Last change
on this file since 1 was 1, checked in by Marek Rychlik, 15 years ago |
First import of a version circa 1997.
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File size:
681 bytes
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1 | ;; This is supposed to prove that the 3 altitudes of a triangle
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2 | ;; intersect at a single point; if consistent, then the altitudes have
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3 | ;; a common point (x,y). Only x3 y3 are treated as parameters, i.e.
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4 | ;; we vary only one vertex; adding all three vertices produces 6 parameters,
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5 | ;; too much to swallow for the software
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6 | (string-grobner-system
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7 | "[X*Y1-U1*Y1-X1*Y+U1*Y+V1*X1-V1*X,X*Y2-U2*Y2-X2*Y+U2*Y+V2*X2-V2*X,X*Y3-U3*Y3-X3*Y+U3*Y+V3*X3-V3*X,-Y1*Y3+V1*Y3+Y1*Y2-V1*Y2-X1*X3+U1*X3+X1*X2-U1*X2,-Y2*Y3+V2*Y3+Y1*Y2-V2*Y1-X2*X3+U2*X3+X1*X2-U2*X1,-Y2*Y3+Y1*Y3+V3*Y2-V3*Y1-X2*X3+X1*X3+U3*X2-U3*X1]"
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8 | '(x y u1 v1 u2 v2 u3 v3)
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9 | '(x1 y1 x2 y2 x3 y3)
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10 | :main-order #'lex>
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11 | :parameter-order #'lex>)
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12 |
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