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Ronan

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12 years, 216 days
East Grinstead, United Kingdom
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Thank you...

Ronan 1207
September 28 2024
0 0

@Scot Gould Nice.

@Kitonum @Rouben Rostamian Thank y...

Ronan 1207
September 28 2024
0 0

@Kitonum @Rouben Rostamian Thank you both for you answers. I decided to go with 

with(LinearAlgebra):
if ((l1 &x l2) . (l1 &x l2)) =0 then....

because this also handles the case of one vector being a multiple of the other. I was looking at the vectors being equal but parallel is more appropiate description.

This is a guaranteed way...

Ronan 1207
September 28 2024
0 0

This works and it handles one vector being a multiple of the other.

with(LinearAlgebra):
((l1 &x l2) . (l1 &x l2))

The application...

Ronan 1207
September 18 2024
0 0

@acer This is the complete procedure. You actually did a lot of work on it a few months ago. 
maplemint is only showing typeset as an undeclarel global variable. Do I just add
global typeset;

The shift seems to work well. What I did find is, have to count from 2nd item in the lists eval(':-shift',Q[2..-1])::float  because the text being the first  my not have an `=`.

I copied in other examples too to give an insight as to what the other parametes do.

 

 

> 

restart
> 

 

> 


Qdim := proc(P1, P2, {Q:=[ ]},
                     {corp::{"cart","proj"}:="cart"},#cartesian or projective
                     {shift::float:=0.5},
                     {vec::list:=[]},
                     {scale::{list,integer}:=1},
                     {leader::{-1,0,1}:= 1},
                     {dimoffset::{1/6,1/5,1/4,3/4,2/3,1/2,1/3,1,3/2,2,3,4,5,6}:=1},
                     {point::list:=['color' = ':-blue', symbol = ':-solidcircle', 'symbolsize' = 12]},
                     {line::list:=['thickness'=3]},
                     {plopts::list:=[]})
description " plots Quadrance symbol and value (Q)";
uses pl=plots, pt=plottools ;#, RationalTrigonometry;

local a,f,g,h,v1,delta,mp, BoxQ,Qsymbol,ldr,pt1,pt2,pt3,pt4,Scl,xpsn,ypsn,zpsn,
      ptxtp1,ptxtp2,txtplt1,txtplt2,plttyp,thk,l12,pts12,perp::boolean:=false,qshift,vshift;
global Projective_Z_Position;
if Projective_Z_Position=1 then   
     xpsn:=2;
     ypsn:=3;
     zpsn:=1;
     else  
     xpsn:=1;
     ypsn:=2;
     zpsn:=3;  
end if;
if P1::{list} and P1[1]::{list,'Vector[row]'(3)} then
   if P1[1]::'Vector[row]'(3) then
      pt1:=[P1[1][xpsn]/P1[1][zpsn],P1[1][ypsn]/P1[1][zpsn]];#print(pt1);
    elif  P1[1]::list then
      pt1:=P1[1];
   end if;     
   plttyp:=`if`(nops(pt1)=3,3,2); # print(pt1,plttyp);
   ptxtp1:=[op(pt1),op(P1[2..-1])];
   txtplt1:=true;  
 else
   if P1::'Vector[row]'(3) then
        pt1:=[P1[xpsn]/P1[zpsn],P1[ypsn]/P1[zpsn]];
    else
        pt1:=P1;
   end if;
   plttyp:=nops(pt1);
   txtplt1:=false;
end if;    

if P2::{list}  and P2[1]::{list,'Vector[row]'(3)} then
   if P2[1]::'Vector[row]'(3)  then
      pt2:=[P2[1][xpsn]/P2[1][zpsn],P2[1][ypsn]/P2[1][zpsn]];

    elif  P2[1]::list then
      pt2:=P2[1];
   end if;     
   plttyp:=`if`(nops(pt2)=3,3,2); # print(pt2,plttyp);
   ptxtp2:=[op(pt2),op(P2[2..-1])];
   txtplt2:=true;  
   
