Ordering monomials of multivariate polynomials --- CAG L11.3

[@marthamulusa3186]

Thank you for the videos you are posting they are very helpful. I am entirely new to this filed of computational algebra and i am kind of finding it had to different the orderings what happens when i apply a particular type of ordering say dp,Dp, ls and many others. without using mathematics symbols, could you please summarise the orderings in plain English?

[@emresertoz]

Thanks for the question. Could you further explain this part of your question "what happens when i apply ... dp,Dp, ls"? Maybe I forgot the notation already. As for orderings, let's start with "lex". With variables x,y,z,w you just pretend that you are writing a word, so x^2y^3z^1w^4 is the word xxyyyzwwww. Now you pretend these words are listed in a dictionary. Which words would come first? For instance xxxyy would come before xxyyyzwwww in a dictionary because the third letter x comes before y. We say a monomial m1 is greater than another monomial m2 if m1 would appear earlier in the dictionary.