#### 7.2.4.2 poly expressions (plural)

A polynomial expression is (optional parts in square brackets):

1. a monomial (there are NO spaces allowed inside a monomial)

       [coefficient] ring_variable [exponent] [ring_variable [exponent] ...]

   monomials which contain an indexed ring variable must be built from `ring_variable` and `coefficient` with the operations `*` and `^`
2. an identifier of type poly
3. a function returning poly
4. polynomial expressions combined by the arithmetic operations `+`, `-`, `*`, `/`, or `^`.
5. a type cast to poly

Example:

    ring r=0,(x,y),dp;
    def R=nc_algebra(1,1);  // make it a Weyl algebra
    setring R;
    R;
    ==> // coefficients: QQ considered as a field
    ==> // number of vars : 2
    ==> //        block   1 : ordering dp
    ==> //                  : names    x y
    ==> //        block   2 : ordering C
    ==> // noncommutative relations:
    ==> //    yx=xy+1
    yx;      // not correct input
    ==> xy
    y*x;     // correct input
    ==> xy+1
    poly f = 10x2*y3 + 2y2*x^2 - 2*x*y + y - x + 2;
    lead(f);
    ==> 10x2y3
    leadmonom(f);
    ==> x2y3
    simplify(f,1);     // normalize leading coefficient
    ==> x2y3+1/5x2y2+3/5xy-1/10x+1/10y+3/5
    cleardenom(f);
    ==> 10x2y3+2x2y2+6xy-x+y+6

User manual for Singular version 4.4.1, 2025, generated by texi2html.