q[5]/4)*Q[8])*Q[4])*Q[4])*(t^2 - 1)) + 2*sqrt(2*sqrt(Q[2]) + 2*Q[10])*t*sqrt(Q[6])/(sqrt(sqrt(Q[2])/(4*a*c - b^2)^2)*sqrt((2*sqrt(Q[2])*a*c^2*e^2 + 2*sqrt(Q[2])*b^2*c^2*f - 8*sqrt(Q[2])*a^3*c*f + 2*sqrt(Q[2])*a^2*b^2*f + 16*sqrt(Q[2])*a^2*c^2*f + 2*sqrt(Q[2])*a^2*c*d^2 - 4*sqrt(Q[2])*a^2*c*e^2 - 8*sqrt(Q[2])*a*c^3*f - 4*sqrt(Q[2])*a*c^2*d^2 + 2*sqrt(Q[2])*a^3*e^2 + 2*sqrt(Q[2])*c^3*d^2 - 2*sqrt(Q[2])*b*c^2*d*e + 4*sqrt(Q[2])*a*b*c*d*e - 2*sqrt(Q[2])*a^2*b*d*e - 4*sqrt(Q[2])*a*b^2*c*f + sqrt(Q[2])*sqrt(2*sqrt(Q[2]) + 2*Q[10])*sqrt(2*sqrt(Q[2]) - 2*Q[10])*Q[7] + 2*Q[11])*signum((sqrt(Q[2])*sqrt(2*sqrt(Q[2]) + 2*Q[10])*sqrt(2*sqrt(Q[2]) - 2*Q[10])*Q[7] + 8*(-(a - c)^2*sqrt(Q[2])/4 + Q[5]/4)*Q[8])*Q[4])*Q[4])*(t^2 - 1)) - 2*a*e + b*d)/(4*a*c - b^2)],

[Q[2] = (a^2 - 2*a*c + b^2 + c^2)*(4*a*c*f - a*e^2 - b^2*f + b*d*e - c*d^2)^2, Q[4] = 1/((a^2 - 2*a*c + b^2 + c^2)*(4*a*c*f - a*e^2 - b^2*f + b*d*e - c*d^2)^2), Q[5] = (a^2 - 2*a*c + b^2 + c^2)*(4*a*c*f - a*e^2 - b^2*f + b*d*e - c*d^2)*(a + c), Q[6] = signum((4*a*c*f - a*e^2 - b^2*f + b*d*e - c*d^2)/(4*a*c - b^2))*(4*a*c*f - a*e^2 - b^2*f + b*d*e - c*d^2)/(4*a*c - b^2), Q[7] = csgn((4*a*c*f - a*e^2 - b^2*f + b*d*e - c*d^2)*(b*I + a - c)*I)*b, Q[8] = 4*a*c*f - a*e^2 - b^2*f + b*d*e - c*d^2, Q[9] = csgn((4*a*c*f - a*e^2 - b^2*f + b*d*e - c*d^2)*(b*I + a - c)*I), Q[10] = (a - c)*(4*a*c*f - a*e^2 - b^2*f + b*d*e - c*d^2), Q[11] = (a + c)*(a^2 - 2*a*c + b^2 + c^2)*(4*a*c*f - a*e^2 - b^2*f + b*d*e - c*d^2)^2]]:

length(Pt);  # was >27,000

5002

(1)

valsh:=[a = -9, b = -9, c = 16, d = -10, e = 7, f = -36]

[a = -9, b = -9, c = 16, d = -10, e = 7, f = -36]

(2)

S1:=eval['recurse'](Pt,valsh)[];

length(%)

 

