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1.2.21. Leading Term (Initial) Ideals, Generic Polynomials |
The following example produces the leading term (initial) ideal of the ideal generated by three "generic" polynomials of degree 2 with respect to the lexicographic term-ordering. |
Example |
Use R ::= Z/(32003)[x[1..4]],Lex; F := DensePoly(2); -- sum of all power-products of degree 2 L := [ Randomized(F) | I In 1..3 ]; -- randomize coefficients LT(Ideal(L)); Ideal(x[1]^2, x[1]x[2], x[1]x[3], x[2]^3, x[1]x[4]^2, x[2]^2x[3], x[2]^2x[4]^2, x[2]x[3]^3, x[2]x[3]^2x[4]^2, x[2]x[3]x[4]^4, x[2]x[4]^6, x[3]^8) ------------------------------- |