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2.4.2 poly expressions

A poly 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] ...]
    
  2. an identifier of type poly
  3. a function returning poly
  4. poly expressions combined by the arithmetic operations +, -, *, /, or ^.
  5. a type cast to poly


Example:
 
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*x(1); // is a valid poly expression, but not 2x(1) (a syntax error)
2*x^3;  // is a valid poly 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;
lead(f);
==> 10x2y3
leadmonom(f);
==> x2y3
simplify(f,1);     // normalize leading coefficient
==> x2y3+1/5x2y2-1/5xy-1/10x+1/10y+1/5
poly g = 1/2x2 + 1/3y;
cleardenom(g);
==> 3x2+2y
int i = 102;
poly(i);
==> 102
typeof(_); 
==> poly

Remark: In the non-commutative case see PLURAL conventions.
Example:
 
ring r=0,(x,y),dp;
ncalgebra(1,1);
// it is a Weyl algebra 
r;
==> //   characteristic : 0
==> //   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


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