 else
   if P2::'Vector[row]'(3)then
      pt2:=[P2[xpsn]/P2[zpsn],P2[ypsn]/P2[zpsn]];
 
    else
      pt2:=P2;
   end if;
   plttyp:=nops(pt2);
   txtplt2:=false;
end if;
#print(Projective_Z_Position,xpsn,ypsn,zpsn);   


if type(scale,'numeric') then
    Scl:=scale;
 else
   if scale[1]::Vector[row](3) then
        pt3:=   [scale[1][xpsn]/scale[1][zpsn],scale[1][ypsn]/scale[1][zpsn]];
    
     else
        pt3:=scale[1];
    end if;
   if scale[2]::Vector[row](3) then
        pt4:=  [scale[2][xpsn]/scale[2][zpsn],scale[2][ypsn]/scale[2][zpsn]];
    
     else
        pt4:=scale[2];
    end if;
    if plttyp = 2 then
       Scl:=evalf(sqrt(((pt3[1]-pt4[1])^2+(pt3[2]-pt4[2])^2)/((pt1[1]-pt2[1])^2+(pt1[2]-pt2[2])^2)));#:-print(Scl);
    
     else
       Scl:=evalf(sqrt(((pt3[1]-pt4[1])^2+(pt3[2]-pt4[2])^2)/((pt1[1]-pt2[1])^2+(pt1[2]-pt2[2])^2)));#:-print(Scl);
  
    end if;
end if;
#print(Scl,pt1,pt2,pt3,pt4);
if plttyp =2 then
     a :=Scl* dimoffset*0.1*leader*[-pt2[2]+pt1[2], pt2[1]-pt1[1]]; #dimension leader 2d lines
  else
     a :=Scl* dimoffset*0.1*leader*[-pt2[2]+pt1[2], pt2[1]-pt1[1],pt2[3]-pt1[3]]; #dimension leader 3d lines
end if;
delta:=Scl*(pt2-pt1);
if Q<>[] and eval(':-shift',Q[2..-1])::float then
         qshift := eval(':-shift',Q[2..-1]);
       else
         qshift := shift;
      end if;
      print("qshift=",qshift);

  if vec<>[] and eval(':-shift',vec[2..-1])::float then
    vshift := eval(':-shift',vec[2..-1]);
  else
    vshift := shift;
  end if;
 print("vshift=",vshift);
 
mp:=(1-qshift)*pt1+qshift*pt2;  #midpoint of line
#:-print(Scl,a,delta,mp);
if plttyp = 2 then
#coorfinates of the sqnbol corners
    BoxQ:=[[a[1]+mp[1]+.05*delta[1]-.01*delta[2],a[2]+mp[2]+.05*delta[2]+.01*delta[1]],
           [a[1]+mp[1]-.05*delta[1]-.01*delta[2],a[2]+mp[2]-.05*delta[2]+.01*delta[1]],
           [a[1]+mp[1]-.05*delta[1]+.01*delta[2],a[2]+mp[2]-.05*delta[2]-.01*delta[1]],
           [a[1]+mp[1]+.05*delta[1]+.01*delta[2],a[2]+mp[2]+.05*delta[2]-.01*delta[1]]];
 else  #3D
    BoxQ:=[[a[1]+mp[1]+.05*delta[1]-.01*delta[2],a[2]+mp[2]+.05*delta[2]+.05*delta[1],a[3]+mp[3]+.05*delta[3]],
           [a[1]+mp[1]-.05*delta[1]-.01*delta[2],a[2]+mp[2]-.05*delta[2]+.05*delta[1],a[3]+mp[3]-.05*delta[3]],
           [a[1]+mp[1]-.05*delta[1]+.01*delta[2],a[2]+mp[2]-.05*delta[2]-.05*delta[1],a[3]+mp[3]-.05*delta[3]],
           [a[1]+mp[1]+.05*delta[1]+.01*delta[2],a[2]+mp[2]+.05*delta[2]-.05*delta[1],a[3]+mp[3]+.05*delta[3]]];
end if;

