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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
==> // 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