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Apply a function to a rationalized expression

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maprat(object, f, options)


As a first step, maprat(object, f, options) calls rationalize(object, options), which generates a rational expression. The maprat function uses the expression returned by rationalize as an input to the function f. As a second step, maprat replaces all variables generated by rationalize with the original subexpressions in object.

See the rationalize help page for details.


Example 1

Find the greatest common divisor (the gcd function) for the following two rationalized expressions. The first argument of maprat is a sequence of the two expressions p, q, which gcd takes as two parameters. Note the brackets around the sequence p, q:

p := (x - sqrt(2))*(x^2 + sqrt(3)*x - 1): 
q := (x - sqrt(2))*(x - sqrt(3)):
maprat((p, q), gcd)

Example 2

The maprat function accepts the same options as the rationalize function. For example, find the least common multiple (the lcm function) for the following two rationalized expressions. Use the FindRelations option to detect trigonometric relations:

p := tan(x)^2 + 1/cos(x)^2: 
q := 1/sin(x)^4 + cot(x)^4:
maprat((p, q), lcm, FindRelations = ["sin"])

Without this option, the result is:

p := tan(x)^2 + 1/cos(x)^2: 
q := 1/sin(x)^4 + cot(x)^4:
maprat((p, q), lcm)

Free the variables for further calculations:

delete p, q:



An arithmetical expression, or a sequence, or a set, or a list of such expressions


A procedure or a functional expression



Approximate floating-point numbers by rational numbers.


Detect algebraic dependencies for subexpressions of specified types.


If the original expression contains subexpressions, rationalize the specified types of subexpressions.


Replace all subexpressions with limits, sums, and integrals by variables.


Replace all subexpressions of the specified types by variables.


Do not rationalize specified types of subexpressions.


Do not rationalize numbers, strings, Boolean constants, NIL, FAIL, PI, EULER, and CATALAN in the set Type::ConstantIdents.

Return Values

Object returned by the function f.

See Also

MuPAD Functions

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