if leader<>0  then
   thk:='thickness'=0
 elif line<>[] then
   thk:=line[op(ListTools:-Search(op(select(has,line,'thickness')),line))];
 else
   thk:='thickness'=0;
end if;
if corp="cart" then
   Qsymbol:=[pt:-line(pt1,pt1+1.05*a,'thickness'=0,plopts[]),
             pt:-line(pt1+a,mp-.05*delta+a,thk,plopts[]),
             pt:-line(op([BoxQ[1],BoxQ[2]]),'thickness'=0,plopts[]),
             pt:-line(op([BoxQ[2],BoxQ[3]]),'thickness'=0,plopts[]),
             pt:-line(op([BoxQ[3],BoxQ[4]]),'thickness'=0,plopts[]),
             pt:-line(op([BoxQ[4],BoxQ[1]]),'thickness'=0,plopts[]),
             pt:-line(pt2+a,mp+.05*delta+a,thk,plopts[]),
             pt:-line(pt2,pt2+1.05*a,'thickness'=0,plopts[])];
  elif (Q[1])=1 or Q[1]::specfunc(typeset) and ormap(is, [op(Q[1])], 1)  and corp="proj"   then
      if leader=0 or leader=1 then ldr:=1 else ldr:=-1 end if;
   Qsymbol:=[pt:-line(mp-.05*delta*dimoffset,mp+ldr*.05*[-delta[2],delta[1]]*dimoffset,thk,plopts[]),
             pt:-line(mp+ldr*.05*[-delta[2],delta[1]]*dimoffset,mp+.05*delta*dimoffset,thk,plopts[])];
             perp:=true;
  else
   Qsymbol:=[pt:-line(pt1,pt1+1.05*a,'thickness'=0,plopts[]),
             pt:-line(pt1+a,mp-.05*delta+a,thk,plopts[]),
             pt:-line(op([BoxQ[1],BoxQ[2]]),'thickness'=0,plopts[]),
             pt:-line(op([BoxQ[2],BoxQ[3]]),'thickness'=0,plopts[]),
             pt:-line(op([BoxQ[3],BoxQ[4]]),'thickness'=0,plopts[]),
             pt:-line(op([BoxQ[4],BoxQ[1]]),'thickness'=0,plopts[]),
             pt:-line(pt2+a,mp+.05*delta+a,thk,plopts[]),
             pt:-line(pt2,pt2+1.05*a,'thickness'=0,plopts[])];
end if;
if point<>[]then           
pts12:=pt:-point([pt1,pt2],point[]);  #end points
else
pts12:=NULL;
end if;

 


if line<>[] then
l12:=pt:-line(pt1,pt2,line[]);
  else
  l12:=NULL;
  end if;
 if plttyp = 2  then
   if perp=false then
     
      f := pl:-textplot([op(((1-qshift)*pt1+qshift*pt2)+1*(a)),op(Q)]);  #Quadrance text
    else
      f:=NULL;    #dont plot value with perp symbol
   end if;
   if txtplt1 then
      g := pl:-textplot( ptxtp1);
    else
      g:=NULL;
   end if;
   if txtplt2 then
      h := pl:-textplot( ptxtp2);
    else
     h:= NULL;
   end if;
   if vec <> [] then
      v1:=pl:-textplot([op(((1-vshift)*pt1+vshift*pt2)), op(vec)]);#`#mover(mi("v"),mo("&rharu;"))`[1,2]   {':-below',':-right'}
    else
      v1:=NULL;
   end if;
 else
   if perp=false then
      f := pl:-textplot3d([op(((1-qshift)*pt1+qshift*pt2)+1*(a)),op(Q)]);
    else
      f:=NULL;    #dont plot value with perp symbol
   end if;
   if txtplt1 then
         g := pl:-textplot3d( ptxtp1);
      else
         g:=NULL;
   end if;
   if txtplt2 then
         h := pl:-textplot3d( ptxtp2);
      else
         h:=NULL;
   end if;
   if vec <> [] then
    
