This method gives the initial forms of a list of polynomials. If the "ideals" option is used, generators for the initial ideal are given. If the "pair" option is used, then the output is a pair of MarkedPolynomialLists.
i1 : QQ[x,y,z] o1 = QQ[x..z] o1 : PolynomialRing |
i2 : L = {x + y, x + z} o2 = {x + y, x + z} o2 : List |
i3 : gfanInitialForms(L, {1,2,1}) o3 = {y, x + z} o3 : List |
i4 : gfanInitialForms(L, {1,2,1}, "ideal"=>true) o4 = {x + z, y} o4 : List |
i5 : gfanInitialForms(L, {1,2,1}, "ideal"=>true, "pair"=>true) o5 = {{x + z, y}, {x + z, y - z}} o5 : List |
i6 : gfanInitialForms({x*y+z, x*z + y}, {1,1,1}, "ideal"=>true) 2 2 o6 = {x*z, y - z , x*y} o6 : List |
gfan Documentation This program converts a list of polynomials to a list of their initial forms with respect to the vector given after the list.Options:--ideal: Treat input as an ideal. This will make the program compute the initial ideal of the ideal generated by the input polynomials. The computation is done by computing a Groebner basis with respect to the given vector. The vector must be positive or the input polynomials must be homogeneous in a positive grading. None of these conditions are checked by the program.--pair: Produce a pair of polynomial lists. Used together with --ideal this option will also write a compatible reduced Groebner basis for the input ideal to the output. This is useful for finding the Groebner cone of a non-monomial initial ideal.--mark: If the --pair option is and the --ideal option is not used this option will still make sure that the second output basis is marked consistently with the vector.--list: Read in a list of vectors instead of a single vector and produce a list of polynomial sets as output.
The object gfanInitialForms is a method function with options.