Ronan

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12 years, 70 days
East Grinstead, United Kingdom

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These are questions asked by Ronan

This is a follow on from and earlier question on tabulation. Some procdures returs up tp eight values. So using a Table make it easier to see what is what. Sometimes the equations returned are very long. Is there a way to truncate what is display in the table using something along the lines of term elision? Say the 1st 300 chatacters for example?  

Edit: Corrected an error in the worksheet.

restart

QQFProj := proc(q12::algebraic, q23::algebraic,
                q34::algebraic, q14::algebraic,
                  prnt::boolean:=true) #{columns:=[QQFproj,Q13proj,Q24proj]}
  description "Projective quadruple quad formula and intermediate 13 and 24 quads. Useful for cyclic quadrilaterals";
  local qqf,q13,q24, sub1,sub2,sub3, R,values,DF,lens;
  uses   DocumentTools;
  sub1:= (q12 + q23 + q34 + q14)^2 - 2*(q12^2 + q23^2 + q34^2 + q14^2) ;
  sub2:=-4*(q12*q23*q34+q12*q23*q14+q12*q34*q14+q23*q34*q14)+8*q12*q23*q34*q14;
  sub3:=64*q12*q23*q34*q14*(1-q12)*(1-q23)*(1-q34)*(1-q14);
  qqf:=((sub1+sub2)^2=sub3);
  q13:=((q12-q23)^2-(q34-q14)^2)/(2*(q12+q23-q34-q14-2*q12*q23+2*q34*q14));#check this
  q24:=((q23-q34)^2-(q12-q14)^2)/(2*(q23+q34-q12-q14-2*q23*q34+2*q12*q14));#check this
  if prnt then
  
   values:=<qqf,q13,q24>;
   DF:=DataFrame(<values>, columns=[`"Values Equations"`],rows=[`#1  QQF`,`#2  Q13`,`#3  Q24`]);
   lens := [4 +8* max(op(length~(RowLabels(DF)))),4+ min(max( 10*(length~(values))),1000)];#op(length~(ColumnLabels(DF)0)
   Tabulate(DF,width=add(lens),widthmode = pixels,weights = lens);
  return qqf,q13,q24
  end if;
  return qqf,q13,q24
end proc:

 q12:=1/2:q23:=9/10:q34:=25/26:q41:=9/130:#Cyclic quadrilateral
q12:=sqrt(17+a)/2:q23:=expand(r^2+t^2)^2/10:q34:=expand((a+b+c)^4/26):q41:=sqrt(17+b)/130:

Q:=QQFProj(q12,q23,q34,q41,true):

#Q[1]

#(Q[2])

#Q[3]

length(Q[1])

2669

(1)

length(Q[2])

1024

(2)

length(Q[3])

1024

(3)
 

 

Download 2024-05-14_Q_Data_Table_Limit_Equation_lentgh.mw

I want to rescale a projective vector. Have been using gcd on the numerators and denominators. This works in simple situations. It doesn;t work well here, admitadely the points have been just made up for the question.  Square roots seem to make it mal-preform. I run into a lot of squate roots in symbolic situations. What would be a better way? I have been wondering if frontend would help?

restart

Prntmsg::boolean:=true;
Normalise_Projective_Point:=1;
ReScl::boolean:=true;

true

 

1

 

true

(1)

 

ProjLP:=overload([

      proc(A::Vector[row],B::Vector[row],prnt::boolean:=Prntmsg)
      description "2 projective points to create a projective line vector";
      option overload;
      local Vp ,gcdn,gcdd,vp ;
      uses LinearAlgebra;
       
      Vp:=CrossProduct(A,B)^%T;#print("2nd ",Vp);
      if ReScl then
         gcdn := gcd(gcd(numer(Vp[1]),numer(Vp[2])), numer(Vp[3]));
         gcdd := gcd(gcd(denom(Vp[1]),denom(Vp[2])), denom(Vp[3]));
         Vp:=simplify(Vp*gcdd/gcdn);
      end if;
      if Prntmsg then
         print("Line vector from two projective points. " );
      end if;
      return Vp
      end proc,



      proc(A::Vector[column],B::Vector[column],prnt::boolean:=Prntmsg)
      description "2 lines to get intersection projective point";
      option overload;
      uses LinearAlgebra;
      local  Vp;
    
      Vp:=CrossProduct(A,B)^%T;
     
     
      if Vp[3]<>0 and Normalise_Projective_Point<>0 then
           Vp:=Vp/Vp[3];
      end if;
      if Prntmsg then
           print("Meet of two Lines ");
      end if;
      return Vp
   end proc
     
