The built-in functions in this topic are useful for decomposing expressions into their component parts.  Some of the functions require that their arguments be polynomials or numbers.


NUMERATOR(u) returns the numerator of the numeric or symbolic expression u.  To put an expression over a common denominator before calling NUMERATOR, factor out its trivial content using the Simplify > Factor commandU08MH3 or the FACTOR function.  For example,

NUMERATOR(FACTOR(a/b + c/d, Trivial, a))

simplifies to a·d + b·c.


DENOMINATOR(u) returns the denominator of the numeric or symbolic expression u.  To put an expression over a common denominator before calling DENOMINATOR, factor out its trivial content using the Simplify > Factor commandU08MH3 or the FACTOR function.  For example,

DENOMINATOR(FACTOR(a/b + c/d, Trivial, a))

simplifies to b·d.


QUOTIENT(u, v) returns the polynomial quotient of u divided by v, where u and v are polynomials.  For example,

QUOTIENT(x^4 + 3·x^3 + 5·x + 6, x^2 - 5)

simplifies to x^2 + 3·x + 5.  QUOTIENT(u, v, x) returns the polynomial quotient of u divided by v, where u and v are polynomials in the variable x.  Use the FLOOR function to find quotients over the ring Z of integers (for details, see the Piecewise Continuous FunctionsPiecewise_Continuous_Functions).


REMAINDER(u, v) returns the polynomial remainder of u divided by v, where u and v are polynomials.  For example,

REMAINDER(x^4 + 3·x^3 + 5·x + 6, x^2 - 5)

simplifies to 20·x + 31.  REMAINDER(u, v, x) returns the polynomial remainder of u divided by v, where u and v are polynomials in the variable x.  Use the MOD function to find remainders over the ring Z of integers (for details, see the Piecewise Continuous FunctionsPiecewise_Continuous_Functions).


POLY_GCD(u, v) returns the polynomial greatest common divisor (gcd) of u and v, where u and v are polynomials.  For example,

POLY_GCD(x^3 + 3·x^2 + 5·x + 6, x^3 + 2·x - 3)

simplifies to x^2 + x + 3.  Use the GCD function to find gcds over the ring Z of integers (for details, see the Number Theory FunctionsNumber_Theory_Functions).


VARIABLES(u) returns a vector of the free variables of u ordered from most to least main.


LHS(u) returns the Left Hand Side (i.e. the left operand) of u if it is an equation, inequality, conjunction, disjunction, union, or intersection.  If u is a vector, LHS(u) returns a vector consisting of the Left Hand Sides of the elements of u.  For example,

LHS([2·x + y = 5, x < y - 3, NOT p AND q, a UNION b])

simplifies to

[2·x + y, x, ¬ p, a]


RHS(u) returns the Right Hand Side (i.e. the right operand) of u if it is an equation, inequality, conjunction, disjunction, union, or intersection.  If u is a vector, RHS(u) returns a vector consisting of the Right Hand Sides of the elements of u.  For example,

RHS([2·x + y = 5, x < y - 3, NOT p AND q, a UNION b])

simplifies to

[5, y - 3, q, b]


Other Built-in Functions and ConstantsBuilt_in_Functions_and_Constants 

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