         v1:=pl:-textplot3d([op(((1-vshift)*pt1+vshift*pt2)),op(vec)]);#`#mover(mi("v"),mo("&rharu;"))`[1,2]   {':-below',':-right'}
     else
         v1:=NULL;
   end if;
end if;
#:-print("pltyp" , plttyp)  ;

if leader = 0 then    
      pl:-display(pts12,f,g,h,v1,Qsymbol,'axes'=':-none','scaling'=':-constrained');
 else       
      pl:-display(pts12,l12,f,g,h,v1,Qsymbol,'axes'=':-none','scaling'=':-constrained');     
end if;
end proc:

 
> 

maplemint(Qdim);

Procedure Qdim( P1, P2, { Q := [], corp::{"cart", "proj"} := "cart",
    dimoffset::{1, 2, 3, 4, 5, 6, 1/2, 1/3, 1/4, 1/5, 1/6, 2/3, 3/2, 3/4} :=
    1, leader::{-1, 0, 1} := 1, line::list := ['thickness' = 3], plopts::list
    := [], point::list := ['color' = ':-blue', symbol = ':-solidcircle',
    'symbolsize'
= 12], scale::{integer, list} := 1, shift::float := .5,
    vec::list := [] } )
  These names were used as global names but were not declared:  typeset

  
> 

Projective_Z_Position:=3:
> 

pp1:=<1|3|2>:pp2:=<2|3/2|1/2>:#projective points
> 

P5:=[1,0]:P6:=[5,2]:
> 

 

> 

#default value of shift=0.5
Qdim([pp1,typeset("P1 ",pp1),align={below, right},color=magenta],pp2,dimoffset=3,Q=[typeset("Q=",3),align=[below,right]],vec=[(\n`#mover(mi("v"),mo("&rharu;"))`[1,2]),align={above,left},font=["century",14]],plopts=[color=blue])
> 

 

> 

 

> 

 

> 

 

> 

 

> 

 

"qshift=", .5

  

"vshift=", .5

  

 
> 

#shift =0.8
Qdim([pp1,typeset("P1 ",pp1),align=[below,right],color=magenta],pp2,dimoffset=3,Q=[typeset("Q=",3),align=[below,right]],vec=[(\n`#mover(mi("v"),mo("&rharu;"))`[1,2]),align={above,left},font=["century",14]],shift=0.8,plopts=[color=blue])

"qshift=", .8

  

"vshift=", .8

  

 
> 

#individual shift values for Q and vec override main shift value
Qdim([P5,typeset("P5 ",P5),align=[below,right],color=magenta],[P6,typeset("P6 ",P6),color="Green",align=right],dimoffset=3,Q=[typeset("Q=",20),colour=blue,align=[below,right],shift=0.35],vec=[(\n`#mover(mi("v"),mo("&rharu;"))`[5,6]),align={above,left},font=["century",14]],shift=0.8,plopts=[color=indigo],line=[thickness=2,linestyle=dash])

"qshift=", .35

  

"vshift=", .8

  

