Dear people in Mapleprimes,
I have a question about the ordering of monomials in a polynomial.
I hope you will help me understand how Maple works about it.
I inputed the polynomial as is written in black below.
Then, the outcome was blue, which ordering I could understand well: total degree ordering where at first
those who have the order of 6 are collected which are 14 x^3*y^3, 6x*y^5, and then the following was those which
have the order of 5: 21*x^5, -35 x^4*y, 9*x^3*y^2,-15*x^2*y^3, ... and so on.
And, among those who have the same order, lexical ordering was done, that is among 14 x^3*y^3, 6x*y^5, one which
came first was the one with the larger degree about x, and among 21*x^5, -35 x^4*y, 9*x^3*y^2,-15*x^2*y^3,
the first was 21*x^5, the second was -35*x^4*y, and so one, which was the ordering following the exponent about x.
And, then, I calculated Factor(polynomial) mod 7, which meaning I know.
Then, the result was 2*(x*y+2)*(3*y^3+x^2+3x*y)y.
I can understand the ordering among x*y and 2 in x*y+2, and that among 3y^3, x^2 and 3x*y in 3y^3+x^2*3x*y.
But, I can't understand why (x*y+2) comes at the first term, with 3 y^3+x^2+3x*y following it, and with y coming last.
This might be a trivial question. But, I hope you will teach me about this.