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4.16.2 poly expressions

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. an int expression (see Type conversion and casting)
  6. a type cast to poly


ring S=0,(x,y,z,a(1)),dp;
2x, x3, 2x2y3, xyz, 2xy2; //  are monomials
2*x, x^3, 2*x^2*y^3, x*y*z, 2*x*y^2; // are poly expressions
2*a(1); // is a valid polynomial expression (a(1) is a name of a variable),
        // but not 2a(1) (is a syntax error)
2*x^3;  // is a valid polynomial expression equal to 2x3 (a valid monomial)
        // but not equal to 2x^3 which will be interpreted as (2x)^3
        // since 2x is a monomial
  ring r=0,(x,y),dp;
  poly f = 10x2y3 +2x2y2-2xy+y -x+2;
==> 10x2y3
==> x2y3
  simplify(f,1);     // normalize leading coefficient
==> x2y3+1/5x2y2-1/5xy-1/10x+1/10y+1/5
  poly g = 1/2x2 + 1/3y;
==> 3x2+2y
  int i = 102;
==> 102
==> poly

See Type conversion and casting; ring.