[-(1/657)*(2*Q[2]^(1/2)+2*Q[10])^(1/2)*Q[6]^(1/2)*(t^2+1)*431649^(1/2)/(Q[2]^(1/4)*((-28903750*Q[2]^(1/2)+Q[2]^(1/2)*(2*Q[2]^(1/2)+2*Q[10])^(1/2)*(2*Q[2]^(1/2)-2*Q[10])^(1/2)*Q[7]-2*Q[11])*signum((Q[2]^(1/2)*(2*Q[2]^(1/2)+2*Q[10])^(1/2)*(2*Q[2]^(1/2)-2*Q[10])^(1/2)*Q[7]-8*((625/4)*Q[2]^(1/2)+(1/4)*Q[5])*Q[8])*Q[4])*Q[4])^(1/2)*(t^2-1))-(2/657)*(2*Q[2]^(1/2)-2*Q[10])^(1/2)*t*Q[6]^(1/2)*Q[9]*431649^(1/2)/(Q[2]^(1/4)*((-28903750*Q[2]^(1/2)+Q[2]^(1/2)*(2*Q[2]^(1/2)+2*Q[10])^(1/2)*(2*Q[2]^(1/2)-2*Q[10])^(1/2)*Q[7]+2*Q[11])*signum((Q[2]^(1/2)*(2*Q[2]^(1/2)+2*Q[10])^(1/2)*(2*Q[2]^(1/2)-2*Q[10])^(1/2)*Q[7]+8*(-(625/4)*Q[2]^(1/2)+(1/4)*Q[5])*Q[8])*Q[4])*Q[4])^(1/2)*(t^2-1))-257/657, (1/657)*(2*Q[2]^(1/2)-2*Q[10])^(1/2)*Q[6]^(1/2)*(t^2+1)*Q[9]*431649^(1/2)/(Q[2]^(1/4)*((-28903750*Q[2]^(1/2)+Q[2]^(1/2)*(2*Q[2]^(1/2)+2*Q[10])^(1/2)*(2*Q[2]^(1/2)-2*Q[10])^(1/2)*Q[7]-2*Q[11])*signum((Q[2]^(1/2)*(2*Q[2]^(1/2)+2*Q[10])^(1/2)*(2*Q[2]^(1/2)-2*Q[10])^(1/2)*Q[7]-8*((625/4)*Q[2]^(1/2)+(1/4)*Q[5])*Q[8])*Q[4])*Q[4])^(1/2)*(t^2-1))-(2/657)*(2*Q[2]^(1/2)+2*Q[10])^(1/2)*t*Q[6]^(1/2)*431649^(1/2)/(Q[2]^(1/4)*((-28903750*Q[2]^(1/2)+Q[2]^(1/2)*(2*Q[2]^(1/2)+2*Q[10])^(1/2)*(2*Q[2]^(1/2)-2*Q[10])^(1/2)*Q[7]+2*Q[11])*signum((Q[2]^(1/2)*(2*Q[2]^(1/2)+2*Q[10])^(1/2)*(2*Q[2]^(1/2)-2*Q[10])^(1/2)*Q[7]+8*(-(625/4)*Q[2]^(1/2)+(1/4)*Q[5])*Q[8])*Q[4])*Q[4])^(1/2)*(t^2-1))-24/73], [Q[2] = 377479229074, Q[4] = 1/377479229074, Q[5] = 114273866, Q[6] = 23123/657, Q[7] = -9, Q[8] = 23123, Q[9] = 1, Q[10] = -578075, Q[11] = 2642354603518]

 

2074

(3)

simplify(S1);# this is  simplify with side retations
length(%)

[-(257/248003853501618)*377479229074^(3/4)*((377479229074^(1/4)*(t^2-1)*((9/377479229074)*377479229074^(1/2)*(2*377479229074^(1/2)-1156150)^(1/2)*(2*377479229074^(1/2)+1156150)^(1/2)+(625/8162419)*377479229074^(1/2)+14)^(1/2)+(1/168849)*657^(1/2)*23123^(1/2)*431649^(1/2)*(2*377479229074^(1/2)-1156150)^(1/2)*(t^2+1))*((9/377479229074)*377479229074^(1/2)*(2*377479229074^(1/2)-1156150)^(1/2)*(2*377479229074^(1/2)+1156150)^(1/2)+(625/8162419)*377479229074^(1/2)-14)^(1/2)+(2/168849)*23123^(1/2)*657^(1/2)*431649^(1/2)*((9/377479229074)*377479229074^(1/2)*(2*377479229074^(1/2)-1156150)^(1/2)*(2*377479229074^(1/2)+1156150)^(1/2)+(625/8162419)*377479229074^(1/2)+14)^(1/2)*(2*377479229074^(1/2)+1156150)^(1/2)*t)/(((9/377479229074)*377479229074^(1/2)*(2*377479229074^(1/2)-1156150)^(1/2)*(2*377479229074^(1/2)+1156150)^(1/2)+(625/8162419)*377479229074^(1/2)-14)^(1/2)*((9/377479229074)*377479229074^(1/2)*(2*377479229074^(1/2)-1156150)^(1/2)*(2*377479229074^(1/2)+1156150)^(1/2)+(625/8162419)*377479229074^(1/2)+14)^(1/2)*(t-1)*(t+1)), -(12/13777991861201)*377479229074^(3/4)*((377479229074^(1/4)*(t^2-1)*((9/377479229074)*377479229074^(1/2)*(2*377479229074^(1/2)-1156150)^(1/2)*(2*377479229074^(1/2)+1156150)^(1/2)+(625/8162419)*377479229074^(1/2)+14)^(1/2)-(1/141912)*657^(1/2)*23123^(1/2)*431649^(1/2)*(2*377479229074^(1/2)+1156150)^(1/2)*(t^2+1))*((9/377479229074)*377479229074^(1/2)*(2*377479229074^(1/2)-1156150)^(1/2)*(2*377479229074^(1/2)+1156150)^(1/2)+(625/8162419)*377479229074^(1/2)-14)^(1/2)+(1/70956)*(2*377479229074^(1/2)-1156150)^(1/2)*t*23123^(1/2)*657^(1/2)*431649^(1/2)*((9/377479229074)*377479229074^(1/2)*(2*377479229074^(1/2)-1156150)^(1/2)*(2*377479229074^(1/2)+1156150)^(1/2)+(625/8162419)*377479229074^(1/2)+14)^(1/2))/(((9/377479229074)*377479229074^(1/2)*(2*377479229074^(1/2)-1156150)^(1/2)*(2*377479229074^(1/2)+1156150)^(1/2)+(625/8162419)*377479229074^(1/2)-14)^(1/2)*((9/377479229074)*377479229074^(1/2)*(2*377479229074^(1/2)-1156150)^(1/2)*(2*377479229074^(1/2)+1156150)^(1/2)+(625/8162419)*377479229074^(1/2)+14)^(1/2)*(t-1)*(t+1))]

