Ronan

1267 Reputation

14 Badges

12 years, 276 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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