 
> 

P1:=[4,5]:P2:=[-1,3]:P3:=[2,-5/2]:
P4:=(1-3/10)*P1+3/10*P2:
P5:=(1-6/10)*P1+6/10*P2:
> 

# Stacking dimensions by using scale, leader and dimoffset. Plus use of colour.
plt7:=Qdim([P1,typeset("  P1=",P1),align=[right],colour=red],[P2,typeset("P2=",P2,"  "),align=[left,above]] ,Q=[typeset("Q12=",29),align =[above,left]] ,leader=-1,dimoffset=5, point=[symbolsize=12,symbol=solidcircle,colour=blue]):
plt8:=Qdim(P1,[P4,typeset("P4=",P4,"   "),align=[left,above]] ,Q=[typeset("Q14=",261/100),align =[above,left]] ,scale=[P1,P2],leader=-1,dimoffset=1, point=[symbolsize=12,symbol=solidcircle,colour=blue]):
plt9:=Qdim(P1,[P5,typeset("P5=",P5,"   "),align=[below,right] ] ,Q=[typeset("Q15=",261/25),align =[above,left]] ,scale=[P1,P2],dimoffset=3,leader=-1,point=[symbolsize=12,symbol=solidcircle,colour=blue],plopts=[colour=blue]):
plots:-display(plt7,plt8,plt9)
> 

 

"qshift=", .5

  

"vshift=", .5

  

"qshift=", .5

  

"vshift=", .5

  

"qshift=", .5

  

"vshift=", .5

  

 
> 

# Form a triangle. More use of colour and leader=0.
plt10:=Qdim(P1,[P3,typeset("P3=",P3),align=[right,below]],leader=0,Q=[typeset("   Q13=",241/4),align =[right]],plopts=[colour=purple]):
plt11:=Qdim(P2,P3,Q=[typeset("Q23=",157/4,"  "),align =[left]],leader=-1,point=[symbolsize=12,symbol=solidcircle,colour=blue],line=[colour="Green",thickness=2],plopts=[colour=purple]):
plots:-display(plt7,plt8,plt9,plt10,plt11,size=[750,750])

"qshift=", .5

  

"vshift=", .5

  

"qshift=", .5

  

"vshift=", .5

  

 
> 

# A diagram with default dimension formats.
plt1:=Qdim([P1,typeset("  P1=",P1),align=[right],colour=red],[P2,typeset("P2=",P2),align=[left,above]] ,Q=[typeset("Q12=",29),align =[below,right]] , point=[symbolsize=12,symbol=solidcircle,colour=blue]):
plt2:=Qdim(P1,[P4,typeset("P4=",P4),align=[left,above]] ,Q=[typeset("Q14=",261/100),align =[below,right]] , point=[symbolsize=12,symbol=solidcircle,colour=blue]):
plt3:=Qdim(P2,P4 ,Q=[typeset("Q24=",1421/100," "),align =[below,right]] , point=[]):
plots:-display(plt1,plt2,plt3,size=[600,600])

"qshift=", .5

  

"vshift=", .5

  

"qshift=", .5

  

"vshift=", .5

  

"qshift=", .5

  

"vshift=", .5

  

 
> 

# Using scale, leader and dimoffset to create a clearer diagram.
plt4:=Qdim([P1,typeset("P1=",P1),align=[right],colour=red],[P2,typeset("P2=",P2),align=[left,above]] ,Q=[typeset("Q12=",Q29),align =[below,right]] , point=[symbolsize=12,symbol=solidcircle,colour=blue]):
plt5:=Qdim(P1,[P4,typeset("P4=",P4,"   "),align=[left,above]] ,Q=[typeset("Q14=",261/100),align =[above,left]] ,scale=[P1,P2],leader=-1,dimoffset=2, point=[symbolsize=12,symbol=solidcircle,colour=blue]):
plt6:=Qdim(P2,P4 ,Q=[typeset("Q24=",1421/100),align =[above,left]] ,scale=[P1,P2],dimoffset=2, point=[]):
plots:-display(plt4,plt5,plt6)

"qshift=", .5

  

"vshift=", .5

  

"qshift=", .5

  

"vshift=", .5

  

"qshift=", .5

  

"vshift=", .5

  

 
> 

 


 

Download 2024-9-18-QA_Applifation.mw

I like you method....

Ronan 1207
September 18 2024
0 0

@mmcdara Very Nice. You should convert it to an asnwer. It is much less brute force than mine.

maplemint or mint...

