︠dd762f20-fe67-47ed-b3ad-9f3971278527s︠ R. = PolynomialRing(ZZ, 3, order='lex') I = Ideal(13*x*y*z+6*x*y+78*x*z+36*x-11*y^2*z-66*y*z, 168*x*y*z+84*x*y+1008*x*z+504*x+12*y^3-154*y^2*z+72*y^2-924*y*z, -168*x^2*y*z^2-84*x^2*y*z-1008*x^2*z^2-504*x^2*z+x*y^3*z+6*x*y^3+154*x*y^2*z^2+6*x*y^2*z+36*x*y^2+924*x*y*z^2-11*y^4*z-66*y^3*z ); gI = R*( I.groebner_basis(algorithm='macaulay2') ) len(gens(gI)) # expected 3 gI ︡54b1356d-140d-46f0-8bc3-9ed7b3bc3b09︡︡{"stdout":"3\n"}︡{"stdout":"Ideal (x*y*z - 6*x*y + 6*x*z - 36*x - 12*y^3 + 11*y^2*z - 72*y^2 + 66*y*z, 84*x*y + 504*x + 156*y^3 - 154*y^2*z + 936*y^2 - 924*y*z, 156*y^3*z + 72*y^3 - 154*y^2*z^2 + 936*y^2*z + 432*y^2 - 924*y*z^2) of Multivariate Polynomial Ring in x, y, z over Integer Ring\n"}︡{"done":true} ︠3f4f59ba-6a3e-45d2-96a0-beb9231e1140si︠ %md this is how to use M2 in a worksheet, but don't do this... ︡2837279f-7386-43fc-9b2c-d080e5ea6265︡︡{"hide":"input"}︡{"md":"this is how to use M2 in a worksheet, but don't do this...\n"}︡{"done":true} ︠332e747e-08de-4912-a038-5aeb637f2780s︠ %macaulay2 R = ZZ[x,y,z,MonomialOrder=>Lex] I = ideal{13*x*y*z+6*x*y+78*x*z+36*x-11*y^2*z-66*y*z, 168*x*y*z+84*x*y+1008*x*z+504*x+12*y^3-154*y^2*z+72*y^2-924*y*z, -168*x^2*y*z^2-84*x^2*y*z-1008*x^2*z^2-504*x^2*z+x*y^3*z+6*x*y^3+154*x*y^2*z^2+6*x*y^2*z+36*x*y^2+924*x*y*z^2-11*y^4*z-66*y^3*z} gens gb I ︡1f9f2154-bb95-47db-8811-901ac2b799ab︡︡{"stdout":"R\n\nPolynomialRing\n\n\n\n 2 3 2 2 2 2 2 2 2 2 3 3 2 2 2 2 2 4 3\nideal (13x*y*z + 6x*y + 78x*z + 36x - 11y z - 66y*z, 168x*y*z + 84x*y + 1008x*z + 504x + 12y - 154y z + 72y - 924y*z, - 168x y*z - 84x y*z - 1008x z - 504x z + x*y z + 6x*y + 154x*y z + 6x*y z + 36x*y + 924x*y*z - 11y z - 66y z)\n\nIdeal of R\n\n| 156y3z+72y3-154y2z2+936y2z+432y2-924yz2 84xy+504x+156y3-154y2z+936y2-924yz xyz-6xy+6xz-36x-12y3+11y2z-72y2+66yz |\n\n 1 3\nMatrix R <--- R"}︡{"done":true} ︠b9195afa-4eb1-437c-88f7-97ea58e183afs︠ v = macaulay2('gens gb I') ︡f371de0b-e8dd-4ae7-9159-5488994c3f1b︡︡{"done":true} ︠7d8c82b7-e28e-44d3-a02d-483fb8bff731s︠ str(v) ︡e554ba25-75a1-449a-93c0-515dc3e5eab0︡︡{"stdout":"| 156y3z+72y3-154y2z2+936y2z+432y2-924yz2 84xy+504x+156y3-154y2z+936y2-924yz xyz-6xy+6xz-36x-12y3+11y2z-72y2+66yz |\n"}︡{"done":true} ︠4ff190fd-5c1e-46d7-8e1f-7e291df67fe2s︠ v.sage_polystring() ︡9c93126d-77b1-473d-b429-002335578429︡︡{"stdout":"'map((R)**1,(R)**{{-4},{-3},{-3}},{{156*y**3*z+72*y**3-154*y**2*z**2+936*y**2*z+432*y**2-924*y*z**2, 84*x*y+504*x+156*y**3-154*y**2*z+936*y**2-924*y*z, x*y*z-6*x*y+6*x*z-36*x-12*y**3+11*y**2*z-72*y**2+66*y*z}})'\n"}︡{"done":true} ︠1a72be16-57ea-4dba-abc1-63156c614310︠