]);

 

proc () option overload; [proc (A::(Vector[row]), B::(Vector[row]), prnt::boolean := Prntmsg) local Vp, gcdn, gcdd, vp; option overload; description "2 projective points to create a projective line vector"; Vp := LinearAlgebra:-CrossProduct(A, B)^%T; if ReScl then gcdn := gcd(gcd(numer(Vp[1]), numer(Vp[2])), numer(Vp[3])); gcdd := gcd(gcd(denom(Vp[1]), denom(Vp[2])), denom(Vp[3])); Vp := simplify(Vp*gcdd/gcdn) end if; if Prntmsg then print("Line vector from two projective points. ") end if; return Vp end proc, proc (A::(Vector[column]), B::(Vector[column]), prnt::boolean := Prntmsg) local Vp; option overload; description "2 lines to get intersection projective point"; Vp := LinearAlgebra:-CrossProduct(A, B)^%T; if Vp[3] <> 0 and Normalise_Projective_Point <> 0 then Vp := Vp/Vp[3] end if; if Prntmsg then print("Meet of two Lines ") end if; return Vp end proc] end proc

(2)

#maplemint(ProjLP)

pt1:=<a|sqrt(b^2+c^2)|1>:
pt2:=<c|sqrt(b^2+a^2)|1>:
pt3:=<f^2/sqrt(a^2+b^2)|f^2/sqrt(c^2+b^2)+sqrt(a^2+b^2)|1>:
pt4:=<b^2/sqrt(a^2+b^2)|f^2/sqrt(c^2+b^2)-sqrt(a^2+b^2)|1>:

 

l1:=ProjLP(pt1,pt2)

"Line vector from two projective points. "

 

Vector[column](%id = 36893490491002736020)

(3)

l2:=ProjLP(pt3,pt4)

"Line vector from two projective points. "

 

Vector[column](%id = 36893490491002712420)

(4)

l3:=ProjLP(pt1,pt4)

"Line vector from two projective points. "

 

Vector[column](%id = 36893490491064062908)

(5)

l4:=ProjLP(pt2,pt4)

"Line vector from two projective points. "

 

Vector[column](%id = 36893490491064037372)

(6)

pl1l2:=simplify(ProjLP(l1,l2))

"Meet of two Lines "

 

Vector[row](%id = 36893490491002741932)

(7)

pl2l3:=simplify(ProjLP(l2,l3))

"Meet of two Lines "

 

Vector[row](%id = 36893490491113907252)

(8)

(ProjLP(pl1l2,pl2l3));
length(%)

"Line vector from two projective points. "

 

Vector[column](%id = 36893490491113907972)

 

6223

(9)

ReScl:=false

false

(10)

# doing nothing seems to work better here than rescaling

(ProjLP(pl1l2,pl2l3));
length(%)

"Line vector from two projective points. "

 

Vector[column](%id = 36893490491125667468)

 

2796

(11)

 


 

Download 2024-05-09_Q_Rescale_projective_vector.mw

I have  4 worksheets with derived equations. So I export the equations and  possibly some procedures (but they can be handled seperately if needed)  from each worksheet as a .mpl file. 

I want to combine the .mpl files  together without using copy/paste. Then I can open that single file in the VS code editor.
There may be other ways to achieve this so I am open to suggestions.

I chased down a problem to factoring a square that has sqrt in the coefficients. All numbers are real,
The code is inside a procedure in a package. Iso I could do with something robust.

expand((sqrt(A+B)*x+sqrt(7-K)*y)^2)
     2      2            (1/2)          (1/2)        2      2
  A x  + B x  + 2 (A + B)      x (7 - K)      y - K y  + 7 y 

factor(%) 

 

I any trying to seperate the real and imaginary components but they are mixed up inside and outside a square root.

Their seems to be a problem displaying the worksheet.

restart



expand((a+I*b)*(a-I*b))
(a+I*b)+(a-I*b)
# z = x *Iy    I need to seperate out solution to [x,y] & [x,-y]
#https://math.stackexchange.com/questions/44391/foci-of-a-general-conic-equation
eq := T*z^2 - (R + S*I)*z +G-K + H*I
sol:=solve(eq,z)
expand(sol[1]*sol[2])=a^2+b^2
simplify(sol[1]+sol[2]=2*a)
simplify(sol[1]-sol[2]=2*b)

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/2024-04-20_Q_Seperate_Real_&_Imaginary.mw .

Download 2024-04-20_Q_Seperate_Real_&_Imaginary.mw

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