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- box% sage
- ┌────────────────────────────────────────────────────────────────────┐
- │ SageMath version 9.2, Release Date: 2020-10-24 │
- │ Using Python 3.8.6. Type "help()" for help. │
- └────────────────────────────────────────────────────────────────────┘
- sage: R.<x1,y1,a,length> = PolynomialRing(QQ, order='lex')
- sage: (x0,y0) = (0,0)
- sage: (x2,y2) = (x1,-y1)
- sage: Q = lambda u, v: (u[0]-v[0])^2 + (u[1]-v[1])^2
- sage: ideal(y1^2-4*a*x1, length^2 - Q((x0,y0),(x1,y1)), length^2 - Q((x1,y1),(x2,y2))).groebner_basis()
- [x1^2 - 3/4*length^2, x1*a - 1/16*length^2, x1*length^2 - 12*a*length^2, y1^2 - 1/4*length^2, a^2*length^2 - 1/192*length^4]
- sage:
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