[1] | 1 | if get('geometry2,'version)=false then load(geometry2);
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| 2 | /* Pappus theorem;
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| 3 | 9 points and 9 lines
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| 4 | Points: a0, a1, a2, b0, b1, b2, c0, c1, c2
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| 5 | line contains points
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| 6 | l0 a0 b1 c0
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| 7 | l1 a0 b2 c1
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| 8 | l2 a1 b0 c0
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| 9 | l3 a1 b2 c2
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| 10 | l4 a2 b0 c1
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| 11 | l5 a2 b1 c2
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| 12 | l6 a0 a1 a2
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| 13 | l7 b0 b1 b2
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| 14 | l8 c0 c1 c2
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| 15 | */
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| 16 | /* Specs */
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| 17 | a00:a10:0; a20:1;
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| 18 | a01:1; a11:0; a21:1;
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| 19 | a12:0; a22:1; /* a02 # 0 */
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| 20 | l06:0; l16:1; l26:0;
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| 21 |
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| 22 | for i:0 thru 2 do (
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| 23 | a[i]:[concat('a0,i),concat('a1,i),concat('a2,i)],
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| 24 | b[i]:[concat('b0,i),concat('b1,i),concat('b2,i)],
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| 25 | c[i]:[concat('c0,i),concat('c1,i),concat('c2,i)]
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| 26 | );
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| 27 |
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| 28 | for i:0 thru 8 do
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| 29 | l[i]:[concat('l0,i),concat('l1,i),concat('l2,i)];
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| 30 |
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| 31 | rel(l,a,b,c):=[l.a,l.b,l.c];
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| 32 |
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| 33 | eqns:append(
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| 34 | [1-v*collinear(c[0], c[1], c[2])],
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| 35 | rel(l[0],a[0], b[1], c[0]),
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| 36 | rel(l[1],a[0], b[2], c[1]),
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| 37 | rel(l[2],a[1], b[0], c[0]),
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| 38 | rel(l[3],a[1], b[2], c[2]),
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| 39 | rel(l[4],a[2], b[0], c[1]),
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| 40 | rel(l[5],a[2], b[1], c[2]),
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| 41 | rel(l[6],a[0], a[1], a[2]),
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| 42 | rel(l[7],b[0], b[1], b[2]));
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| 43 |
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| 44 |
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| 45 | vars:append(makelist(l[j],j,0,7),
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| 46 | makelist([c[i]],i,0,2),[a[2],b[2]]);
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| 47 | params:makelist([a[i],b[i]],i,0,1);
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| 48 | vars:''vars;
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| 49 | params:''params;
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| 50 | vars:listofvars(vars);
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| 51 | params:listofvars(params);
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| 52 | cover:expand([[[],[]]]);
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| 53 | eqns:expand(''eqns);
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| 54 | cover:expand(''cover);
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| 55 | stringout("pappus4.out",eqns,vars,params,cover);
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