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Can someone validate this counterexample from gpt-5.6 sol (-(1+xy)^2 z - y^3(1+xy), 2x(1+xy)z + (1+xy)^3 w + y^2(7+12xy+4x^2y^2), 2x^2z + 3x(1+xy)^2w + 2y(1+10
by dragonmage65535 2mo ago
Can someone validate this counterexample from gpt-5.6 sol
(-(1+xy)^2 z - y^3(1+xy), 2x(1+xy)z + (1+xy)^3 w + y^2(7+12xy+4x^2y^2), 2x^2z + 3x(1+xy)^2w + 2y(1+10xy+6x^2y^2), 2x - 4x^2y - x^3w): C^4 → C^4 has Jacobian determinant 4, and sends (-2,0,1,0) and (-1,0,1,-2), (1,−2,−7,14), (2,−1,0,3) to (-1,-4,8,-4)
https://xcancel.com/__alpoge__/status/2079091571316912542 https://xcancel.com/__alpoge__/status/2079091571316912542
- taegee 2mo agohttps://www.wolframalpha.com/input?i=Det%5BD%5B%7B-%281%2Bxy%29%5E2+z+-+y%5E3%281%2Bxy%29%2C+2x%281%2Bxy%29z+%2B+%281%2Bxy%29%5E3+w+%2B+y%5E2%287%2B12xy%2B4x%5E2y%5E2%29%2C+2x%5E2z+%2B+3x%281%2Bxy%29%5E2w+%2B+2y%281%2B10xy%2B6x%5E2y%5E2%29%2C+2x+-+4x%5E2y+-+x%5E3w%7D%2C+%7B%7Bw%2Cx%2Cy%2Cz%7D%7D%5D%5D https://www.wolframalpha.com/input?i=Det%5BD%5B%7B-%281%2Bxy...