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Ronan

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14 years, 30 days
East Grinstead, United Kingdom
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ReScaliing a projective vector...

Ronan 1401 Maple 2024
gcd frontend
May 09 2024
0 1

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

Can .mpl type files be combined?...

Ronan 1401 Maple 2024
filetools mpl concatenation
April 29 2024
1 2

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.

How do I get this to factor?...

Ronan 1401 Maple 2024
April 28 2024
2 0

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(%)

 

Seperate Real and Imaginary...

Ronan 1401 Maple 2024
imaginary real evalc
April 19 2024
1 3

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

Return only two specific values from a p...

Ronan 1401 Maple 2024
procedure
April 13 2024
1 2

I have a proceure that returns 7 values. I cac get it to return ang single specific value ousing e.g [2] to get the second.
Or a range[3..6] for the third to sixth.

Is there a way to get specific seperated values e.g [1] and[[6]. The procedure is burried in a package so it is difficult to post.

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