|  |  7.2.4.2 poly expressions (plural) 
A polynomial expression is (optional parts in square brackets):
 
a monomial (there are NO spaces allowed inside a monomial)
monomials which contain an indexed ring variable
 must be built from|  | [coefficient] ring_variable [exponent] [ring_variable [exponent] ...]
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 ring_variableandcoefficientwith the operations*and^
an identifier of type poly
a function returning poly
polynomial expressions combined by the arithmetic operations +,-,*,/, or^.
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
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