 

2316

(4)

simplify(%%);
length(%)

[-(1/71716466988)*(-2471*706^(1/2)+249218)^(1/2)*(2471*706^(1/2)+249218)^(1/2)*((73^(1/2)*(t^2+1)*(46246*706^(1/2)-1156150)^(1/2)+(257/3)*706^(1/4)*(14+2*706^(1/2))^(1/2)*t^2)*(-14+2*706^(1/2))^(1/2)+2*73^(1/2)*(t*(46246*706^(1/2)+1156150)^(1/2)*(14+2*706^(1/2))^(1/2)-257*706^(1/4)))*706^(1/4)/(t^2-1), (1/71716466988)*(-2471*706^(1/2)+249218)^(1/2)*((73^(1/2)*(t^2+1)*(46246*706^(1/2)+1156150)^(1/2)-72*706^(1/4)*(14+2*706^(1/2))^(1/2)*t^2)*(-14+2*706^(1/2))^(1/2)-2*73^(1/2)*((14+2*706^(1/2))^(1/2)*(46246*706^(1/2)-1156150)^(1/2)*t-216*706^(1/4)))*(2471*706^(1/2)+249218)^(1/2)*706^(1/4)/(t^2-1)]

 

744

(5)

 

S2:=eval['recurse'](eval['recurse'](Pt,valsh)[]);# I find this interesting
length(%)

[-(1/162938531750563026)*(2*377479229074^(1/2)-1156150)^(1/2)*23123^(1/2)*657^(1/2)*(t^2+1)*431649^(1/2)*377479229074^(3/4)/(((9/377479229074)*377479229074^(1/2)*(2*377479229074^(1/2)-1156150)^(1/2)*(2*377479229074^(1/2)+1156150)^(1/2)+(625/8162419)*377479229074^(1/2)+14)^(1/2)*(t^2-1))-(1/81469265875281513)*(2*377479229074^(1/2)+1156150)^(1/2)*t*23123^(1/2)*657^(1/2)*431649^(1/2)*377479229074^(3/4)/(((9/377479229074)*377479229074^(1/2)*(2*377479229074^(1/2)-1156150)^(1/2)*(2*377479229074^(1/2)+1156150)^(1/2)+(625/8162419)*377479229074^(1/2)-14)^(1/2)*(t^2-1))-257/657, (1/162938531750563026)*(2*377479229074^(1/2)+1156150)^(1/2)*23123^(1/2)*657^(1/2)*(t^2+1)*431649^(1/2)*377479229074^(3/4)/(((9/377479229074)*377479229074^(1/2)*(2*377479229074^(1/2)-1156150)^(1/2)*(2*377479229074^(1/2)+1156150)^(1/2)+(625/8162419)*377479229074^(1/2)+14)^(1/2)*(t^2-1))-(1/81469265875281513)*(2*377479229074^(1/2)-1156150)^(1/2)*t*23123^(1/2)*657^(1/2)*431649^(1/2)*377479229074^(3/4)/(((9/377479229074)*377479229074^(1/2)*(2*377479229074^(1/2)-1156150)^(1/2)*(2*377479229074^(1/2)+1156150)^(1/2)+(625/8162419)*377479229074^(1/2)-14)^(1/2)*(t^2-1))-24/73]

 

1283

(6)

simplify(S2); #
length(%)

 

[-(1/406325592)*(14+2*706^(1/2))^(1/2)*(((181442/3)*(14+2*706^(1/2))^(1/2)*t^2+706^(3/4)*73^(1/2)*(46246*706^(1/2)-1156150)^(1/2)*(t^2+1))*(-14+2*706^(1/2))^(1/2)+2*(46246*706^(1/2)+1156150)^(1/2)*73^(1/2)*706^(3/4)*(14+2*706^(1/2))^(1/2)*t-362884*73^(1/2))*(-14+2*706^(1/2))^(1/2)/(t^2-1), (14+2*706^(1/2))^(1/2)*((-2*706^(3/4)*73^(1/2)*(46246*706^(1/2)-1156150)^(1/2)*t-50832*(-14+2*706^(1/2))^(1/2)*t^2)*(14+2*706^(1/2))^(1/2)+(304992+(t^2+1)*(46246*706^(1/2)+1156150)^(1/2)*706^(3/4)*(-14+2*706^(1/2))^(1/2))*73^(1/2))*(-14+2*706^(1/2))^(1/2)/(406325592*t^2-406325592)]

 

705

(7)
 

 

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