Ronan 1207
September 14 2024
0 0

@acer I use the VS code editor with the Maple addin. Is there a difference between mint and maplemint. The code editor can run the command line version of maple and maplemint, which is very useful.
I don't find maplemint much good inside maple though.

Yes......

Ronan 1207
September 13 2024
0 0

@Kitonum I was bored at work.I didn't see that one. I was looking at you solution too.

On vectors v1,v2, I would use the determinat of the vector matrix as gives the signed area of a rectangle (so could be negative).

 

M:=<v2|v1> #
S1:=LinearAlgebra:-Determinant(M)/2;
simplify(S1, {a*b=24}); # The answer

 

Very interesting....

Ronan 1207
September 11 2024
0 0

@Carl Love @Kitonum Thank you for your answers. I often struggle with the has select I never knew about primpart. I have two applications for simplifying one internal insde a packake and the other a commmand in another package. In the internal case I don not need to know the factors so primpart will be very useful there. Can you explain "searched for (disjunctively)"

On the command version the factors are be useful to have returned. 

Took a while to see that...

Ronan 1207
September 06 2024
0 0

@acer Thank you. I had to look at that eval(colour, styles1) for a couple of minutes befor it dawned on me why! Very Nice.

Ahh.. iquo irem...

Ronan 1207
September 06 2024
0 0

@acer I was going for that through divide and trunc. Forgot about iquo and irem 

What is was most stuck in was trying to get the color list out of the styles list. Realised I can do the following. Is there a more efficient way?

styles1:=[symbol=solidcircle,colour = [red,green,blue,magenta],symbolsize=20];
   
for i to nops(styles1) do
if has(styles1[i],colour) then
#print(i);
  Cc:=rhs(styles1[i]);
  break;
end if;
end do

 

An idea for an approach....

Ronan 1207
September 02 2024
0 0

@mmcdara I am basilally plotting points and lines. Using a tetrahedron for example. 4 points and 6 line segments with can be plotted using the plottools:-line command.display the 3Dplot. Using an orientation matrix and it's projection onto 2D can the (X,Y) actual plotted coords of the 3D points be accessed. Then do a 2D plot of these points and lines and plot  the text based on these points. The 2D plot would have to update if the 3D plot is rotated. I know that would not scale the height and length of the text.
 I have a procedure now for aligning text based on two points or a point and line/vector that alows shifting it back and forth parallel to the line/vector alongwith changing it's offset from the line to suit text size. I can modify it to share, because at present it calls other procedures in my package. 

can you post the image file...

Ronan 1207
September 02 2024
0 0

@mmcdara Thank you for answering. You code is looking for some file img.jpg. Could you upload a copy. 
I sort of figured there is no good solution. I noticed even if one transforms a 2d plot to 3d the text looses alignment. 

Fixed it....

Ronan 1207
August 26 2024
0 0

I found the problem. I write the packace and procedures in the VS code editor. That can run CMaple which is useful. But to test the prcedures on their own I have to put in the line "uses RationalTrigonometry;" This then must be "# out" before building the package in Maple. Otherwise one get all sorts of warnings depending which proceduses it is used in. I found if because on a procedure I altered started producing warning about types being overwritten where as the previouse version of it did not. Of course i nthe process of tyring to find what was wrong, I uninstalled and reinstalled Maple thinking it must be some form of corruption.  All seems ok now.

My Package...

Ronan 1207
August 24 2024
0 0

@nm @C_R I have am writing my own RationalTrigonometry package. It has as two subpackages UHG and RT Projective.

It has been through various incarnations over the past few years. Some of the commands have changed. I was using the aliases to maintain compatability with older worksheets. The are turning out to be more trouble than they are worth.

As I said the problem began a few nights ago.

Glad it worked...

Ronan 1207
August 20 2024
0 0

@mmcdara Oh Good.. The download from Google Docs worked for me.  Interesting post.

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